ELECTRONIC TUNING OF SEMICONDUCTOR LASERS WITH …

ELECTRONIC TUNING OF SEMICONDUCTOR LASERS

WITH MULTIPLE QUANTUM WELL DEVICES

Submitted to University of London in Fulfillment of the Requirements for

the Degree of Philosophiae Doctor

Thesis Author: BO CAIThesis Supervisor: ALWYN SEEDS

Department of Electronic and Electrical Engineering University College London

Torrington Place, London WC1E 7JE October, 1991

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Electronic Tuning of Semiconductor Lasers

With Multiple Quantum Well Devices

Abstract

This thesis has been devoted to theoretical and experimental work on tunable semiconductor lasers, devices which play an important role in optical communication. The use of multiple quantum well (MQW) materials as tuning elements has been studied.

In theoretical work the static and dynamic characteristics of single and multi-cavity tunable laser systems have been investigated in considerable detail. The various tuning structures were discussed. The refractive index change in MQW materials has been modelled and comparison between MQW and bulk materials has been made. The design details of integrated MQW-Bragg phase modulators are given. The possibility of integrated tunable semiconductor laser utilizing refractive index change in MQW materials was investigated.

In experimental work, the electric field induced refractive index change in a PIN MQW device has been used in an electronically tuned external cavity GaAs/AlGaAs laser system. Discontinuous and continuous tuning experiments have been carried out using this structure. The experimental

oresults show a discontinuous tuning range of over 600GHz (14A in wavelength) for a 6 V change in device bias with less than 0.6 dB variation in laser output power and a continuous tuning range of over 2 GHz without significant output power change. The results also confirm the predicted refractive index change from absorption measurement. The optical FM Response was also measured using a high resolution Fabry-Perot interferometer and birefringent fibre filter system. A flat modulation response from very low frequencies up to 200 MHz was observed and no thermal tuning effect was found.

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Acknowledgement

I am grateful to Dr. A J. Seeds for his supervision, for his support of this thesis and for his dedication and patience in reading and correctingthe manuscript. His helpful comments and constructive suggestions forimproving the manuscript are greatly appreciated.

I would also like to thank the many staff and students in this department who have helped during the course of this work. In particular, I would like to thank Professor G. Parry and his students for their help in the theoretical and experimental aspects of MQW modulators. I havebenefitted tremendously from their pioneer work in this area. Thanks are also due to Mr. A. Rivers, Mr. C. Watson and Mr. F. Stride for their help and supervision on device processing. Dr. J. Roberts in SERC III-Vsemiconductor Centre of the University of Sheffield has given generous help in the aspects of MQW material growth.

It is a pleasure to acknowledge my close association with my fellow students, N. Gomes, I. Benchflower, R. Ramos, C. Zaglanikis, and most recently S. Hoskyns. They have been a fertile source of ideas and comments.

I would also like to acknowledge the generous support and encouragement of my former colleagues at the Institute of Optics and Electronics of the Chinese Academy of Sciences.

The Chinese Academy of Sciences and the U.K University Vice Chancellor’s Committee have financially supported my study in the U.K. through an Overseas Postgraduate Scholarship and an Overseas Research Student Award.

Finally I would like to thank my wife for her understanding and support during the course of this work.

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TABLE OF CONTENTS

Contents Page No.Cover Page 1Abstract 2Acknowledgement 3Table of Contents 4List of Figures 7List of Tables 10List of Symbols 11

Chapter One: Introduction 201.1 Needs for Tunable Semiconductor Lasers 201.2 Historical Review 211.3 Structure of this Thesis 28References 33

Chapter Two: Static Theory of Tunable Semiconductor Lasers 392.1 Introduction 392.2 Single Cavity Structures 402.3 Multiple Cavity Structures 442.4 Conclusion 54References 56

Chapter Three: Dynamic Theory of Tunable Semiconductor Lasers 583.1 The Limitation of Tuning Speed 583.2 Operating Speed of Tuning Elements 593.3 Dynamic Characteristics of Mode Selection 64

3.3.1 The Fabry-Perot Resonator with Gain Medium 643.3.2 The Round Trip Effect in a Fabry-Perot Filter 663.3.3 Mode Switching Time 68

3.4 Dynamic Characteristics of Continuous Tuning 693.4.1 Use of Parametric Resonators for Frequency Tuning 69

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Table of Contents

Contents Page No.3.4.2 Oscillation in a Parametric Resonator 703.4.3 FM Response for a Sinusoidally Modulated Resonator 733.4.4 Three Special Cases 74

3.5 Conclusion 75References 77

Chapter Four: Refractive Index Change in Quantum Well Materials 794.1 Introduction 794.2 Effective Mass Approximation Model 814.3 Exciton Absorption 83

4.3.1 Solution Under Zero Field 844.3.2 Solution Under Applied Field 864.3.3 Light Hole Absorption Peak Red Shift 874.3.4 Oscillation Strength 88

4.4 Continuum Band Absorption 904.5 Binding Energy 924.6 Absorption Spectrum Broadening 944.7 Refractive Index Change 1004.8 Summary 101References 104

Chapter Five: Comparison of Various Tuning Mechanisms 1075.1 Introduction 1075.2 Application Requirements and Performance Targets 1085.3 Quantum Confined Stark Effect 111

5.3.1 Phase Shift and Insertion Loss 1115.3.2 The Upper Cutoff Frequency 112

5.4 Franz-Keldysh Effect 1175.4.1 Theoretical Model of FKE Induced Band Gap Shift 1175.4.2 Comparison Between FKE and QCSE 119

5.5 Carrier Injection Effect 1215.5.1 Plasma Effect 1225.5.2 Band Gap Shift With Injection Carrier Density 1235.5.3 Carrier Density Modulation 1255.5.4 Thermal Effect 128

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Table of Contents

Contents Page No.5.5.5 Comparison Between CIE and QCSE 129


Chapter Six: MQW Tuned External Cavity Laser Experiments 1366.1 Introduction 1366.2 Discontinuous Tuning Experiments 136

6.2.1 Experimental Arrangement 1366.2.2 Experimental Results 1436.2.3 Discussion 145

6.3 Continuous Tuning Experiments 1496.3.1 Experimental Arrangement 1496.3.2 Experimental Results 150 ‘6.3.3 Discussion 153

6.4 Measurements of the Dynamic Tuning Characteristics 1556.4.1 Fast Tuning Elements 1556.4.2 Fabry-Perot Interferometer Method 1566.4.3 Birefringent Filter Method 164


Chapter Seven: Conclusion 1707.1 Tunable Laser Structures 1707.2 Tuning Mechanisms 1717.3 MQW Tuned External Cavity Laser Experiments 1717.4 Proposed Work 1737.5 Summary 173

AppendicesA: Antireflection Coating of Semiconductor Laser Facet 176B: Data for HLP-1400 Semiconductor Lasers 183C: Design of Semiconductor Bragg Reflectors 185D: Measurements of Semiconductor Bragg Reflectors 193E: Device Processing 197

