Modeling And Simulation Of Quantum Dot Devices And Their Applications In Optical Communications

Al-AZHAR University Faculty of Engineering Dept. of Electrical Engineering

Modeling and Simulation of Quantum Dot Devices and Their Applications in Optical Communications Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Electrical Engineering (Electronics and Communications) By

Eng. Mohamed Nady Abdul Aleem Dept. of Microwave Engineering Electronics Research Institute (ERI) Under the Supervision of

Prof. Dr. Abd-El-HadiAbd-El-Azim Ammar Dept. of Electrical Engineering Faculty of Engineering Al-AZHAR University

Assoc. Prof. Khalid Fawzy Ahmed Hussein Dept. of Microwave Engineering Electronics Research Institute (ERI)

2014

ACKNOWLEDGEMENT All gratitude is to Allah for every thing. Without his blessing this research wouldn't have been possible. I wishe to express my deep thanks to Prof. Dr. Abd-ElHadiAbd-El-Azim Ammar and Asst. Prof. Khalid Fawzy Ahmed Hussein for their invaluable assistance and continuous encouragement during the research. I, also, wishe to express my thanks to the staff of the microwave engineering department of the Electronics Research Institute (ERI). My special thanks should be extended to my parents, brothers, for their encouragement support during the research. Finally I would like to show my thanks to my wife, for her taking care of our sons, while I was writing. And thanks to our lovely sons Abdul Rahman, Eyman, Doaa and my brothers's sons Omar and Rahma.

2014

Abstract The importance of semiconductor optical amplifiers (SOAs) as key components in optical communications and integrated optics, covering a wide range of applications for the 1550- and 1300-nm optical windows, has grown in recent years. All-optical signal processing, including wavelength conversion, optical logic gates and signal regeneration, etc, is one of the most important enabling technologies to realize optical switching, including optical circuit switching, optical burst switching and optical packet switching. SOAs are very promising in all-optical signal processing since they are compact, easy to manufacture and power efficient. The need for all-optical elements for increasing the capacity of current and future communication networks and optimizing the operation of optical switching networks has been one of the main motivations for considering SOAs as essential elements in all-optical switching scenarios in recent years. This present work is concerned with the analysis of the QD-SOA-based MachZehnder Interferometer (MZI) and its fundamentals and applications. This analysis is carried out using the rate equations model. The dissertation starts with the dissection of foundation of the quantum dot laser and amplifier. This includes a brief introduction to the development of quantum dots and quantum dot lasers. Advantages and disadvantages of the latter are discussed as well as the progress in manufacturing. In the discussion of the QD amplifier we concerned on the gain and gain saturation. Some important parameters are also considered in this background such as the Linewidth Enhancement Factor, the Amplified Spontaneous Emission, and the simulation methods of Quantum-Dot Semiconductor Optical Devices. Then, this dissertation proceeds to study the QD laser using the Multi Population Rate Equations MPRE model. In which, equations

for

the

quantum-dot

laser

we have solved the rate

considering

homogeneous

and

inhomogeneous broadening of optical gain numerically using fourth-order

Runge-Kutta method. The dynamic (relation with the time) and static (relation with the current) characteristics of proposed QDL are presented in chapter three. This chapter studies also the effect of the FWHM of homogeneous broadening and the injected current on the rise and fall time, hence on the bit rate. These later results aims to study the possibility of using the QDL as a pulse source for high bit rate data transmission. Then the dissertation proposes a theoretical model of a QD SOA-MZI based ultrafast all-optical signal processor. The QD SOA-MZI operation has been analyzed theoretically by solving the rate equations of the QD-SOA dynamics, optical wave propagation equations in an active medium, and the MZI equations. A brief review for the QD SOA-MZI and its transfer function that will be used to analyze this device are introduced. The rate equations model of the QD SOA is also introduced then the QD-SOA characterizations are theoretically investigated and demonstrated. Two direct applications of QD SOA-MZI; all-optical W.C. and 3R are also introduced. Then the all-optical QD-SOA-based MZI switch is used to design three alloptical logic gates; XOR, AND, and OR. For each all-optical logic gate the principle of operation, the proposed design, and the simulation results are presented. Finally and for the first time, a new scheme for all-optical full adder using fife QD-SOA based Mach–Zehnder interferometers is theoretically investigated and demonstrated. The proposed scheme consists of two XOR, two AND, and one OR gate. The impact of the peak data power as well as of the QD-SOAs current density, maximum modal gain, and QD-SOAs length on the Extinction Ratio ER and Q-factor of the switching outcome are explored and assessed. The operation of this system is demonstrated with 160 Gbit/s.

Table of Contents ABSTRACT

II

Table of Contents

IV

List of Symbols

IX

List of Abbreviations

XII

List of Figures

XIV

Chapter (1):

Introduction 1.1 Context

1

1.2 Motivation

2

1.3 Thesis objectives and outline

5

Chapter (2):

Quantum Dot Devices 2.1 Quantum Dot

8

2.1.1 Semiconductor lasers

8

2.1.2 Density of States

10

2.1.3 Progress in fabricating QD

11

2.1.3.1 Self-assembled growth

12

2.4 Inhomogeneous broadening

13

2.2 Quantum Dot Laser

14

2.2.1 Advantages of quantum dot lasers

15

2.3 Quantum Dot Amplifier

15

2.3.1 Operation Principles of SOA

16

2.3.2 SOA Gain

18

2.3.3 Gain Saturation

21

2.4 Linewidth Enhancement Factor

23

1.6 Simulation Methods of QD Semiconductor Lasers and Amplifiers

25

Chapter (3):

Semiconductor Quantum Dot Laser 3.1 Semiconductor Quantum Dot Laser

27

3.2 Multi Populations Rate Equations Model

28

3.3 Numerical Results

34

3.3.1 Dynamic Characteristics of InAs/InP (113) B Self-Assembled 35 Quantum Dot Lasers 3.3.2 Static Characteristics of InAs/InP (113) B Self-Assembled Quantum 41 Dot Lasers 3.3.3 Semiconductor Quantum Dot Lasers as pulse Sources for High Bit rate 47 Data Transmission

Chapter (4):

QD-SOA-Based Mach–Zehnder Interferometer 4.1. SOA-MZI (Brief review)

55

4.1.1. SOA-MZI Gate

57

4.1.2. SOA-MZI Transfer Function

59

4.2. Rate Equations

61

4.3. QD-SOA CHARACTERIZATION

65

4.4. Wavelength Conversion (WC)

70

4.5. 3R Regeneration (Re-amplification, Re-shaping and Re-timing)

78

Chapter (5):

All-Optical Logic Gates 5.1 All-Optical Logic Gates

84

5.2 All-Optical AND Gates

86

5.2.1 Principle of Operation of Proposed AND Gate

87

5.2.2 Numerical Results of Proposed AND Gate

89

5.3 All-Optical XOR Gates

96

5.3.1 Principle of Operation of Proposed XOR Gate

97

5.3.2 Numerical Results of Proposed XOR Gate

99

5.4 All-Optical OR Gates

106

5.4. 1 Principle of Operation of Proposed OR Gate

106

5.4.2 Numerical Results of Proposed OR Gate

107

Chapter (6):

Ultrafast All-Optical Full Adder Using Quantum-Dot Semiconductor Optical Amplifier-Based Mach-Zehnder Interferometer 6.1 All optical Full adders

116

6.2 Principle and Design of Proposed All-Optical Full Adder

119

6.3 Simulation Results of the All-Optical Full Adder

120

Chapter (7):

Conclusions and Suggestion of Future Work 7.1 Conclusions

130

7.2 Suggestions for Future Work

133

Appendix (A):

4th Order Runge-Kutta Integrator 4th Order Runge-Kutta Integrator

134

Appendix (B):

Design Metrics B.1 Extinction Ration ER

137

B.2 Amplitude Modulation AM

137

B.3 Q-Factor

138

B.4 Pseudo-Eye-Diagram PED

139

References

140

Published Papers

152

Arabic Abstract

List of Symbols

jth

threshold current density

k

Wave vector

Jo

transparency current density

gmat

The material gain

gCDP

carrier density pulsation

N

carrier density

τCH

CH recovery time

G

gain of an amplifier

g

Modal gain (differential gain)) the optical angular frequency atomic transition angular frequency

PS

Saturation power of the gain medium. gain spectrum

г

confinement factor

V

volume of the active region

N0

transparency carrier density

a

Differential gain coefficient (a = dg/dN).

I

injection current carrier lifetime effective cross section of the waveguide node

υ

input signal frequency linewidth enhancement factor cavity length capture time to ES Relaxation time from ES to GS thermally reemitted time spontaneous emission time carrier number in the WL reservoir,

and

are the filling

probabilities of the ES and GS, WL volume (

)

coefficients for phonon assisted relaxation related to the WL and the ES

(

)

coefficients for Auger assisted relaxation related to the WL and the ES filling probabilities of the ES filling probabilities of the GS ES carrier number in the nth subgroup GS carrier number in the nth subgroup effective density of states in the WL Boltzmann constant electron effective mass in the WL refractive index number of photons emitted from exited state at the mode number m number of photons emitted from ground state at the mode number m photon lifetime overlap integral between the envelope functions of an electron and a hole band gap energy

Δ

spin-orbit interaction energy of the QD material homogenous broadening factor FWHM of the inhomogeneous broadening linewidth enhancement factor electron transitions from WL to ES electron transitions between ES and GS relaxation time from GS to ES electron escape transitions from ES back to WL spontaneous radiative time in QDs

group velocity effective cross section speed of the light in vacuum wavelength of the incident light maximum modal gain effective thickness of the active layer material absorption coefficient peak power FWHM of the input pulse BD

bit duration

List of Abbreviations 3R

3r regeneration (re-amplification, re-shaping and re-timing)

AM

Amplitude modulation am

ASE

Amplified spontaneous emission

CH

Carrier heating

CW

Continuous wave

DWDM

Dense wavelength division multiplexing

EDFA

Erbium doped optical amplifier

EES

Excited-state energy

EGS

Ground-state energy

ER

Extinction ration

ES

Exited state

FWHM

Full-width at half-maximum

FWM

Four-wave mixing

GAAS

Gallium-arsenide

GS

Ground state

IB

Inhomogeneous broadening

INAS

Indium-arsenide

LEF

Linewidth enhancement factor

MPRE

Multi population rate equations model

MQW

Multi-quantum well

MQW

Multi-quantum well

MZI-SOA

Mach-zehnder interferometer with a soa in each arm

NRZ

Non-return-to-zero

O

Eye opening

OADM

Optical add/drop multiplexers

OEO

Optical-electrical- optical

OXC

Optical cross connect

PED

Pseudo-eye-diagram

PED

Pseudo-eye-diagram

PLC

Planar lightwave circuit

PRBS

Pseudorandom binary sequences

QD

Quantum dot

QDL

Quantum dot laser

Q-FACTOR Quality factor QW

Quantum well

RZ

Return-to-zero

SHB

Spectral hole burning

SLALOM

Semiconductor laser amplifier loop optical mirror

SOA

Semiconductor optical amplifier

TCDD

Total carrier density depletion

TDM

Time domain multiplexing

TOADS

Terahertz optical asymmetric demultiplexers

UNI

Ultrafast nonlinear interferometer

UNI

Ultrafast nonlinear interferometer

W.C.

Wavelength conversion

WDM

Wavelength division multiplexing

WL

Wetting layer

WSC

Wavelength selective coupler

XGM

Cross gain modulation

XPM

Cross phase modulation

XPOLM

Cross polarization modulation

List of Figures Fig. (2.1)

Schematic view of a separate confinement double heterostructure laser.

Fig. (2.2)

Illustrative light-current curve of a semiconductor laser.

Fig. (2.3)

Density of states in materials of different dimensionality: (a) 3D (bulk), (b) 2D (QW), and (c) 0D (QD).

Fig. (2.4)

(a) A schematic of an ideal QD system and, (b), a real QD system, where inhomogeneous broadening is illustrated. (EGS: ground-state energy; EES: excited-state energy; EC: the bottom of the conduction band).

Fig. (2.4)

Simplified band structure of a direct band-gap semiconductor in quasi-equilibrium [77]

Fig. (2.5)

GaAs-based waveguide structure of a QD-SOA including n and p cladding layers and multi-layer QD active region. Energy band diagram of a sample QD is also sketched

Fig. (2.6)

Temporal evolution of conduction band free carrier density distribution after exciting by a picoseconds optical pulse

Fig. (2.7)

SOA gain characteristic versus output signal power

Fig. (2.8)

LEF at the ground state transition of InGaAs QD amplifier as a function of pump-probe relative delay for different bias currents [85]

Fig. (2.9)

3 dB saturation output power as a function of device length for bulk, QW and QD-SOA [88]

Fig. (3.1)

The interaction between the cavity-mode photons and the carriers in the quantum dots via homogeneous broadening of gain.

Fig. (3.2)

Energy diagram of the laser-active region and diffusion, recombination, and relaxation processes

Fig. (3.3)

photon-characteristics for N=M=0 and Current Density CD= (a) 160A/cm2, (b) 240A/cm2, and (c) 380A/cm2

Fig. (2.4)

photon-characteristics at

=50meV,

and

Current Density CD= 16, 25, 50, and 100 A/cm2 Fig. (2.5)

photon-characteristics for

=50meV and

and

Current Density CD= 16, 25, 50, and 100 mA/cm2 Fig. (3.6)

photon-characteristics at

=50meV and Current Density CD=

100 A/cm2 at (a) Fig. (3.7)

and (b)

photon-characteristics at

=20meV and Current Density CD=

100 A/cm2 at Fig. (3.8)

photon-characteristics at

=20meV and

and

Current Density CD= 100 A/cm2 at different coefficient for phonon relaxation(Aw) Fig. (3.9)

Light-Current characteristics of SAQD-LD at N=M=0

Fig. (3.10)

Optical gain-Current characteristics of SAQD-LD at N=M=0

Fig. (3.11)

Light-Current characteristics of SAQD-LD for

=20meV at

different Fig. (3.12)

Light-

characteristics of SAQD-LD for

=20meV at

different injected current Fig. (3.13)

Light-Current characteristics of SAQD-LD for

=20meV at

equals (a) 0.1meV and (b) 10meV Fig. (3.14)

Optical gain-Current characteristics of SAQD-LD for and

Fig. (3.15)

=20meV

=10meV at different Aw

Light-Current characteristics of SAQD-LD for

=20meV and

=10meV at different Aw Fig. (3.16)

Normalized photon-characteristics at

and Current

Density; J= 180 A/cm2 Fig. (3.17)

Normalized Injected Current Pulse, (b) photon-characteristics at =20 meV,

and J= 100, 250, 500, and 1000

A/cm2 Fig. (3.18)

Depends of the Rise time (a), fall time (b) of the number of photons, and Bit rate (c) on the injected current at

=20 meV,

Fig. (3.19)

photon-characteristics at

=20 meV,

and

Current Density J= 100, 250, 500, and 1000 A/cm2 Fig. (3.20)

Rise time versus the Homogenous broadening factor;

at

different injected current Fig. (3.21)

Fall time versus the Homogenous broadening factor;

at

different injected current Fig. (3.22)

Bit rate versus the Homogenous broadening factor;

at

different injected current Fig. (3.23)

photon-characteristics at

=20meV and

and

Current Density CD= 1000 A/cm2 at different coefficient for phonon relaxation(Aw) Fig. (3.24)

Rise(a), fall(b) time and Bit rate(c) versus the coefficient of phonon relaxation(Aw) at

Fig. (4.1)

=20meV,

SMZ configuration and nonlinear phase response cancel out mechanism

Fig. (4.2)

Structure of SOA and hybrid-integrated SMZ gate

Fig. (4.3)

Schematic of SOA incorporated MZI structure

Fig. (4.4)

(a) Schematic diagram of a QD-SOA, (b) energy band diagram of a QD system and the WL.

Fig. (4.5)

(The considered spatio-temporal grid on which the 4th order Runge-Kutta method is applied. L: the QD-SOAs length. N=10 the number of uniform segments that the QD-SOA is divided into. Δz: the length of each spatial segment. Δt: the temporal interval between two consecutive samples of an input pulse.

Fig. (4.6)

Variation of minimum instantaneous QD-SOA gain versus peak input data power. The difference ΔP = 4 dBm denotes the deviation of the QD-SOA bias point chosen as fixed for the simulation analysis from the 3 dB input saturation power.

Fig. (4.7)

Instantaneous QD-SOA gain variation for different (a) Peak input power (b) maximum modal gain (c) current density

Fig. (4.8)

Instantaneous QD-SOA gain variation for (a) J = 1 kA/cm2, (b) J

= 3 kA/cm2 Fig. (4.9)

(a) Wavelength conversion scheme based on cross-gain modulation in an SOA and (b) mechanism of XGM-based on gain saturation

Fig. (4.10)

Schematic of SOA-MZI configuration for wavelength conversion based on cross phase modulation effect

Fig. (4.11)

Realization of WC by XPM between the data signal A with and CW-light with

. for the bit rate

160Gb/s. Fig. (4.12)

Variation of extinction ratio (ER) with (a) peak data power, (b) the maximum modal gain, (c) the current densities, and (d)QDSOA length.

Fig. (4.13)

waveforms of wavelength conversion-based QD-SOA MZI, where (a) input data stream A, (b) output with ER=20.7dB, (c) output with ER=4.8dB

Fig. (4.14)

Simulated waveforms with pseudo-eye-diagram (PED) where (a) input data stream A, (b) output with O=99%, (c) output with O=67%

Fig. (4.15)

Schematic configuration used for 3R regeneration in an QD-SOS MZI

Fig. (4.16)

Waveforms of 3R-based QD-SOA MZI, where (a) Noisy input data stream A, (b) Regenerated output, (c) Clock

Fig. (4.17)

Variation of 3R extinction ratio (ER) with (a) peak data power, (b) the maximum modal gain, (c) the current densities, and (d)QD-SOA length.

Fig. (4.18)

Waveforms of 3R-based QD-SOA MZI, where (a) Noisy input data, (b) Output with ER=17dB, (c) Output with ER=3.92dB

Fig.(4.19)

Simulated waveforms with pseudo-eye-diagram (PED) where (a) Noisy input data stream A, (b) output with O=98%, (c) output with O=59.5%

Fig. (5.1)

Simulated setup of QD-SOA-based MZI configured for Boolean

AND operation between data A and B. Fig. (5.2)

Variation of Q-Factor with peak data power for different current densities, keeping other parameters fixed.

Fig. (5.3)

Variation of Q-Factor with the maximum modal gain for three different QD-SOAs length, keeping other parameters fixed

Fig. (5.4)

Variation of Q-Factor with current densities for two different QDSOAs length, keeping other parameters fixed

Fig. (5.5)

Variation of extinction ratio (Q-Factor) with QD-SOA length for two different peak data power, keeping other parameters fixed.

Fig. (5.6)

Variation of Q-Factor with electron relaxation time from the ES to the GS for two different QD-SOAs length, keeping other parameters fixed

Fig. (5.7)

waveforms of AND gate -based QD-SOA MZI, where (a) input data stream A, (b) input data stream B, (c) Output with Q=15.15, (d) Output with Q=2.5

Fig. (5.8)

Simulated waveforms with pseudo-eye-diagram (PED) where (a) input data stream A, (b) output with O=92%, (c) output with O=22%

Fig. (5.9)

Gain response of QD-SOA1 to data stream A of Fig. (5.7). for (a) Q=15.15, (b) Q=2.5

Fig. (5.10)

(a) Simulated setup of QD-SOA-based MZI configured for Boolean XOR operation between data A and B and (b) its truth table.

Fig. (5.11)

waveforms of XOR gate -based QD-SOA MZI, where (a) input data stream A, (b) input data stream B, (c) A XOR B

Fig. (5.12)

Simulated waveforms with pseudo-eye-diagram (PED) for A XOR B

Fig. (5.13)

(a) Gain response of QD-SOA1 to data stream A, (b) Gain response of QD-SOA2 to data stream B

Fig.(5.14 )

Delay between the two input pulses

Fig. (5.15)

Variation of (a) ER, (b) AM, and (C) Q-factor with the delay

Fig. (5.16)

waveforms of XOR gate -based QD-SOA MZI, where (a) delay equals zero, (b) delay equals 1 ps.

Fig. (5.17)

Simulated waveforms with pseudo-eye-diagram (PED) for A XOR B at delay equals 1 ps

Fig. (5.18)

Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in the peak input power.

Fig. (5.19)

waveforms of XOR gate -based QD-SOA MZI, where the difference in the peak power equals (a) zero, (b) 0.5dBm.

Fig. (5.20)

Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in length

Fig. (5.21)

waveforms of XOR gate -based QD-SOA MZI, where the difference in length equals (a) zero, (b) 0.5mm.

Fig. (5.22)

Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in maximum modal gain

Fig. (5.23)

waveforms of XOR gate -based QD-SOA MZI, where difference in maximum modal gain equals (a) zero, (b) 0.2 cm-1.

Fig. (5.24)

Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in relaxation time from ES to GS

Fig. (5.25)

(a) Simulated setup of QD-SOA-based MZI configured for Boolean OR operation between data A and B and (b) its truth table.

Fig. (5.26)

Variation of AM with the peak input power for two different current density, keeping other parameters fixed.

Fig. (5.27)

Variation of AM with the current density for two different lengths, keeping other parameters fixed.

Fig.(5.28)

Variation of AM with the maximum modal gain

Fig. (5.29)

Variation of AM with the length

Fig.(5.30)

waveforms of OR gate -based QD-SOA MZI, where (a) input data stream A, (b) input data stream B, (c) A OR B

Fig. (5.31)

Simulated waveforms with pseudo-eye-diagram (PED) for A OR B

Fig. (6.1) Fig (6.2)

(a) Full adder logic diagram and (b) its Truth table Configuration of the proposed all-optical full adder using fife symmetrical QD-SOAs based MZI interferometers

Fig (6.3)

Variation of extinction ratio (ER) with peak data power for different current densities, keeping other parameters fixed.

Fig (6.4)

Variation of extinction ratio (ER) with QD-SOA length for different peak data power, keeping other parameters fixed.

Fig (6.5)

Variation of ER with current densities for three different QDSOAs length, keeping other parameters fixed

Fig (6.6)

Variation of ER with the maximum modal gain for three different QD-SOAs length, keeping other parameters fixed

Fig (6.7)

Variation of ER with electron relaxation time from the ES to the GS.

Fig (6.8)

Variation of Q- Factor with current densities for three different maximum modal gains, when the other parameters are kept constant

Fig (6.9)

Variation of Q- Factor with current densities for three different QD-SOA lengths, when the other parameters are kept fixed.

Fig (6.10)

waveforms of all-optical full adder, where (a) input data stream A, (b) input data stream B, (c) input data stream C ( sum-bit S and (e) output carry-bit (

Fig (6.11)

), (d) output

).

Simulated output waveforms with pseudo-eye-diagram (PED)

Chapter (1) Introduction 1.1 Context The advent of digital telecommunications has been preponderant in the recent history of Humanity. The International Telecommunications Union has estimated that in 2008 there were 61 mobile phone subscriptions per 100 inhabitants in the world, while 23% of the world’s population used the Internet and 11% had a broadband connection [1]. We have now grown to be used to being connected anywhere, anytime and with large enough bandwidth to access our email, to browse the web, to chat over an instant messaging service, to make a phone call, to listen or watch an audio or video stream, among several other services the Internet provides us with. The user content generated websites, such as blogs, video hosting sites, online marketplaces and also social networking sites, have changed the way we use the Internet, since everyone can very easily publish personal content online and make it available to a very large number of people. One other major use of the internet is file sharing, namely through peer-to-peer applications. All this variety of services has rendered the Internet as almost indispensable for the regular daily life. As a consequence of the Internet, traffic in telecommunications networks has changed from being mainly local and low bandwidth intensive to world wide and large bandwidth consuming. Telecommunication service providers have to deliver an increasingly larger amount of bandwidth, either wired or wirelessly, at a low price to the end user. As a result, telecommunication system vendors have nowadays the challenge of providing networks that have high transmission capacity, are simple to set up and operate, support a multitude of network services, are flexible, reliable and fault tolerant, and all this at a low cost per transmitted bit. Moreover, energy consumption is

becoming a key factor when operators pick the supplying vendor, for both cost and environmental impact reasons. It is foreseen that the current technology, based on electrical processing, of network nodes is not scalable at the present rate of growth of bandwidth demand [2]. In fact, router capacity has been growing 2-fold every 18 months, just barely enough to keep up with the4-fold traffic demand increase over three years of AT&T; one of the largest network operators in the world [3]. Optical technology seems to alleviate the electronic processing limitations, enabling more scalable network nodes. However, optical technology performance is not yet comparable to its electronic counterpart for system vendors to employ it in a commercial system. In this context, this Thesis intends to contribute towards implementing the new generation of optical networks, by studying the semiconductor quantum dot laser and amplifier down to all-optical devices and techniques, which hold the promise of being the right technology to build larger capacity, more energy efficient, cheaper and more transparent optical networks.

1.2 Motivation The optical fibre is the principal enabler of the large data transmission capacity we have today, with reported capacity times distance product of 112×1015km×bit/s [4], achieved with 155 µm wavelength channels at 100 Gb/s over 7200 km. This record represents an increase of over seven orders of magnitude over 35 years, since the beginning of optical telecommunications [5]. Dense wavelength division multiplexing (DWDM) and time domain multiplexing (TDM) are key technologies for achieving such high transmission bit rates, of the order of tens of terabits per second. Typically, at the network node, the incoming data are converted to the electrical domain, the data headers are processed and the data are then forwarded to the correct output port. With a data rate of tens of terabits per second per fibre arriving at a network node, it is a hard task for the electronics to handle such amount of data due to the limited electronic bandwidth of the order of tens of gigabit per second per channel.

Therefore, there is a bottleneck effect, where the fibre provides very large bandwidth capacity, but at the network nodes there are not enough processing capabilities to take advantage of the fibre capacity. Despite the very large increase of fibre data transmission capacity and different technologies involved, the optical network nodes have always been based in optical-electrical- optical (OEO) conversion, until the adoption of optical add/drop multiplexers (OADM). This was the first optical solution to be adopted, where the traffic is routed in the optical domain, on a wavelength basis. The next solutions, which are currently being adopted, are the reconfigurable OADM (ROADM) and the optical cross connect (OXC), where the OADM functionality is retained, with the added capability of remotely rerouting the traffic without local user intervention. Although, the OADM, ROADM and OXC provide wavelength routing, neither regeneration nor routing at a finer granularity are possible. Therefore, all-optical processing schemes are being proposed to avoid OEO conversion and take advantage of the optical processing capabilities. Regeneration, wavelength conversion, packet routing, optical TDM, bit-wise logic, and various other functions have been demonstrated all-optically, as will be described in detail in the next chapters. By and large, all-optical processing is seen to be key in future optical networks [6]. All-optical processing functions have been mainly achieved by exploiting nonlinear effects on both fibres and semiconductors. The semiconductor optical amplifier (SOA) stands out from other all-optical processing devices since it is integrable, provides gain and requires small optical input powers for non-linear operation. Due to the SOA integrability, interferometric structures have been proposed, which have stable operation when compared to their fibre-based counterparts. The integrated SOA structures allow more optical processing functions than the SOA alone, and at a faster bit rate, as will be shown in the next chapter. In particular, the Mach-Zehnder interferometer with a SOA in each arm (MZI-SOA), and moreover, MZI-SOA integrated arrays have been

used to demonstrate several all-optical functions at 40 Gb/s. Therefore, both the SOA and the MZI-SOA are considered key elements for all-optical processing sub-systems and consequently for future generation optical networks. For this reason, the MZI-SOA was chosen to be the third centerpiece of the optical processing study presented in this dissertation. One drawback of SOA based devices relates to long carrier lifetimes (typically tens to hundreds of picoseconds) which result in significant pattern effect limiting the maximum pattern-effect-free bit rate. The advent of QDSOAs has promised higher pattern free operation capabilities of SOA-based devices. Therefore, QD-SOA is the second centerpiece of this dissertation. As mentioned before, Semiconductor devices are among the most promising candidates for all-optical processing devices due to their high-speed capability up to 160Gb/s, low switching energy, compactness, and optical integration compatibility [6]. Their performance may be substantially improved by using quantum dots in the active region characterized by a low threshold current density, high saturation power, broad gain bandwidth, and a weak temperature dependence as compared to bulk and multi-quantum well (MQW) devices [7].For this reason, the quantum dot laser was chosen to be the first centerpiece of the optical processing study presentedhere. In future high-speed optical communication systems, logic gates will play important roles, such as signal regeneration, addressing, header recognition, data encoding and encryption [8]. In recent years, people have demonstrated optical logic using different schemes, including using dual semiconductor optical amplifier (SOA) Mach-Zehnder interferometer (MZI) [9, 10], semiconductor laser amplifier (SLA) loop mirror [11], ultrafast nonlinear interferometer (UNI) [12], four-wave mixing (FWM) in SOA [13] and cross gain (XGM)/cross phase (XPM) modulation in nonlinear devices [14]. Among above schemes, the SOA based MZI has the advantage of being relatively stable, simple and compact. The final centerpiece presented here is the all optical logic gates based on QD-SOA MZI.