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LIST OF FIGURES

Figures Page No.Fig. 1.2.1 Grating external cavity semiconductor laser 25Fig. 1.2.2 Continuously tunable grating external cavity laser 25Fig. 1.2.3 External cavity laser with an additional reflection

surface 26Fig. 1.2.4 Continuously tunable twin segment Fabry-Perot laser 26Fig. 1.2.5 Discontinuous tuning twin segment Fabry-Perot laser 30Fig. 1.2.6 Multiple segment DFB laser 30Fig. 1.2.7 Twin guide DFB laser 31Fig. 1.2.8 Three segment DBR laser 31Fig. 1.2.9 Example of various tunable structures 32

Fig.2.2.1 Single Fabry-Perot resonator 41Fig.2.3.1 The multiple cavity structure 45Fig.2.3.2 Block A: a multilayer stack 45Fig.2.3.3 External cavity laser 49Fig.2.3.4 Modelling of mode selection 51Fig.2.3.5 Tuning characteristics of external cavity lasers 53

Fig.3.2.1 The equivalent circuit of a MQW device 60Fig.3.2.2 Cutoff frequency as a function of device size 62Fig.3.2.3 A structure for fast MQW modulators 63Fig.3.3.1 Fabry-Perot resonators as filters 67Fig.3.4.1 General model for tunable lasers 72Fig.3.4.2 Model for tunable external cavity lasers 72Fig.3.4.3 Relative peak frequency deviation as a function

modulation frequencyof

76

Fig.4.3.1 An n region system 85Fig.4.3.2 Eigen energies of electron, light and heavy holes

under applied field 89

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List of Figures

Figures Page No.Fig.4.3.3 The square of the electron-hole overlap 89Fig.4.4.1 The shape of exciton in QW 91Fig.4.4.2 Dimensional coefficient Tl1 and Tih 93

dim dimFig.4.5.1 Binding energy (+, * from reference 12) 93Fig.4.6.1 Well thickness floating due to interface roughness 96Fig.4.6.2 Applied field induced Gaussian broadening 96

oFig.4.6.3 Absorption spectra of 47A well 99

oFig.4.7.1. Refractive index change in 47A well 99Fig.4.8.1 Block diagram of MQW modelling 103

Fig.5.2.1 Long (a) and short (b) path Structures 109Fig.5.3.1 Insertion loss A and its change AA for QCSE 109

in inFig.5.3.2 Particle redistribution due to applied field 114Fig.5.4.1 FKE induced absorption coefficient change 114Fig.5.4.2 FKE induced refractive index change 120Fig.5.4.3 Insertion loss A and its change AA. for FKE 120

in inFig.5.5.1 CIE induced absorption coefficient change 126Fig.5.5.2 CIE induced refractive index change 126Fig.5.5.3 Typical modulation frequency response of CIE 130Fig.5.5.4 Insertion loss A and its change AA. for CIE 130

in in

Fig.6.2.1 MQW device structure 138Fig.6.2.2 Electro-absorption and electro-refraction spectra of

MQW device (MV246) 139Fig.6.2.3 Refractive index and absorption coefficient changes in

MQW devices 140Fig.6.2.4 MQW tuned semiconductor laser 141Fig.6.2.5 Laser mode selection 144Fig.6.2.6 Continuous tuning results 146Fig.6.2.7 Continuous tuning modelling 147Fig.6.2.7 Continuous tuning modelling 148Fig.6.3.1 Continuous tuning result 1 151Fig.6.3.2 Continuous tuning result 2 152Fig.6.3.3 Frequency shift as a function of bias 154Fig.6.4.1 100pm MQW tuning element with Bragg reflector 157

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List of Figures

Figures Page No.Fig.6.4.2 MQW phase modulator processing 158Fig.6.4.3 Power of carrier, 1st and 2nd sidebands in FM

optical spectrum 159Fig.6.4.4 Dynamic FM measurement using Fabry-Perot interferometer 160Fig.6.4.5 FM optical spectra (frequency deviation Av = 100 MHz) 161Fig.6.4.6 Theoretical modelling of FM optical spectra (frequency

deviation Av = 100 MHz) 162Fig.6.4.7 Comparison between experimental and theoretical FM

spectra 163Fig.6.4.8 An ordinary birefringent filter FM detection system 165Fig.6.4.9 FM measurement using phase-adjustable birefringent

filter 166Fig.6.4.10 FM response of modulation frequency 168

Fig.7.4.1 Proposed MQW Tuned DBR Laser 175

Fig.A.l Setup for SiO anti-reflection coating 177Fig.A.2 Laser- detector sub-mount 178Fig.A.3 Antireflection coating monitoring signal 180Fig.A.4 Optical power-current curves before and after

anti-reflection coating 181Fig.B.l Structure of HLP-1400 laser 183Fig.B.2 Current-output power of HLP-1400 laser 184

Fig.C.l Spectra of semiconductor Bragg reflectors 191Fig.D.l Measurement setup 195Fig.D.2 Measured spectrum 196Fig.E.l MQW-Bragg wafer structure 200Fig.E.2 Mask set for device processing 201

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LIST OF TABLES

Tables Page No.Table 4.6.1 Parameter used in modelling 98Table 5.3.1 Comparison between QW and optical resonators 115Table 5.4.1 Fitted coefficients for unpumped GaAs 124

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LIST OF SYMBOLS

initial acceleration due to applied field

speed of light in vacuum

thickness of intrinsic layer

Fermi-Dirac distribution function

cutoff frequency

Fermi-Dirac distribution function

gain/relative wavelength

Planck Constant

h/2n

integer

grating rotating arm/resonator length

active region length

external cavity length

lengths of active section

distance between two adjacent interfaces

lengths of phase adjusting section

physical length of the optical path for k phase shift

largest integer

element of optical property matrix




11

List of Symbols

m effective mass in conduction bandc

m effective mass of electrone

mh effective mass of heavy hole

m - effective masses of electron in Z directione_L

mel| effective masses of electron in the plane of the layers

r n ^ effective masses of hole in Z direction

m effective masses of hole in the plane of the layersh II

m effective mass of particle pp

m effective mass in valence bandV

nij^. effective mass of particle p in i region

n refractive index

nQ refractive index of unpumped materials

ni refractive index of active region

n refractive index of AlGaAsAlGaAs

n effective refractive index of waveguide layereff

n. refractive index in i region

q value of electron charge

r relative position of electron and hole in the plane of

the layer

r amplitude reflection ratio of cavity interface A

r amplitude reflection ratio of cavity interface Bb

rjj radius of exciton in the plane of QW layer

r£ radius of exciton perpendicular to QW layer

t starting time

u+ backward travelling waves

u’ forward travelling waves

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List of Symbols

optical input

x position

A maximum insertion lossin

Ap complex amplitude at point p

A spontaneous emission of amplitude

Ai() Airy Function

Bi() Airy Function

C effective capacitance

C thermal capacity

D device diameter

E eigen energy

Eq band gap tail energy

E* forward travelling electric field

E& backward travelling electric field

El binding energyb

Ee p binding energy of electron and light or heavy holesb

E£ energy level in conduction band

Ep edge of continuum bandc

Eg energy of electron

E band gapg

El energy of holeh

Ef absorption rise at high energy

E* forward travelling electric field

E‘ backward travelling electric field

Ey energy level in valence band

Fc Fermi energy for pumped materials in conduction band

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List of Symbols

F „ effective finesse of laser resonatorserf

Fy Fermi energy for pumped materials in valence band

F ^ applied perpendicular field

G^hco) Gaussian broadening function

H effective-mass electron-hole Hamiltonian

Hkb kinetic energy operator of electron-hole interaction

Hke kinetic energy operator of electron

H kinetic energy operator of hole

H kinetic energy operator of particle p in the region i.

J input carrier density

JQ particle current densities of the average injection

current

J particle current densities of material for positive gain

particle current densities at lasing threshold

K refractive index ratio in Bragg structures

Kp(hco) Sommerfeld factor

L resonator optical length

Lp Lorentzian lineshape

L. width of the region i

L well widthw

oscillation strength of electron- light or heavy holes

N carrier density

Nq average carrier density

Nc Carrier density in conduction band

Ng electron density

N hole densityh

14

List of Symbols

Np density of carrier p (p = electron or hole)

Nv Carrier density in valence band

PQut The output power

Pp optical power at point p

P spontaneous emission powerspon

P . stimulated emission powerstim

R reflectance

R. load resistancein

Ryp Rydberg constant for particle p

S area of a PIN junction

T transmittance of interface Bb

Tpp transmission function of a Fabry-Perot resonator

U. spectrum of u.m m

UQut output spectrum

V light velocity at position x in a resonator

V& volume of active region

VL Coulomb potential energy of electron and hole

Ve potential energy of electron

VL potential energy of holes

V potential energy of particle p in region i

Zg coordinates perpendicular to the plane of the layer for

electron

Z coordinates perpendicular to the plane of the layer forh

hole

IM. optical property matrix of layer i

M optical property matrix of stack of layers

15

List of Symbols

a absorption coefficient

a Q absorption coefficient for unpumped intrinsic material

a absorption coefficient of continuum at zero fieldcon

a? continuum absorption at zero applied field

a effective absorption coefficient of a resonatorerf

a* exciton absorption values at zero applied field

a. absorption coefficient in region i

a background absorption at low photon energy

a maximum absorption coefficient changemax

Pr linear coefficient for absorption rise at high energy

8 optical phase

8E^ stress-related energy shift

8E^ stress-related energy shift in a 10 nm thick well for

GaAs/AlAs

8 spontaneous emission rate per unit volumemq

a photon lifetime

standard deviation of Gaussian broadening function

standard deviation of interface roughness

a* effective interface roughness

e dielectric constant

e dielectric constant in vacuumo

<j> photon density

<j>0 average photon density

<b initial phasestar

y heat conducting constant between the device and the heat

sink

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List of Symbols

Yp, ratio of exciton and continuum absorptionex/com

rj constant dependent upon interface roughness

rjb coupling coefficient between Bragg grating and waveguide

layers

ri p dimensional coefficientdim

y wave function

y wavefunction related to electron-hole interaction

y wavefunction of electrone

y u wavefunction of holeh¥p0 wavefunction of particle p without applied field

y wavefunction of particle p with applied field

X wavelength

A, long wavelength limits of Bragg reflection band

short wavelength limits of Bragg reflection band

11 reduced effective mass of electron and hole

vQ optical central frequency

pc state density in conduction band

p* amplitude reflection ratio

p‘ amplitude reflection ratio

Pv state density in valence band

x inter-band relaxation time

x+ forward travelling time

x backward travelling time

x round trip timeo

x light travel time

x time for output reaching half of the final power

17

List of Symbols

T* forward amplitude transmission ratio of interface i

x| backward amplitude transmission ratio of interface i

Td thermal damping time constant

T thermal time constanttco optical angular frequency

coQ resonance angular frequency

cofc oscillation frequency of k mode

X relative pumping level

£ input photon density

initial grating arm angle/polariser angle

Ap broadening function

Ag relative wavelength change

A1 resonator length change

An refractive index change

An change of effective refractive index of waveguide layereff

An maximum refractive index changemax

Ax A1 mole fraction difference between well and barrier

AA maximum change in insertion loss for a jc phase shiftin

AJ amplitude of current density modulation

AT temperature difference between the device and the heat

sink

AZ average moving distance of a particle

AA, wavelength change

Av optical frequency change

At maximum variation of single trip time

A$ grating angle change

18

List of Symbols

r Lorentzian linewidthp

r° Lorentzian linewidth at zero fieldp

r confinement factor

CHAPTER ONE

INTRODUCTION

1.1 Need for Tunable Semiconductor LasersIn recent years, there has been increased interest in coherent optical

communication systems1,2 which promise higher transmission quality and higher information capacity. Research in this area has established a clear need for tunable sources. Such sources are one of the essential components in systems for wavelength division multiplexing, optical frequencymodulation and local oscillator tuning.

Although in the early stages of coherent optical communicationexperiments, the He-Ne Gas laser was used to demonstrate the basicprinciple3, considering its size and reliability, it is almost impossible to operate such a system out of laboratories. There is a general consensus inthe literature that the best solution will be to develop tunable semiconductor lasers.

Depending on the application, several performance parameters are required. For use in wavelength division multiplexing, a tuning range as large as several thousand gigahertz is desirable, although the tuning is allowed to be a combination of large range discontinuous tuning and small range continuous tuning. In principle, the gain bandwidth of several hundredoA in m -V semiconductor lasers allows a correspondingly large tuning range to fulfil the large tuning range requirements. On the other hand, for optical frequency modulation, only a few gigahertz tuning range is demanded, but high tuning speed, flat frequency modulation response and continuity of tuning become the critical requirements.

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Chapter One: Introduction

1.2 Historical ReviewMost of the early tunable semiconductor laser experiments were

associated with attempts to achieve single longitudinal mode operation of semiconductor lasers which normally operate in multiple longitudinal modes. Single longitudinal mode operation has been successfully realised by two different approaches: the first4'13 utilizes frequency-selective opticalfeedback obtained with a diffraction grating, while the second14'25 employs a composite resonator formed by the intrinsic diode cavity in conjunction with an external mirror or cavity. Both approaches provide tunability of the semiconductor laser.