1.3 Thesis objectives and outline The goal of this Thesis is to contribute to the advancement of optical technology enabling the future generations of optical networks. Optical processing is believed to be the path to this goal and therefore all-optical circuits were studied for this purpose. The QD-SOA MZI shows very attractive optical processing capabilities and therefore one objective is to investigate these optical processing capabilities with a focus on its direct use to achieve important functions such as wavelength conversion and 3R regeneration. The characteristics of the quantum dot laser and amplifier which can significantly degrade the performance of the QD-SOA MZI have been investigated to be another objective of this thesis. In the third objective, all-optical QD-SOAbased MZI switches are used to design three all-optical logic gates; XOR, AND, and OR. The final objective and for the first time, a new scheme for alloptical full adder using fife QD-SOA based Mach–Zehnder interferometers is theoretically investigated and demonstrated. The proposed scheme is driven by three input data streams; two operands and a bit carried in from the next less significant stage. The proposed scheme consists of two XOR, two AND, and one OR gate. The following structure in seven chapters was adopted to describe the studies: This first introductory chapter exposes the social and technological context of the Thesis, as well as the motivation and objectives behind the work here presented. It is expected to motivate the reader for the next chapters where the deeper and more arduous content lies. The second chapter introduces the background of the quantum dot laser and amplifier. This includes a brief introduction to the development of quantum dots and quantum dot lasers. Advantages and disadvantages of the latter are discussed As well as the progress in manufacturing. In the discussion of the QD amplifier we concerned on the gain and gain saturation. Some important parameters are also considered in this background such as the Linewidth Enhancement Factor and the Amplified Spontaneous Emission. Finally,

Simulation Methods of Quantum-Dot Semiconductor Optical Devices are outlined. In the third chapter Multi population rate equations model is used to analyze the dynamic characteristics of the InAs/InP (113) B quantum dot laser. In which,

We have solved the rate equations for InAs/InP (113) B self-

assembled quantum-dot laser considering homogeneous and inhomogeneous broadening of optical gain numerically using fourth-order Runge-Kutta method. In the result section, the dynamic (relation with the time) and static (relation with the current) characteristics of proposed QDL are presented. Finally, this chapter studies the effect of the FWHM of homogeneous broadening and the injected current on the rise and fall time, hence on the bit rate. These final results aims to study the possibility of using the QDL as a pulse source for high bit rate data transmission. The fourth chapter proposes a theoretical model of a QD SOA-MZI based ultrafast all-optical signal processor which under certain conditions can simultaneously carry out WC, and 3R regeneration of the distorted optical signals.

The QD SOA-MZI operation has been analyzed theoretically by

solving the rate equations of the QD-SOA dynamics, optical wave propagation equations in an active medium, and the MZI equations. This chapter begins to introduce a brief review for the QD SOA-MZI and its transfer function that will be used to analyze this device. The rate equations model of the QD SOA is also introduced then the QD-SOA characterizations are theoretically investigated and demonstrated. The final two sections of this chapter are devoted to the alloptical W.C. and 3R where the principle, design, and the numerical simulation results will be introduced. In the fifth chapter the all-optical QD-SOA-based MZI switch introduced in chapter four are used to design three all-optical logic gates; XOR, AND, and OR. For each all-optical logic gate this chapter introduces the principle of operation, the proposed design, and the simulation results. In the sixth chapter and for the first time, a new scheme for all-optical full adder using fife QD-SOA based Mach–Zehnder interferometers is

theoretically investigated and demonstrated. The proposed scheme is driven by three input data streams; two operands and a bit carried in from the next less significant stage. The proposed scheme consists of two XOR, two AND, and one OR gate. The impact of the peak data power as well as of the QD-SOAs current density, maximum modal gain, and QD-SOAs length on the Extinction Ratio ER and Q-factor of the switching outcome are explored and assessed. The operation of this system is demonstrated with 160 Gbit/s. The seventh chapter summarized the main conclusions of this work. Future work following from the work presented in this thesis is also suggested here.

Chapter (2) Quantum Dot Devices

Introduction In this chapter, the background of the quantum dot laser and amplifier is introduced. This includes a brief introduction to the development of the semiconductor laser down to the quantum dot lasers. Section 2.1 discusses the concept of the QD starting from semiconductor lasers down to QD laser and its progress in manufacturing taking into account the Inhomogeneous broadening property of the QD. A review of advantages and disadvantages of the quantum dot laser QDL is presented in section 2.2. The quantum dot amplifier and its gain as well as the gain saturation concept are discussed in section 2.3. Sections 2.4 and 2.5 are devoted to the Linewidth Enhancement Factor and the Amplified Spontaneous Emission, respectively. Finally, Section 2.6 introduces the numerical methods used to model the QD laser and amplifier.

2.1 Quantum Dot Semiconductor devices are among the most promising candidates for alloptical processing devices due to their high-speed capability up to 160Gb/s, low switching energy, compactness, and optical integration compatibility. Their performance may be substantially improved by using quantum dots in the active region characterized by a low threshold current density, high saturation power, broad gain bandwidth, and a weak temperature dependence as compared to bulk and multi-quantum well (MQW) devices. This section discusses the concept of the QD starting from semiconductor lasers down to QD laser

2.1.1 Semiconductor lasers Semiconductor lasers are one of the most important inventions of the 20th century. Since their invention in the early 1960s, semiconductor lasers

have been among the most extensively used lasers. Nowadays, semiconductor lasers appear in various areas of our daily life. They present a critical component in optical communication systems [8] and in many commercial products, such as compact disk players [15], laser printers [15], and pointers. Unlike other types of lasers, a semiconductor laser is pumped by electric current and its basic structure is a p-n junction. For this reason, semiconductor laser is also called injection laser or diode laser. Fig.(2.1)shows an example of a separate confinement double heterostructure semiconductor laser. Different layers in such a laser are made of semiconductor materials with different band gaps. Electrons and holes are injected from the n- and p-cladding layers, respectively. In the active region, electrons and holes recombine via spontaneous and stimulated recombination thus generating photons. The generated emission is confined within the waveguide layer (optical confinement layer). Photons leaving the cavity from its facet(s) form the output of a laser.

Fig. (2.1)Schematic view of a separate confinement double heterostructure laser. A key characteristic of a semiconductor laser is the light current curve. It presents the output optical power versus the pump current (Fig. (2.2)). The more linear is this curve, or the larger is its slope, or the closer is the starting point of the curve to the origin, the better is the laser diode. The current density

at which lasing starts is defined as the threshold current density jth. The lower jth, the higher is the output optical power at a given injection current density. The temperature dependence of jth can be empirically described by an exponential function (Fig. (2.2)), where T0 is a figure of merit called the characteristic temperature. The higher T0, the higher is the temperature stability of jth. Lowering jth and improving its temperature stability have been important objectives in the development of semiconductor lasers [16].

Fig. (2.2)Illustrative light-current curve of a semiconductor laser.

2.1.2 Density of States Nowadays, QW lasers almost completely took the place of bulk heterostructure lasers and dominate over the semiconductor laser market. Hence, the quantum confinement effect has already led to high performance QW lasers. To achieve even better performance, a natural approach was to further restrict the motion of carriers in the remaining two directions. This led to the concept of quantum dot (QD) lasers [15]. In a QD laser, the active region consists of a layer (or layers) with a large number of QDs (with a typical QD size on the order of 10 nanometers). Due to the complete confinement of carriers in all three directions, the transitions between the electron and hole levels in QDs are analogous to those between the discrete levels in individual atoms. Fig.(2.3)shows the density of states in semiconductor materials of

different dimensionality. The density of states describes the number of states per unit volume per unit energy. With reducing dimensionality of the active region, the density of states profile becomes narrower and hence a smaller number of states should be filled by carriers to achieve the population inversion required for lasing. As a result, the threshold current is reduced [17]. As seen from Fig. (2.3), with the transition from a bulk (3D) to a quantum well (2D) medium, the density of states remains continuous. A qualitative change to a discrete, delta-function density of states [Fig. (2.3)(c)] occurs only when a QD (0D) medium is used. Radically reduced jth would thus be expected in QD lasers. Another important advantage of QD lasers is high temperature stability of operation. In an ideal QD laser, the injection current should go entirely into the recombination in QDs and the charge neutrality in QDs should hold [8, 15]. In such a case, the threshold current would not depend on temperature and hence the characteristic temperature would be infinitely high [17].

Fig. (2.3)Density of states in materials of different dimensionality: (a) 3D (bulk), (b) 2D (QW), and (c) 0D (QD).

2.1.3 Progress in fabricating QD Although low threshold current and high temperature stability [17] have been predicted for QD lasers in the 1980s, the realization of lasing was lagged

due to the lack of an appropriate technology at that time. Lasing properties of three-dimensionally quantized carriers were first investigated indirectly by placing QW lasers in strong magnetic fields [17], which demonstrated an increase in the characteristic temperature. There have been several approaches to the realization of QD structures. A traditional way was to selectively etch QW structures. In 1987, Miyamoto et al [18].demonstrated electrically pumped light emission from a QD structure, which was realized from an MOCVDgrown GaInAsP/InP QW by applying the holographic process, etching, and overgrowing [18]. The authors reported a Fabry-Perot-mode-like spectrum, which suggested a possible stimulated emission. Later efforts yielded a laser operation, but the devices exhibited high jth (7.6 kA/cm2 at 77 K under pulsed operation), most probably due to a high density of surface states created during etching.

2.1.3.1 Self-assembled growth As mentioned above, the idea of producing semiconductor structures to provide three dimensional confinements was initially thought to require lithography and etching of a planar structure. This was until the self-assembly of small crystal islands was found: InAs has a 7% strain mismatch with GaAs which means that InxGa1−xAs alloys grown on a GaAs substrate accumulate strain as they are deposited. Under the correct growth conditions, InAs initially deposited on the growth surface will form a compressively strained pseudo morphic wetting layer (WL). Further deposition of InAs then increases the strain mismatch until coherent three dimensional islands spontaneously form when the cost in energy for deforming the surface becomes lower than continuing to form the next planar layer. This is called the Stranski-Krastanow [15] growth mode. Importantly, once the islands have been grown they must then be buried into the host crystal; partly so that the islands can be integrated into bulk-crystal heterostructure devices and also to isolate them from the deleterious effects of surface states. Both the formation and burying (or

capping) processes must be controlled so as to keep the islands coherent with the host crystal and to control the size, composition and strain state of the QD. When the island material grown in the Stranski-Krastanow, mode has a lower energy gap than its host matrix, a potential well in all three spatial dimensions can be created in the band structure. These islands are then called quantum dots (QDs) and can confine electrons leading to localized states with well defined energies within the energy gap of the host matrix. The energies of these states are controlled by the size, shape, composition and strain-state of the QD. To decrease the energy of the lowest state (the ground-state or GS) the QD must either be larger in size, have a higher in composition or be under less compressive-strain from the host crystal. The resultant QDs are roughly lens or pyramidal-shaped and have sizes on the order of a 20-30 nm per side square base and 5-10 nm height [19]. The shape and composition of self-assembled quantum dots are properties quite demanding to determine and often only available by indirect means. Precise knowledge of these parameters, [19] on which optical and electrical properties depend, is of major interest.

2.4 Inhomogeneous broadening The self-assembly process discussed before is driven by random fluctuations during growth and therefore unavoidably causes the positions of the QDs to be random and gives a statistical spread in the size-distribution. The random positioning of the QDs is not important for laser devices, as the dimensions of the device enclose enough QDs as to always be dealing with a representative ensemble. However the latter effect causes inhomogeneous broadening (IB) of the ensemble’s optical properties. Because of the way QDs are grown, there is a Gaussian distribution of sizes with a corresponding Gaussian distribution of emission frequencies, Fig. (2.4).These effects lead to inhomogeneous broadening. At cryogenic temperatures, IB is several orders of magnitude wider than the transition linewidth [20]. Assuming that each QD is isolated from the rest, only QDs whose peak emission energy is separated

Fig. (2.4)(a) A schematic of an ideal QD system and, (b), a real QD system, where inhomogeneous broadening is illustrated. (EGS: ground-state energy; EES: excited-state energy; EC: the bottom of the conduction band). from a laser mode by less than their homogeneous linewidth (in the region of 510 meV at room-temperature and increases for higher carrier densities [20]) are able to contribute to its oscillation having an inhomogeneous line-width that is greater than the homogeneous broadening will limit the laser’s efficiency. Therefore growth recipes that result in lower inhomogeneous broadening are desirable. For quantum dots, typical value of homogeneous broadening of few μeVs are normally reported in the literature for low temperature [21]. At room temperature the rate between homogeneous and inhomogeneous broadening is around 4, typical value of homogeneous broadening is on the order of 10-20 meV [20] and inhomogeneous broadening around 40-60 meV.

2.2Quantum Dot Laser A quantum dot laser (QDL) is a semiconductor laser that uses quantum dots as the active laser medium. Quantum dot lasers acquired more importance after significant progress in nanostructure growth in the 1990 such as the selfassembling growth technique for InAs QDs. The first demonstration of a quantum dot laser with low threshold density was reported in 1994 [22]. Room temperature QD edge-emitting lasers, were demonstrated later on [23] and now

match or surpassquantum-well performance. In the following paragraphs a review of advantages of QDL laser is presented.

2.2.1 Advantages of quantum dot lasers The advantages in using quantum dot lasers compared to quantum well lasers are several. A quantum dot laser emits at wavelengths determined by the energy levels of the dots, rather than the band gap energy. Thus, they offer the possibility of improved device performance and increased flexibility to adjust the wavelength. They have the maximum material and differential gain, at least 2-3 orders higher than QW lasers [24]. QDL are expected to show a broader modulation bandwidth, higher temperature stability and lower power consumption than quantum well counterparts, primarily due to the discrete energy states of electrons and holes under three-dimensional quantum confinement by quantum dots [24]. They show superior temperature stability of the threshold current [23]. QD lasers suppress the diffusion of non-equilibrium carriers, resulting in reduced leakage from the active region. Quantum-dot lasers operable at high pulse-repetition rates are capable of reaching pulse energies that will allow modifying living cells, e.g., making accurately controlled incisions in cell structures, while minimizing the attendant effects on cellular environments. Also forming high-density indium-arsenide (InAs) quantum dots on the surface of a gallium-arsenide (GaAs) substrate, improves the laser’s operation speed and enabling a significant improvement over previous technologies. This new technology is expected to be employed nextgeneration high-speed data communications above 100 Gbps [15].

2.3 Quantum Dot Amplifier The development of semiconductor optical amplifiers (SOAs) happened soon after the invention of the semiconductor laser. A SOA is very similar to a semiconductor laser without (or with negligible) optical facet feedback. An incoming signal injected into the SOA propagates along its optical waveguide

and is amplified by stimulated emission. The optical gain is achieved by inverting the carrier population in the active region via electrical pumping. The SOA offers a cost competitive alternative to the Erbium doped Optical Amplifier EDFA when used as an inline amplifier in metro networks, as a power booster and as a preamplifier. Also, in nonlinear operation they can perform all-optical signal processing due to their strong nonlinearities and their fast dynamics[25]. Advent of new SOA generation in the last decade (i.e. quantum well-SOAs and quantum dot-SOAs) has promised enormous improvements over traditional bulk- SOAs. SOAs with quantum wells or dots in their active region have presented higher output power, lower threshold current, good temperature stability, lower noise characteristics and interesting nonlinear properties compared with bulk SOAs. Quantum-dot SOAs (QDSOAs) specially have attracted great interest recently due to interesting specifications of quantum dots and have developed along with quantum dot lasers in recent years. Low-threshold current, high output saturation power, fast gain dynamics and low noise level of QD-SOAs have been proved and it has emphasized that these elements can be utilized as building blocks of all-optical systems. Multi-channel operation capability of QD-SOAs such as multichannel amplification and wavelength conversion provides a great chance for development of WDM network as well as demonstration of all-optical networks [25].

2.3.1 Operation Principles of SOA The operation principle of the SOA lies in the creation of an inversion in the carrier population used to amplify the input optical signal via stimulated emission. The population inversion is achieved by electric current injection into the SOA. Fig.(2.4)shows the simplified band structure of a direct-gap semiconductor. The conduction band and the valence band are separated by the band-gap energy Eg. The current injection leads to free electron–hole pair generation in the conduction band and valence band, respectively. In quasiequilibrium the relaxation times for transitions within either of the bands are

much shorter than the relaxation time between the two bands. So, the carrier distribution within each band can be described by two quasi-Fermi levels denoted by Efc and Efv. The position of the quasi-Fermi levels is determined by the current injection. If the current injection is sufficiently large the separation between the quasi-Fermi levels exceeds the band gap energy (Efc - Efv>Eg) and the semiconductor acts as an amplifier for optical frequencies (υ) with EgΔEf) and the material acts as an attenuator [25].

Fig. (2.4)Simplified band structure of a direct band-gap semiconductor in quasi-equilibrium [25] In a QD-SOA, an optical signal pulse with a wavelength resonant to the GS can be amplified due to stimulated recombination of the GS excitons which lead to GS carrier depletion and consequently the empty states are refilled by fast carrier relaxation from the ES. This fast relaxation from ES to GS is a result of two features: the large energy splitting between the dot levels which ensure slow thermal excitation of carriers, and a high WL carrier density resulting in fast Auger-assisted relaxation. Thus, the ultrafast gain recovery is achieved by the ES level, which acts as a nearby carrier reservoir for the GS level. This recovery time can occur in very short time scale (e.g. 140 fs) [26]. The next optical pulse can only be amplified if the gain has recovered after the first optical excitation. The ultrafast gain recovery following a single pulse excitation is promising for QD-SOA-based ultrafast all-optical signal

processing in the Tb/s range. However, since the carrier capture process from the WL into the dot is slower than intradot relaxation, the ES level recovers on a longer time-scale (picoseconds). The refilling rate of the WL is much longer and is essentially determined by the injection current and the spontaneous recombination rate of the WL and occurs in nanosecond time scale. A schematic of QD-SOA structure including the waveguide structure based on GaAs substrate, p-doped and n-doped cladding layers and QD stacks as active region is illustrated in Fig. (2.5) Also, the energy band diagram of a sample QD in Fig. (2.5) illustrates the amplification mechanism in a QD amplifier.

Fig. (2.5)GaAs-based waveguide structure of a QD-SOA including n and p cladding layers and multi-layer QD active region. Energy band diagram of a sample QD is also sketched

2.3.2 SOA Gain The gain of the SOA results from transitions between the conduction and valence bands which depend on the carrier density and distribution in both bands. There dynamical processes that determine the gain variation after propagating an optical pulse through the SOA can be categorized into interband and intraband classes and the gain coefficient may be described as a combination of these processes [8, 50] ⏟

( )

⏟ (

)

(

)

(2.1)

Where gCDP (carrier density pulsation) is due to interband processes (e.g. spontaneous emission, stimulated emissions and absorption) depended on the carrier density whereas gCH and gSHB are because of the intraband processes (e.g. carrier heating and spectral hole burning). The interband dynamic refers to

the exchange of carriers between the conduction band and the valence band which affects the carrier density and the interband energy gap determines the recovery of the carrier density (N) which is a slow process with a time constant in the range of several tenths of picoseconds. This time constant depends on the SOA geometry and the operating conditions. Interband mechanism dominates the SOA dynamics when long optical pulses are used. On the other hand, when the SOA is operated using pulses shorter than few picoseconds, intraband effects become important. They change the electron distribution within the conduction band and the hole within the valence band. When a short optical pulse arrives to the SOA, it interacts with only a certain part of the carrier distribution, depended on the photon energy and the spectral width of the pulse. The pulse causes a reduction (hole) in the carrier distribution at the particular photon energy (a deviation from the Fermi distribution). This effect is called the spectral hole burning (SHB). The time τSHB, which is the time needed to restore the Fermi distribution by scattering processes (mainly carrier-carrier scattering), is typically several tens of femtoseconds. Carrier heating process (CH) tends to increase the temperature of the carrier distribution above the lattice temperature. The distribution cools down to the lattice temperature through phonon emission. The CH recovery time τCH is several hundreds of femtoseconds to a few picoseconds. The evolution processes of conduction band free carrier distribution after exciting by a picosecond pulse are schematically illustrated in Fig. (2.6).

Fig. (2.6) Temporal evolution of conduction band free carrier density distribution after exciting by a picoseconds optical pulse As it was justified, the average temperature of carriers increase when the optical pulse leaves the SOA, meanwhile the carrier cooling process with a

time constant of τCH redistribute the Fermi distribution to the initial condition and the electrical current injection refills the empty states of the lost carrier. The gain of an amplifier (bulk, QW, or QD-SOA) can be generally defined as (2.2) where the input and output optical powers of the amplifier are denoted by Pin = P (z = 0) and Pout = P (z = L). The amplifier length in the growth direction (z) is given by L. The propagation of light power along the z-axis in an amplifying medium can be described by

(2.3)

P

The solution of the above equation for a constant gain g is in the form of P(z) = Pinexp (gz) which results in the amplifier Gain by extracting output power at z = L as

exp(

(2.4)

)

Since the optical gain depends on the input signal intensity and frequency, it is common to model the frequency-dependant gain coefficient with a homogeneously broadened two-level system ( )

(

⁄

)

where g0 is the maximum value of the gain, of the incident signal,

(2.5)

is the optical angular frequency

is the atomic transition angular frequency, T is the

dipole relaxation time, P the optical power of the incident signal and PS is the saturation power of the gain medium. Thus, the frequency-dependant relation between the amplifier gain G and the optical gain g can be written as G ( ) = exp (g ( ) L). For input signal powers much smaller than the saturation power (P << PS), the gain coefficient reduces to ( )

(

)

which describes a Lorentzian-shape gain spectrum with maximum at

(2.6) =

.

The optical gain bandwidth is defined as the full-width-at-half-maximum

⁄

(FWHM) of the gain spectrum given by

⁄ . Hence, the

amplifier bandwidth (FWHM of G( )) can be obtained through Eq. (2.4) (

)

(2.7)

It is clear from the above equation that the amplifier bandwidth is smaller than the optical gain bandwidth due to the exponential dependence of the amplifier gain to the optical gain. Also, this simplistic model of a homogeneously broadened two level system cannot be applied to QD-SOAs with inhomogeneously broadened gain spectrum [48].

2.3.3 Gain Saturation Increasing the input signal power to the amplifier will result in depletion of the carriers in the active region and consequently decreasing the amplifier gain. This fact is referred as gain saturation which is common between amplifiers and lasers and leads to signal distortion. A typical SOA gain versus output signal power characteristic is displayed in Fig. (2.7) where the 3 dB saturation power is defined as the amplifier output power at which the amplifier gain is half the small-signal gain. Combining Eqs. (2.3 & 2.5)at the maximum gain frequency,

, yields

Fig. (2.7) SOA gain characteristic versus output signal power

(2.8) ⁄ The solution of the above equation when P is comparable to PS, (large signal) will result in the amplifier gain given by (

(2.9)

)

whereG0 = exp (g0L) is unsaturated gain at small input powers. According to the definition presented above for 3 dB saturation power,

(

)

⁄ G,

one can obtain (2.10)

)

In bulk and QW amplifiers the peak gain depends linearly on first order carrier density given by (

⁄ )(

)

(2.11)

where г is the confinement factor, V is the volume of the active region, N0 is the transparency carrier density and a is the differential gain coefficient (a = dg/dN). The carrier density rate equation can then described by ( where I, P,

,

)

(2.12)

and υ are injection current, input signal power, carrier

lifetime, effective cross section of the waveguide node and input signal frequency, respectively. For t >>

(CW operation), Eq. (2.12) may find

stationary solution (dN/dt = 0). By substituting the obtained carrier density in Eq. (2.11), the gain saturation and saturation power in bulk and QW amplifiers, g and PS, can relate to each other through ⁄

=(

⁄ )(

⁄

) (2.13)

Using a 2-level rate equation model for QDs in CW operation mode, the saturation power in the limit of high-inversion condition under high current density where the QD states and the WL band edge are completely filled, can be expressed by [27]

( Where

)

(2.14)

are the characteristic capture time and spontaneous

recombination lifetime of the GS which are typically ~2 ps and ~1 ns respectively. Thus, SHB of the WL (capture time into dot states) determines the saturation power. In the above approximation the WL band edge is assumed to be completely filled while this condition is not fulfilled due to thermal degradation or lasing. It can be concluded by comparing Eqs. (2.13 and2.14) for bulk, QW, and QD amplifiers that a much larger saturation power is expected for QD-SOAs since the carrier capture time is much smaller than the carrier lifetime. It might be worthy to note that the dominant gain saturation mechanism in QD-SOAs can be either SHB or total carrier density depletion (TCDD) depending on the injection current density and input signal power [28]. In small injection currents compared with the signal power the QD states are mostly empty due to amplification process and the gain recovery is achieved through injection current after several carrier capture and escape processes via the common carrier reservoir of the QW-like capping layer since the carrier relaxation processes are incoherent. This gain saturation process is known as TCDD and occurs in bilk or QW-SOAs with a typical recovery time of 0.1–1 ns [29]. In high injection currents compared with the signal power, the QD states are relatively full and the removed carriers through stimulated recombination are replaced from the ES or the WL states. Therefore, the gain saturation in the signal wavelength is attributed to SHB which recovers in less than a few picoseconds [30].

2.4 Linewidth Enhancement Factor An important parameter for the performance of semiconductor optical amplifiers and lasers is the linewidth enhancement factor (LEF), also called parameter (

H).

It is defined as the ratio between the change of the refractive

index and gain (real and imaginary parts of the susceptibility), induced by the carrier-density (N) change. This parameter not only affects the linewidth of a

semiconductor amplifier and laser but also directly connects to the chirp, i.e. the change of emission wavelength during a change of the carrier density. The physical origin of this shift is related to the coupling of the real and imaginary parts of the complex susceptibility in the gain medium. A variation of gain due to a change of carrier density N leads to a variation of the refractive index that modifies the phase of the optical mode in the laser cavity. The coupling strength is defined by the linewidth enhancement factor via the expression [31] ⁄ where

and

(2.15)

are the density-induced variations of the modal refractive

index and of the modal gain, λ is the light wavelength and g is the material gain respectively. A high value of

leads to self-focusing and therefore to

filamentation, which limits the performance of high-power semiconductor lasers. In SOAs, the LEF has become a powerful tool for predicting the nonlinear phase shift observed in connection with gain nonlinearities. In the ideal case of a perfect Gaussian energy distribution the gain spectrum is perfectly symmetric around the peak gain energy and α = 0, i.e. chirp-free. Yet, due to the influence of the carrier density and thermal effects due to heating, the linewidth enhancement factors is neither constant nor zero. Values between 0 and 10, and even negative values have been reported depending on the measurement method and the operating condition [28]. Quantum dot based amplifiers in principle offer the potential to achieve zero LEF due to their atom-like density of states which results in a symmetric gain spectrum. Recent measurements of the LEF in InGaAs/GaAs QD lasers and amplifiers have indicated values of

below 1, however only at low injection currents

near/below transparency or at low temperatures [31]. A smaller LEF at photon energies above the GS, eventually reaching even negative values above the ES, was also observed [31].

1.6 Simulation Methods of QD Semiconductor Lasers and Amplifiers In modeling a semiconductor optical amplifier, one would first consider how the carrier dynamics are modeled. Secondly, one would be concerned about how to model the optical field propagation. There exist many SOA models of different accuracies. The most accurate way of modeling an SOA is to solve the semiconductor bloch equation (SBE) but this is extremely timeconsuming. The computation time is not acceptable for the system applications of SOA-based devices, where many optical pulses have to be transmitted through the SOA to evaluate the system performance. A simplified approach is to include certain physical processes phenomenologically, as it is done in rateequation models. These models enjoy the much faster calculation speeds. Although the accuracy for sub-picosecond pulses is not as good as the SBE calculations, the rate equation models are quite successful in explaining the experimental results for both laser diodes and SOAs. In early 1990s, Mørk et al [32]. introduced the concept of the local carrier density in the SOA modeling and by doing so, intra-band carrier dynamics such as spectral hole burning, carrier heating and free carrier absorption can be modeled with great success to explain the pump-probe experimental results. Numerical modeling is always necessary to understand the working principle of the devices and to optimize their performance. It is also useful to verify a novel idea before implementing it in the lab. It also allows the applications engineer to predict how an SOA or cascade of SOAs behaves in a particular application. It means, physical modeling of complex devices including SOA, such as all-active MZIs, is necessary in order to understand their potential and limitations. In addition, a reliable physical model may be used to investigate new configurations leading to superior ways of operating devices, or possibly to development of entirely new device structures. The main purpose of modeling a QD a laser and QD SOA is to relate the internal variables of the amplifier to measurable external variables such as the output signal power, saturation output power and amplified spontaneous emission (ASE) spectrum. This aids the design and optimization of SOA for a

given application. As the SOA model equations contain coupled derivatives of time and space, thus they have rarely analytical solutions. However, analytical solutions of SOA equations can give a deep understanding on how internal variables of the device vary by external conditions such as injection current, input pump, temperature, etc. Also, an analytical solution may exactly exhibit the limitation of the operation since it contains the influence of physical phenomena explicitly. Due to the mentioned difficulties of obtaining an analytical solution, a numerical solution is required in most of applications. Numerical techniques are usually more complex but make fewer assumptions and are often applicable over a wide range of operating regimes. With the advent of fast personal computers, numerical techniques are beginning to supersede analytical techniques. In spite of intensive research on numerical modeling of QD-SOAs, both theoretically and experimentally, there still remains an unexplored area. This involves the development of equivalent circuit models for QD-SOAs suitable for circuit simulation by using standard packages like SPICE. Considering the fact that numerical techniques as the solution of the rate equations require long and tedious computational time, analysis of equivalent circuit models with circuit programs reduces the computational time several orders [48]. In the next two chapters, we introduce two forms of the rate equations model. Specifically, in chapter two the Multi Population Rate Equations model (MPRE) is used to analyze the dynamic characteristics of the InAs/InP (113) B quantum dot laser. In which, We have solved the rate equations for InAs/InP (113) B self-assembled quantum-dot laser considering homogeneous and inhomogeneous broadening of optical gain numerically using fourth-order Runge-Kutta method, the details of this method is presented in appendix A. On the other hand, in chapter three the simple rate equations model is used to analyze the dynamic characteristics of the quantum dot amplifier. In this chapter, we use the simple rate equations model because it enjoys the much faster calculation speeds than the MPRE.

Chapter (3) Semiconductor Quantum Dot Laser

Introduction Semiconductor quantum dot laser is a recent class of laser sources which is an alternative to the conventional bulk and quantum well lasers. In the development of laser sources an important step concerns the modeling of the devices to be realized, and this requires the use of good methods able to incorporate various physical phenomena present in real devices. In this chapter, the characteristics of the InAs/InP (113) B quantum dot laser are studied by Multi population rate equations model. Section 3.1 introduces a brief dissection about the semiconductor quantum dot laser. QD laser analyzing theory based on the multi population rate equations model is described in section 3.2. Section 3.3 is devoted to our numerical results in which there are three different sets of analysis are introduced. The first two sets are the dynamic and static characteristics. In the third one, the effect of the critical parameters on the rise time, fall time, and the bit rate will be treated. Finally, section 3.4 summarizes the concluded remarks that may be obtained from the displayed results.

3.1 Semiconductor Quantum Dot Laser As mentioned in previous chapters, semiconductor devices are among the most promising candidates for all-optical processing devices due to their highspeed capability up to 160Gb/s, low switching energy, compactness, and optical integration compatibility [6]. Their performance may be substantially improved by using quantum dots in the active region characterized by a low threshold current density, high saturation power, broad gain bandwidth, and a weak temperature dependence as compared to bulk and multi-quantum well (MQW) devices [7].Therefore the moment QD laser has been proposed, and more and more researchers are attracted to this area [33, 34].As a result, thanks to QDs lasers, several steps towards cost reduction can be reached such as

improving the laser resistance to temperature fluctuation in order to remove temperature control elements, or designing a feedback resistant laser for isolator-free transmissions and optics-free module. Most investigations reported in the literature deal with In(Ga)As QDs grown on GaAs substrates [35-37]. Also numerous theories about carrier dynamics in these structures have been introduced [35]. It is however important to stress that In(Ga)As/ GaAs QDs devices do not allow a laser emission above 1.35 µm which is detrimental for optical transmission. In order to reach the standards of long-haul transmissions, 1.55 µm InAs QD lasers on InP substrate have been developed. Recent experimental studies conducted on these devices have shown that a second laser peak appears in the laser spectrum as the injection power increased. The double laser emission is a common property found independently by different research groups for In(Ga)As/GaAs as well as for InAs/InP systems [37]. As mentioned above, Semiconductors lasers with quantum dots in their active regions are expected to exhibit many superior properties. However, we know that actual QDs do not always satisfy our expectations because of the energy level broadening (homogeneous broadening) and size distributions (inhomogeneous broadening) and phonon bottleneck. Thus, for an accurate modeling of quantum dot laser diode performance, we must take into account all these actual aspects of QDs [35].

3.2 Multi Populations Rate Equations Model In the following, a numerical model is used to study carrier dynamics in the two lowest energy levels of an InAs/InP (113) B QD system. Its active region consists of a QD ensemble, where different dots are interconnected by a wetting layer (WL). For simplicity the existence of higher excited states is neglected and a common carrier reservoir is associated to both the WL and the barrier. In order to include the inhomogeneous broadening of the gain due the dot size fluctuation, and to describe the interaction between the QDs with different resonant energies through photons, we divide the QD ensemble into n

= 1, 2,... 2N+1 groups, depending on their resonant energy for the interband transition; of the ES,

, and of the GS,

. As a result, number of

longitudinal cavity photon modes are constructed in the cavity equals to 2M+1, as shown in Fig. (3.1). M =N corresponds to the central group and the central mode with

and

[38]. We take the energy width of each group equals to

the mode separation of the longitudinal cavity photon modes which equals to ⁄ where

(3.1)

is the cavity length. The energy of the n-th QDs group is represented

by (

)

(3.2)

wheren =1,2,...,2N +1.

Fig. (3.1) The interaction between the cavity-mode photons and the carriers in the quantum dots via homogeneous broadening of gain.

Fig. (3.2) Energy diagram of the laser-active region and diffusion, recombination, and relaxation processes

The QDs are assumed to be always neutral and electrons and holes are treated as eh-pairs and thermal effects and carrier losses in the barrier region are not taken into account. Fig.(3.2) shows a schematic representation of the carrier dynamics in the conduction band of the n-th QD sub-group in the active region. First, an external carrier injection fills directly the WL reservoir with I being the injected current. Some of the eh-pairs are then captured on the fourfold degenerate ES of the QD ensemble with a capture time the ES, carriers can relax on the twofold GS WL reservoir time

. Once on

, be thermally reemitted in the

or recombine spontaneously with a spontaneous emission

or by stimulated emission of photons with ES resonance energy. The

same dynamic behavior is followed for the carrier population on the GS level with regard to the ES. This approach has been previously developed for the In(Ga)As/GaAs system [39] but in the case of InAs/InP (113)B system it is assumed that at low injection rates, the relaxation processes are phononassisted while the Auger effect dominates when the injection gets larger [35, 39]. In order to include this effect, a modified model has been considered introducing a direct relaxation channel

to the standard cascade relaxation

model as shown in Fig. (3.2) (dashed line) [39]. It is attributed to a single Auger process involving a WL electron captured directly into the GS by transferring its energy to a second WL electron [35]. Carriers are either captured from the WL reservoir into the ES or directly into the GS within the same time

. This assumption has been made

after analysis of the kinetic curves in [35] where the ES and GS populations gave raise simultaneously 10 ps after excitation. On the other hand carriers can also relax from the ES to the GS. The other transition mechanisms remain the same as in the cascade model. The capture and the relaxation times are then calculated through a phenomenological relation depending on the carrier density in the WL reservoir [40], the ES and GS occupation probabilities, and the existence probability of the ES and GS transitions

(3.3) (

)⁄

(

)(

) (3.4)

(

)⁄

(

)(

) (3.5)

( where (

)⁄

(

)(

)

is the carrier number in the WL reservoir, )

(

is the WL volume and

) are the coefficients for phonon and Auger-assisted relaxation,

respectively, related to the WL and the ES.

and

are the filling

probabilities of the ES and GS, respectively, in the nth subgroup of dots given by (3.6) where

being the ES and GS carrier number in the nth subgroup, the degeneracy of the considered confined states,

density,

is the QD surface

are the width and length of the active region, and

the number of QD layers.

and

being

are the probabilities of recombination

with EESn and EGSn energy, respectively. To calculate them, a Gaussian QD size distribution has been considered with a consequent Gaussian distribution of the QD recombination energies [35]. √

(

)

where the FWHM of the inhomogeneous broadening is given by

(3.7) .

The eh-pairs escape times have been derived considering a Fermi distribution for the ES and GS carriers for the system in quasi-thermal equilibrium without external excitation [40]. To ensure this, the carrier escape time is related to the carrier capture time as follows: (3.8)

)⁄

(

(

)⁄

(3.9)

⁄

where (

(3.10)

)⁄

(

) [41] is the effective density of states in the

WL and EWL is its emission energy,

is the Boltzmann constant. The

numerical model is based on the Multi Populations Rate Equations MPRE analysis already reported in [42]. According to all those assumptions the MPRE system, describing the change in carrier number of the three electronic energy levels; WL, ES, and GS, can be written as ∑

(3.11)

∑ (

) (3.12) ∑ (

) (3.13)

∑ with

being the refractive index and

is the optical confinement factor.

In order to calculate the entire emission spectrum, the model has been extended considering also the presence of many cavity longitudinal modes, Fig. (3.1), hence the photon number with resonant energy of the

mode is

depicted by (3.14)

∑ ∑(

(

)

)

∑ (3.15) ∑(

(

)

)

Where

and

are the number of photons emitted from exited and

ground state at the mode number m, respectively, and

is the total number of

photons at the mth mode which equals to photons (

emitted ⁄

out ( ⁄

(

of )

. The rate of

the

cavity

is

,

with

) being the photon lifetime [42]. The contribution

of the spontaneous emission to the lasing mode is calculated as the ES and GS spontaneous transitions multiplied by the spontaneous emission coupling factor , assumed to be constant. In equations (3.12-3.15), the material gain is described by the set of equations |

|

(

)

(

) (3.16)

|

|

(

)

(

) (3.17)

where H is the average height of the QD and |

|is the density matrix

momentum [43] given by | where

|

|

|

(3.18)

represents the overlap integral between the envelope functions of an

electron and a hole; we take it equals one, and

( Where

is the band gap,

)

(3.19)

is the electron effective mass, is the spin-orbit

interaction energy of the QD material [43]. Furthermore, let us emphasize that the various QD population are coupled by the homogeneous broadening of the stimulated emission process assumed to be Lorentzian such as (

) ⁄ (

(3.20) )

(

⁄

)

with

being the full-width at half-maximum (FWHM) of the homogeneous (

broadening and(

)

) being the mode energy.

All parameters used in the calculations are summarized in Table I.

Parameter

Value

Emission 1.05 eV energy of the Spontaneous WL 500ps emission from Spontaneous ES 1200ps emission from Spontaneous GS 500ps emission from WL WL phonon Aw 1.35·1010s-1 assisted ES phonon relaxation AE 1.5·1010s-1 assisted WL Auger relaxation Cw 5·10-15m3 s-1 coefficient ES Auger CE 9·10-14m3 s-1 coefficient ES central EES0 0.840 eV energy GS central transition EGS0 0.792 eV energy Average QD transition R 1.55·10-6 cm radius Average QD H 2·10-7 cm hight QD Surface 1011 cm2/QD ND density layer Number of QD NW 6 layers Optical 0.036 Confinement Mirror factor R1=R2 0.33 reflectively Cavity internal 10 cm-1 i loss Table I : Parameters Used for Simulation of InAs/InP (113) B quantum dot laser EWL

3.3 Numerical Results The Multi Populations Rate Equations MPRE model together with the photons rate equations Eq.(3.11-3.15) have been solved using the fourth order Runge-Kotta method with the help of the optical gain equations, Eq.(3.16, 3.17). In this section there are three sets of analysis are presented. These sets can be described as follows, In the first set, we achieve dynamic response and analyze photon time evolution of mentioned QD laser at different injected currents and FWHM of homogeneous broadening. Then, the effects of the initial relaxation oscillation time are treated on the number of photons characteristics. While in the second set,we achieve static response and analyze powercurrent evolution of mentioned QD laser at different injected currents and FWHM of homogeneous broadening. Then, the effects of the initial relaxation oscillation time are treated on the power-current and gain-current characteristics. Finally, in the third setwe study the effect of the FWHM of homogeneous broadening and the injected current on the rise and fall time, hence on the bit rate. Finally, the effects of the initial relaxation oscillation time are treated.

3.3.1 Dynamic Characteristics of InAs/InP (113) B Self-Assembled Quantum Dot Lasers In this section the dynamic analysis will be studied. Fig.(3.3) shows the simulation results of photon-characteristics when the inhomogeneous broadening will be neglected, N=M=0. As can be seen from the transient response of the GS and ES shown in Fig.(3.3), the turn on delay decreased as current increases. The ground state lasing starts first and the lasing of the ES delayed when the current is 160A/cm2 and the steady state of the GS is higher. As the current increases the ES lasing becomes faster and the steady state of the two levels increases and comparable to each other. as can be seen from the figure at current density equals 380A/ cm2 the steady state of the ES is higher than that of the GS which known in the published papers by the two states

lasing or double wavelength lasing. All the above can be explained by that as the current increases the carriers supplied to the active region required to starting the lasing is faster and the turn on delay decreased. The two lasing phenomena is due to the direct relaxation process of the carriers from WL to GS. The results shown in Fig.(3.3) is in a good agreement of the that published in [44].

Fig. (3.3) photon-characteristics for N=M=0 and Current Density J= (a) 160A/cm2, (b) 240A/cm2, and (c) 380A/cm2 In the following results the number of groups and modes equals 15, i.e. N=M=7 and we will group the number of photons of the ES and GS in one parameter S, S=SGS+SES. Fig.(3.4) shows the number of photons characteristics of the central mode at =50 meV and

for different current densities, J=16, 25, 50,

and 100A/cm2. Fig.(3.5) shows the same results of Fig.(3.4) except for the homogenous broadening, in Fig(3.5), As can be seen from these two figures, Fig.(3.4, 3.5), as the current increases the turn on delay decreases and the steady state becomes higher. The photons reach its steady state faster for the smaller homogenous broadening factor

. These results can be explained by considering the effect of the

homogeneous broadening of the optical gain of a single dot. When the

homogeneous broadening is negligible with respect to the inhomogeneous broadening, dots with different energies have no correlation to each other since they are spatially isolated from each other. Then, all dots that have an optical gain above the lasing threshold start lasing independently, leading to broadband lasing emission and they reach the steady state independently with no

Fig. (3.4) photon-characteristics at =50meV, Density J= 16, 25, 50, and 100 A/cm2

and Current

influence of any group on the others. The quantum-dot laser at this situation behaves in the same way as if it included independent lasing media in the same cavity. When homogeneous broadening is comparable to inhomogeneous broadening, lasing mode photons are emitted not only from energetically resonant dots, central group, but also from other non resonant dots within the scope of the homogeneous broadening of the central group. Since carriers of non resonant dots are brought into the central lasing mode by stimulated

emission, lasing emission with a narrow line takes place and the steady state of the lasing mode will be slower [50]. So, in quantum-dot lasers, homogeneous broadening of optical gain connects spatially isolated and energetically different quantum dots, leading to the collective lasing of dot ensemble.

Fig. (3.5) photon-characteristics for

=50meV and

and J=

16, 25, 50, and 100 mA/cm2 From a physics standpoint, it is interesting that homogeneous broadening leads to an interaction of spatially and energetically isolated quantum dots through photons, and that collective lasing is achieved. With respect to technology, it is important that the interaction leads to a narrow lasing line at room temperature via collective interaction of energetically non resonant and spatially isolated dots.

To insure the above concept, the following two figures explain the effect of the homogenous broadening. Fig.(3.6) shows photon-characteristics of all modes at

=50meV and J= 100 A/cm2 and (a)

and (b)

.

Fig. (3.6) photon-characteristics at

=50meV and Current Density J= 100

A/cm2 at (a)

and (b)

As can be seen in this figure, for

, all modes start lasing

independently and they reach the steady state independently with no influence of any group on the others. On the other hand, for

lasing

mode photons are emitted not only from energetically resonant dots, central group, but also from other non resonant dots within the scope of the homogeneous broadening. Since carriers of non resonant dots are brought into

the central lasing mode by stimulated emission, as a result, the steady state of the lasing mode will be slower. Figure (3.7) shows the photon-characteristics at

=20meV and J= 100

A/cm2 for different homogenous broadening

these

results are another insurance of the above concept. As can be seen in the figure, as the

decreases the steady state is reached faster.

Fig. (3.7) photon-characteristics at

=20meV and Current Density J= 100

A/cm2 at

Fig. (3.8) photon-characteristics at

=20meV and

and

Current Density J= 100 A/cm2 at different coefficient for phonon relaxation(Aw)

The final result in this section is the study of the initial carrier relaxation which corresponds to phonon bottleneck. Fig.(3.8) shows the photoncharacteristics at

=20meV and

and Current Density J= 100

A/cm2 at different coefficient for phonon relaxation; Aw=0.35*1010, 2.35*1010, 5.35*1010, and 10.35*1010s-1. As shown in Fig.(3.8), as the Aw coefficient increases which means the initial carrier relaxation time decreases, referred to Eqs.(3.3, 3.5), the turn on delay decreases and the steady state value becomes higher. This is because, the injected carriers are consumed in the WL and thus do not contribute to lasing oscillation.

3.3.2 Static Characteristics of InAs/InP (113) B Self-Assembled Quantum Dot Lasers In this section the static analysis will be studied. Fig.(3.9) shows the simulation results of light-current characteristics when the inhomogeneous broadening will be neglected; N=M=0. In this figure, the calculated ES and GS output power are reported as functions of the injection current density. It shows two thresholds corresponding to the two laser emissions. When the ES stimulated emission appears, only a slight decrease of the GS slope efficiency is predicted. At the same time, the global slope efficiency increases. Here, the double laser emission seems to result from the efficient carrier relaxation into the GS due to the increase of the Auger effect for larger injection rates [105]. Although the competition between GS and ES transitions of different QDs is not taken into account in this figure, these numerical results give a good qualitative understanding of the experimental results recently reported for an optical pumped InAs/InP (113)B diode laser [45] and it is in a good agreement of the that published in [44]. Fig.(3.10) shows optical gain-current characteristics for the same case of the results shown in Fig.(3.9); N=M=0. The first point, it seems that optical gain increases to the threshold gain and then becomes fixed with enhancing of the injection current. Actually, what happens when the current is increased to a

value above threshold is that the carrier density and gain initially (by the order of a nanosecond) elevate to values above their threshold levels, and the photon density grows. But then, the stimulated emission rate also heightens that leads to reducing of the carrier density and gain until a new steady-state balance is created [35]. The second point, due to the threshold current of the GS is small than the ES, the GS gain reaches its steady-state value faster than the ES.

Fig. (3.9) Light-Current characteristics of SAQD-LD at N=M=0

Fig. (3.10) Optical gain-Current characteristics of SAQD-LD at N=M=0

Fig. (3.11) Light-Current characteristics of SAQD-LD for

=20meV at

different In the following results the number of groups and modes equals 15, i.e. N=M=7 and we will group the number of photons of the ES and GS in one parameter S, S=SGS+SES. Fig.(3.11) shows light-current characteristics of SAQD-LD for FWHM of inhomogeneous broadening broadening

;

= 20meV at different FWHM of homogeneous

= 0.1, 3, 7, 10, 15, and 20 meV.

In this figure, there are three points have to be highlighted. The first one, the relation between the output power and the injected current is no longer linear as it is in the first case; Fig.(3.9). As can be seen in Fig.(3.12), the nonlinearity appears at

light-current characteristics. This point can be

explained by considering the effect of the homogeneous broadening of the optical gain of a single dot. When the homogeneous broadening is negligible, dots with different energies have no correlation to each other since they are spatially isolated from each other. Then, all dots that have an optical gain above the lasing threshold start lasing independently, leading to broad-band lasing emission and the relation between the output power and the injected current will be linear with no influence of any group on the others. The quantum-dot laser at this situation behaves in the same way as if it included independent lasing media in the same cavity. When homogeneous broadening

is larger, lasing mode photons are emitted not only from energetically resonant dots, central group, but also from other non resonant dots within the scope of the homogeneous broadening of the central group. Since carriers of non resonant dots are brought into the central lasing mode by stimulated emission, lasing emission with a narrow line takes place and the relation between the output power and the injected current will be nonlinear [50]. So, in quantumdot lasers, homogeneous broadening of optical gain connects spatially isolated and energetically different quantum dots, leading to the collective lasing of dot ensemble. The second point in Fig.(3.11), Slope efficiency (external quantum differential efficiency) heightens as the FWHM of homogeneous broadening increases from 0.1 to 10meV then it starts to decline for higher

. It

can be concluded from this point that there is a better value of corresponding to

to extract the maximum output optical power from the

device. To insure this conclusion, Fig.(3.12) shows Lightof SAQD-LD for

characteristics

=20meV at different injected current; I=0.3024 and

0.5184A. As can be seen in Fig.(3.12), there is a better value of

for the

maximum output power which equals in this case 12meV. Also it is clear in this figure, as the injected current increases the output power increases. The third point we want to highlight in Fig.(3.11) is the threshold current. As can be seen in Fig.(3.13) as the

increases the threshold current decreases.

For more explanation of this point, Fig.(3.13) shows the Light-Current characteristics of SAQD-LD for

=20meV at

equals (a) 0.1meV and (b)

10meV. In this figure, the threshold current equals 0.25A for while it equals 0.08A for

=0.1meV,

=10meV. The explanation of this is that as the

increases, carriers of non resonant dots are brought into the central lasing mode by stimulated emission. As a result, the lasing starts faster which means lower threshold current. In the final runwe study the effect of the initial carrier relaxation which corresponds to phonon bottleneck. Fig.(3.14) and Fig.(3.15) show the Optical gain-Current and Light-current, respectively, characteristics of SAQD-LD for

=20meV and

=10meV at different Aw; Aw=0.035*1010, 0.35*1010,

1.35*1010, and 10.35*1010s-1.

Fig. (3.12) Light-

characteristics of SAQD-LD for

=20meV at different

injected current

Fig. (3.13) Light-Current characteristics of SAQD-LD for (a) 0.1meV and (b) 10meV

=20meV at

equals

Fig. (3.14) Optical gain-Current characteristics of SAQD-LD for and

=20meV

=10meV at different Aw

Fig. (3.15) Light-Current characteristics of SAQD-LD for

=20meV and

=10meV at different Aw As shown in Figs.(3.14& 3.15), as the Aw coefficient decreases which means the initial carrier relaxation time increases, referred to Eqs.(3.3, 3.5),the optical gain reaches its steady state (fixed value) slower and the slope efficiency of the Light-current curve declines. This is because, the injected carriers are consumed in the WL and thus do not contribute to lasing oscillation. In other words, the effect of increasing Aw coefficient with respect to the QD region is

equivalent to the increase of the injected current, which means increasing the supplied carriers to the QD region

3.3.3 Semiconductor Quantum Dot Lasers as pulse Sources for High Bit rate Data Transmission A critical part of the design of a communication system is the choice of the transmitter or source laser. High bit rate optical time-division multiplexed (OTDM) systems in particular demand reliable short pulse generation at high repetition rates. Semiconductor lasers are becoming increasingly attractive and viable for such applications. Semiconductor lasers can be compact sources of picoseconds,

high

repetition

rate

pulses

of

light

at

the

popular

telecommunication wavelength of 1.5 μm [46]. Recent advances in semiconductor processing and cavity design have led to the advent of ultrastable [46] and ultralow-noise performance. Single-channel, single polarization transmission rates up to 160 Gb/s [47] have been successfully demonstrated using mode-locked semiconductor lasers, and detailed characterization of their noise properties [47] indicate that they may be useful sources for transmission rates beyond 1 Tb/s. In this section, the effect of the injected current, the FWHM of homogeneous broadening, and phonon bottleneck on the rise time, fall time, and the bit rate will be treated. Fig.(3.16) shows the simulation results of photon-characteristics when the inhomogeneous broadening is neglected, N=M=0. In this figure the normalized number of photons (normalized to its maximum) and the injected current pulse are plotted versus time. The results of Fig.(3.16) represent the ideal case which cannot practically be realized. As seen in this figure, the rise time is exactly equal to the turn-on delay and the time of the relaxation oscillations which is less than 20 psec. On the other hand, the fall time is negligible as it is less than 10 psec.

Fig. (3.16) Normalized photon-characteristics at

and Current

Density; J= 180 A/cm2 In the following investigations, the number of groups as well as the number of modes are set to 15, i.e. N=M=7. Fig.(3.17) shows the normalized number of photons versus time at

=20 meV,

and at

different injected current densities; J=100, 250, 500, and 1000 A/cm2. As shown in Fig. (3.17), the current injected takes the form of a square pulse of width 250 psec. It is shown in this figure that, as the injected current increases the rise time decreasesand the fall time also decreases. And it is also shown that, the rate of decreasing the number of photons during the fall time is much smaller than the rate of decreasing the number of photons during the rise time. If we consider that an injected current pulse represents a logic "1" whereas the absence of the current pulse represents a logic "0", then the bit duration is the time duration of the injected current pulse. If a stream of bits is represented by successive current pulses, the rise and fall times of the signal will limit the speed of transmission. It is known that, the maximum bit rate is the inverse of the bit duration and the minimum bit duration (corresponds to the maximum bit rate), in this work, is taken equal to the rise time. Therefore, the maximum possible bit rate increases with increasing the injected current amplitude.

(a)

(b)

Fig. (3.17.a) Normalized Injected Current Pulse, (b) photon-characteristics at =20 meV, and J= 100, 250, 500, and 1000 A/cm2 All the above can be explained by that as the current increases the number of carriers supplied to the active region required to start lasing is reached faster and the turn-on delay decreases. As a result, the rise time decreases. On the other hand, for high current, when the current is switched off, the number of existing carriers is high enough to increase the rate of stimulated emission and as a result, the fall time decreases.

Figure (3.18) shows dependence of the rise, fall time and bit rate on the injected current. As can be seen from this figure, as the injected current increases the rise time decreases and the fall time alsodecreases. The rate of decreasing the fall time is small with respect to the rate of the decreasing the fall time. Therefore, the bit rate increases with the increase of the injected current.

Fig. (3.18) Depends of the Rise time (a), fall time (b) of the number of photons, and Bit rate (c) on the injected current at =20 meV, To demonstrate the effect of reducing the homogenious broadening on the rise and fall time, the number of generated photons is plotted against time for as shown in Fig. (3.19).

Fig. (3.19) photon-characteristics at =20 meV, Current Density J= 100, 250, 500, and 1000 A/cm2

and

In comparison to the case presented in Fig.(3.17), it is found that the number of generated photons reaches its steady state faster and hence the rise and fall times are smaller for lower FWHM of the homogenous broadening. Figures (3.20), (3.21) and (3.22) show the dependence of the rise time, fall time, and the bit rate on the FWHM of the homogenous broadening,

.

In these results, the current density is used as a parameter and its value are; J=1000, 500, 250, 100 A/cm2. Again, these figures explain that, as the increases, the rise and fall times increase. Hence, the bit rate decreases. These results can be explained by considering the effect of the homogeneous broadening of the optical gain of a single dot. When the homogeneous broadening is negligible with respect to the inhomogeneous broadening, dots with different energies have no correlation to each other since they are spatially isolated from each other.Then, all dots that have an optical gain above the lasing threshold start lasing independently, leading to broadband lasing emission and they reach the steady state and decay independently with no influence of any group on the others. The quantum-dot laser at this situation behaves in the same way as if it included independent lasing media in the same cavity. When homogeneous broadening is comparable to inhomogeneous broadening, lasing mode photons are emitted not only from energetically resonant dots, central group, but also from other non resonant dots within the scope of the homogeneous broadening of the central group. Since carriers of non resonant dots are brought into the central lasing mode by stimulated emission, lasing emission with a narrow line takes place and the time to reach steady state and decay time of the lasing mode will be slower [50].

Fig. (3.20) Rise time versus the Homogenous broadening factor; different injected current

at

Fig. (3.21) Fall time versus the Homogenous broadening factor; different injected current

at

Fig. (3.22) Bit rate versus the Homogenous broadening factor; different injected current

at

Fig. (3.23) photon-characteristics at =20meV and and 2 Current Density CD= 1000 A/cm at different coefficient for phonon relaxation(Aw)

Fig. (3.24) Rise(a), fall(b) time and Bit rate(c) versus the coefficient of phonon relaxation(Aw) at =20meV, The final result is the study of the initial carrier relaxation which corresponds to phonon bottleneck. Fig. (3.23) shows the photon-characteristics at

=20meV and

and Current Density J= 100 A/cm2 at

different coefficient for phonon relaxation; Aw=0.35*1010, and 10.35*1010s-1. As shown in Fig.(3.23), as the Aw coefficient decreases which means the initial carrier relaxation time increases, referred to Equations.(3.3, 3.5), the turn on delay increases and the steady state value becomes lower. This is because, the injected carriers are consumed in the WL and thus do not contribute to lasing oscillation. It can be seen also that, the effect of this parameter on the rise and fall time is weak. To see this effect, we plot in Fig.(3.24) the dependence of rise and fall time and the bit rate on the Aw coefficient.