External grating cavity semiconductor laser experiments, as shown inFig. 1.2.1, were first carried out by Edmonds and Smith4 in 1970. In theirexperiment, the oscillation of the internal modes of the Fabry- Perot cavityformed by the cleaved surfaces of the diode was prevented by ananti-reflection coating on one of the diode cleaved surfaces. The actualresonator was formed by the external grating and the other cleaved surfaceof the diode. By rotating the grating, the grating diffraction wavelength

aiulwas changed ^ thus wavelength tuning was obtained. Because of the anti-reflection coating on one of the cleaved surfaces, oscillation occurred in the modes defined by the resonator formed by the uncoated cleaved surface and the grating. The tuning involved selecting these modes and was therefore discontinuous, although due to the long external part of the cavity, themode spacing was very small.

A similar experiment was carried out by Thomas5. Although hisexperimental arrangement was similar to the a b c / e * there was a significant difference: there was no anti-reflection coating on the diode cleavedsurfaces, therefore the internal modes of the diode were selected by the grating and tuning was obviously discontinuous because of the large mode spaci*/^. In both experiments, the gratings were u^ed as mode selection elements to select but not shift the modes. A large^'continuous tuning range and narrow linewidth was obtained.

In order to achieve continuous tuning, an optical length change has tobe introduced in the resonator defining the mode to shift the modes. Basedon this idea, in later experiments10, a shift which alters the length of the

21


resonator, in cooperation with rotating of the grating, was introduced by using a carefully designed mechanical structure. A typical structure isshown in Fig. 1.2.2. Instead of rotating around its own centre Axis O, the grating rotates around Axis O’ by introducing an arm connecting the grating and Axis O’. This movement not only causes a grating angle change Ad, so that, the grating diffraction wavelength changes, but also causes aresonator length change A1 which shifts the wavelength of the resonator modes. By carefully designing the length of the rotating arm 1 and initial angle d , it is possible to match the mode shift caused by A1 and the gratingdiffraction wavelength change caused by Ad within a certain range, andachieve continuous tuning in this range.

Although this technique has demonstrated the potential of the semiconductor laser for large tuning range operation, it is obviouslyincapable of producing high speed tuning because of its dependence of themechanical movement of the grating, and is difficult to use in a practicalsystem because of its large physical size and poor mechanical reliability.

In order to achieve fast electronic tuning, a different approach inobtaining frequency selective optical feedback was adopted by C.K Tang et

1113al ' using an external electro-optical birefringent filter cavity. It displayed a high speed tuning potential due to the extremely short responsetime for electro-optical crystals. With this system, discontinuous tuningover a large range was achieved and the tuning speed was potentially high due to the speed of the electro-optic effect. The major difficulty for the use of these kinds of systems in an optical communication system is the incompatibility of electro- optic crystals with semiconductor materials andthe need for large controlling voltages.

The use of an additional reflecting surface outside the laser cavity to obtain single longitudinal mode operation was first proposed by Kleinman and Kishliuk11. The additional reflecting surface and adjacent laser cavityfacet form a composite mirror(shown in Fig. 1.2.3). This wavelength dependent mirror works as a mode selecting element. As the feedback from theadditional surface is extremely weak, the modes to be selected are definedby cleaved laser cavity. Although this technique has • been successfullyapplied to several laser systems16 to provide single longitudinal mode

22


operation, it is less convenient for achieving tunability in semiconductorlasers. To do so, a precise variation in external cavity length is required. Several researchers managed to design some very precise experiments17'22 to demonstrate the tuning capability of semiconductor laser by this technique. In their experiments, precise variations in optical lengths of external

17cavities were achieved by mechanical movements , thermal expansion or22carrier injection induced refractive index changes . A tuning range as

large as 15 nm was observed22. Obviously, all of these tuning experimentswere discontinuous, since no effort was made to prevent oscillation of internal modes.

Continuous tuning has been realized through injection current26 27 28 29modulation and temperature variation . In these experiments, the

optical lengths of the semiconductor resonators which define the oscillating modes were changed by the refractive index changes induced by carrier density change or temperature effects, while in the former experiments therewere no changes in the mode defining resonators. So the former can beendescribed as a procedure of "mode selecting" and the latter as "mode shifting".

To achieve narrow linewidth and large tuning range, most of the early research on tunable lasers has been concentrated on external cavity Fabry-Perot lasers with or without AR-coating to eliminate the laser internal modes. Although these kinds of tunable lasers can not compete with recently developed all- integrated tunable semiconductor lasers in terms of more compactness, reliability, stability and economy, they do have some distinct advantages such as, the ability to tune the wavelength over the entire gain bandwidth of the semiconductor, extremely narrow linewidth oscillation, independent control of the oscillation wavelength and output power, very high modulation speed of the optical frequency freedom to utilize virtuallyany of the well-developed laser structures with proven long lifetimes, and the potential for the development of high-power tunable sources. In recentyears, great effort has been made to improve the compactness, reliability and stability of the external cavity lasers. As a result, miniature packaged

30 32external cavity tunable lasers have been produced ' . More importantly for this work, the external cavity laser structures are a very useful approach for investigating various tuning structures and mechanisms.

e.g. using birefringent crystal filters

23


As semiconductor processing techniques developed and optical communication increased the demand for compact, inexpensive and reliable tunable sources, some new ideas and designs appeared. They benefited from new semiconductor processing techniques such as double epitaxy and accurate etching to achieve monolithic integrated and electronically tuned semiconductor lasers which included multiple segment Fabry- Perot cavities22’25, distributed feedback (DFB)33"44 and distributed Bragg reflector (DBR)45,46 semiconductor lasers.

The earliest developed integrated tunable lasers were multiple segment Fabry- Perot lasers22'25. In Reinhart and Logan’s work24, a 15 GHz continuous tuning range was obtained from a two segment Fabry- Perot laser. In their structure, the modulator and amplifier shared a single waveguide and light amplification was performed in a tapered active waveguide layer(shown in Fig. 1.2.4). With this structure, the optical length change produced by the modulator will introduce continuous tuning. This arrangement also provided good electrical isolation between the modulator and amplifier, which made reverse bias operation of the modulator possible.

In order to achieve a larger tuning range, Tsang et al developed a different two-segment Fabry- Perot laser . Apart from a forward biased modulator, the most significant difference was that the modulator and laser sections had separate waveguides and hence the modulator, as acleaved-coupled-cavity to the laser section, acted as a mode selectionelement(shown in Fig. 1.2.5). The tuning achieved in this case was discontinuous.

In principle, by combining these two structures, continuous tuning over a large range can be achieved in the form of a three segment Fabry- Perot laser. In such a structure, as the tuning range depends on the opticallength difference between laser cavity and coupled cavity, the tradeoff has to be made between stability and tuning range. The coordination needed between mode shifting and mode selecting sections, to obtain smoothcontinuous tuning over a large region will be very difficult.