As can be seen, the rise time increases and the fall time decrease as the Aw coefficient increases. As a result, the bit rate increases. These results can be explained by noting that, the effect of increasing Aw coefficient is equivalent to the increase of the injected current, which means increasing the supplied carriers to the QD region

Chapter (4) QD-SOA-Based Mach-Zehnder Interferometer (MZI) Introduction Practical implementation of all-optical signal processing unit requires integrated all-optical devices for ease of manufacturing, installation, and operation. The semiconductor optical amplifier Mach–Zehnder interferometer (SOA-MZI) is an integrated all-optical logic gate which can fulfill these requirements.

Conceptually,

SOA-MZI-based

logic

gate

operation

is

straightforward, relying on optically inducing XGM, XPM or other nonlinear phenomena between the SOAs located in each of the two interferometer arms. This chapter proposes a theoretical model of a QD SOA-MZI based ultrafast all-optical signal processor which under certain conditions can simultaneously carry out wavelength conversion WC and 3R Regeneration of the distorted optical signals. The QD SOA-MZI operation has been analyzed theoretically by solving the rate equations of the QD-SOA dynamics, optical wave propagation equations in an active medium, and the MZI equations. Section 4.1 introduces a brief review for the QD SOA-MZI and its transfer function that will be used to analyze this device. The rate equations are introduced in section 4.2 while the QD-SOA characterizations are theoretically investigated and demonstrated in section 4.3. Sections 4.4 and 4.5 are devoted to the all-optical W.C. and 3R where the principle, design, and the numerical simulation results will be introduced. Finally, section 4.6 summarizes the concluded remarks that may be obtained from the displayed results.

4.1. SOA-MZI (Brief review) Realization of future all-optical switching networks regardless of their exact operational specifications strongly depends on all-optical signal processing methods and elements. Advanced all-optical signal processing functions such as all-optical header recognition, buffer, switching, wavelength

conversion, logic gates, flip-flop memory, etc. should be realized. In particular, wavelength conversion is very crucial in all of optical switching schemes including optical circuit switching, optical burst switching and optical packet switching [48, 49]. All-optical signal processing functions are usually performed using nonlinear optical effects that occur in a device under certain conditions. All-optical signal processing based on optical fibers profit several advantages such as easy coupling to the transmission link, low operation noise and ultrafast nonlinear phenomena (tens of femotoseconds) which make them attractive for high-speed all-optical signal processing beyond 1 Tb/s. However, these elements suffer from bulky nature of fiber-based devices which is demanded for observation of noticeable nonlinear effect and prevent the integration of the processing unit. Also, due to small nonlinear coefficient, the input optical power (usually more than 20 dBm) is too high for practical application in ultra-high bit rate all-optical signal processing systems. Semiconductor optical amplifier-based devices have been proposed to suitable alternatives in all-optical signal processing due to the gain and nonlinear properties, operation at low powers and small device dimensions. One drawback of SOA based devices relates to long carrier lifetimes (typically tens to hundreds of picoseconds) which result in significant pattern effect limiting the maximum pattern-effect-free bit rate. The advent of DQ-SOAs has promised higher pattern free operation capabilities of SOA-based devices. Although several studies have been done to increase the operation speed and gain recovery time of QD-SOAs as discussed in previous chapters. In recent years considerable progress has beenmade in SOA-based all-optical signal processing including demonstration of complicated logic devices which are mainly based on SOA nonlinear phenomena like cross gain modulation (XGM), cross phase modulation (XPM), four wave mixing (FWM) and cross polarization modulation (XPolM). Combination of these effects has yielded state of the art all-optical devices and functions such as high-speed all-optical wavelength conversion at 320 Gb/s, 640 Gb/s-to-40 Gb/s all-optical demultiplexing, penalty-free all-optical 3R regeneration (re-amplification,

reshaping and re-timing) at 84 Gb/s, 8-state optical flip-flop memory, optical shifter register, an optical pseudo-random binary series generator, optical half adder and full adder [49]. In these complicated systems, optical logic gates play a significant role. Optical logic gates, specifically, XOR gates, are actually used to realize packet address recognition in the IST-LASAGNE project [49]. These examples clarify the importance of SOA-based devices in all-optical signal processing.

Fig. (4.1) SMZ configuration and nonlinear phase response cancel out mechanism

4.1.1. SOA-MZI Gate Practical implementation of all-optical signal processing unit requires integrated all-optical devices for ease of manufacturing, installation, and operation. The semiconductor optical amplifier Mach–Zehnder interferometer (SOA-MZI) is an integrated all-optical logic gate which can fulfill these requirements.

Conceptually,

SOA-MZI-based

logic

gate

operation

is

straightforward, relying on optically inducing XGM, XPM or other nonlinear phenomena between the SOAs located in each of the two interferometer arms. Figure 4.1 shows the configuration of a SOA-MZI gate also known as symmetric Mach–Zehnder (SMZ) where SOAs used as nonlinear elements are placed in both arms of a MZI [49]. The control light governs the dynamics of nonlinear optical effects and the probe light experiences the nonlinear optical effects. The control and probe beams can be either return-to-zero (RZ) pulses,

as in Fig. 4.1, or non-return-to-zero (NRZ) light. The control pulse induces carrier depletion and thus modulates the gain and phase of the probe light which are called XGM and XPM, respectively. These nonlinear optical effects induced through the carrier density change in semiconductors, are generally highly efficient, which means that device operation can be realized in a compact size and with low power control beam. In addition to this, the control light, which depletes carriers, is amplified in SOA and thus, lowers the required power of input control light. Differential arrangement of SOAs on both arms of the MZI with an appropriate time delay,

resolves the low gain recovery time

since the similar phase responses of the SOAs cancel out each other as depicted schematically in Fig. (4.1). The operation of the proposed device can be explained as follows: Control pulses with a specified duration and repetition rate cause the change in the total carrier number or the carrier density in SOAs.

Fig. (4.2) Structure of SOA and hybrid-integrated SMZ gate Short control pulses cause depletion in the carrier density and the slow recovery in the carrier density is compensated by exciting both arms with an interval of

. In this timing interval the gating window for the probe beam

opens while outside this interval the destructive interference for the probe beam at the output of the Mach–Zehnder interferometer is maintained even though the carrier density in the SOAs on both arms is slowly recovered. Therefore, the rising and falling of the gate window are defined by the control pulse

duration [50]. The technology of integrating optical circuits is an important key for developing practical MZI-based all-optical gates. SOAs incorporated into Mach–Zehnder interferometers can be used as appropriate unit call for optical logic gates. The integration of active and passive waveguides for SMZ gates has been developed both in a hybrid manner and in a monolithic manner. Figure (4.2) depicts a hybrid integrated device where SOAs are mounted on a silica-based planar lightwave circuit (PLC) [48]. Monolithic integration of SMZ gates with other active devices, such as input and output optical amplifiers and fixed or tunable diode lasers and significant reduction in the footprint of Mach–Zehnder optical circuits using photonic-crystal waveguides [51] are important technological outcomes in the way of realizing integrated all-optical signal processing devices.

4.1.2. SOA-MZI Transfer Function

Fig. (4.3) Schematic of SOA incorporated MZI structure QD-SOAs incorporated with MZI are one of the most applicable configurations in optical logic gates. Similar to other fiber-based devices including QDSOAs as nonlinear element such as semiconductor laser amplifier loop optical mirror (SLALOM) and terahertz optical asymmetric demultiplexer (TOAD), SOA in MZI structure presented in Fig. 4.3can be modeled with a nonlinear device with a gain effect and phase shift applied on input signal. Thus, the transfer function of such a structure can be obtained through following manner. In the above configuration (A1, A2) and (D1, D2) are input and output lightwaves, respectively, (k1, k2) are normalized coupling coefficients of the input and output couplers and (B1, B2) and (C1, C2) are

input and output lightwaves to the QDSOAs, respectively. The gain and phase shift of each QDSOA is considered with (G1, Ф1) and (G2, Ф2) for upper and lower arm QDSOAs [5]. The time-dependent gain can be expressed as ( )

( )

(

( )) where

( ) is the SOA modal gain and

( )is the active medium length. Considering each pair of input and output lightwaves one can write [127] (

)

(

)(

) (4.1)

An optical signal travelling through the amplifier will experience an amplification of √ and a phase shift of Ф. Therefore,

( )

(

√

)(

√

)

(4.2)

Then, the transfer function can be described as (

)

(

)(

) (4.3)

Where (

)

(

)√

(

)

(

)√

(

(

)

(

)√

(

)

(

)√

)

(

(

)

(

)√

(

)

(

)√

)

(

)

(

)√

(

)

(

)√

(4.4)

Denoting the input and output signal powers with PA1, PA2, PD1 and PD2 and assuming an ideal 3 dB coupler (

( )

( )

√ ⁄ ) the transfer

function reduces to |[

]

|

[

√

]

|[

]

|

[

√

]

(4.5)

(4.6)

(4.7) As mentioned above, when the control signals A1 and/or A2 are fed intothe two SOAs they modulate the gain of the SOAs and give rise to the phase modulation of the co-propagating CW signal due to the linewidth enhancement factor (LEF)α[8, 51]. LEF values may vary in a large interval from the experimentally measured value of LEF =0.1in InAs QD lasers near the gain saturation regime [51] up to the giant values of LEF =60measured in InAs/InGaAs QD lasers [52]. However, such limiting cases can be achieved for specific electronic band structure [54]. The typical values of LEF in QD lasers are

[53]. Detailed measurements of the LEF dependence on

injection current, photon energy, and temperature in QD SOAs have also been carried out [31]. For low-injection currents, the LEF of the dot GS transition is between 0.4 and 1 increasing up to about 10 with the increase of the carrier density at room temperature [31]. The phase shift at the QD SOA-MZI output is given by [10]

(4.8) It is seen from (4.8) that the phase shift the gain. For the typical values of LEF

is determined by both LEF and , gain

, and

the phase shift of about π is feasible

4.2. Rate Equations In the QD SOA-MZI, optical signals propagate in an active medium with the gain determined by the rate equations for the electron transitions in QD-SOA between WL, GS and ES [55, 56]. In this model, we have taken into account the two energy levels in the conduction band: GS and ES. The diagram of the energy levels and electron transitions in the QD conduction band is shown in Fig. (4.4).The stimulated and spontaneous radiative transitions occur from GS to the QD valence band level.

Fig. (4.4) (a) Schematic diagram of a QD-SOA, (b) energy band diagram of a QD system and the WL. The system of the rate equations accounts for the following transitions: 1) the fast electron transitions from WL to ES with the relaxation time ; 2) the fast electron transitions between ES and GS with the relaxation time from ES to GS

and the relaxation time from GS to ES

; 3) the slow electron escape transitions from ES back to WL with the electron escape time

.

The balance between the WL and ES is determined by the shorter time of QDs filling. Carriers relax quickly from the ES level to the GS level, while the former serves as a carrier reservoir for the latter [40]. In general case the radiative relaxation times depend on the bias current. However, it can be shown that for moderate values of the WL carrier density this dependence can be neglected [36, 50]. The spontaneous radiative time in QDs

remainslarge enough:

(

)

[55, 56].

For the case of the signal detuning smaller than the QD spectrum homogeneous broadening the electron rate equations have the form [99] (

)

(4.9)

( ( (

) (

)

)

(4.10)

(

)

( (

)

)

(4.11)

)

(4.12)

where variable Z is the longitudinal direction along the QD-SOAs length L, i.e. Z=0, means for the input and Z=L for the output facet of each QD-SOA, variable t is the local time measured in a coordinate system moving with the pulse group velocity

. The functions used in the derivatives [Eqs. (4.9-4.12)]

are the photon density of input data signals, which is related to their power (

(

), with the equation as

)

(

)⁄(

),where

is the effective cross section of the QD-SOAs, the group velocity of the propagating signal, and (

, where

is is the photon energy

is the speed of the light in vacuum and

wavelength of the incident light). The electron density in WL is

is the , and the

electron occupation probability in the ES and GS is h and f , respectively. (

Also,

)

,

where

maximum modal gain, where l,

and

effective thickness of the active QD layers, of the resonant QDs, and

is the number, surface density and is the homogeneous linewidth

is the material absorption coefficient, J is the injection current the electron relaxation time from the WL to

the surface density of QDs, the

effective thickness of the active

the electron escape time from the ES to the WL,

radiative lifetime in the WL, GS,

the

the inhomogeneous linewidth of the QD ensemble

density, e the electron charge,

layer,

is

is the resonant cross section of the carrier-photon interaction [57].

Furthermore,

the ES,

√

the spontaneous

the electron relaxation time from the ES to the

the electron escape time from the GS to the ES and

radiative lifetime in the QDs [41 - 43].

the spontaneous

Fig. (4.5) (The considered spatiotemporal grid on which the 4th order Runge-Kutta method is applied. L: the QD-SOAs length. N=10 the number of uniform segments that the QD-SOA is divided into. Δz: the length of each spatial segment. Δt: the temporal interval

between

two

consecutive

samples of an input pulse. The system of coupled Equations (4.9-4.12) is numerically solved in a step-wise manner for pulses that belong to a data signal. For this purpose, each input pulse is sampled over its period at discrete intervals, Δt, while the QDSOA is divided into 10 uniform segments of length Δz, as shown in Fig. (4.5). The 4th order Runge-Kutta method (Appendix A) is then applied on the created spatio-temporal grid of size Δt x Δz= Δt x L/10 ≈ 4 ps µm to find the amplification factor, which by definition is ( )

)⁄ (

(

), where L is

the QD-SOA length. This procedure is followed for typical QD-SOA parameters' values taken from the literature [58, 59], which include ,

=

0.25µm,

,

,

and

.

It has to be noted that, the above model specifically Eq.(5, 6) vary depending on the application. In remaining of this thesis we use this model for different applications (wavelength conversion, 3R Regeneration, all-optical logic gates and circuits) and we explain the difference in each case. Furthermore, the input data pulse streams are belong to a 160 Gbit/s pseudorandom binary sequence and have a Gaussian power profile[41, 42, 48]: ( where

)

(

is their peak power and

( )(

)

)

(4.13)

=2 ps is their full width at half

maximum, FWHM. BD= 6.25ps is the bit duration.

4.3. QD-SOA CHARACTERIZATION Given the central role of the QD-SOA in the operation of the MZI configured as logic gate it is important to characterize the dynamical behaviour of this device with respect to several critical operational parameters. This is necessary in order to be able to properly interpret in next sections and chapters the simulation results obtained when QD-SOAs are incorporated in the MZI. In fact the information given by most of previous reported works [5862] as part of the study on the performance of a QD-SOA-based MZI intended for use in the implementation of all- optical logic gates at ultrafast bit rates is not sufficient or complete for the pursued goal. More specifically, [59] have dealt with the QD- SOA carrier dynamics and the temporal evolution of the occupation probabilities in the discrete levels of the QD system. In [62] the temporal dependence of the gain has been obtained both for a single input pulse and a non return-to-zero (NRZ) input pulse train. In the first case the result concerns the saturation and quick recovery of the QD-SOA caused by the pulse as it enters and leaves the device, respectively. In the other case the focus is on the gain that is modulated by the NRZ input pulse train and it is shown to respond directly to the input data pattern, i.e., the gain is saturated as long as logic ones enter the QD-SOA and it recovers when one or more logic zeros appear at the input. The same study examines also the change of the QD-SOA gain dynamics by a NRZ input pulse train for different values of

which

shows that the decrease of this parameter speeds up the gain recovery of the QD-SOA. Moreover in [58], the temporal dependence of the gain is derived for the case of a single input RZ pulse and for different values of J and τ

The

results for J indicate that the increase of this parameter accelerates the gain recovery of the QD-SOA, while the results for τ

reveal that this parameter is

a limiting factor for the QD-SOA gain dynamics. Finally, regarding the QDSOA saturation properties, in [62] the steady-state static gain has been obtained as a function of the input power for different values of J, which shows that the gain begins to saturate as the input power is increased and that the saturation power is increased with J. This dependence on J can also be noticed in [61],

where the 3 dB input saturation power, Pin,sat, is calculated as a function of J for different values of QD-SOA length. This unveils that if the current density is kept constant the QD-SOA saturation power is decreased as its length is increased. This means that the longer the device is, the more easily it can be saturated by a smaller input power. Despite the significant contribution of the aforementioned works, a more comprehensive characterization of a QD-SOA intended for use as nonlinear element for interferometric switching should take into account the impact of a whole set of critical parameters. This task is of a greater importance when the mode of operation is pulsed and the strain imposed on the operating conditions is quite demanding [63], as in our case. Therefore we have focused on the QDSOA gain dynamics and their dependence on these parameters, since it is expected that they will affect the performance of the proposed logic function. Specifically, in Figs. (4.7& 4.8) we examine the instantaneous QD-SOA gain variation for different values of the critical parameters, Ppeak, GmaxJ, L, and

.

This task is accomplished for a few pulses, which have been selected to be the last four pulses in the longest run of these bits inside the PRBS. This is done in order to ensure that a saturation equilibrium has been established for the QD-SOA gain dynamics and thus that the conducted characterization is as realistic as possible. For this purpose the process that is followed is to change each time one parameter while keeping the rest constant. Specifically, the typical values chosen to be fixed for, Gmax, J, L, and

are

15/cm, 3 kA/cm2, 3mm, and 0.15 ps, respectively. On the other hand the choice for the peak input data power has been dictated by the gain saturation of the QD- SOA that occurs under pulsed mode of operation. In this context the saturated gain, which is defined as the minimum of the instantaneous gain that is dropped after the pulse has acted on the QD-SOA has been plotted as a function of this parameter in Fig. (4.6).

Fig. (4.6) Variation of minimum instantaneous QD-SOA gain versus peak input data power. The difference ΔP = 4 dBm denotes the deviation of the QD-SOA bias point chosen as fixed for the simulation analysis from the 3 dB input saturation power. From this figure we see that the 3 dB saturation input power [32] is Pin,sat= 7.5dBm. Thus in order for the QD-SOA to be adequately saturated for the needs of this characterization while at the same time keep Ppeak reasonable we set Ppeak,fixed= 11.5 dBm. The incremental deviation of this fixed value from the 3 dB QD-SOA saturation input power under pulsed mode of operation defines an interval, which is indicated in Fig. 4.6 by the vertical dotted lines and the arrows attached on either side of them. The extent of this interval is determined by the, dimensionless, relative difference ΔP = Ppeak,fixed - Pin,sat= 4 dB, within which the QD-SOA single pass gain has been reduced by 5.96 dB. Therefore the remarks that will be extracted for the QD-SOA characterization conducted under the specific bias condition will also hold for a lower saturation level. Figure (4.7a) shows the instantaneous QD-SOA gain variation for different values of the peak input data power. First, it is observed that the initial level of the gain is not its maximum modal gain value, which also holds for Figs. (4.7. b, c, dand4.8. a, b). This happens because as already mentioned the examined pulses are the last four pulses. For this reason when this pulses enter the QD-SOA it encounter a gain that has been partially recovered after it have been saturated by the preceding mark. Now the amount that the gain is dropped from its maximum value, ΔG, becomes larger as Ppeak is increased.

Fig. (4.7) Instantaneous QD-SOA gain variation for different (a) Peak input power (b) maximum modal gain (c) current density (d) Length

This is consistent with Fig. (4.6) and the fact that as Ppeak is changed in this direction the QD-SOA becomes more saturated because of carrier depletion. Furthermore, this gain drop is favourable to impart a differential phase between the decomposed components of probe pulse (Fig.(4.1)) as close as possible to π and hence achieve full switching. Then the dynamic gain response for different values of the QD-SOA maximum modal gain is illustrated in Fig. (4.7. b). Notably the drop of the gain from its unsaturated value is greater for larger maximum modal gain. More specifically, for gmax = 11/cm the drop is ΔG ≈ 0.97 dB, while for gmax =15cm-1 ΔG ≈ 2.7dB. Thus similarly to the case of the peak input data power the extent of the QD-SOA saturation quantified by ΔG becomes larger as gmax is increased, which as mentioned is helpful for creating the desired phase difference between the MZI arms. Moreover, Fig. (4.7c) shows the instantaneous QD-SOA gain variation for different values of current density. The increase of J from 2 to 4 kA/cm2 supplies the GS with more carriers that are available for the gain recovery process and thus the latter is accelerated. However, if J is further increased to 5 kA/cm2 the effect on the dynamical behavior of the gain is not so pronounced. This happens because the ES and WL, which act as carrier reservoirs for the GS, have been adequately filled and the additionally supplied carriers do not fully participate in the QD-SOA gain recovery process. Finally, in Fig. (4.8a) we present the instantaneous QD-SOA gain variation for different electron relaxation times from the ES to the GS and for the chosen fixed value of current density. With the decrease of

from 1.3 to 0.3 ps carriers relax faster

from the ES to the GS and so the process of gain recovery is made faster. At the same time there are more carriers involved in the amplification process which leads to less intense saturation and gain modulation. This also holds for the case in which

is decreased down to 0.15 ps. But when the QD-SOA

becomes saturated subject to the consecutive bits of the PRBS, more carriers relax to the GS. Therefore they are depleted in the upper levels, i.e., the ES and the WL, eventually becoming insufficient for speeding up the QD-SOA gain recovery. Nevertheless, if the current density is

Fig. (4.8) Instantaneous QD-SOA gain variation for (a) J = 1 kA/cm2, (b) J = 3 kA/cm2. concurrently increased, the behavior of the gain is altered in a common manner for all considered changes of investigating the impact of

, as shown in Fig. (4.8b). This means that when on the switching capability of the logic gate it is

also necessary to take into account the simultaneous effect of J.

4.4. Wavelength Conversion (WC) Cross-gain modulation based wavelength conversion is one of simplest schemes to achieve all-optical wavelength conversion which employs gain saturation effect in active region of SOAs. The principle of this scheme for a QD-SOA based wavelength converter is illustrated in Fig. (4.9a). the input data signal at the wavelength

and a co-propagating CW-beam at the wavelength

are coupled into the SOA. Due to high optical power of data signal, it causes total carrier depletion in the active region and therefore the gain saturation occurs. The CW-signal at

experiences this change in the gain

so that CW-beam traversing the SOA with a mark (in data signal) will experience a lower gain than light traversing with a space. This scenario is sketched in Fig. (4.9b). Therefore, the SOA output contains a copy of the original data signal with inverted polarity at

. A filter should be placed at

the output of the SOA in this technique to omit the

and pass the

. This

filter can be omitted if the two signals counter-propagate through the SOA.

Fig. (4.9) (a) Wavelength conversion scheme based on cross-gain modulation in an SOA and (b) mechanism of XGM-based on gain saturation The main disadvantageous of this method are: 1)The chirped output signal caused by XGM [48]. This arises from the frequency shift at the leading and trailing edges of the converted pulses due to carrier dynamics which results in a severe penalty in polarity conversion scheme and hence limits the transmission distance in a dispersive fiber. 2) The smaller differential gain for longer wavelengths. This results in smaller output extinction ratio for upconversion (conversion to longer wavelengths) than for down-conversion (conversion to shorter wavelengths). 3) The possible polarity conversion-based problems in signal processing. The polarity conversion-based problem of the introduced structure becomes much important in the case of using RZ data format. Since the polarity inversion is associated with pulse inversion, devices employing this scheme should have identical RZ pulse shapes. Cross-phase modulation based wavelength conversion is another technique that doesn’t have the limitations of the XGM-based schemeFigure (4.10) schematically shows the structure of which consists Mach–Zehnder interferometer with two SOAs on both arms of the interferometer [48].

Wavelength conversion in this scheme is achieved according to the different phase changes experienced by the CW beam in two interferometric arms of MZI. The data signal at the wavelength

coupled to the port 1 modulates the

carrier density and therefore the refractive index of the active region of SOA due to its high power. Meanwhile, the CW beam at the wavelength

is

coupled to port 3 of the MZI-SOA structure and is split into two equal parts (if the coupler is 3 dB) travelling through the upper and lower interferometer arms. The CW beam in the lower arm experiences a constant phase change, φ2, which depends on the lower SOA bias current while the phase change experienced by the CW beam in the upper arm, φ1, depends on the bit pattern of the input data signal. Therefore, at the output of the MZI the split CW beams can combine constructively or destructively to transfer the data signal pattern to the CW beam. The theoretical analysis of the proposed ultrafast QD SOA-MZI processor is based on the combination of the MZI model with the nonlinear characteristics and the QD-SOA dynamics. At the output of MZI, the CW optical signals from the two QD SOAs interfere giving the output intensity [10, 53]. [ [ where via

]

√

(4.15)

]

√

(4.14)

is the CW or the clock stream optical signal divided and introduced the

symmetric

coupler

into

the

two

QD-SOAs.

are the non inverted converted and the inverted converted output, respectively. System of equations (4.9-4.12) constituting a complete set of equations describing XGM and XPM in QD SOA are essentially nonlinear and extremely complicated. Their analytical solution in a closed form is hardly possible, and for this reason, this system of equations has been solved numerically for the same typical parameters values of the QDSOA which are stated in previous section.

Fig. (4.10) Schematic of SOA-MZI configuration for wavelength conversion based on cross phase modulation effect The situation here is like that, there is only one data signal interacts with the CW-light signal as shown in Fig. (4.10). In such a case, WC occurs between the input signal at the wavelength

propagating through

the upper arm of QD SOA-MZI and the CW-light with

. Figure

(4.11) shows the input waveform (data A) and the simulated output waveforms, specifically, the non-inverted converted version of input data and the inverted version. It can be seen from this figure that the quality of the non-inverted output is better than the quality of the inverted one. Therefore, in the remaining of this section we will study the effect of the important parameters on the ER for the non-inverted output.

Fig. (4.11)

Realization of WC by XPM between the data signal A with and CW-light with . for the bit rate 160Gb/s.

Figure (4.12) illustrates the effect on the ER with; (a) peak power of the input data signals, (b) maximum modal gain, (c) the current densities, and (d) QD-SOA length. In each case the other parameters are kept fixed.

As it can be observed from Fig. (4.12.a), the obtained curve exhibits a bell-like variation with a maximum point at around 11dBm, on either side of which the ER is decreased. In order to interpret this behavior we recall from Figures (4.6, 4.7) that the peak input data power determines the extent of the QD-SOA gain excursions, ΔG, which in turn makes the phase difference between the MZI arms lie in different intervals [82]. This affects analogously the magnitude of switching and accordingly the ER. Thus initially the ER is

Fig. (4.12) Variation of extinction ratio (ER) with (a) peak data power, (b) the maximum modal gain, (c) the current densities, and (d)QD-SOA length. increased with the peak input data power, because QD-SOA1 is progressively brought into deeper saturation and the phase difference approaches closer to its optimum value of π. However as the examined parameter is increased further beyond 11dBm, the additional differential gain that is induced causes the phase difference to diverge away from π [82]. As a result the ER does not continue to improve but it is declined with a steeper slope than that of its rising part due to the stronger carrier depletion. The ER is acceptable within a total input power dynamic range of roughly 5.5dBm, whose central peak power of 11dBm which can be provided by commercial erbium doped fiber amplifier. Fig. (4.12.b) shows the dependence on maximum modal gain. It can be noticed that there is a similarity between the obtained curve and that of Fig.

(4.12.a). This is attributed to the common impact that both parameters have on the QD-SOAs dynamical behaviour, as demonstrated in Section 4.3. Therefore, as this parameter is altered the phase difference created between the replicas of CW-light undergoes a variation analogous to that described in the context of Fig. (4.12.a). This means that in order to achieve switching as anticipated according to the requirements of wavelength conversion an efficient level of maximum modal gain is necessary. The ER remains above 10 on either side of a maximum modal gain of approximately 15 cm-1, where it becomes a maximum. For given QD- SOAs length this maximum modal gain range can be achieved in a feasible manner by intervening in the number of the QD layers when designing the QD-SOA structure [71], as discussed in section 4.2.

Figure (4.12.c) illustrates the ER versus the QD-SOAs current density. For small current densities, the ER is sharply increased, and after exceeding its required minimum, it becomes almost independent of this parameter. This happens because a lower current density facilitates the saturation of a QD-SOA [61]. As a result the gain of QD-SOA1 is dropped to a greater extent and it becomes more difficult for it to recover closer to its unsaturated value, which is additionally verified by Fig. (4.7c). Consequently, the ER is very low and hence totally inadmissible. In contrast, a larger current density offers a redundancy of supplied carriers and thus permits the dynamical optical properties of QD-SOA1 to reach an equilibrium state, which has a positive impact on the considered metric. Fig. (4.12.c) shows that if J is adjusted to be over 2.17 kA/cm2 then the ER is made acceptable. The corresponding bias current is 260.4 mA, which lies within reasonable limits and can be practically supplied by commercial current sources [61]. Therefore a moderate current density is fine for allowing the proposed wavelength conversion circuit to be realized at least with an adequate performance. Figure (4.12.d) shows the ER as a function of the QD-SOAs length. It can be noticed that there is an apparent similarity between the obtained curve and that of Figures (4.12.a & b) for the peak data power and the maximum modal gain, respectively. This is attributed to the common impact that these parameters

have on the QD-SOAs dynamical behavior and subsequently on the switching performance. In particular the QD-SOAs length determines the extent that the gain of each QD-SOA is dropped from its unsaturated level [58] and subsequently the amount of the differential gain created between the MZI arms. Since this quantity imparts through the line width enhancement factor a differential phase shift, it can be realized that the changes of

also affect φ

and hence the ER in a way analogous to that described in the context of Fig. (4.12.a). this reason the three ER diagrams resemble in shape both having a rising and a falling part, although the effect on the ER magnitude is more pronounced for the QD-SOAs length because the gains G1 and G2 that enter in the expressions of the characteristic transfer functions are influenced directly by its variation ,Eq. (4.5). The ER remains above 10 dB on either side of a QD-SOAs length of 3mm, where it becomes maximum, and within a range of approximately 1.1mm, which for given QD-SOAs maximum modal gain can be achieved by intervening in the number of the QD layers when designing the QD-SOA structure. Design Parameters According thus to Figs. (4.12a-d) it can be inferred that the requirements for the critical parameters, to have a good performance with reasonable amplification,

are

,

, mm, and

. By

following these guidelines and using the combination of values ,

J=

,

L=3mm,

,

respectively,

which

obviously is not unique and it fall within the specified boundaries, a more than adequate ER of about 15dB can be obtained, which is reflected on the high quality of pulse stream obtained at the output [8]. On the other hand, when we use another combination of values such as

, J=

, L=4mm,

, respectively. These

values are not falling within the specified boundaries. ER in this case equals 4.8dB, which is reflected on the low quality of pulse stream obtained at the

output. The input waveforms and the simulated output waveforms are shown in Figs. (4.13a-c), respectively.

Fig. (4.13) waveforms of wavelength conversion-based QD-SOA MZI, where (a) input data stream A, (b) output with ER=15dB, (c) output with ER=4.8dB

Fig. (4.14) Simulated waveforms with pseudo-eye-diagram (PED)where (a) input data stream A, (b) output with O=98%, (c) output with O=62% Figures (4.14 a-c) demonstrate Simulated waveforms with pseudo-eyediagram (PED) for (a) input data stream A, (b) output with ER=15dB, and (c) output with ER=4.8dB. As can be seen from these figures, the quality of case (b) is better than that of case (c). The relative eye opening (O) in case (b) equals 98%, whilst it equals 62% for case (c).These values indicate a quite good response of the circuit under consideration at its output terminals in case (b).

4.5. 3R Regeneration (Re-amplification, Re-shaping and Re-timing) Short optical pulses propagating in optical fibers are distorted due to the fiber losses caused by material absorption, Rayleigh scattering, fiber bending, and due to the broadening caused by the material dispersion, waveguide dispersion, polarization-mode dispersion, intermodal dispersion [8, 64]. 3R regeneration is essential for the successful logic operations because of the ultrafast data signal distortions. 3R regeneration requires an optical clock and a suitable architecture of the regenerator in order to perform a clocked decision function [48]. In such a case, the shape of the regenerated pulses is defined by the shape of the clock pulses [65, 66].

Fig. (4.15) Schematic configuration used for 3R regeneration in an QD-SOS MZI The proposed QD SOA-MZI ultrafast all-optical processor can successfully solve three problems of 3R regeneration. Indeed, the efficient pattern-effect free optical signal re-amplification may be carried out in each arm by QD-SOAs. WC based on the all-optical logic gate provides the reshaping since noise cannot close the gate, and only the data signals have enough power to close the gate [48]. The retiming in QD-SOA-MZI based processor is provided by the optical clock which is also essential for the reshaping [66]. Hence, if the CW signal is replaced with the clock stream, the 3R regeneration can be carried out simultaneously with logic operations. The analysis shows that for the strongly distorted data signals a separate processor is needed providing 3R regeneration before the data signal input to the logic gate.

In our model, there is only one data signal interacts with the clock signal as shown in Fig. (4.15). In such a case, 3R occurs for the optical signal A at the wavelength

propagating through the upper arm of QD SOA-MZI

with the help of the clock signal with

.

Fig. (4.16) Waveforms of 3R-based QD-SOA MZI, where (a) Noisy input data stream A, (b) Regenerated output, (c) Clock Figure (4.16) shows the noisy input waveform (data A), the regenerated output waveforms, and clock waveforms. It can be seen from this figure that the quality of the regenerated output is excellent and it depends basically on the clock waveforms. Therefore, in the remaining of this section we will study the effect of the important parameters on the ER for the regenerated output. Figure (4.17) illustrates the effect on the ER with; (a) peak power of the input data signals, (b) maximum modal gain, (c) the current densities, and (d) QDSOA length. In each case the other parameters are kept fixed. As it can be observed from Fig. (4.17.a), the obtained curve exhibits a bell-like variation with a maximum point at around 12dBm, on either side of which the ER is decreased. In order to interpret this behaviorwe recall from Figures (4.6, 4.7) that the peak input data power determines the extent of the QD-SOA gain excursions, ΔG, which in turn makes the phase difference between the MZI arms lie in different intervals [82]. This affects analogously the magnitude of switching and accordingly the ER. Thus initially the ER is

increased with the peak input data power, because QD-SOA1 is progressively brought into deeper saturation and the phase difference approaches closer to its optimum value of π. However as the examined parameter is increased further beyond 12dBm, the additional differential gain that is induced causes the phase difference to diverge away from π [82]. As a result the ER does not continue to improve but it is declined with a steeper slope than that of its rising part due to the stronger carrier depletion. The ER is acceptable within a total input power dynamic range of roughly 1.9dBm, whose central peak power of 12dBm which can be provided by commercial erbium doped fiber amplifier.

Fig. (4.17) Variation of 3R extinction ratio (ER) with (a) peak data power, (b) the maximum modal gain, (c) the current densities, and (d)QD-SOA length. Fig. (4.17.b) shows the dependence on maximum modal gain. It can be noticed that there is a similarity between the obtained curve and that of Fig. (4.17.a). This is attributed to the common impact that both parameters have on the QD-SOAs dynamical behaviour, as demonstrated in Section 4.3. Therefore, as this parameter is altered the phase difference created between the replicas of CW-light undergoes a variation analogous to that described in the context of Fig. (4.17.a). This means that in order to achieve switching as anticipated according to the requirements of wavelength conversion an efficient level of maximum modal gain is necessary. The ER remains above 10 on either side of a maximum modal gain of approximately 15 cm-1, where it becomes maximum.

For given QD- SOAs length this maximum modal gain range can be achieved in a feasible manner by intervening in the number of the QD layers when designing the QD-SOA structure [71], as discussed in section 4.2.

Figure (4.17.c) illustrates the ER versus the QD-SOAs current density. For small current densities, the ER is sharply increased, and after exceeding its required minimum, it becomes almost independent of this parameter. This happens because a lower current density facilitates the saturation of a QD-SOA [61]. As a result the gain of QD-SOA1 is dropped to a greater extent and it becomes more difficult for it to recover closer to its unsaturated value, which is additionally verified by Fig. (4.7c). Consequently, the ER is very low and hence totally inadmissible. In contrast, a larger current density offers a redundancy of supplied carriers and thus permits the dynamical optical properties of QD-SOA1 to reach an equilibrium state, which has a positive impact on the considered metric. Fig. (4.17.c) shows that if J is adjusted to be over 2.8 kA/cm2 then the ER is made acceptable. The corresponding bias current is 336 mA, which lies within reasonable limits and can be practically supplied by commercial current sources [61]. Therefore a moderate current density is fine for allowing the proposed wavelength conversion circuit to be realized at least with an adequate performance. Figure (4.17.d) shows the ER as a function of the QD-SOAs length. It can be noticed that there is an apparent similarity between the obtained curve and that of Figures (4.17.a & b) for the peak data power and the maximum modal gain, respectively. This is attributed to the common impact that these parameters have on the QD-SOAs dynamical behavior and subsequently on the switching performance. In particular the QD-SOAs length determines the extent that the gain of each QD-SOA is dropped from its unsaturated level [58] and subsequently the amount of the differential gain created between the MZI arms. Since this quantity imparts through the line width enhancement factor a differential phase shift, it can be realized that the changes of

also affect φ

and hence the ER in a way analogous to that described in the context of Fig. (4.17.a). this reason the three ER diagrams resemble in shape both having a

rising and a falling part, although the effect on the ER magnitude is more pronounced for the QD-SOAs length because the gains G1 and G2 that enter in the expressions of the characteristic transfer functions are influenced directly by its variation ,Eq. (4.5). The ER remains above 10 dB on either side of a QD-SOAs length of 3mm, where it becomes maximum, and within a range of approximately 0.29mm, which for given QD-SOAs maximum modal gain can be achieved by intervening in the number of the QD layers when designing the QD-SOA structure. Design Parameters According thus to Figs. (4.17a-d) it can be inferred that the requirements for the critical parameters, to have a good performance with reasonable amplification,

are

,

, mm, and

.

By following these guidelines and using the combination of values ,

J=

,

L=3mm,

,

respectively,

which

obviously is not unique and it fall within the specified boundaries, a more than adequate ER of about 10.5dB can be obtained, which is reflected on the high quality of pulse stream obtained at the output [8].

Fig. (4.18) Waveforms of 3R-based QD-SOA MZI, where (a) Noisy input data, (b) Output with ER=10.5dB, (c) Output with ER=2.8dB

On other hand, when we use another combination of values such as , J=

, L=4mm,

, respectively. These values

are not falling within the specified boundaries. Therefore, ER in this case equals 2.8dB, which is reflected on the low quality of pulse stream obtained at the output. The input waveforms and the simulated output waveforms in the two cases are shown in Figs. (4.18a-c), respectively.

Fig. (4.19) Simulated waveforms with pseudo-eye-diagram (PED)where (a) Noisy input data stream A, (b)output with O=93%, (c) output with O=42.5%

Figures (4.19 a-c) demonstrate Simulated waveforms with pseudo-eyediagram (PED) for (a) input data stream A, (b) output with ER=10.5dB, and (c) output with ER=2.8dB. As can be seen from these figures, the quality of case (b) is better than that of case (c). In other words, the relative eye opening (O) in case (b) equals 93%, whilst it equals 42.5% for case (c).These values indicate a quite good response of the circuit under consideration at its output terminals in case (b).

Chapter (5) All-optical Logic Gates Introduction All-optical logic gates are indispensable modules for making feasible the concept of signal processing exclusively by means of light in order to take full advantage of the potential of optical fibers in modern networks without problematic conversions in the electronic domain. In This chapter, all-optical QD-SOA-based MZI switch introduced in chapter four are used to design three all-optical logic gates; XOR, AND, and OR. Section 5.1 introduces a brief review for the all-optical logic gates. The next three sections(5.2 – 5.4) are devoted to our proposed all-optical logic gates; XOR, AND, and OR gate, respectively. In each of these three sections, principle and design of proposed all-optical gate will be introduced. In addition, these sections contain the simulation results of its gate. Finally, some of the concluding remarks and discussions are contained in section 5.5.

5.1 All-Optical Logic Gates In future high-speed optical communication systems, logic gates will play important roles, such as signal regeneration, addressing, header recognition, data encoding and encryption [8]. In recent years, people have demonstrated optical logic using different schemes, including using dual semiconductor optical amplifier (SOA) Mach-Zehnder interferometer(MZI) [9, 10], semiconductor laser amplifier (SLA) loop mirror [11], ultrafast nonlinear interferometer (UNI) [12], four-wave mixing (FWM) in SOA [13] and cross gain (XGM)/cross phase (XPM) modulation in nonlinear devices [14]. Among above schemes, the SOA based MZI has the advantage of being relatively stable, simple and compact. As mentioned in previous chapters, operation speeds of these schemes are limited by no more than 40 Gb/s. In order to realize higher speed data processing, faster device and schemes are needed. The emergence of quantum-dot (QD) SOAs in recent years provided a better

device for signal processing at communication band. Up till now, such device has experimentally demonstrated high saturated output power and low noise figure [32, 67], ultrafast carrier relaxation between QD energy states [68] and a much smaller carrier heating (CH) impact on gain and phase recovery [69]. In recent years, rate equations approach is widely used to simulate these logic operation based on QD-SOAs [70]. In this chapter,all-optical QD-SOA-based MZI switch introduced in chapter four are used to design three all-optical logic gates; XOR, AND, and OR. The reason to choose these gates is that they will be combined in one logic circuit to perform an all optical full adder in next chapter. It is worth referring to that the mathematical model that is used in these analyses is the model introduced in chapter 4. In which, the system of coupled Equations (4.9-4.12) is numerically solved in a step-wise manner for pulses that belong to a data signal Eq. (4.13). For this purpose, each input pulse is sampled over its period at discrete intervals, dt, while the QD-SOA is divided into n uniform segments of length dZ. The 4th order Runge-Kutta method is then applied on the created spatio-temporal grid of size , to find the amplification factor, which by definition is (

)

(

). This procedure is followed for typical QD-SOA parameters'

values taken from the literature [58, 71]. The general and common parameters used in the calculations of the proposed gates are summarized in Table (5.1). Parameter

Value

Value

2 cm

1.2ps

1200ps

0.4ns

3ps Lw

Parameter

-1

NQ

0.25µm

4.5

1ns

0.2ns

width

3 µm

Pulse duration

6.25 ps

Pulse width

2ps

Table 5.1 : Parameters Used for Simulation of the AllOptical AND

5.2 All-Optical AND Gates The AND gate is indispensable for achieving lightwave broadband communications networks as it is involved in the accomplishment of numerous tasks in the optical domain both in fundamental and system-oriented level, such as buffering, address comparison, add-drop multiplexing, packet clock and data recovery, packet header and payload separation, binary pattern recognition, binary counting, analog-to-digital conversion, digital encoding and comparison, data regeneration, waveform sampling, binary addition, multiplication, construction of other logic gates and of combinational logic circuits [48, 72, 73]. Given its importance, multi-lateral role the AND gate has attracted intense research interest and among the technological options that exist for its implementation those that exploit a semiconductor optical amplifier (SOA) are well established [48]. In fact, besides being employed for classical applications such as signal generation, amplification, and modulation [48, 71], SOAs have also demonstrated their potential as nonlinear switching elements for performing all-optical AND logic, either as stand-alone entities [73, 74] or incorporated in an interferometric configuration [75]. Nevertheless, the extension of the use of these digital logic modules as AND gate at ultrafast data rates is limited by the inherently slow SOA gain recovery time and the associated pattern- dependent performance degradation [29]. The negative byproduct of this fact is that it is not possible to satisfy the unceasing demand for more bandwidth since single channel data rates are upgrading to magnitudes that exceed by far the SOAs ultrafast potential [76]. As mentioned in chapter 4, QD-SOAs with their special structure are very promising devices thanks to their distinctive physical properties that have been constantly improving during recent years over conventional SOAs. Owing to its attractive features the QDSOA-based MZI has been the primary choice for the demonstration of alloptical logic functions [77-80].Therefore we introduce in this section a simple, affordable and versatile way implement the AND gate using the classic MZI scheme [48]. The adopted approach requires only two distinct data trains between which the AND function is directly executed, with only one of them

being strong and inserted in only one QD-SOA. The feasibility of the scheme is thoroughly investigated by applying a numerical model that takes into account the dynamical behaviour of QD-SOAs in order to simulate the operation of the standard MZI configured as AND gate when it receives a pair of fully-loaded pseudorandom binary sequences (PRBS) as inputs. This is done at 160 Gb/s where it will be shown that the conducted theoretical analysis allows thoroughly investigating and assessing the impact of these parameters on the metric of Q-factor (the definition of the Q-factor is presented in Appendix B). Then we extract a set of design rules for their selection and combination within their specified allowable range so that the AND function can be executed at the target ultrafast data rate both with logical correctness and high quality.

5.2.1 Principle of Operation of Proposed AND Gate The configuration of the proposed AND gate considered in the conducted theoretical treatment is shown in Fig. (5.1). and the output power can be expressed as [

√

]

(5.1)

All parameters are explained in previous chapters. The configuration is based on the symmetrical MZI architecture, in which the same QD-SOAs, QD-SOA1 and QD-SOA2, are placed in the upper and lower arm, respectively. A data-carrying signal A enters through a wavelength selective coupler (WSC) QD-SOA1, while a data-carrying signal B is inserted in the MZI and is split via the input 3 dB coupler C1 into a pair of identical parts, which travel separated along the QD-SOAs located in their path. Signal A should be at least an order of magnitude stronger than signal B [58]. These signals are discriminated by using different wavelengths, such that their

Fig. (5.1) Simulated setup of QD-SOA-based MZI configured for Boolean AND operation between data A and B. detuning in the 1550nm region is less thanthe homogeneous broadening of QDSOA1 [58]. In this manner only signal A can modify the nonlinear optical properties of QD-SOA1 and induce a change on the gain and phase of signal B. Now if B = `0' then regardless of the binary content of A we get nothing at output port (O/P), simply because there is no input signal on which to imprint any perturbation of the initially balanced MZI and to transfer to the O/P, as can be extracted from Eq. (5.1). This is a trivial situation, which changes when B = `1', namely when data sequence B contains a pulse. In this case the result at O/P depends on the existence or not of a pulse in the same bit slot of data sequence A. More specifically, if A = `0', QD-SOA1 remains intact to the same dynamical state as QD-SOA2 so that the decomposed constituents of B perceive the same gain. Thus when they recombine at 3 dB coupler C2 they interfere destructively, which results in a space at O/P. But if A = `1' QDSOA1 undergoes a radical change of its gain compared to the non-driven QDSOA2. Consequently the copy of B in the upper MZI arm acquires via crossphase modulation [81] a nonlinear phase shift against its counterpart in the lower MZI arm, which eventually creates a relative phase difference between these components. If this quantity is ideally made equal to π then it is possible to maximize the amount of the power that emerges at O/P and hence the amplitude of the obtained mark. According to this mode of operation a pulse occurs at O/P if and only if a pulse is present in both signals A and B whilst no pulse appears at the specific terminal if a pulse is absent from either A or B or

from both of them. In other words O/P = `0' when (A, B) = (0, 0), (0, 1) or (1, 0), and O/P = `1' when A, B = (1, 1). These combinations of logical pairs and their outcome form the truth table of Boolean AND logic executed between A and B, which means that the QD-SOA-based MZI in the setup of Fig. (5.1) is configured as AND gate.

5.2.2 Numerical Results of Proposed AND Gate In order to examine whether the proposed QD-SOA-based MZI scheme can be configured as ultrafast AND gate at 160 Gb/s we evaluate its performance against the Q-factor. In order to ensure acceptable performance, the Q-factor must satisfy the criterion to be over six. Details of the design metrics; ER, AM, Q- Factor, and PED are presented in Appendix B. Thus in the following we investigate whether this goal can be achieved at 160 Gb/s in terms of the critical operational parameters, which include the peak input data power as well the QD-SOAs maximum modal gain, current density and electron relaxation time from the ES to the GS.Fig. (5.2) illustrates the effect on the Q-factor with peak power of the input data signals for three different current density values, when the other parameters are kept fixed.

Fig. (5.2) Variation of Q-Factor with peak data power for different current densities, keeping other parameters fixed.

As it can be observed, the obtained curve exhibits a bell-like variation with a maximum point at around 11dBm for J=3kA/cm2, on either side of which the Q-factor is decreased. In order to interpret this behavior we recall from Figures (4.6, 4.7) that the peak input data power determines the extent of the QD-SOA gain excursions, ΔG, which in turn makes the phase difference between the MZI arms lie in different intervals [82]. This affects analogously the magnitude of switching and accordingly the Q-factor. Thus initially the Qfactor is increased with the peak input data power, because QD-SOA1 is progressively brought into deeper saturation and the phase difference approaches closer to its optimum value of π. However as the examined parameter is increased further beyond 11dBm, the additional differential gain that is induced causes the phase difference to diverge away from π [82]. As a result the Q-factor does not continue to improve but it is declined with a steeper slope than that of its rising part due to the stronger carrier depletion. The Qfactor is acceptable within a total input power dynamic range of roughly 4dBm, whose central peak power of 10.8 dBm which can be provided by commercial erbium doped fiber amplifier; we consider the Q- factor = 10 as a limit. Another point, the common characteristic of all curves is that the maximum value changes and shifted to the right as the current density becomes larger. From a physical perspective this happens because the current density determines the power required to alter the optical properties of a QD-SOA and properly saturate its gain, and the higher it is the more power is necessary for this purpose [61]. This fact also explains that as we move well enough into the falling slope of the curves a larger current density is necessary to enhance the Q-Factor and hence improve performance for a given power. This in turn allows selecting the peak data power from a wider range of permissible values, which potentially offers greater flexibility in the design of the AND gate. Figure(5.3) shows the Q-factor against the QD-SOAs maximum modal gain for three different QD-SOAs length, when the other parameters are kept fixed. It can be noticed that there is a similarity between the obtained curve and that of Fig. (5.2).This is attributed to the common impact that both parameters

have on the QD-SOAs dynamical behaviour, as demonstrated in Section 4.3. Therefore, as this parameter is altered the phase difference created between the replicas of input data signal B undergoes a variation analogous to that described in the context of Fig. (5.2).This means that in order to achieve switching as anticipated according to the requirements of AND operation an efficient level of maximum modal gain is necessary. The Q-factor remains above 10 on either side of a maximum modal gain of approximately 16 cm-1 for L=4mm, where it becomes maximum. For given QD- SOAs length this maximum modal gain range can be achieved in a feasible manner by intervening in the number of the QD layers when designing the QD-SOA structure [71], as discussed in section 4.2. It can also note in this figure; the common characteristic of all curves is that the maximum value is shifted tothe right as the QD-SOAs length becomes smaller. The smaller value of the maximum modal gain requires the longer QD-SOAs length to obtain the maximum value of Q-factor.

Fig. (5.3) Variation of Q-Factor with the maximum modal gain for three different QD-SOAs length, keeping other parameters fixed

Figure (5.4) illustrates the Q-factor versus the QD-SOAs current density for two different QD-SOA lengths, when the other parameters are kept fixed. For small current densities, the Q-factor is sharply increased, and after exceeding its required minimum, it becomes almost independent of this

parameter. This happens because a lower current density facilitates the saturation of a QD-SOA [61]. As a result the gain of QD-SOA1 is dropped to a greater extent and it becomes more difficult for it to recover closer to its unsaturated value, which is additionally verified by Fig. (4.7c). Consequently, the Q-factor is very low and hence totally inadmissible. In contrast, a larger current density offers a redundancy of supplied carriers and thus permits the dynamical optical properties of QD-SOA1 to reach an equilibrium state, which has a positive impact on the considered metric. Fig.(5.4) shows that if J is adjusted to be over 1.7 kA/cm2 then the Q-factor is made acceptable. The corresponding bias current is 204 mA, which lies within reasonable limits and can be practically supplied by commercial current sources [61]. Therefore a moderate current density is fine for allowing the proposed AND gate to be realized at least with an adequate performance. The second point which can be noted from this figure is that the higher value of J requires the longer QDSOAs length to obtain the same value of Q-factor.

Fig. (5.4) Variation of Q-Factor with current densities for two different QDSOAs length, keeping other parameters fixed Figure (5.5) illustrates the effect on the Q-factor with QD-SOAs length for two different peak powers of the input data signals, when the other parameters are kept fixed. The common characteristic of these curves is that the Q-factor is increased with QD-SOAs length to a certain value after that it is

dropped. The maximum value is shifted to the left as the peak power becomes larger. The smaller value of the QD-SOA length requires the larger peak control power to obtain the maximum value of Q-factor.

Fig. (5.5) Variation of extinction ratio (Q-Factor) with QD-SOA length for two different peak data power, keeping other parameters fixed.

Fig. (5.6) Variation of Q-Factor with electron relaxation time from the ES to the GS for two different QD-SOAs length, keeping other parameters fixed Figure (5.6) depicts the Q-factor as a function of the QD- SOAs electron relaxation time from the ES to the GS for two QD-SOAs length, when the other parameters are kept fixed. This figure demonstrates that in order for the proposed scheme to operate without logical errors, this parameter must not be

chosen arbitrarily fast, as it would be expected from the evidence available on the implementation of another basic logic function using the QD-SOA-based MZI [59]. In fact

must not be too small neither too large so as to avoid

impairing the quality of switching in terms of the Q-factor. More specifically, for

>0.32ps the Q-factor starts becoming degraded and as

is increased

further in this region the performance of the proposed AND gate is strongly deteriorated due to the slower QD-SA1 gain recovery process described in the QD-SOA characterization. On the other hand for

<0.32ps the very fast

relaxation of the carriers from the ES to the GS causes the carrier density in the upper energy levels of the discrete QD-SOA energy diagram to be dramatically decreased. This results in lack of supplied carriers, which limits the ultrafast operation of the MZI and renders the Q-factor unacceptable. Thus we need to take jointly into account the contribution of the current density, as inferred from the discussion of the QD-SOA characterization (section 4.3). To this end the current density must be properly chosen as specified from Fig. (5.4). The Q-factor remains over 6 against

within approximately 1.17 ps. The values

lying in this range as well as the maximum of 0.95 ps are typical for

[83].

Design Parameters According thus to Figs. (5.2-5.6) and their interpretation, it can be inferred that the requirements for the critical parameters are ,

, , and

mm,

0.3ps.

By following these guidelines and using the combination of values ,

J=

,

L=4mm,

,

and

,

respectively, which obviously is not unique, which fall within the specified boundaries, a more than adequate Q-factor of about 15.15dB and ER of about 14 dB can be obtained, which is reflected on the high quality of pulse stream obtained at the output [8].On other hand, when we use another combination of values such as

, J=

, L=2mm,

, and

, respectively. These values are not falling within the specified

boundaries. ER in this case equals 5dB, and Q-factor of about 2.5dB which is reflected on the low quality of pulse stream obtained at the output. The input waveforms and the simulated output waveforms for the two cases are shown in Figs. (5.7), respectively.

Fig. (5.7) waveforms of AND gate -based QD-SOA MZI, where (a) input data stream A, (b) input data stream B, (c) Output with Q=15.15, (d) Output with Q=2.5 Figs. (5.8 a-c) demonstrate Simulated waveforms with pseudo-eyediagram (PED) for (a) input data stream A or B, (b) output with Q=15.15, and (c) output with Q=2.5. As can be seen from these figures, the quality of case (b) is better than that of case (c). The relative eye opening (O) in case (b) equals 92%, whilst it equals 22% for case (c).These values indicate a quite good response of the circuit under consideration at its output terminals in case (b). Concurrently, for the case shown in Fig. (5.7c), the marks are sufficiently balanced and the difference between their peak amplitudes is only 0.1 dB, as verified by Fig. (5.9.a). In this figure, the uniform drop of QD-SOA1 gain in response to data signal A can be easily noted. On the other hand, for the case shown in Fig. (5.7.d), the marks are unbalanced and the difference between their peak amplitudes is higher than 0.1 dB, as verified by Fig. (5.9.b). In this figure, the inconsistent drop of QD-SOA1 gain in response to data signal A can be easily seen.

Fig. (5.8) Simulated waveforms with pseudo-eye-diagram (PED)where (a) input data stream A, (b) output with O=92%, (c) output with O=22%

Fig. (5.9) Gain response of QD-SOA1 to data stream A of Fig. (5.7). for (a) Q=15.15, (b) Q=2.5

5.3 All-Optical XOR Gates XOR logic gate is one of the most applicable gates in optical signal processing and is a key element to implement primary systems for binary address and header recognition, binary addition and counting, pattern matching, decision and comparison, generation of pseudorandom binary sequences, encryption and coding. This gate has been demonstrated at 40 Gb/s and 80 Gb/s [80] using SOA-MZI differential schemes that have been deployed to overcome the speed limitations imposed by the bulk SOAs slow recovery time.

However, it is predicted that QD-SOA based XOR gates have the potential to operate above 160Gb/s bit rates [53]. A 0 0 1 1

B 0 1 0 1

XOR 0 1 1 0 (b)

(a)

Fig. (5.10) (a) Simulated setup of QD-SOA-based MZI configured for Boolean XOR operation between data A and B and (b) its truth table.