24


Laser Diode Lens Grating

Fig. 1.2.1 Grating External Cavity Semiconductor Laser

A0

Laser Diode Lens Grating

Fig. 1.2.2 Continuous Tuning Grating External Cavity Laser

25


Laser Diode r External M irror

Composite Mirror

Fig. 1.2.3 External Cavity Laser With an Additional Reflection Surface

Substrate

p Waveguide n TaperedActive Laser

Fig. 1.2.4 Continuous Tuning Twin Segment Fabry- Perot Laser

n + ModulatorReverse Bias

26


The development of DFB and DBR lasers provided a new dimension for tunable sources. For a DFB laser, the tuning is ideally realised by a refractive index change in the whole laser waveguide region. With AR coating on both facets, this refractive index change will cause an optical period change in the Bragg structure, thus, the operation wavelength will change. The mode shifting and selecting functions are naturally combined together. In practice, to give independent control of output power and tuning, therefractive index change is performed in part of the laser waveguide in theform of a multiple segment or twin guide DFB laser.

In a multiple segment structure(shown in Fig. 1.2.6), the electrode contact region is divided into two or more sections along the longitudinal direction. Some of these sections are used to obtain tuning and the rest areadjusted accordingly to keep a constant output. The tuning, in this case, isnot purely achieved by changing the optical period of the Bragg structure but also by other factors such as a change in the gain distribution.

In the twin guide structure(shown in Fig. 1.2.7), the waveguide includes three layers; the tuning layer, electrode layer and active layer. Thewaveguide transmission characteristics are changed by a refractive index change in the tuning layer. As the tuning is performed over the whole Bragg structure region, it is an ideal structure from the point of view of DFB laser tuning. Drawbacks for this structure are its complicated transverse structure and the inevitable compromise between lasing and tuning performance.

A large continuous tuning range can also be realised by a three segment DBR laser44,45 shown in Fig. 1.2.8, which consists of an active region to provide laser emission, a phase shift region to provide mode shift, (continuous tuning) and a tunable Bragg reflector region to provide modeselection. The capabilities of individually controlling these three segments give extra freedom in controlling the performance of the laser. With careful coordination of the control of each segment, it is possible to achieve largerange continuous tuning with constant output emission power. This structure overcomes some difficulties faced by either multiple segment Fabry- Perot or DFB lasers. The disadvantages are that the structure is relatively hard to fabricate and, when the tuning is provided by carrier injection effect, the tuning speed is limited by the carrier recombination time in the transparent

27


Bragg and phase control regions as both regions are passive.

As a summary, various tunable semiconductor laser structures and their relations are illustrated in Fig. 1.2.9.

The development of semiconductor processing techniques also make it possible to grow some very fine structure such as quantum well (QW) or multiple quantum well (MQW) structures. These interesting materials provide many new possibility in optoelectronic devices and some new devices such as

46 47 48 52low threshold QW lasers ’ , high speed intensity modulators ' and some integrated devices53'55 have already been developed. Although most devices are based on QW electroabsorption or photo-luminescence properties, there is clear theoretical and experimental evidence56-60 for electric Field induced refractive index changes in QW materials. Since the refractive index changes are the most essential requirement in various tunable semiconductor laser structures, this fast electric field induced refractive index change in QW materials created a new approach for very fast electronic tuning of semiconductor lasers61. As a wide tuning range has been demonstrated in grating external cavity MQW laser9, there is also potential for an integrated MQW tunable laser with wide tuning range.

Using MQW materials to realize tunable semiconductor lasers is a natural and straightforward idea for two major reasons: first, MQW materials provide a fast refractive index change which is about ten times larger in magnitude than electro-optic crystals; second, MQW tuning elements have good compatibility with semiconductor or MQW structures, for example, wide gain-bandwidth MQW lasers, MQW photo-detectors and modulators, widely used in optical communication systems so there is a potential for integrated structures.

1.3 Structure of the ThesisThe goals of this thesis are to investigate the possibility of using

MQW materials in tunable semiconductor lasers experimentally and theoretically. The investigations involve the general theory for tunable systems including continuous and discontinuous tuning systems, the theoretical investigation of MQW material properties and the experimental

28


investigation of MQW tuned external cavity semiconductor lasers. The structure of the thesis is as follows:

The second chapter is devoted to a theoretical analysis of the static properties of tunable lasers. The results will be used in later chapters to design and explain the experiments. The dynamic properties of the tunable laser are discussed in the third chapter, where the tuning speed limits of both continuous and discontinuous tuning are given and the influences of device structure are discussed. The optical properties of QW material are investigated in the fourth chapter. The computer modeling of electro-optic properties of QW materials is carried out. The emphasis was on producing a model practically usable in device design and assessment rather than on the detailed QW physics. The fifth chapter is devoted to the comparisons of various mechanisms which provide the optical length changes needed by a tunable semiconductor laser. These comparisons give a clear view of the superiority of the quantum confined Stark effect in QW material over other mechanisms. The sixth chapter describes the MQW tuned external cavity laserexperiments to give an example of using MQW material in tunablesemiconductor lasers as the tuning element. Experimental results arediscussed and compared with some previous work. Finally, in the seventh chapter, the potential of QW tuned semiconductor lasers is discussed interms of the possibilities for monolithically integrated devices and the conclusions for the whole thesis are drawn.

29


Substrate

Seperate Waveguide

Active Region

Laser Bias

Modulator Region

M odulator Bias

Fig. 1.2.5 Discontinuous Tuning Twin Segment Fabry- Perot Laser

Electrically Isolated Sections W aveguide

Substrate

Fig. 1.2.6 Multiple Segment DFB Laser

30


n layer W aveguide

ilay e r active

p lay e r electrode

i layer tuning

n layer

Substrate

Fig. 1.2.7 Twin Guide DFB Laser

Active Region Phase Control Mode SelectionRegion Region

Substrate

W aveguide

Fig. 1.2.8 Three Segment DBR Laser

31


COG 60• t-H<£! .3■4—*• rHX oDooDTO

1300O T3s Gcd

>

60 >-> c /£o ^

^ U ”5 <D oo Oh <L> • tTTO ^O 3S S

>

ext.S

60 >> C .3 5 >cd

u<Doo

<DTOOs

60C00

oo•Sn

\ 1

s a in p r m s lu o u o d u io ^ )p n g

sainpru)<$ p9iBj§Qiuj

32

Fig.

1.2.

9 E

xam

ples

of

Var

ious

Tu

ning

S

truc

ture

s

1


References

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20. K.R. Preston, K.C. Woollard and K.H. Cameron, External CavityControlled Single Longitudinal Mode Laser Transmitter Module, E l e c t r o n . L e t t . 17, 931

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23. S. Ikeda, A. Shimizu, Y. Sekiguchi, M. Hasegawa, Wide-range Wavelength Tuning of an Asymmetric Dual Quantum Well Laser With Inhomogeneous Current Injection, Appl. Phys. Lett., 55, 2057, 1989

24. F.K. Reinhart and R.A. Logan, Integrated Electro-Optic Intracavity Frequency Modulation of Double-Heterostructure Injection Laser, Appl. Phys. Lett. 27, 532, 1975

25. I.H. White, JJ.S. Watts and B. Garrett, Experimental Observation of Spectral Tuning in Twin-Segment Double Quantum Well (DQW) AlGaAs Diode Laser, Electron. Lett., 25, 953, 1989

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27. S. Kobayashi, Y. Yamamoto, M. Ito and T. Kimura, Direct Frequency Modulation in AlGaAs Semiconductor Laser, I E E E . J . Q u a n t u m E l e c t r o n ., QE-18, 582

28. T. Celia, N.K. Dutta, A.B. Piccirilli and R.L. Brown, Monolithically Integrated Thermoelectrically Tunable Distributed Bragg Reflector Laser, E l e c t r o n . L e t t . 23, 1032

29. N.K. Dutta, T. Wessel, T. Celia and R.L. Brown, Continuously Tunable Distributed Feedback Laser Diode, Appl. Phys. Lett., 47, 981, 1985

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31. J.M. Kahn, C.A. Burras and G. Raybon, Hifg-stability 1.5 |im Extemal-Cavity Lasers for Phase-lock Applications, IEEE Photon. Technol. Lett., 1, 159, 1989

32. C.Y. Kuo, E.J. Wagner, D.A. Ackerman, C.H. Henry, Y. Shani, M.I. Dahbura and R. Kistler, Uniform Frequency Modulation Response in Narrow Linewidth (£ 200kHz) Compact Hybrid Lasers, Electron. Lett. 26, 270, 1990

33. M. Kuznetsov, Theory of Wavelength Tuning in Two-segment Distributed Feedback Lasers, IEEE J. Quantum Electron., QE-24, 1837, 1988

34. H. Olesen, X. Pan and B. Tromborg, Theoretical Analysis of Tuning Properties for a Phase-tunable DFB Laser, IEEE J. Quantum Electron., QE-24, 2367, 1988

35. H. Kawaguchi, K. Magari, H. Yasaka, M. Fukuda and K. Oe, Tunable Optical-Wavelength Conversion Using an Optically Triggerable Multielectrode Distributed Feedback Laser Diode, IEEE J. Quantum Electron., QE-24, 2153, 1988

36. S. Illek, W. Thulke, C. Schanen, H. Lang and M.C. Amann, Over 7 nm (875 GHz) Continuous Wavelength Tuning by Tunable Twin-guide (TTG) Laser Diode, Electron. Lett., 26, 46, 1990

37. Y. Yoshikuni and G. Motosugi, Multielectrode Distributed Feedback Laser for Pure Frequency Modulation and Chirping Suppressed Amplitude Modulation, J. Lightwave Technol., LT-5, 516, 1987

35


38. M. Kitamura, M. Yanaguchi, K. Emura, I. Mito, K. Kobayashi, Lasing Mode and Spectral Linewidth Control by Phase Tunable Distributed Feedback Laser Diodes With Double Channel Planar Buried Heterostructure (DFB-DC-PBH LD’S), IEEE J. Quantum Electron., QE-21, 415, 1985

39. S. Murata, I. Mito and K. Kobayashi, Frequency Modulation and Spectral Characteristics for an 1.5 pm Phase-tunable DFB Laser, Electron. Lett., 23, 12, 1987

40. Y. Yoshikuni, K. Oe, G. Motosugi and T. Matsuoka, Broad Wavelength Tuning Under Single-mode Oscillation with a Multi-electrode distributed Feedback Laser, Electron. Lett., 22, 1153, 1986

41. Y. Nakano, Y. Itaya, M. Fukuda, Y. Noguchi, H. Yasaka and K. Oe, 1.55 pm Narrow-linewidth Multielectrode DFB Laser for Coherent FSK Transmission, Electron. Lett., 23, 826, 1987

42. N.K. Dutta, A.B. Piccirilli, T. Celia and R.L. Brown, ElectronicallyTunable Distributed Feedback Lasers, Appl. Phys. Lett., 48, 1501, 1986

43. S. Murata, I. Mito and K. Kobayashi, Over 720 GHz (5.8 nm) FrequencyTuning by an 1.5 pm DBR Laser with Phase and Bragg Wavelength ControlRegions, Electron. Lett., 23, 403, 1987

44. Y. Tohmori, K. Komori, S. Arai, Y. Suematsu and H. Oohashi, WavelengthTunable 1.5 pm GalnAsP/InP Bundle-integrated-guide Distributed BraggReflector (BIG-DBR) Lasers, Trans. IECE Japan, 48, 84, 1985

45. Y. Kotaki, M. Matsuda, M. Yano, H. Ishikawa and H. Imai, 1.55 pm Wavelength Tunable FBH-DBR Laser, Electron. Lett., 23, 325, 1987

46. S.P. Cheng, F. Brillouet and P. Correc, Design of Quantum WellAlGaAs-GaAs Stripe Lasers for Minimization of Threshold Current-Application to Ridge Structures, IEEE J. Quantum Electron., QE-24, 2433, 1988

47. Y. Arakawa, A. Yariv, Quantum Well Lasers -Gain, Spectra, Dynamics, IEEE J. Quantum Electron., QE-22, 1887, 1986

48. T.H. Wood, C.A. Burrus, D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard and W. Wiegmann, High-speed Optical Modulation with GaAs/GaALAs Quantum Wells in a p-i-n Diode Structure, Appl. Phys. Lett., 44, 16, 1984

36


49. T.H. Wood, C.A. Burrus, D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard and W. Wiegmann, 131 ps Optical Modulation in Semiconductor Multiple Quantum Wells(MQW’s), IEEE J. Quantum Electron., QE-21, 117, 1985

50. P.J. Stevens and G. Parry, Limits to Normal Incidence Electroabsorption Modulation in GaAs/(GaAl)As Multiple Quantum Well Diodes, J. Lightwave Technol., 7, 1101, 1989

51. P. Barnes, P. Zouganeli, A. Rivers, M. Whitehead, G. Parry, K. Woodbridge and C. Roberts, GaAs/AlGaAs Multiple Quantum Well Optical Modulator Using Multilayer Reflector Stack Grown on Si Substrate, Electron. Lett., 25, 995, 1989

52. I. Kotaka, K. Wakita, O. Mitomi, H. Asai and Y. Kawamura, High-speed InGaALAs/InALAs Multiple Quantum Well Optical Modulators with Bandwidths in Excess of 20 GHz at 1.55 |im, IEEE Photon. Tech. Lett., 1, 100, 1989

53. Y. Arakawa, A. Larsson, J. Paslaski and A. Yariv, Active Q Switching in a GaAs/AlGaAs Multiquantum Well Laser with an intracavity Monolithic Loss Modulator, Appl. Phys. Lett., 48, 561, 1986

54. U. Das, P.R. Berger and P.K. Bhattacharya, InGaAs/GaAs Multiquantum-well Electroabsorption Modulator with Integrated Waveguide, Opt. Lett., 12, 820, 1987