5.3.1 Principle of Operation of Proposed XOR Gate The configuration of the proposed XOR gate considered in the conducted theoretical treatment is shown in Fig. (5.10.a).The output power can be expressed as [70] [

√

]

(5.2)

It is based on the symmetrical MZI architecture, in which the same QD-SOAs; QD-SOA1 and QD-SOA2, are placed in the upper and lower arm, respectively. A first input data (A) enters through a wavelength selective coupler (WSC) QD-SOA1, and a second input data (B) enters through a wavelength selective coupler (WSC) QD-SOA2. While a clock stream, with the same repetition rate as the data input but it has a power less than the power of the data input by at least one order of magnitude, is inserted in the MZI and is split via the input 3 dB coupler C1 into a pair of identical parts, which travel separated along the QD-SOAs located in their path [58]. These signals are discriminated by using different wavelengths, such that their detuning in the 1550nm region is less than the homogeneous broadening of QD-SOA1. In this manner the first input data A modify the nonlinear optical properties of QD-SOA1 and induce a change on the gain and phase of the upper part of the clock stream and the

second input data B do the same thing on the lower part of the clock stream. Now if both A and B equal '0' or '1' then QD-SOA1 remains intact to the same dynamical state as QD-SOA2 so that the decomposed constituents of the clock stream perceive the same gain. Thus when they recombine at 3 dB coupler C2 they interfere destructively, which results in a space or pulse free at output port. On the other hand, if one of A or B equals '1' and the other equals '0' then one of QD-SOA1 or QD-SOA2 undergoes a radical change of its gain compared to the non-driven QD-SOA (which has input equals '0'). Consequently, the copy of the clock stream in one MZI arm acquires via cross-phase modulation [70] a nonlinear phase shift against its counterpart in the other MZI arm, which eventually creates a relative phase difference between these components. If this quantity is ideally made equal to π then it is possible to maximize the amount of the power that emerges at output port and hence the amplitude of the obtained logic one. According to this mode of operation a pulse occurs at output port if and only if a pulse is present in only one input data (A or B) whilst no pulse appears at the specific terminal if A and B are similar. The truth table is shown in Fig. (5.10.b.). From the above description and the truth table one can deduce that if the two inputs (A and B) are exactly equals and the two amplifiers (QD-SOA1 and QD-SOA2) are exactly the same (the parameters in each amplifier are equals) the output will be perfect, i.e. Q-Factor and ER will be very high and the AM will be very low. To confirm this concept, the input waveforms and the simulated output waveform are shown in Figs. (5.11.a, b, c), respectively while Fig. (5.12) shows a pseudo-eye-diagram [10]. As can be seen from these figures, the quality of the diagram is very high where ER = 41.2 dB, Q-Factor= 52.5, and the O = 99%. These values indicate an excellent response of the circuit under consideration at its output terminals. Verification to the above concept is presented in Fig (5.13). It is clear from this figure that there is a uniform drop of QD-SOA1 gain in response to input data A and QD-SOA2 gain in response to input data B. Therefore, based on the above discussion, we study in the next section the effect of the difference in the values of important parameters between the two

amplifiers, as well as, the two input data; A and B. In other words, we study the effect of the delay between the two input data A and B and the effect of power deference between them. In addition, the deference in QD-SOAs length, maximum modal gain, and the relaxation time from ES to GS between the two amplifiers; QD-SOA1 and QD-SOA2 will also be explained.

Fig. (5.11) waveforms of XOR gate -based QD-SOA MZI, where (a) input data stream A, (b) input data stream B, (c) A XOR B

Fig. (5.12) Simulated waveforms with pseudo-eye-diagram (PED) for A XOR B

5.3.2 Numerical Results of Proposed XOR Gate In these numerical results we will concentrate on the influence of the delta Δ parameters on the three popular metrics; Extinction Ratio ER, Amplitude Modulation AM, and the Q-Factor. The delta Δ is the value added to the studying parameters in one QD-SOA and it did not added to the another amplifier. Specifically, Δ represents the delay in time, in the first case and the

difference in the input peak power, in the second case, between the two input data; A and B. Then it represents the difference in QD-SOA Length, QD-SOA maximum modal gain, and finally, the electron relaxation time from ES to GS between the two QD-SOAs.

Fig. (5.13) (a) Gain response of QD-SOA1 to data stream A, (b)Gain response of QD-SOA2 to data stream B

Fig. (5.14 ) Delay between the two input pulses

Fig. (5.15) Variation of (a) ER, (b) AM, and (C) Q-factor with the delay

Figure (5.14) shows the meant by delay. The delay is time difference between the two input data in one bit duration. Fig. (5.15) demonstrates the influence of this delay on the ER, AM, Q-factor, respectively. As it is expected, the performance of the XOR gate worse as the delay increases. The ER and QFactor degrade while the AM increases. As can be also seen from this figure, the delay must be below 0.45 ps because this value is the minimum critical value for the three metrics. Above this value the ER is under 10dBm which is the lower limit for the good communications. Although, the delays up to 0.58 ps the Q-factor is still reasonable and up to 0.73 ps the AM is still acceptable, but we will take the lower limit for the three metrics. We compare in Fig. (5.16) between the XOR outputs for the two input stream represented in Fig.(5.11.a, b) in two cases; case (a) delay equals zero, and case (b), delay equals 1 ps.

Fig. (5.16) waveforms of XOR gate -based QD-SOA MZI, where (a) delay equals zero, (b) delay equals 1 ps. Degradation in performance is very clear in case (b) compared to case (a) in which the XOR output is very good. For case b (1 ps), the bad quality of the XOR operation is also confirmed by the corresponding pseudo-eye diagram (PED) [72] which has been plotted in Fig.(5.17) for a 127 bit-long data stream. An eye-diagram with large eyes indicates a clear transmission with a low bit error rate and vice versa. Here, we get PED O=18%. This value indicates a bad response of the circuit under consideration at its output terminals.

Fig. (5.18) illustrates the effect on the three metrics with the difference in the input peak power between the two input data. As can be seen from theses curves, ER is the less affected metric than AM and Q-Factor. Differences in peak power up to 0.28dBm means a good performance with respect to all metrics and up to 0.44dBn reflect an acceptable performance with respect to ER and Q-Factor. We compare in Fig. (5.19) between the XOR outputs for the two input stream represented in Fig.(5.11.a, b) in two cases; case (a), peak power difference equals zero, and case (b), equals 0.5dBm. As can be seen from this figure, high AM is very clear but still ones and zeros can be distinguished from each other which mean the ER is still acceptable.

Fig. (5.17) Simulated waveforms with pseudo-eye-diagram (PED) for A XOR B at delay equals 1 ps Fig.(5.20) shows the effect on the three metrics with the difference in lengths between the two QD-SOAs. As is shown in this figure, the AM is the first metric affected by this difference then the Q-Factor. Differences up to 0.3mm the performance is acceptable with respect to ER and Q-Factor. Above this value the Q-Factor will be less than 6 and the performance no longer reasonable. We compare in Fig. (5.21) between the XOR outputs for the two input stream represented in Fig. (5.11.a, b) in two cases; case (a), difference in Length equals zero, and case (b), equals 0.5mm. It can be noted from this figure that high AM is very clear but still ones and zeros can be distinguished from each other which means the ER is still acceptable.

Fig. (5.18)Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in the peak input power

Fig. (5.19) waveforms of XOR gate -based QD-SOA MZI, where the difference in the peak power equals (a) zero, (b) 0.5dBm. Figure (5.22) shows the effect on the three metrics with the difference in the maximum modal gain between the two QD-SOAs. Also it is obvious from this figure; the three metrics are very sensitive to the difference in the maximum modal gain between the two amplifiers. This difference has to be less than 0.025cm-1 to avoid higher AM. Whilst, it has to be less than 0.08cm-1 to obtain a good performance with regarding to ER and Q-Factor. We compare in Fig. (5.23) between the XOR outputs for the two input stream represented in Fig. (5.11. a, b) in two cases; case (a), difference in maximum modal gain equals zero, and case (b), equals 0.2 cm-1. It can be noted from this figure that the performance in case (b) is very bad; zeros and ones cannot be distinguished from each other and this comes from lower ER and Q-Factor.

Fig. (5.20) Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in length

Fig. (5.21) waveforms of XOR gate -based QD-SOA MZI, where the difference in length equals (a) zero, (b) 0.5mm. Finally, the effect of the difference in the electron relaxation time from ES to GS between the two amplifiers on the three metrics is explained in Fig. (5.22). Like all the above parameters except delay in time between the two data, the AM is the first metric affected by this difference. Differences up to 0.28ps the performance is acceptable with respect to ER and Q-Factor. Above this value the Q-Factor will be less than 6 and the performance no longer reasonable. From the observation and interpretation of Figs.(5.14 to 5.24) it can be deduced that the difference in each parameter between the two QD-SOAs has to be less than some values to avoid degradation the XOR performance.

Fig. (5.22) Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in maximum modal gain

Fig. (5.23) waveforms of XOR gate -based QD-SOA MZI, where difference in maximum modal gain equals (a) zero, (b) 0.2 cm-1.

Fig. (5.24) Variation of (a) ER, (b) AM, and (C) Q-factor with the difference in relaxation time from ES to GS

5.4 All-Optical OR Gates A Boolean logic OR gate is one of the essential logic gate devices and is capable of forming more complex all-optical functional blocks, modules, or subsystems. Several SOA-based logic OR gates have been demonstrated. An OR gate based on cross-gain modulation effect in a single SOA has a simple configuration but low extinction ratio and relatively large chirp [84]. OR logic gates based on cross-phase modulation (XPM) [85] own advantages of high extinction ratio or high contrast ratio at the cost of complex interferometer configurations. In this section all optical OR gate based on QD-SOA MZI will be investigated.

5.4. 1 Principle of Operation of Proposed OR Gate The configuration of the proposed OR gate considered in the conducted theoretical treatment is shown in Fig. (5.25). and the output power can be expressed by Eq. (5.2). It is based on the symmetrical MZI architecture, in which the same QD-SOAs; QD-SOA1 and QD-SOA2, are placed in the upper and lower arm, respectively. The input data, call it D, enter through a wavelength selective coupler (WSC) QD-SOA1, these input data D consist of the two data we want to OR them; data A and B, which combined through a wavelength selective coupler (WSC). while a clock stream with the same reputation rate as the data input but it has a power less than the power of the data input by at least one order of magnitude is inserted in the MZI and is split via the input 3 dB coupler C1 into a pair of identical parts, which travel separated along the QD-SOAs located in their path[50]. These signals are discriminated by using different wavelengths, such that their detuning in the 1550nm region is less than the homogeneous broadening of QD-SOA1, as shown in Fig. (5.25). In this manner only the input data (D) can modify the nonlinear optical properties of QD-SOA1 and induce a change on the gain and phase of the clock stream. Now if D = `0' which means the two data; A and B equal zero, then QD-SOA1 remains intact to the same dynamical state as QDSOA2 so that the decomposed constituents of the clock stream perceive the

same gain. Thus when they recombine at 3 dB coupler C2 they interfere destructively, which results in a space or pulse free at output port. The output equals zero. But if D = `1' which means at least one of the two data; A and B equals one, QD-SOA1 undergoes a radical change of its gain compared to the non-driven QD-SOA2. Consequently, the copy of clock stream in the upper MZI arm acquires via cross-phase modulation [50] a nonlinear phase shift against its counterpart in the lower MZI arm, which eventually creates a relative phase difference between these components. If this quantity is ideally made equal to π then it is possible to maximize the amount of the power that emerges at output port and hence the amplitude of the obtained logic one. According to this mode of operation a pulse occurs at output port of the OR gate if and only if a pulse is present at any of the input data A and B whilst no pulse appears at the specific terminal if a pulse is absent from both, as shown in Fig.(5.25.b). In other words O/P = '1' when (A,B)= (0,1), (1,0) or (1,1), and O/P = '0' when (A,B) = (0,0). These combinations of logical pairs and their outcome form the truth table of Boolean OR logic executed between A and B, which means that the QD-SOA-based MZI in the setup of Fig. (5.25.a) is configured as OR gate. It is noteworthy that when both of the input signals are ‘1’ the upper SOA lies in high saturation mode and the output power will be higher than the situation where only one of the inputs is ‘1’. Therefore, it is important to select the input powers such that the QD-SOA works in the saturation region in the presence of only of input data stream.

5.4.2 Numerical Results of Proposed OR Gate In order to evaluate the performance of the scheme it is necessary to select the appropriate metric. This can be done with the help of the truth table of the OR gate (Fig. 5.25.b). More specifically, we observe that of the four logical possibilities, three concerns a mark and one a space. Now since the latter case is the outcome of both data signals A and B being not present and thus affecting similarly the respective QD-SOAs dynamical behavior, this means that the resultant ‘0’ is expected to be fully extinguished and so there is

no need to worry about it as it can be clearly distinguished from the ‘1’s. Therefore we must focus on the ‘1’s and their peak amplitudes for which although ideally we would desire them to be as equal as possible yet in practice we could tolerate a maximum relative fluctuation so as to avoid the pattern effect and its deleterious consequences [29, 86].

A 0 0 1 1

B 0 1 0 1

OR 0 1 1 1

(b)

(a)

Fig. (5.25)(a) Simulated setup of QD-SOA-based MZI configured for Boolean OR operation between data A and B and (b) its truth table. In this context the most suitable metric for comparing their level and assessing the degree of their uniformity is by definition the amplitude modulation (AM) [87]. In general there is no absolute upper limit for the AM but according to the information that is available on the performance of SOAbased switches [88] a value that does not exceed 1dB should be acceptable for the OR gate [89]. The satisfaction of this requirement depends in turn on the peak power of the data signals A and B, Ppeak as well as on the QD-SOAs injected current density, J, maximum modal gain gmax, time from the ES to the GS,

electron relaxation

and QD-SOAs length. For this purpose in the

following the impact of these critical parameters on the AM is investigated and assessed through the observation and interpretation of the numerically derived curves shown in Figs. (5.26-5.30). These figures have been obtained by setting them to the fixed values Ppeak =12 dBm, J=3kA/cm2, gmax =16 and

, L=4mm,

, which are representative of practical QD-SOA devices [58, 59],

and then scanning one after the other.

Fig. (5.26)Variation of AM with the peak input power for two different current density, keeping other parameters fixed. Fig. (5.26) depicts the AM against the equal peak power of data signals A and B for two values of J. As it can be observed, the AM becomes minimum at around 11dBm for J=2kA/cm2 and 12dBm for J=3kA/cm2 and on either side of this point there are two distinct areas where the AM is drastically varied in a parabolic like manner. In order to interpret this behavior we note first that the change of the data power launched into QD-SOAs 1 and 2 defines their degree of saturation and subsequently the reduction of their gains whose relative ratio, G1/G2, determines in turn the amount of the phase difference, ⁄ ) (

(

⁄

), Eq. (4.8), induced between the copies of the clock

stream. Thus depending on the level of the driving data power this quantity is made to lie in different intervals [88], which affects analogously the magnitude of switching and accordingly the AM. In this context we note further with the help of the truth table of the Boolean OR operation and the transfer function (

that can be extracted from Eq. (4.5), (

√

)), that there are three values to R depending on the input data binary

pairs. Specifically,

(

)

(

)

(

)

(

)

(

)

is not in AM interest

because it corresponds to the zero output. In all times, G2=Gss because QDSOA2 receives no data. Therefore, the value of G1 controls the phase difference and this in turn change the value of cosine in the transfer function. Since the cosine is a trigonometric function it has minima and maxima. Therefore the effect of the data power on the AM can be qualitatively estimated by means of

the impact that different φ at border points of the trigonometric circle have on the previous transfer functions. More specifically, when the provided peak φ

power is such that this condition for

(

then

φ

)[ √

(

)

φ

)

Now since under

as a result

this

is mostly

. On the other hand, when the provided peak power is

⁄ then

such that φ for

(

]

QD-SOA1 is not saturated but operates close to the

small signal gain regime then related to

√

(

)(

) Now since under this condition

QD-SOA1 is saturated and operates far from the small signal gain

regime. This

is mostly related to

(

)

these means that the amplitude of the

minimum ‘1’ at the output of the MZI will deviate much away from the maximum ‘1’, thereby making the AM of the OR gate surpass 1 dB. Therefore, to achieve an acceptable AM it has to incur the proper ratio between required for bringing closer

(

)

and

(

)

From this point on ward things

begin to significantly improve with the launch of more power since the cosine term in (

(

changes sign and adds to the sum (

)

) approach

more to

(

).

At Ppeak=11dBm for J=2 kA/cm2 and

Ppeak=12dBm for J=3kA/cm2. Concurrently, (

)

and

(

)

), thus making

φ

π and the convergence of

becomes maximum, which is translated to a minimum AM. By

continuing to increase the data power φ exceeds π and as it successively runs through the other two quadrants of values the process described above is repeated in the inverse order causing the AM to exhibit again a similar trend of deterioration. Nevertheless this variation is not exactly a mirror image of that undergone before since

are now modified from a lower initial gain

level and in this case the AM is higher when comparing points that are located equidistantly from its specified minimum, which results in some asymmetry between the opposite slopes. Overall what matters is whether the AM can be eventually made acceptable and this is indeed possible within a total power dynamic range of roughly 8dB that can be achieved by means of erbium doped fiber amplifiers (EDFAs). Another point can be noted from Fig. (5.26) is that the minimum value changes and shifted to the right as the current density

becomes larger. From a physical perspective this happens because the current density determines the power required to alter the optical properties of a QDSOA and properly saturate its gain, and the higher it is the more power is necessary for this purpose [61].

Fig. (5.27)Variation of AM with the current density for two different lengths, keeping other parameters fixed. Figure (5.27) illustrates the AM versus the QD-SOAs current density. As it can be seen, for values less than 0.8 kA/cm2 the AM is very high and thus inadmissible. This is explained by the fact that the current density determines the saturation power of a QD-SOA [61] in such way that the lower it is the easier can the QD-SOA be saturated. The result of this correlation is that the gain

deviates much away from the small signal gain

and according to

the previous paragraph so do the corresponding transfer functions in which they are involved,

(

)

and

(

)

. It can be noted that, as J is increased the

AM is sharply decreased and when it exceeds the threshold of 1 kA/cm2 the AM becomes almost constant and independent of this critical parameter. This evolution is a byproduct of the satisfaction of a sufficient and of a necessary condition, which together make the AM take the specific form. The first condition is that the amount of injected carriers is such that it can force the excursions of the QD-SOAs gains to occur closer to the same average level. The second condition is that the mark density of the OR output is high, i.e.0.75, and thus it increases the probability of having a pair of marks within the switched sequence whose amplitude fluctuation is less than 1dB, as required

for the AM. Then provided that J is adjusted to be over its identified minimum its final selection is dictated by the requirement that the equivalent bias current can be supplied by the commercially available current sources while it is not prohibitive for the practical use of QD-SOAs [61]. Therefore a moderate current density value of the order of 3kA/cm2should be fine for this purpose.

Fig.(5.28)Variation of AM with the maximum modal gain Figure (5.28) shows the AM as a function of the QD-SOAs maximum modal gain. As it can be noticed there is an apparent similarity between the obtained curve and that of Fig. (5.26) for the peak data power, which is attributed to the common impact that both parameters have on the QD-SOAs dynamical behavior and subsequently on the switching performance. In particular the maximum modal gain determines the extent that the gain of each QD-SOA is dropped from its unsaturated level [58] and subsequently the amount of the differential gain created between the MZI arms. Since this quantity imparts through the line width enhancement factor a differential phase shift, it can be realized that the changes of

also affect φ and hence the AM

in a way analogous to that described in the context of Fig. (5.26). For this reason the two AM diagrams resemble in shape both having a falling and a rising part, although the effect on the AM magnitude is more pronounced for the small signal gain because the gains G1 and G2 that enter in the expressions of the characteristic transfer functions are influenced directly by its variation. The AM remains below 1 dB on either side of a maximum modal gain of approximately 17cm-1, where it becomes minimum, and within a range of

approximately 3.5cm-1, which for given QD-SOAs length can be achieved by intervening in the number of the QD layers when designing the QD-SOA structure, see section 4.2.

Fig. (5.29)Variation of AM with the length Figure (5.29) shows the AM as a function of the QD-SOAs length. It can be noticed that there is an apparent similarity between the obtained curve and that of Fig. (5.26, 5.28) for the peak data power and the maximum modal gain, respectively. This is attributed to the common impact that these parameters have on the QD-SOAs dynamical behavior and subsequently on the switching performance. In particular the QD-SOAs length determines the extent that the gain of each QD-SOA is dropped from its unsaturated level [58] and subsequently the amount of the differential gain created between the MZI arms. Since this quantity imparts through the line width enhancement factor a differential phase shift, it can be realized that the changes of

also affect φ

and hence the AM in a way analogous to that described in the context of Fig. (5.26). this reason the three AM diagrams resemble in shape both having a falling and a rising part, although the effect on the AM magnitude is more pronounced for the QD-SOAs length because the gains G1 and G2 that enter in the expressions of the characteristic transfer functions are influenced directly by its variation ,Eq. (4.5). The AM remains below 1 dB on either side of a QDSOAs length of approximately 4mm, where it becomes minimum, and within a range of approximately 1.4mm, which for given QD-SOAs maximum modal

gain can be achieved by intervening in the number of the QD layers when designing the QD-SOA structure.

Fig.(5.30)waveforms of OR gate -based QD-SOA MZI, where (a) input data stream A, (b) input data stream B, (c) A OR B Design Parameters From the observation and interpretation of Figures (5.26 to 5.29) it can be deduced that the requirements for the critical parameters are ,

, .

, J=

mm,

Thus using the combination of values

, L=4mm,

, and τ

,

which fall within the specified boundaries, the OR gate can be realized according to the desired performance standards. This can be seen in Fig. (5.30) where the OR logic has been executed for convenience of visual representation between two input data stream shown in Fig. (5.30.a, b). In fact pulses emerge only at the bit slots of A and B that are not simultaneously occupied by '0' or equivalently if just one of these inputs is in the ‘1’ logical state, and are extinguished when both A and B are ‘1’. This proves that the OR operation is correctly executed for 160 Gb/s RZ data according to its truth table in Fig. (5.25.b), as it can be alternatively confirmed by comparing the resultant sequence in Fig. (5.30.c) with the expected one ̅̅̅̅ Moreover, despite the nonuniformity among the output marks, the quality of the logical outcome is more

than adequate since the difference in their amplitudes is strongly suppressed and its maximum does not exceed 0.5 dB. The existing pattern dependence is inevitable and cannot be fully eliminated due to the special nature of switching, which demands combating the amplitude fluctuations of marks that correspond to a high percentage, 75%, of the output logical possibilities. Despite the difficulty of this task, the proposed scheme, provided that it is designed by following the extracted guidelines, can render the AM acceptable to a greater extent than other SOA-based MZI circuits having the same aim but more complicated configuration and much lower speed capability [89]. The above observation is further verified by the pseudo-eye-diagram [10]shown in Fig. (5.31). An eye-diagram with large eyes indicates a clear transmission with a low bit rate. Here, we get PED O=89.3%. This value indicates a good response of the circuit under consideration at its output terminals.

Fig. (5.31)Simulated waveforms with pseudo-eye-diagram (PED) for A OR B

Chapter (6) Ultrafast All-Optical Full Adder Using Quantum-Dot Semiconductor Optical Amplifier-Based Mach-Zehnder Interferometer

Introduction Interferometric devices have drawn a great interest in all-optical signal processing for their high-speed photonic activity. Quantum-dot semiconductor optical amplifier (QD-SOA) - based gate has added a new momentum in this field to perform all-optical logic and algebraic operations. In this chapter, for the first time, a new scheme for all-optical full adder using fife QD-SOA based Mach–Zehnder interferometers is theoretically investigated and demonstrated. The proposed scheme is driven by three input data streams; two operands and a bit carried in from the next less significant stage. The proposed scheme consists of two XOR, two AND, and one OR gate. The impact of the peak data power as well as of the QD-SOAs current density, maximum modal gain, and QDSOAs length on the ER and Q-factor of the switching outcome are explored and assessed. The operation of the system is demonstrated with 160 Gbit/s. section 6.1 introduces a brief review for the all-optical full Adder. Principle and design of proposed all-optical full adder will be explained in section 6.2. Section 6.3 is devoted to introduce the numerical simulation results of our proposed design. Finally, section 6.4 summarizes the concluded remarks that may be obtained from the displayed results

6.1 All optical Full adders The demand for faster optical communication networks has been on the rise in recent years. As mentioned in chapter one to accommodate this demand, the new generation of optical communication networks is moving towards terabit per second data rates. Such data rates can be achieved if the data remain in the optical domain eliminating the need to convert the optical signals to

electronic signals and back to optical signals. Therefore, to be successfully able to achieve higher data rates, advanced optical networks will require all optical ultra-fast signal processing such as wavelength conversion, optical logic and arithmetic processing, add–drop function, etc [90, 91]. All -optical combinational circuits are required for managing of the contentions and the switch control in a node of an optical packed switched network. Calculating the addition of Boolean numbers is an important functionality to perform packet header processing [92]. In recent years, optical logic gates based on several different schemes are demonstrated and reported, which are based on dual semiconductor optical amplifier (SOA) Mach–Zehnder interferometer (MZI), semiconductor laser amplifier (SLA) loop mirror, ultrafast nonlinear interferometers, and four-wave mixing process in SOA [72], etc.All-optical binary adders have been reported by using many optical designs such as terahertz optical asymmetric demultiplexers (TOADs) [93] and ultrafast nonlinear interferometers [94].An all-optical half adder using an SOA-assisted Sagnac interferometer has been suggested and demonstrated by several groups of researches [95-97]. A scheme for an ultrahigh-speed all-optical half adder based on four-wave mixing in SOAs has been demonstrated by Li [96]. The operation of a half adder/subtractor arithmetic using the dark–bright soliton conversion control has been reported by Phongsanam et al. [95]. Menezes et al. have suggested alloptical half adder using the symmetric planar three-core non-linear directional coupler, operating with a short light pulse [97]. Finally, M. Scaffardi et al. have introduced all-optical full adder using a single SOA as a basic building block [92] Among different topologies, monolithically integrated SOA-based MZI switches are the most promising candidates for all-optical signal processing devices due to their compact size, thermal stability, high-speed capability, low switching energy, relative stability, and optical integration compatibility [98]. The technology of quantum-dot SOAs (QD-SOAs) is very appropriate owing to its remarkably ultrafast response, which, combined with its attractive

characteristics, distinguishes them from conventional SOAs [99, 100]. They have larger unsaturated gain than bulk SOAs, resulting in higher power optical amplifiers, but also have enough gain at low injected currents to enable operation with low power consumption. Their saturation power can be controlled by changing the injected current with the unsaturated gain kept constant, thus enabling easy tuning of the operating point for signal amplification and processing. QD-SOAs exhibit much faster gain recovery after gain compression than bulk SOAs, enabling amplification and processing of short pulses with negligible pulse-shape distortion. The all-optical logic gates, optical wavelength conversion, and optical regeneration based on a QDSOA MZI are promising candidates for faster speed of operation compared with bulk and MQWSOAs due to the comparatively small electron relaxation times in QDs [77 - 79]. This chapter introduces for the first time (to the knowledge of the authors) a theoretical model of an ultrafast all-optical full adder based on fife QD SOA-MZIs. The all-optical adder is potential to execute the addition in the optical domain up to 160 Gbit/s.

(a)

A 0 0 0 0 1 1 1 1 (b)

B 0 0 1 1 0 0 1 1

C 0 1 0 1 0 1 0 1

Sum 0 m 1 1 0 1 0 0 1

Fig. (6.1) (a) Full adder logic diagram and (b) its Truth table

Carry 0 y 0 0 1 0 1 1 1

6.2 Principle and Design of Proposed All-Optical Full Adder A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A, B, and C; A and B are the operands, and C is a bit carried in from the next less significant stage. The full-adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit wide binary numbers. As it is known, the full adder is a combinational logic circuit performing addition of three binary digits. The carry-bit is logic 1 when at least two inputs have logic 1. Otherwise, it is logic 0. The sum-bit represents the least significant bit of the three bits binary summation. The truth table shown in Fig. (6.1.b) explains all the expected cases for the full adder. While, Fig.(6.1.a) shows the concept upon which the all-optical full adder circuit is designed [101]. From the standpoint of optics, Fig.(6.2) shows the configuration of the proposed all-optical full adder. It consists of fife symmetrical QD-SOA-based MZIs (QD-SOAMZI-1 to QD-SOA MAZI-5) with the same QD-SOA placed in each of its arms. In the first and second gates (MZI-1, and MZI-2), the first XOR and the first AND, respectively, the input data are A and B. On the other hand, the third and fourth gates, (MZI-3, and MZI-4), the second XOR and the second AND, respectively, the input data are C and the XOR output of the MZI-1. Finally, the fifth gate, OR (MZI-5), the input data are the AND outputs of the MZI-2 and MZI-4.The circuit described in Fig. (6.2) can be divided into three types of gates; XOR, AND, and OR gates which have been explained and studied in chapter (5). It has to be noting that, the output of any one of these gates has to be attenuated before using it as input to the next gate to avoid the cascading amplification.