55. A. Larsson, P.A. Andrekson, P. Andersson, S.T. Eng, J. Salzman and A. Yariv, High-speed Dual-wavelength Demultiplexing and Detection in a Monolithic superlattice p-i-n waveguide Detector Array, Appl. Phys. Lett., 49, 233, 1986

56. H. Nagai, Y. Kan, M. Yamanishi and I. Suemune, Electroreflectance Spectra and Field-induced Variation in Refractive Index of a GaAs/ALAs Quantum Well Structure at Room Temperature, Japan. J. Appl. Phys., 25, L640, 1986

57. T. Hiroshima, Electric Field Induced Refractive Index Changes in GaAs-Al^Gaj ^As Quantum Wells, Appl. Phys. Lett., 50, 968, 1987

58. H. Yamamoto, M. Asada and Y. Suematsu, Electric-field-induced Refractive Index Variation in Quantum-well Structure, Electron. Lett., 21, 579, 1985

37


59. J.E. Zucker and T.L. Hendrickson, Electro-optic Phase Modulation inGaAs/AlGaAs Quantum Well Waveguides, Appl. Phys. Lett., 52, 945, 1988

60. J.E. Zucker and T.L. Hendrickson, C.A. Burrus, Low-voltage PhaseModulation in GaAs/AlGaAs Quantum Well Optical Waveguides, Electron. Lett., 24, 112, 1988

61. B. Cai, A.J. Seeds, A. Rivers and J.S. Roberts, Multiple QuantumWell-tuned GaAs/AlGaAs Laser, Electron. Lett., 25, 145, 1989

38

CHAPTER TWO

STATIC THEORY OF TUNABLE SEMICONDUCTOR LASERS

2.1 IntroductionThe structures of tunable Fabry- Perot semiconductor lasers can be

classified into two categories by operating principles. One is single cavity structures in which the tuning is achieved by altering the optical length of the laser resonator, i.e. mode shifting. The tuning obtained is continuous1.The other is multiple cavity structures in which the tuning is achieved by altering the feedback wavelength of external cavities, i.e. mode selection.

2 5The tuning obtained is discontinuous * .Although the above tuning structure classification is primarily for

tunable Fabry- Perot lasers, it can also be adaptable for other forms of tunable lasers. For tunable DBR lasers6’8, these two classifications represent modulation in the form of phase control and Bragg period change.

9 12For DFB lasers , which can be considered as a composition of a vastnumber of very short Fabry- Perot resonators arranged in such a way that their emissions reinforce each other at the operation wavelength,theoretically, the tuning can be analyzed in each individual resonator. Thetuning in each resonator can be considered as a single cavity situation,

9 11although, when the changes in each resonator are different ’ , the overalltuning performance has to be analyzed in a much more complicated multiple cavity structure.

In this chapter, the above tuning structures are discussed in section2.2 and 2.3 respectively. Emphasis is laid on the static analyses of the tuning procedures; aspects associated with tuning speed are not taken into account although they could be vital in high speed tuning systems; furtherconsideration of these will be given in Chapter 3. These analyses willdeduce a set of basic formula about the static characteristic of tunable semiconductor lasers and will be useful static theoretical preparations for further chapters.

39

Chapter Two: Static Theory of Tunable Semiconductor Laser

2.2 Single Cavity StructuresTo shift modes of a Fabry-Perot resonator continuously, the resonator

parameters have to be altered. In the case of semiconductor lasers in which the Fabry-Perot resonators are formed by two flat reflectors, the mode shifting can be simply achieved by altering the optical length between the two reflectors. The relationship between this optical length variation and mode shift can be deduced from the single cavity structures. I ,

Consider a Fabry-Perot resonator shown in Fig.2.2.1, a is thepower power . . , ,^absorption coefficient and g the, \pain. In the active medium | g | > | a | . ra,

r are the amplitude reflection ratio of the cavity interfaces A and B. Theb

refractive index n is uniform throughout the cavity and the length of cavity is 1. If there is a spontaneous emission of amplitude A and initial phase <b near interface A, after one round trip in the cavity, A ,the

star pcomplex amplitude at point p, becomes

+ A,u;r. V exp { 4 ^ ^ , J +(s-a >1}

= A 1 + rj V exp( + (g-a)l)}

After N round trips, the complex amplitude can be described as a contribution of N + 1 individual beams:

N

A = A •p star exp0V ;Eo{r.v exp( + (8'a)1)}

1 - { r. V exp( j + (S'®)1)}= A -exp(j(j) )

star star

1 - W exp( + (g' a)1)We omit the initial phase <|> which is not important in our analyses, and

let R = | r r b | , G = exp |(g -a )lj, 8 = and the above equation can berewritten:

1 - [R G-exp(j28)]NA = A •---------------------------- 2.2.1

p surl - R G exp(j25)

At point p the emission power P = | a | 2. From Eq 2.2.1, emission power isp p

obtained by:

40


A s tar 6tar

g, a, n

B

Tb

r b

Fig. 2.2.1 Single Fabry-Perot Resonator

41


1 - 2(R G)n c o s ( 2 N 8 ) + ( R G ) 2Np - I A 2______________________________________ 2 2 2

p sur (1-R-G)2 + 4 R - G s i n 2 (8 )When the laser system reaches a stable situation, N tends to infinity and ina laser system since the output power can not be infinite, R G must be lessthan 1, therefore (R G)N tends to zero.

Ia I 2P = _____________ i l i l - 2 .2 .3

p (1-R-G)2 + 4 R G s i n 2(8)

If this system is considered as an amplifier, then, when sin 8 = 0 its amplification reaches the maximum and the oscillation should occur in thiscondition. Let P and P be spontaneous and stimulated emission power

spon stimrespectively at oscillation condition. Then the spontaneous emission, as background noise, can be obtaiifdfrom:

Ia t I2p _ s t a r

Jpon (1 + R -G )2 and stimulated emission

P = P - Pstun p spon

Then, the power ratio of the stimulated and spontaneous emissions at oscillating situation can be obtained by the expression

P 4 R Gs t tm

P (1-R G )2spon

Following the theory of an ordinary Fabry-Perot etalon13, we introduce a new quantity: the effective coefficient of finesse Feff

PF = 5tim 2.2.4

eff pspon

The output power from interface B, P ^ can be easily obtained by Pout= P T b where T is transmittance of interface B. After normalization:

bl

P = ---------------------------------------------------- 2.2.5out ■»—* • 2 o1 + F -sm o

e f f

The oscillation condition is 8 = nm, when m is an arbitrary integer, i.e

X = 2-n-l/m 2.2.6

42


For an optical length change An-1, a consequent wavelength change A X can be expressed as

Consider that m is the largest integer which is less than 2n-lA then from Eq. 2.2.6

On the other hand, when the change in the optical length is larger than a half wavelength, from Eq. 2.2.7 we know that m will change with n. That means the oscillation is transformed from the old mode to a new mode. Therefore the continuous tuning of a single cavity tuning structure has a limited range. From

An-1 < A/2

we can obtain the maximum continuous tuning range A X

This is identical with the expression for the wavelength interval between two adjacent modes for Fabry-Perot resonators; the mode space of a Fabry-Perot resonator.