MZI 3

WSC MZI 1 WSC

Data A CLK

C1

CLK

C1

C2

QD-SOA1

SUM

WSC

Data C

WSC

Data B

C2

QD-SOA1

QD-SOA2

QD-SOA2

WSC

Data C

MZI 4

C1

QD-SOA1

C2

WSC

QD-SOA2

WSC

Data A Data B

MZI 2

C1

WSC

C2

QD-SOA1

CLK WSC

MZI 5

C1

QD-SOA1

C2 Carry

WSC QD-SOA2

QD-SOA2

Fig (6.2) Configuration of the proposed all-optical full adder using fife symmetrical QD-SOAs based MZI interferometers

6.3 Simulation Results of the All-Optical Full Adder In order to study the performance of the proposed QD-SOA based MZI, we have solved the coupled Eqs.(4.9-4.12)numerically in a step wise manner for pulses of input data A, B, and C that belong to a 160 Gbit/s pseudo-random binary sequence and have a Gaussian power profile[175]: (

)

(

( )(

)

) (6.1)

where

is their peak power and

=2 ps is their full width at half

maximum. BD= 6.25ps is the bit duration. Then the 4th order Runge-Kutta method is applied to find the amplification factors in both MZI arms, which are expressed by

(

)

(

)

(6.2)

(

)

(

)

(6.3)

In this QD-SOA model the values of the different parameters are taken from the literature on other QD-SOA based interferometric gates [77, 79]. All parameters used in the calculations are summarized in Table 6.1. In order to assess the performance of the full adder circuit at 160 Gbit/s, we have to choose which output (Carry or SUM)) we will study?And what is the suitable metric for this purpose? Parameter

Value

Value

14 cm-1

0.16ps

2 cm-1

1.2ps

1200ps

0.4ns

3ps NQ Lw

Parameter

0.25µm

Pmax

11dBm

L

4mm

J

4KA/cm2

1ns

4.5

0.2ns Table 6.1 : Parameters Used for Simulation of the AllOptical Full Adder We will study the Carry bit because it deals with a higher number of gates (4 gates) than the SUM bit (2 gates). With respect to chose the suitable metric, this can be done with the help of the truth table of the full adder shown in Fig. (6.1.b).More specifically, we observe that of the eight logical possibilities, marks (1) and spaces (0) are equal (4 times for each case).Therefore, we must focus on how to distinguish marks from the spaces. Hence, the most suitable metric for this purpose is the extinction ratio and the Quality factor[8]. Fig. (6.3) illustrates the effect on the ER with peak power of the input data signals for three different current density values, when the other

parameters are kept fixed. The common characteristic of all curves is that the ER is increased with power up to a certain value after that it is decreased. The maximum value changes and shifted to the right as the current density becomes larger. From a physical perspective this happens because the current density determines the power required to alter the optical properties of a QD-SOA and properly saturate its gain, and the higher it is the more power is necessary for this purpose [61]. This fact also explains that as we move well enough into the falling slope of the curves a larger current density is necessary to enhance the ER and hence improve performance for a given power. This in turn allows selecting thepeak data power from a wider range of permissible values, which potentially offers greater flexibility in the design of the full adder circuit.

Fig (6.3)Variation of extinction ratio (ER) with peak data power for different current densities, keeping other parameters fixed. Fig.(6.4) shows the variation of ER with QD-SOAs length for three different peak control powers. The common characteristic of all curves is that the ER is increased with QD-SOAs length to a certain value after that it is dropped. The maximum value is shifted to the left as the peak power becomes larger. The smaller value of the QD-SOA length requires the larger peak control power to obtain the maximum value of ER. Thus from Figs.(6.4 and 6.5), we say that larger current density and longer QD-SOAs length are

preferable for obtaining a satisfactory performance in terms of the ER with reduced control power lying in a wider span. In reality, however, this choice is technically limited by the fact that the extra bias current, which is required either for providing a higher current density in a given QD-SOA device or achieving the same current density in a longer QD-SOA, might not be reasonable for practical QD-SOAs [61, 103].

Fig (6.4) Variation of extinction ratio (ER) with QD-SOA length for different peak data power, keeping other parameters fixed. Figure (6.5) shows the variation of ER with current densities for three different QD-SOA lengths. From this figure, it is observed that among the three QDSOAs lengths the ER becomes acceptable only for 3.5 and 4 mm. This in turn allows keeping the current density below 4 kA/cm, since after reaching its defined minimum the ER becomes almost independent of this parameter because there is an oversupply of carriers and the QD-SOA is sufficiently biased to the desired point. Figure(6.6) shows the variation of ER with the maximum modal gain for three different QD-SOAs lengths. The common characteristic of all curves is that the ER is increased with the maximum modal gain to a certain value after that it is dropped. The maximum value is shifted to the right as the QD-SOAs

length becomes smaller. The smaller value of the maximum modal gain requires the longer QD-SOAs length to obtain the maximum value of ER.

Fig (6.5) Variation of ER with current densities for three different QD-SOAs length, keeping other parameters fixed

Fig (6.6) Variation of ER with the maximum modal gain for three different QD-SOAs length, keeping other parameters fixed Figure (6.7) shows that the ER is very sensitive to the variations of the electron relaxation time from the ES (excited state) to the GS (ground state) since the

slope of the curve is decreased in an exponential-like manner as this relaxation time is increased, finally becoming more smoother near the left edge of the diagram. So the transition time between ES and GS must be kept below some value and ideally be as fast as possible. In this curve it has to be below 0.25ps to obtain ER a round 10dB. Figure (6.8) illustrates the effect on the Q-factor with current densities for three different maximum modal gains, when the other parameters are kept constant. The common characteristic of all curves is that the Q-factor is increased with current density up to a certain value after that it is decreased. The maximum value of Q-factor is dropped when the value of gmax outside the certain range. So the value of gmax must be fixed at particular value to achieve the maximum Q-factor value.

Fig (6.7) Variation of ER with electron relaxation time from the ES to the GS.

Fig (6.8) Variation of Q- Factor with current densities for three different maximum modal gains, when the other parameters are kept constant.

Fig (6.9) Variation of Q- Factor with current densities for three different QDSOA lengths, when the other parameters are kept fixed. Figure (6.9) shows the variation of Q-factor with current densities for three different QD-SOA lengths. From this figure, it is observed that among the three QD-SOAs lengths the Q-factor becomes acceptable only for 4 mm. Thus from Figs.(6.8 and 6.9), we say that increasing of injection current up to a value approximately 3.5 kA/cm , more carriers are injected to the wetting layer. Thus

each energy level in the QD can recover to its initial carrier density faster after carrier depletion by the injected pulse. So, up to a certain value approximately 3.5 kA/cm of the injection current, the Q-factor value increases. After a value (approximately, above 3.5 kA/cm) of the injection current, more carriers in the conduction band will be depleted due to stimulated emission. So the QD energy states will take much longer time to recover their carrier density level, hence decrease the output quality. Design Parameters According thus to Figs. (6.3-6.9) and their interpretation, it can be inferred that the requirements for the critical parameters are ,

, , and

0.3ps. By following these guidelines

and using the combination of values L=4mm,

mm,

, and

, J=

,

, respectively, which obviously is

not unique and fall within the specified boundaries, a more than adequate Qfactor of about 12.5dB and ER of about 11.7dB can be obtained, which is reflected on the high quality of pulse stream obtained at the output [8]. The input waveforms and the simulated output waveforms are shown in Figs. (6.10.a-e), respectively. The eye-diagram is the superposition of the outputs for the repetition period of the inputs. Fig.(6.11) is not a classical eye-diagram because it is not as informative in the sense that degrading effects, normally observed in the point-to-point communication links[72], such as noise source, are added by the detector and optical fibers. This diagram is called a pseudoeye-diagram [10]. The relative eye opening (O) is defined as )

, where

and

(

are the minimum and maximum powers at 1-

state and 0-state, respectively. An eye-diagram with large eyes indicates a clear transmission with a low bit rate. Here, we get PED O=92%. This value indicates a quite good response of the circuit under consideration at its output terminals. The cascadeability refers to the ability of a switch to drive directly from its main output to another input where the signal responsible for switching is launched and constitutes a key requirement for the perspective of building

combinational circuits. In the cascading stages, the extinction ratio will be decreased and Q-factor value maybe increased at the output. In the cascading circuit, high input power at the previous stages is required to provide sufficient pump power at the input of the subsequent cascading stages. This high pump power degrades the extinction ratio at the subsequent stages of the subsystem. Moreover, it leads to improvement of the output Q-factor value and the power transfer function of the QD-SOA becomes steeper due to the deep gain saturation caused by the incoming pulses in cross gain modulation operation. It is also noted that the performance of the subsequent system, which are limited by the degradation of the extinction ratio is expected to be significantly enhanced using saturable absorbers[104].

Fig (6.10) waveforms of all-optical full adder, where (a) input data stream A, (b) input data stream B, (c) input data stream C ( (e) output carry-bit (

), (d) output sum-bit S and ).

Fig (6.11)Simulated output waveforms with pseudo-eye-diagram (PED)

Chapter (7) Conclusion and Suggestions for Future Work 7.1 Conclusions In the first part of this work, the homogeneous and inhomogeneous broadening of the optical gain are considered through solving the Multi Populations Rate Equations MPRE model numerically using fourth-order Runge-Kutta method. Then three sets of results are introduced. Firstly, we analyzed the dynamic characteristics of InAs/InP (113) B quantum dot laser. Turn on delay and steady-state photons improve as the current increases. With decreasing the full width at half maximum (FWHM) of homogeneous broadening, turn-on delay decrease and the laser reaches its steady state faster due to enhancing of central group carriers. As the time of the initial relaxation becomes longer by decreasing the coefficient of phonon relaxation Aw, the turn on delay decreases and the steady state value becomes higher. This is because, the injected carriers are consumed in the WL and thus do not contribute to lasing oscillation. Secondly, we analyzed the static characteristics of InAs/InP (113) B quantum dot laser. We observe the double laser emission phenomena which results from the efficient carrier relaxation into the GS due to the increase of the Auger effect for larger injection rates. The nonlinearity appears at light-current characteristics due to the effect of FWHM of the homogeneous broadening which connects spatially isolated and energetically different quantum dots. As a result, the lasing mode photons are emitted not only from energetically resonant dots, central group, but also from other non resonant dots within the scope of the homogeneous broadening of the central group. Simulation results of the static-characteristics of InAs/InP (113) B SAQD-LD show that there is a better value of

corresponding to

to extract the

maximum output optical power from the device. Also it shows that as the increases the threshold current decreases. Then, we find that, the

effect of increasing Aw is equivalent to increase the injected current, which means increasing the supplied carriers to the QD region. Finally, we analyzedthe effect of the injected current, the FWHM of the homogenous broadening, and the initial relaxation (phonon bottleneck) on the rise, fall time, and the bit rate of the optical pulse. It is founded that, as the injected current increases the rise time increases while the fall time decreases. As a result, the bit rate of the optical pulse increases. With respect to the FWHM of the homogenous broadening

, as the

increases, the rise and fall

times increase. Consequently, the bit rate decreases. In the second part of this work, the feasibility of realizing an all-optical wavelength conversion and 3R at 160 Gb/s using a properly driven QDSOA-MZI has been theoretically investigated and demonstrated. By conducting numerical simulation, a set of curves have been obtained for the impact of the involved critical parameters on the ER. Based on a detailed characterization of the dynamical behavior of a QD-SOA that is subject to an ultrafast data pulse stream, the simulation results have been analyzed and interpreted. In this manner, the operating conditions, which are favorable in order for the employed metric to meet its desired criterion, have been derived. These suggest that it would be possible to achieve the pursued logic function with error-free performance and high quality for a combination of moderate values for all involved parameters, which can be well supported by state-of-the-art QD-SOA technology. This prediction can enhance the capability of the QD-SOA-based MZI as switching module. Also itcan complement the suite of bitwise Boolean functions that it can execute and facilitate its exploitation in more sophisticated circuits and subsystems such optical logic gates which are introduced in the chapter (5). The obtained results are interpreted with the help of a complete characterization of the QD-SOA response to an ultrafast data pulse stream. This allows specifying the requirements that the critical parameters must satisfy to achieve acceptable performance.

To be more close to the concept of all optical devices, in chapter (5), the feasibility of realizing all-optically the Boolean AND, XOR, and OR gates at 160 Gb/s RZ data using a single QD-SOA-based MZI has been theoretically investigated and demonstrated. The influence of the identified critical parameters on the performance of the gate in terms of the amplitude modulation has been assessed by conducting numerical simulation. The results of AND gate indicate that in order for the defined metric; Q-Factor to be acceptable the peak data power must be such that the QD-SOAs are biased to operate in the 3 dB saturation regime, while they must be driven by a current and provide a nominal maximum modal gain of the order of 204 mA and 16 dB, respectively. Furthermore their length must be chosen to be between (3.7 and 4.2 mm). On the other hand, the results of XOR gate indicate that the difference in each parameter between the two QDSOAs or between the two input streams has to be less than some values to avoid degradation the XOR performance. Finally, the results of OR gate indicate that in order for the defined metric; AM to be acceptable the peak data power must be such that the QD-SOAs are biased to operate in the 3 dB saturation regime, while they must be driven by a current and provide a nominal maximum modal gain of the order of 250 mA and 17 dB, respectively. Furthermore their length must be chosen to be between (3.6 and 5.1 mm). Provided that these operational conditions are satisfied, which is technologically feasible, these logic functions can be executed both with logical correctness and high quality, in a straightforward, affordable, efficient, cascadable, scalable and competent manner. Therefore the proposed scheme can constitute a useful choice to be adopted for implementing the logic gates and employing it as logical unit in the design of more complex photonic circuits and subsystems. In chapter (6), one of these complex logic circuits, specifically, the all-optical full adder is theoretically investigated and demonstrated. To give a good application to our algorithm, the feasibility of realizing an ultrafast all-optical full adder using fife QD-SOA based Mach-

Zehnderinterferometers is theoretically investigated and demonstrated in chapter (6). The impact of the peak data power as well as of the QD-SOAs current density, maximum modal gain, and QD-SOAs length on the ER and Q-factor at the output has been thoroughly investigated. The performance of this optical circuit is extremely fast and operation of the system is demonstrated with 160Gbit/s. It is important to note that the predetermined values of the intensities of laser light for incoming pluses and input data signals are needed to send optical signal in desired channels. In our proposed design, the measured values of ER and Q-factor are about 11.7 dB and 12.5, respectively, which are more adequate for all-optical logic based information processing systems. This circuit can be used to design many complex all-optical circuits. The model can be extended for studying more complex all-optical circuits of enhanced functionality in which this proposed circuit developed in this thesis may be assumed as the basic building blocks.

7.2 Suggestions for Future Work

 The Multi Populations Rate Equations model can be used to study the semiconductor optical amplifiers and absorbers. In turn, we can use it to model the Quantum Dot Mode-Locked Lasers using Quantum Dot Saturable Absorbers

 Using the all-optical QD-SOA-based MZI switch introduced in chapter four to design another optical logic gates such as Not, NOR, NAND, ….

 Using the all- optical logic gates to design more complex circuits such as all optical multiplier, Multiplexer, Demultiplexer, All-Optical FlipFlop, …

 All optical signal processing systems and all-optical switching architecture which utilize QD SOA-based logic gates and circuits as their

basis

foundation

can

also

be

implemented.

All-Optical

Header/Payload Separation, All-Optical Correlator, and All-Optical Packet Routing are examples of these systems.

Appendix (A) 4thOrder Runge-KuttaIntegrator The Runge-Kutta integrator of 4th order [105] represents a four step algorithm for the approximate numerical solution of ordinary differential equations, such as the rate equations.Let us briefly review the implementation of this method. Given a differential equation of the form (

(A1)

)

We are interested in obtaining the function y(x) starting from its derivative. The Runge-Kutta method (which is an improvement of the Euler method), in its 4th-order form states that the function evaluated at a step i+1 depends on the function evaluated at the step iand a weighted average of the function evaluated at intermediate steps between iand i+1. In the following we list this result in an appropriate way [105]

(

) (

(

)

)

(

)

(

)

(

)

(A2)

Simple Rate Equations: Now these equations have to be translated into our set of equations (Eq. (4.9 to 4.12)) for photon density S, the electron density in WL Nw, the electron occupation probability in the ES and GS h, f, respectively,to allow for a numerical implementation. In our problem y must be read as S, Nw, h, f;

is

the time step dtbecause our equations are time-dependent (thus, x must be translated to t). The values k0, k1, k2 and k3 arecalculated for each of the state

variables and represent the differential rate equations in Eq. (4.9-4.12). This means the program will solve 4 x 4 = 16 equations per iteration. The fourthorder Runge-Kuttaroutine developed is based on the equations below (A3) ( ( ( (

[

) ) ) )]

(

(A4)

)

(

[

) (A5)

(

)

(

)] (

)

(

[

) )

(

)]

(

)

(

[

(A6)

(

)

(

)

(

)] (

[

(A7)

) ( ) ( ) ] ( ) ( )

(A8)

As it can be seen in Eqs. (A3-A8) our data structure for the output variable y consists on a matrix having 4 rows (1st forphoton density, 2ndfor the electron density in WL, 3rdfor the electron occupation probability in the ES and the fourth for the electron occupation probability in the GS) and as many columns as the time vector is long (because our implementation is fixed-steplike). The variables assigned to k0. . . k3are column-vectors because they contain the solution of every rate equation; these variables are supposed to be cleared after the end of each step (only after being computed in the output y). In equations. (A4 –A7) the notationkS(Nw,

h, f)

stands for the solution of the

corresponding rate equation for photon density (the photon density, the electron density in WL, electron occupation probability in the ES, electron occupation probability in the GS). Multi Population Rate Equation MPRE For the Multi Population Rate Equation MPRE model, the same procedure as the simple rate equations model is followed except for that each equation replaced by a number of equations represents the modes and groups. Specifically, Equation of Nwl , Eq. (3.11) remains one equation Equation of NES, Eq. (3.12) is replaced by n equations, (n number of groups) Equation of NGS, Eq. (3.13) is replaced by n equations, (n number of groups) Equations of SES and SGS;Eqs. (3.14, 3.15) each is replaced by m equations, (m number of modes) Therefore, if we have 15 groups and 15 modes, the rate equation actually are 61 equations. This means the program will solve 4 x 61 = 244 equations per iteration. In this situation the function k in Eq. (A1) is one of the rate equations; Eq. (3.11) to Eq. (3.15) and

is represented by

[

( ( ( ( (

) ) ) ) )]

(A9)

Appendix (B) Design Metrics

Through this work there are four design metrics have been used to study the influence of some important parameters on the performance of the device under test. These metrics are Extinction Ration ER, Amplitude Modulation AM, Q-Factor, and Pseudo-Eye-Diagram PED. This appendix introduces a briefreview for these metrics.

B.1 Extinction Ration ER In telecommunication, ER is the ratio of to optical power levels of a digital signal generated by an optical source. The ER may be expressed as a fraction, in dB, or as a percentage [8]. It may be given by (

)

(

)

(B1)

which means that this extinction ratio (ER) is performed between the minimum and maximum peak output powers of the marks and spaces,

and

,

respectively, occurring at the output of the device. This metric must be over 10 dB [8, 106] so that the ‘1’s can be clearly distinguished from the ‘0’s, which is the basic measure of the capability to execute Boolean logic functions according to the expected performance standard. In other words, the higher the ER the more clearly can the ‘1’s be distinguished from the ‘0’s,

B.2 Amplitude Modulation AM In some cases such as OR gate the resultant ‘0’ is expected to be fully extinguished and so there is no need to worry about it as it can be clearly distinguished from the ‘1’s. Therefore we must focus on the ‘1’s and their peak amplitudes for which although ideally we would desire them to be as equal as

possible yet in practice we could tolerate a maximum relative fluctuation so as to avoid the pattern effect and its deleterious consequences [86]. In this context the most suitable metric for comparing their level and assessing the degree of their uniformity is by definition the amplitude modulation (AM) [29] ( where

and

)

(

(B2)

)

are the maximum and minimum peak powers,

respectively, among the‘1’s that are contained in the sequence that is switched at the output port of the device. In general there is no absolute upper limit for the AM but according to the information that is available on the performance of SOA-based switches a value that does not exceed 1dB should be acceptable for the logic gates [86]. In general the lower the AM the more uniform is the level of the output ‘1’s and the smaller is the related pattern effect

B.3 Q-Factor The quality factor for the output waveforms can be expressed as (B3)

Where

are the average value of all the out coming "1" and "0" data's

peak power, respectively.

are their standard deviations. The Q-factor

is related to the bit error rate in terms of [8] (

√

)

⁄ )

(

(B4)

√

The approximate form of BER is obtained by using the asymptotic expansion [8] of

( ) and is reasonably accurate for √

. The BER improves as Q

increases and becomes lower than 10−12 for Q >7. Therefore, In order to ensure acceptable performance, the Q-factor must satisfy the criterion to be over six [8].

B.4 Pseudo-Eye-Diagram PED This visual quality indicator is obtained by superimposing the marks and spaces in the data stream of interest on top of each other and displaying them within a single bit period. According to this generation method the PED consists in the general case of two distinct curves, one for the marks and one for the spaces, while its form depends on the quality of these bits, both individually and in relation to each other. It is important to note that, thisindicatoris not a classical eye-diagram because the superimposed curves are not as informative in the sense that degrading effects, normally observed in the point-to-point communication links such as noise source, which are added by the detector and optical fibers. Therefore, thisdiagram is called a pseudo-eyediagram [10, 102]. The relative eye opening (O) is defined as ( where

and

)

(B5)

are the minimum and maximum powers at 1-state and 0-

state, respectively. An eye-diagram with large eyes indicates a clear transmission with a low bit rate.

References 1. International Telecommunication Union, Measuring the Information Society

–

The

ICT

Development

index.

2009.

Available

online

at

http://www.itu.int/pub/D-IND-ICTOI-2009http://www.itu.int/ITUT/ 2. I. Keslassy, S. Chuang, K. Yu, D. Miller, M. Horowitz, O. Solgaard, andN.

McKeown, "Scaling Internet routers using optics (extended version)," tech. rep., Stanford HPNG Tech. Rep. TR03-HPNG-080101 (Stanford University, 2003), available online at http://yuba.stanford.edu/techreports/TR03-HPNG-080101.pdf. 3. K. Tse, "AT&T’s photonic network," in Proc. Optical Fiber Communication

Conference (OFC), vol. NMC1, 2008. 4. M. Salsi, H. Mardoyan, P. Tran, C. Koebele, E. Dutisseuil, G. Charlet, and

S. Bigo, "155x100Gbit/s coherent PDM-QPSK transmission over 7,200km ," in Proc. Optical Fiber Communication Conference (OFC), p. PD2.5, 2009. 5. E. Desurvire, "Capacity Demand and Technology Challenges for Lightwave

Systems in the Next Two Decades," IEEE/OSA Journal of Lightwave Technology, vol. 24, no. 12, pp. 4697–4710, 2006. 6. Dong, J.; Zhang, X.; Fu, S.; Xu, J.; Shum, P. & Huang, D. "Ultrafast all-

optical signal processing based on single semiconductor optical amplifier," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 14, No. 3, pp. 770-778, 2008. 7. Sugawara, M.,Ebe, H.,Hatori, N., Ishida,M., Arakawa, Y., Akiyama,

T.,Otsubo, K. & Nakata, Y. "Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers," Phys. Rev. B, Vol. 69, No. 23, pp. 235332-1-39, 2004. 8. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley,

(2002).

9. J. Kim, Y. Jhon, Y. Byun, S. Lee, D. Woo, and S. Kim, "All-optical XOR

gate using semiconductor optical amplifiers without additional input beam," IEEE Photon. Technol. Lett. 14(10), 1436–1438, 2002. 10.

Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. B. Piccirilli, and

N. K. Dutta, "Study of all-optical XOR using Mach-Zehnder interferometer and differential scheme," IEEE J. Quantum Electron. 40(6), 703–710, 2004. 11.

T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L.

Occhi, G. Guekos, S. Hansmann, H. Burkhard, and R. Dall’Ara, "10 Gbit/s all-optical Boolean XOR with SOA fiber Sagnac gate," Electron. Lett. 35(19), 1650, 1999. 12.

C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H.

Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, and R. Dall’Ara, "20Gb/s all optical XOR with UNI gate," IEEE Photon. Technol. Lett. 12(7), 834–836, 2000. 13.

K. Chan, C. Chan, L. Chen, and F. Tong, "Demonstration of 20 Gb/s

all-optical XOR gate by four-wave mixing in semiconductor optical amplifier with RZ-DPSK modulated inputs," IEEE Photon. Technol. Lett. 16(3), 897– 899, 2004. 14.

Z. Li, Y. Liu, S. Zhang, H. Ju, H. de Waardt, G. D. Khoe, H. J. S.

Dorren, and D. Lenstra, "All-optical logic gates using semiconductor optical amplifier assisted by optical filter," Electron. Lett. 41(25), 1397, 2005. 15.

E. A. Avrutin, M. A. Cataluna, E. U. Rafailov, "Ultrafast Lasers Based

on Quantum-dot Structures: Physics and Devices," Wiley, 2011. 16.

Zh. I. Alferov, "Double heterostructure lasers: early days and future

perspectives," IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 6, pp. 832– 840, 2000. 17.

L. V. Asryan and S. Luryi, "Quantum dot lasers: theoretical overview,"

Boston: Artech House, 2004. 18.

Y. Miyamoto, M. Cao, Y. Shingai, K. Furuya, Y. Suematsu, K. G.

Ravikumar, and, S. Arai,"Light-emission from quantum-box structure by current injection," Jpn. J. Appl. Phys., vol. 26, no. 4, pp. L225–L227, 1987.

19.

J. A. Barker and E. P. O’Reilly, "Theoretical analysis of electron-hole

alignment in InAs-GaAs quantum dots," Phys. Rev. B, 61(20):13840–13851, 2000. 20.

P. Lunnemann and J. Mørk, "Reducing the impact of inhomogeneous

broadening

on

quantum

dot

based

electromagnetically

induced

transparency," Appl. Phys. Lett., 94(7):071108, 2009. 21.

W. Ouerghui, A. Melliti, M.A. Maaref, and J. Bloch, "Dependence on

temperature of homogeneous broadening of InGaAs/InAs/GaAs quantum dot fundamental transitions," Physica E: Low-dimensional Systems and Nanostructures, 28(4):519–524, 2005. 22.

N.N. Grundmann, M. Bimberg, D. Ustinov, V.M. Ruvimov, S.S.

Maximov, M.V. Kop’ev, P.S. Alferov, Zh.I.; Richter, U.

Werner, P.

Gosele, U. Heydenreich, J. Kirstaedter, N. Ledentsov, "Low threshold, large T0 injection laser emission from (InGa)As quantum dots," Electron. Lett., 30,1416–1417, 1994 23.

R. Mirin, A. Gossard, and J. Bowers, "Room temperature lasing from

InGaAs quantum dots," Electronics Letters, 32(18):1732, 29, 1996. 24.

W. Chow, "Studies on the relative advantages of quantum-dot and

quantum-well gain media in lasers and amplifiers," In Conference on Lasers and Electro- ptics/International Quantum Electronics Conference, page CMV1. Optical Society of America, 2009. 25.

C. Schubert, R. Ludwig, H.-G. Weber, "High-speed optical signal

processing using semiconductor optical amplifiers," J. Opt. Fiber Commun. Rep. 2, 171–208, 2004. 26.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A.E. Zhukov, V.M.

Ustinov, N. N. , Ledentsov, Z.I. Alferov, D. Ouyang, D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3 lm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633– 2635,2001

27.

T.W. Berg, "Quantum dot semiconductor optical amplifiers," Physics

and application. In: Department of Communications, Optics & Materials (COM), Technical University of Denmark, Lyngby, 2004. 28.

J. Kim, M. Laemmlin, C. Meuer, D. Bimberg, G. Eisenstein, "Small-

signal cross-gain modulation of quantum-dot semiconductor optical amplifiers," IEEE J. Quantum Electron. 45, 240–248, 2009. 29.

Mork, J., Nielsen, M.L., Berg, T.W., "The dynamics of semiconductor

optical amplifiers: modeling and applications," Opt. Photon. News 14, 42– 48, 2003. 30.

Dommers, S., Temnov, V.V., Woggon, U., Gomis, J., Pastor, J.M.,

Laemmlin, M., Bimberg, D, "Complete ground state gain recovery after ultrashort double pulses in quantum dot based semiconductor optical amplifier," Appl. Phys. Lett. 90, 033508–033510, 2007. 31.

Schneider, S., Borri, P., Langbein, W., Woggon, U., Sellin, R., Ouyang,

D., Bimberg, D., "Linewidth enhancement factor in InGaAs quantum-dot amplifiers," IEEE J. Quantum Electron. 40, 1423–1429,2004. 32.

Mecozzi A. and Mørk, J., "Saturation effects in non-degenerate Four-

Wave mixing between short optical pulses in semiconductor laser amplifiers," IEEE J. Sel. Topics Quantum Electron., vol. 3, no.5, pp. 11901207, 1997. 33.

M. Sugawara, R. K. Willardson, E. R. Weber, "Self-Assembled

InGaAs/GaAs Quantum Dots (Semiconductors and Semimetals)," Academic Press, 1999. 34.

A. E. Farghal, S. Wageh, and A. E.-S. Abou-El-Azm, "The Effect of

Electrode Materials on the Optical Characteristics of Infrared Quantum DotLight Emitting Devices", Progress In Electromagnetics Research C, Vol. 19, 47-59, 2011 35.

D. Ghodsi, H. Arabshahi and M. RezaeeRokn-Abadi, " ANALYSIS OF

DYNAMIC AND STATIC CHARACTERISTICS OF InGaAs/GaAs SELFASSEMBLED QUANTUM DOT LASERS", Armenian Journal of Physics, vol. 3, issue 2, pp. 138-149, 2010.

36.

A.S. Naeimi, DavoudGhodsiNahri and S.A. Kazemipour, "Analysis of

Dynamic Characteristics of Self-Assembled Quantum Dot Lasers", World Applied Sciences Journal, Vol. 11 No. 1, pp. 6-11, 2010. 37.

D. GhodsiNahri and A.S. Naeimi, "Simulation of Static Characteristics

of Self-Assembled Quantum Dot Lasers", World Applied Sciences Journal, Vol. 11 No. 1, pp. 12-17, 2010. 38.

Sugawara,M., Hatori,N.,Ebe, H.,Arakawa,Y., Akiyama, T.,Otsubo, K.,

and Nakata, Y. "Modelling room-temperature lasing spectra of 1.3 mm homogeneous broadening of optical gain under current injection," J. Appl. Phy., Vol. 97, No. 4, p. 043523, 2005. 39.

F. Grillot, K. Veselinov, M. Gioannini, I. Montrosset, J. Even, R. Piron,

E. Homeyer, and S. Loualiche, "Spectral analysis of 1.55 µm InAs–InP (113) B quantum-dot lasers based on a multipopulation rate equations model," IEEE J. Quantum Electron. Vol. 45, No. 7, pp. 872–878, 2009. 40.

Berg, T. W., Bischoff, S., Magnusdottir, I., Mork, J. "Ultrafast gain

recovery and modulation limitations in self assembled quantum-dot devices," IEEE Photonics Technol. Lett. Vol.13, No. 6, pp.541-543, 2001. 41.

M. Gioannini and I. Montrosset, "Numerical Analysis of the Frequency

Chirp in Quantum-Dot Semiconductor Lasers", IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 10, 2007. 42.

M. Gioannini, A. Sevega, and I. Montrosset, "Simulations of differential

gain and linewidth enhancement factor of quantum dot semiconductor lasers," Opt. Quantum Electron., vol. 38, No, 4, pp. 381–394, 2006. 43.

M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, "Effect of

homogeneous broadening of optical gain on lasing spectra in self-assembled In Ga As/GaAs quantum dot lasers," Phys. Rev. B., vol. 61, no. 11, pp. 7595–7603, 2000. 44.

K. Veselinov, F. Grillot, A. Bekiarski and S. Loualiche, "Modelling of

the two-state lasing and the turn-on delay in 1.55 mm InAs/InP (113)B quantum dot lasers", IEE Proc.-Optoelectron., Vol. 153, No. 6, PP. 3.8:311, 2006.

45.

Platz, C., Paranthoen, C., Caroff, P., Bertru, N., Labbe, C., Even, J.,

Dehaese, O., Folliot, H., Le Corre, A., Loualiche, S., Moreau, G., Simon, J.C., and Ramdane, A. "Comparison of InAs quantum dot lasers emitting at 1.55 mm under optical and electrical injection", Semicond. Sci. Technol., 20, pp. 459–463, 2005. 46.

H.Yokoyama, "Highly reliable mode-locked semiconductor lasers",

IEICE Trans. Electron., E85-C (1), 27–36,2002. 47.

U. Feiste, R. Ludwig, C. Schubert, J. Berger,C. Schmidt, H. G.Weber,B.

Schmauss,A. Munk, B. Buchold, D. Briggmann, F. Kueppers, and F. Rumpf, "160 Gbit/s transmission over 116km field-installed fiber using 160 Gbit/s OTDM and 40 Gbit/s ETDM", Electron. Lett., Vol. 37, No. 7, pp. 443–445, 2001. 48.

Ishikawa, H. (ed.) "Ultrafast All-Optical Signal Processing Devices,"

Wiley, New York (2008) 49.

Ramos, F., Kehayas, E., Martinez, J.M., Clavero, R., Herrera, J.,

Seoane, J., Nielsen, P.V., et al. "IST-LASAGNE: towards all-optical label swapping employing optical logic gates and optical flip-flops," IEEE J. Lightwave Technol. 23, 2993–3011,2005. 50.

A.

Rostami,

H.

Baghban, and

R.

Maram "Nanostructure

Semiconductor Optical Amplifiers", Springer (2011) 51.

Nakamura, H., Sugimoto, Y., Kanamoto, K., Ikeda, N., Tanaka, Y.,

Nakamura, Y., Ohkouchi, S., Watanabe, Y., Inoue, K., Ishikawa, H., Asakawa, K. "Ultra-fast photonic crystal/quantum dot all-optical switch for future photonic networks," Opt. Express 12, 6606–6614,2004. 52.

T. C. Newell, D. J. Bossert, A. Stinz, A. Fuchs, and K. J. Malloy, "Gain

and linewidth enhancement factor in InAs quantum-dot laser diodes," IEEE Photon. Technol. Lett., vol. 11, no. 12, pp. 1527–1529, Dec. 1999. 53.

H. Sun, Q. Wang, H. Dong, and N. K. Dutta, "XOR performance of a

quantum dot semiconductor optical amplifier based Mach–Zender interferometer," Opt. Exp., vol. 13, no. 6, pp. 1892–1899, Mar. 2005.

54.

B. Dagens, A. Markus, J. X. Chen, J.-G. Provost, D. Make, O. de

Gouezigou, J. Landreau, A. Fiore, and B. Thedrez, "Giant linewidth enhancement factor and purely frequency modulated emission from quantum dot laser," Electron. Lett., vol. 41, no. 6, pp. 323–324, 2005 55.

O. Qasaimeh, "Optical gain and saturation characteristics quantum-dot

semiconductor optical amplifiers," IEEE J. Quantum Electron., vol. 39, no. 6, pp. 793–798, Jun. 2003. 56.

O. Qasaimeh,

"Characteristics

of cross-gain (XG) wavelength

conversion in quantum dot semiconductor optical amplifiers," IEEE Photon. Technol. Lett., vol. 16, no. 2, pp. 542–544, Feb. 2004. 57.

Uskov, A. V., J. Mork, B. Tromborg, T. W. Berg, I. Magnusdottir, and

E. P. O'Reilly, "On high-speed cross-gain modulation without pattern effects in quantum dot semiconductor optical amplifiers," Optics Communications, Vol. 227, No. 4, 363-369, 2003. 58.

Han, H., M. Zhang, P. Ye, and F. Zhang, "Parameter design and

performance analysis of an ultrafast all-optical XOR gate based on quantum dot

semiconductor

optical

amplifiers

in

nonlinear

Mach-Zehnder

interferometer," Optics Communications, Vol. 281, No. 20, 5140-5145, 2008. 59.

Rostami, A., H. B. A. Nejad, R. M. Qartavol, and H. R. Saghai, "Tb/s

optical logic gates based on quantum-dot semiconductor optical amplifiers," IEEE Journal of Quantum Electronics, Vol. 46, No. 3, 354-360, 2010. 60.

Feng, C., J. Wu, K. Xu, and J. Lin, "Simple ultrafast all- optical AND

logic gate," Optical Engineering, Vol. 46, No. 12, Art. No. 125006, 2007. 61.

Yang, W., M. Zhang, and P. Ye, "Analysis of all-optical demultiplexing

from 160/320 Gbit/s to 40 Gbit/s using quantum- dot semiconductor optical amplifiers assisted Mach-Zehnder interferometer," Microwave and Optical Technology Letters, Vol. 52, No. 7, 1629-1633, 2010. 62.

Yang, W., M. Zhang, and P. Ye, "Analysis of 160 Gb/s all-optical NRZ-

to-RZ data format conversion using quantum- dot semiconductor optical

amplifiers assisted Mach-Zehnder interferometer," Optics Communications, Vol. 282, No. 9, 1744-1750, 2009. 63.

Uskov, A. V., E. P. O'Reilly, R. J. Manning, R. P. Webb, D. Cotter, M.

Laemmlin, N. N. Ledentsov, and D. Bimberg, "On ultrafast optical switching based on quantum-dot semiconductor optical amplifiers in nonlinear interferometers," IEEE Photonics Technology Letters, Vol. 16, No. 5, 1265-1267, 2004. 64.

Agrawal, G.P. "Applications of Nonlinear Fiber Optics," Academic

Press, New York, (2001). 65.

Z. Zhu, M. Funabashi, Z. Pan, L. Paraschis, D. Harris, and S. J. B. Yoo,

"High-performance optical 3R regeneration for scalable fiber transmission system applications," J. Lightw. Technol., vol. 25, pp. 504–511, Jan. 2007. 66.

G. T. Canellos, D. Petrantonakis, D. Tsiokos, P. Bakopoulos, P.

Zakynthinos, N. Pleros, D. Apostolopoulos, G. Maxwell, A. Poustie, and H. Avramopoulos, "All-optical 3R burst-mode reception at 40 Gb/s using four integrated MZI switches," J. Lightw. Technol., vol. 25, no. 1, pp. 184–192, 2007. 67.

T.

Akiyama,

M.

Sugawara,

and

Y.

Arakawa,

"Quantum-dot

semiconductor optical amplifiers," Proc. IEEE 95(9), 1757–1766,2007. 68.

P. Reithmaier, and G. Eisenstein, "Semiconductor optical amplifiers

with nanostructured gain material," in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008 69.

P. Borri, W. Langbein, J. M. Hvam, F. Heirichsdorff, M. Mao, and D.

Bimberg, "Spectral hole-burning and carrier-heating dynamics in quantumdot amplifiers: comparison with bulk amplifiers," Phys. Stat. Solidi. B 224(2), 419–423, 2001. 70.

Ben-Ezra, Y.; Lembrikov, B.I. &Haridim, M. "Ultra-Fast All-Optical

Processor Based on Quantum Dot Semiconductor Optical Amplifiers (QDSOA)," IEEE Journal of Quantum Electronics, Vol. 45, No.1, pp. 34-41, 2009.

71.

Uskov, A. V., J. Mork, B. Tromborg, T. W. Berg, I. Magnusdottir, and

E. P. O'Reilly, "On high-speed cross-gain modulation without pattern effects in quantum dot semiconductor optical amplifiers," Optics Communications, Vol. 227, No. 4-6, 363-369, 2003. 72.

Kim, S. H., J. H. Kim, J. W. Choi, C. W. Son, Y. T. Byun, Y. M. Jhon,

S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using cross gain modulation in semiconductor optical amplifiers," Optics Express, Vol. 14, No. 22, 10693-10698, 2006. 73.

Kim, J. H., B. C. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H.Woo, and

S. H. Kim, "All-optical AND gate using cross-gain modulation

in

semiconductor optical amplifiers," Japanese Journal of Applied Physics, Vol. 43, No. 2, 608-610, 2004. 74.

Sharaiha, A., J. Topomondzo, and P. Morel, "All-optical logic AND-

NOR gate with three inputs based on cross-gain modulation in a semiconductor optical amplifier," Optics Communications, Vol. 265, No. 1, 322-325, 2006. 75.

Singh, S. and Lovkesh, "Ultrahigh speed optical signal processing logic

based on an SOA-MZI," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 18, No. 2, 970-977, 2012. 76.

Mulvad, H. C. H., M. Galili, L. K. Oxenlowe, H. Hu, A. T. Clausen, J.

B. Jensen, C. Peucheret, and P. Jeppesen, "Demonstration of 5.1 Tb/s data capacity on a single-wavelength channel," Optics Express, Vol. 18, No. 2, 1438-1443, 2010. 77.

Dimitriadou, E. and K. E. Zoiros, "On the design of ultrafast all-optical

NOT gate using quantum-dot semiconductor optical amplifier-based MachZehnder interferometer," Optics and Laser Technology, Vol. 44, No. 3, 600607, 2012. 78.

Dimitriadou, E. and K. E. Zoiros, "Proposal for all-optical NOR gate

using single quantum-dot semiconductor optical amplifier- based MachZehnder interferometer," Optics Communications, Vol. 285, No. 7, 17101716, 2012.

79.

Dimitriadou, E. and K. E. Zoiros, "On the feasibility of ultrafast all-

optical NAND gate using single quantum-dot semiconductor optical amplifier-based

Mach-Zehnder

interferometer,"

Optics

and

Laser

Technology, Vol. 44, No. 6, 1971-1981, 2012. 80.

Dimitriadou, E. and K. E. Zoiros, "Proposal for ultrafast all- optical

XNOR gate using single quantum-dot semiconductor optical amplifier-based Mach-Zehnder interferometer," Optics and Laser Technology, Vol. 45, No. 1, 79-88, 2013. 81.

Ben-Ezra, Y.; Haridim, M.; Lembrikov, B.I. & Ran, M., "Proposal for

All-optical Generation of Ultra Wideband Impulse Radio Signals in MachZehnder Interferometer with Quantum Dot Optical Amplifier," IEEE Photonics Technology Letters, Vol. 20, No. 7, pp. 484-486, 2008 82.

Zoiros, K. E., P. Avramidis, and C. S. Koukourlis, "Performance

investigation of semiconductor optical amplifier-based ultrafast nonlinear interferometer in nontrivial switching mode," Optical Engineering, Vol. 47, No. 11, Art. No. 115006, 2008. 83.

Sugawara, M., T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H.

Ishikawa, "Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160 Gbs-1 and a new scheme of 3R regenerators," Measurement Science and Technology, Vol. 13, No. 11, 1683-1691, 2002. 84.

A. Hamie, A. Sharaiha, and M. Guegan, "Demonstration of an all-

optical logic OR gate using gain saturation in an SOA," Microw. Opt. Technol. Lett., vol. 39, no. 1, pp. 39–42, Oct. 2003. 85.

J. -Y. Kim, J.-M. Kang, T. -Y. Kim, and S. -K. Han, "10 Gbit/s

alloptical composite logic gates with XOR, NOR, OR and NAND functions using SOA-MZI structures," Electron. Lett., vol. 42, no. 5, pp. 303–304, 2006. 86.

Webb RP, Dailey JM, Manning RJ. "Pattern compensation in SOA-

based gates," Optics Express, 18, 13502–9, 2010. 87.

Houbavlis T, Zoiros KE, Kanellos G. "Design rules for implementation

of 10-Gb/s all-optical Boolean XOR gate using semiconductor optical-

amplifier-based Mach–Zehnder interferometer," Optical Engineering, 43, 1334–40, 2004. 88.

Xu J, Zhang X, Mørk J. "Investigation of patterning effects in ultrafast

SOA- based optical switches," IEEE Journal of Quantum Electronics, 46, 87–94, 2010. 89.

Ye X, Ye P, Zhang M. "All-optical NAND gate using integrated SOA-

based Mach–Zehnder interferometer," Optical Fiber Technology, 12, 312–6, 2006. 90.

J. N. Roy, "Mach–Zehnder interferometer-based tree architecture for all-

optical logic and arithmetic operations," Optik 120, 318–324, 2009 91.

A. K. Garg, R. S. Kaler, "Novel optical burst switching architecture for

high speed networks," Chinese Optics Letters, 6, 11, 807-811,2008. 92.

M. Scaffardi, P. Ghelfi, E. Lazzeri, L. Poti, A. Bogoni, "Photonic

processing for digital Comparison and Full addition based on semiconductor optical amplifiers," IEEE J. Sel. Quantum Electron. 14(3),826-832, 2008. 93.

Z. Chen, "Simple novel all-optical half adder," Opt. Eng., vol. 49, no. 4,

pp. 043201–6, 2010. 94.

D. Tsiokos, E. Kehayas, K. Vyrsokinos, T. Houbavlis, L. Stampoulidis,

G. T. Kanellos, N. Pleros, G. Guekos, and H. Avramopoulos, "10-Gb/s alloptical half adder with Interferometric SOA gates," IEEE Photon. Technol. Lett., vol. 16, no. 3, pp. 284–286, 2004. 95.

P. Phongsanam, S. Mitatha, C. Teeka, and P. P. Yupapin, "All optical

half adder/ subtractor using dark-bright soliton conversion control," Microw. Opt. Technol. Lett., vol. 53, no. 7, pp. 1541–1544, 2011. 96.

P.-L. Li, D.-X. Huang, X.-L. Zhang, and G.-X. Zhu, "Ultrahigh speed

all-optical half adder based on four-wave mixing in semiconductor optical amplifier," Opt. Exp., vol. 14, no. 24, pp. 11839–11847, 2006. 97.

J. W. M. Menezes, W. B. Fraga, A. C. Ferreira, G. F. Guimaraes, A. F.

G. F. Filho, C. S. Sobrinho, and A. S. B. Sombra, "All-optical half adder using all-optical XOR and AND gates for optical generation of "Sum" and "Carry"," Fiber Integr. Opt., vol. 29, no. 4, pp. 254–271, 2010.

98.

J. Y. Kim, J. M. Kang, T. Y. Kim, and S. K. Han, "All-optical multiple

logic gates with XOR, NOR, OR, and NAND functions using parallel SOAMZI structures: Theory and experiment," J. Lightw. Technol., vol. 24, no. 9, pp. 3392–3399, 2006. 99.

X. Li and G. Li, "Comments on "Theoretical analysis of gain recovery

time and chirp in QD-SOA," IEEE Photon. Technol. Lett., vol. 18, no. 22, pp. 2434–2435, 2006. 100.

Y. Ben-Ezra, B. I. Lembrikov, and M. Haridim, "Acceleration of gain

recovery and dynamics of electrons in QD-SOA," IEEE Journal of Quantum Electronics, vol. 41, no. 10, pp. 1268–1273, 2005. 101.

M. Morris Mano, "Digital Logic and Computer Design," Prentice-Hall

1979. 102.

E. Dimitriadou and K. E. Zoiros, "On the feasibility of 320 gb/s all-

optical and gate using quantum-dot semiconductor optical amplifier-based mach-zehnder interferometer," Progress In Electromagnetics Research B, Vol. 50, 113-140, 2013. 103.

J. F. Pina, H. J. A. da Silva, P. N. Monteiro, J. Wang, W. Freude, and J.

Leuthold, "Cross-gain modulation-based 2R regenerator using quantum-dot semiconductor optical amplifiers at 160 Gbit/s," in Proc. Conf. ICTON, vol. 1, pp. 106–9, 2007. 104.

T. Nakahara and R. Takahashi, "Self-stabilizing optical clock pulse-

train generator using SOA and saturable absorber for asynchronous optical packet processing", Optics Express, Vol. 21, Issue 9, pp. 10712-10719 (2013) 105.

E. Kreyszig, "Advanced Engineering Mathematics," 8th Edition, John

Wiley, 2006 106.

Hinton K, Raskutti G, Farrell PM, Tucker RS "Switching energy and

device size limits on digital photonic signal processing technologies," IEEE Journal of Selected Topics in Quantum Electronics, 14, 938–45, 2008.

Published Papers 1. M. Nady Abdul Aleem, K. F. A. Hussein, and A.-E.-h. A. Ammar, "Semiconductor quantum dot lasers as pulse sources for high bit rate data transmission," Progress In Electromagnetics Research M(PIER M), Vol. 28, 185-199, 2013. 2. M. Nady, , Khalid F. A. Hussein, Abd-El-hadi A. Ammar, " Analysis of Dynamic Characteristics of InAs/InP (113) B Self-Assembled Quantum Dot Lasers Using Multi- Population Rate Equations MPRE Model", 30th National Radio Science Conference (NRSC2013), April, 16-18, 2013, NTI, Cairo, Egypt. 3. M. Nady, , Khalid F. A. Hussein, Abd-El-hadi A. Ammar, " Analysis of Static Characteristics of InAs/InP (113) B Self-Assembled Quantum Dot Lasers Using Multi- Population Rate Equations MPRE Model", 2nd conference on New Paradigms in Electronics and Informatics Technologies ( PEIT '013 ), Nov. 2013, Luxer, Egypt. 4. M. Nady Abdul Aleem, K. F. A. Hussein, and A.-E.-H. A. Ammar, "Ultrafast all-optical full adder using quantum-dot semiconductor optical amplifier-based mach-zehnder interferometer," Progress In Electromagnetics Research B, Vol. 54, 69-88, 2013.

‫ملخص الرسالة‬ ‫نمذجة ومحاكاة أجهزة النقاط الكمية وتطبيقاتها في االتصاالت الضوئية‬

‫لقد ازدادت في السنوات األخيرة أهمية مكبرات اشباه الموصالت الضوئية (‪ )SOA‬باعتبارها‬ ‫عنصر رئيسيي في االتصاالت الضوئية والدوائر الضوئية المتكاملة والتي تغطي مجموعة واسعة من‬ ‫التطبيقات في الحيز الترددي‬

‫‪ 0551‬و ‪ 0011‬نانومتر‪.‬تعتبر جميع المعمالت على اإلشارات‬

‫الضوئية‪ ،‬بما فيها تحويل الطول الموجي‪ ,‬البوابات المنطقية الضوئية و إعادة توليد اإلشارات‪ ،‬الخ واحدة‬ ‫من أهم التكنولوجيات الميسرة لتحقيق المبدل الضوئي‪ ،‬مبدل الدوائر الضوئية المنفجر و مبدل الحزمة‬ ‫الضوئية‪ .‬مكبرات اشباه الموصالت الضوئية واعدة جدا في معالجة اإلشارات الضوئية حيث تتميز‬ ‫بصغر الحجم‪ ,‬سهولة التصنيع و بكفاءة الطاقة‪ .‬ان الحاجة إلى العناصر الضوئية الخالصة لزيادة القدرة‬ ‫الحالية والمستقبلية من شبكات االتصال و تحسين عملية شبكات التبديل الضوئية أحد أهم الدوافع العتبار‬ ‫مكبرات اشباه الموصالت الضوئية من العناصر األساسية في جميع سيناريوهات التبديل الضوئية في‬ ‫السنوات االخيرة‪.‬‬ ‫يهتم هذا العمل بتحليل متداخل ماك زندر القائم على اشباه الموصالت الضوئية القائمة على‬ ‫النقاط الكمية ‪ QD-SOA‬باالضافة الى اساسياته وتطبيقاته‪ .‬ويتم تنفيذ هذا التحليل باستخدام نموذج‬ ‫المعادالت معدل‪.‬‬

‫تتكون الرساله من سبعة أبواب وملحقين‬ ‫يحتوى الباب األول وعنوانه "مقدمة"‬ ‫الكش ففن ا ففا الال ففاعي االتك ففعاي لالتكحلل ففللي لالدلا ففوا هد ففو ا ففا الف ف لاه لا ف ف ان ل اد‬

‫فف ا‬

‫العكل‪.‬‬

‫يهتم الباب الثانى وعنوانه "اجهزة نقاط الكم"‬ ‫بمناقشة اساسيات ليزر النقاط الكمية ومكبر الضوء‪ .‬وهذا يشتمل على مقدمة موجزةعن‬ ‫تطويرفزياء النقاط الكمية و ليزر النقاط الكمية ‪ .‬يتم مناقشة مزايا وعيوب ليزر النقاط الكمية‬ ‫باالضافة الى التقدم المحرز في كيفية تصنيعه‪ .‬يتم التركيز في مناقشة مكبر الضوء القائم على نقاط‬ ‫الكم على الكسب و تشبع الكسب‪ .‬يتم ايضا في هذا الجزء مناقشة بعض العوامل الهامة مثل تأثير‬

‫االستعراض الغير متجانس لشعاع الليزر الخارج واالنبعاث التلقائي المكبر‪ .‬واخيرا اساليب محاكاة‬ ‫أجهزة أشباه الموصالت الضوئية القائمة على النقاط الكمية‪.‬‬

‫و يحتوى الباب الثالث وعنوانه " ليزر النقاط الكمية أشباه الموصالت "‬ ‫على دراسة ليزر النقاط الكميةة باسةتخدام نمةوذج معةدل السةكان متعةدد المعةادالت ‪" MPRE‬‬ ‫‪ ."Multi Populations Rate Equations‬فةي هةةذا النمةوذج يقةوم الطالةب بحةل معةادالت المعةةدل‬ ‫لليةةزر النقةةاط الكميةةة باسةةتجدام طريقةةة رون ة كوت ةة ذات الدرجةةة الرابعةةة اخةةذا فةةي االعتبةةار التشةةتت‬ ‫المتجانس والغير متجانس للكسب‪ .‬يدرس هذا الباب ايضا الخصائص الثابتة والمتغيرة مع الزمن لليةزر‬ ‫النقاط الكمية ‪ .‬كما يتناول هذا الباب تأثير التشتت المتجانس و تيار الدخل على الوقت الصةاعد والنةازل‬ ‫وبالتالي على معدل االشارات وذلك بهدف معرفة امكانية استخدام ليزر النقةاط الكميةة كمصدراشةارات‬ ‫في االنظمة التي تحتاج الى اشارات ذات معدل نبض عالي‪.‬‬

‫ويحتوى الباب الرابع وعنوانه" متداخل ماك زندر القائم على مكبر النقاط الكمية"‬ ‫على نموذج نظري لمتداخل ماك زندر القائم علةى مكبةر النقةاط الكميةة‪ .‬ثةم يقةوم بتحليةل تشةغيل‬ ‫متداخل ماك زندر القائم على مكبةر النقةاط الكميةة نظريةا بحةل معةادالت المعةدل الخاصةة بمكبةر النقةاط‬ ‫الكمية ومعادلة انتشار الموجات في المواد النشةطة باالضةافة الةى معادلةة متةداخل مةاك زنةدر‪ .‬يبةدأ هةذا‬ ‫الجزء بمراجعة مختصرة عن متداخل ماك زندر القائم على مكبر النقاط الكمية والمعادلة التةي تحكمةه‪.‬و‬ ‫يتضمن هذا الباب ايضا دراسة لمعادالت المعدل لمكبر النقاط الكمية ويتحقة مةن خصائصةه ‪ .‬يقةدم هةذا‬ ‫الباب تطبقين مباشرين لمتداخل ماك زندر القائم على مكبر النقاط الكميةة همةا محةول الطةول المةوجي و‬ ‫معيد االنتاج ذي الثالث وظائف (إعادة التضخيم‪ ،‬إعادة تشكيل وإعادة توقيت)‪.‬‬

‫ويتعرض الباب الخامس وعنوانه " بوابات منطق تعمل ضوئيا"‬ ‫ال ستخدام متداخل ماك زندر القائم على مكبةر النقةاط الكميةة لتصةميم ثةالث بوابةات منطة التةي‬ ‫تعمةةل ضةةوئيا‪ .‬هةةذة البوابةةات هةةي ‪ ،AND ،XOR‬و ‪ .OR‬يعةةرض هةةذا البةةاب مبةةدأ العمليةةة‪ ،‬والتصةةميم‬ ‫المقترح‪ ،‬ونتائ المحاكاة لكل بوابة منطقية‪.‬‬

‫يقدددم البدداس السددادا وعنواند " الجدداما الكامددل الفددائق السددرعة الددذي يعمددل ضددوئيا باسددتخدام‬ ‫متداخل ماك زندر القائم على مكبر النقاط الكمية "‬ ‫مخطط جديد للجامع الكامل الذي يعمل ضوئيا بشكل كلي باستخدام خمس بوابات منطقية والتي‬ ‫تم دراستها في الباب الساب ‪ .‬ويتكون المخطط المقترح من بوابتين من النوع ‪ XOR‬واثنين من النوع‬

‫‪ AND‬وبوابة من النوع ‪ . OR‬يوضح ويقيم هذا الباب تأثير كال من ذروة قدرة اشارة البيانات‪ ,‬كثافة‬ ‫التيار‪ ,‬اقصى كسب مشروط للمكبر المستخدم في بناء هذة البوابات وكذلك دراسة طول مكبر النقاط‬ ‫الكمية على نسبة التمييزبين النبضات المنطقية "‪"Extinction Ratio‬ومعامل الجودة للبيانات الخارجة‪.‬‬ ‫تتم هذة الدراسة عند معدل نقل بيانات قدره ‪.160 Gbit/s.‬‬

‫ويقدم الباب السابع وعنوانه "ملخص المضمون واالستنتاجات والعمل المستقبلي"‬

‫تلخيص للرسالة واهم النقاط المستخلصة من هذة الدراسة وكذلك العمل المستقبلي المقترح‬ ‫من الطالب‪.‬‬ ‫ويتعرض الملحق االول االعالاعت لداقو ‪. 4th Runge - Kutta Integrator‬‬ ‫ويتعرض الملحق الثاني لتعدان كقعااس التصكام الكالتخ كو هي الدالعلو‪.‬‬

‫لعكعفو ا ز ف ففد‬

‫كلافو الهح الفو‪-‬القع دة‬ ‫قالم الهح الو الكهدباو‬

‫نمذجة ومحاكاة أجهزة النقاط الكمية وتطبيقاتها في االتصاالت‬ ‫الضوئية‬

‫رسالة مقدمـة من‬

‫المهـندس‪ /‬محمد نادي عبد العليم‬ ‫قالم ح الو الكللعت الكاكدلئاو‬ ‫كعه بالث اإللكتدلحاعت‬

‫للاصلل الى دلو الععلكاه (ال كتلداه الفلالفو)‬ ‫هي الهح الو الكهدباو (االكتدلحاعت لااتصعات الكهدباو)‬ ‫إشدان‬

‫أ‪.‬د‪ .‬عبد الهادى عبد العظيم عمار‬ ‫قالم الهح الو الكهدباو ‪ -‬كلاو الهح الو‬ ‫لعكعو ا ز د‬

‫أ‪.‬م‪.‬د‪ .‬خالد فوزى أحمد حسين‬ ‫قالم ح الو الكللعت الكاكدلئاو‬ ‫كعه بالث اإللكتدلحاعت‬

‫‪2104‬‬