There are two important results from the discussion above: the first,in single Fabry-Perot cavity structures, the relative change of thewavelength is equal to the relative change of the refractive index, and the second, this wavelength change is limited to one mode space.

It is also important to notice that there are two pre-conditions under which all the results are deduced. The first, the output emission is stable so that N tends to infinity; and the second, which is less obvious, the gaing in the active medium is fixed, although it should vary with photon densityin the cavity until equilibrium is reached.

A . =2-A(n-l)/m

If the physical length of the resonator 1 is fixed, then

AX = ^ -A n

2.2.7

thereforeA X _ An ~ X n 2.2.8

max

max2.2.9

43


2.3 Multiple Cavity StructuresMost external cavity tuning experiments have been carried out with

2 5multiple cavity structures ’ . Even with anti-reflection coatings, theinterfaces cannot be totally neglected. In both external multiple and single cavity experiments, the multiple cavity structure model is useful in analyzing either mode stability for the mode selection or output powervariation caused by residual reflection from the anti-reflection coating in continuous tuning.

For convenience of analysis, a multiple cavity laser is simplified to asingle cavity laser constructed by two composite mirrors A and B, each ofwhich consists of a multiple layer stack (shown in Fig. 2.3.1). For each ofthe composite mirrors at a given wavelength, there is an equivalentamplitude reflection coefficient r and transmission coefficient t. A composite mirror can be treated just as a simple mirror with the same amplitude reflection r and transmission t at the given wavelength, although,in general, r and t will be complex.

First of all, we consider block A shown in Fig.2.3.2 and deduce r anda

t .a

At interface i, the electric field satisfies:

Here E+ and E* are the electric fields near interface i in region ii i » »travelling forward and backward respectively; E*+i and E|+i are the electric fields near interface i travelling forward and backward respectively but in region i+1; p*, p‘, x* and x‘ are the amplitude reflection and transmission ratios forward and backward at interface i. From Eq.2.3.1 and 2.3.2, we

y y

isolate E+ and E'i+i i+i


Interface

ta

Interface

Block A Block B

Fig. 2.3.1 The Multiple Cavity Structure

i+ l m+1

ET i+i E ’i+i

Fig. 2.3.2 Block A: A Multilayer Stock

45


Notice th a tifx +-x’- p+-p> 1, x = x+= x’ and p= p+= -p'. Eq.2.3.3 and1 1 1 1 i i i r i r i r i ^

Eq.2.3.4 can then be converted to 1

E+ , = — ( E+ + E;-p.) 2.3.5i + i _ i i iTi

lE: , = — •( Ht-p. + E!) 2.3.6

1+1 _ 1 1 1Ti

The electric field at interface i and i+1 can be linked by

E+ = E+’ exp( j8.) 2.3.7i+i i+i r J i

E' = E‘ exp(-j8.) 2.3.8i+i i+i r J iwhere

2 jc-N-15 = ------ — 2.3.9

and

N= n+ ja 2.3.10i 1 * i.norm lised field

where n. and a. are the refractive index and, .absorption coefficient respectively. 1 is the distance between two adjacent interfaces. When there is a coupling loss between adjacent regions, a stands for the effective absorption coefficient which takes into account coupling loss. If in a region the efficiency of coupling optical power into this region is % the region length 1 and the medium absorption coefficient is a , then, the effective absorption coefficient can be calculated by

a = a + -J— ln% 2.3.11eff j

Substituting Eq.2.3.5 and Eq.2.3.6 in Eq.2.3.7 and Eq.2.3.8 yields1

E+ = E+ l exp( j8.) = — •( E+ + E‘ p.) exp( j8)i+i i+i r J i _ i i r i r J ix.i1

E: = e : -expC-jS.) = — •( E+ p. + E') exp(-j8.)i+i i+i i . i r i i r J ixior, more conveniently, in matrix form

46


—1 tn + 1i+l

E‘ XL i+iJ i

exp( j5.) p.-exp(j5.)

_ p. exp(-j5.) exp(-j8.)

K iE'

2.3.12

Let

E =E+i + l

i + lJ

1and M = —

1 x.

exp( j5.) p.-exp(j5.)

_ p. -exp(-j8.) exp(-j5.)

The whole system can be characterized bym+ 1

E = n M.-Ea 11 i 1i = 1

where a is the total number of regions. Notice that at region 1'0

2.3.13

E* = 0 or Er ,EL 1JE+ and E' can be solved as functions of E . Since E \ E+ and E‘ are in fact

a a 1 a a 1the incident, reflected and transmitted electric fields, we can easily calculate r and t :

r =a

t =

E+a

E ‘a

E '

2.3.14

2.3.15

Applying the same procedure to block B to calculate r and t . observingb b

that rfa is defined in the opposite direction to that in block A,

r = -b

E+l

With equivalent reflection and transmission of both blocks, we can thenapply the single cavity formula to the system shown in Fig.2.3.1. Unlike asimple interface, r , t , r and t normally have imaginary parts. Therefore

a a b bthere will be a phase change 2i3 in the interface. Let

r r = R-exp(j2,d) 2.3.17a b

Following single cavity structures, the normalizing output power can beexpressed as

47


1P 2.3.18

out 1 + F -sm2(5 + fl)e ff

where again F stands for the power ratio of the stimulated and spontaneous emissions at oscillating situation and is calculated by Eq.2.2.4. Although Eq.2.2.5 and Eq.2.3.18 share some similarity in form, there is a great difference between them: in the former case, F „ is

effconstant, and in the later, F and ft change with wavelength.

Using the above formulas we analyze one simple situation; a three boundary system which can be constructed, in practice, simply by a laser diode and an external mirror (shown in Fig.2.3.3).

Assume region 1 is the laser cavity and region 2 is the external cavity formed by the external mirror and one of the laser diode’s facets. Block A consists of only one interface, therefore r and t can be simply obtained

a aby

and Block B consists of interface 1 and interface 2. At interface 1

at interface 2

' exp( j5 ) p exp( j5 )'m2=

[ p2-exp(-j52) exp(-jS2)

Using Eq.2.3.13, we obtain

p2-exp( jS2) + Pj-exp(-j82)r =bb P, P2 exp( j8 2) + exp(-j82)

( P, + P2) 2- 4p1-p2-sin2822.3.19

48


\\\\N\N\NNNNNNNNNNSNNNNS

49


1d = —tan"1

2

Assume pQ= - 0.55, 1 = 0.3 mm, n = 3.5, G = 3.2, 1= 15 mm, p= 0.1, andn2= 1 which are typical for a laser diode - GRIN rod lens - MQW reflector structure . The oscillation conditions are sin(5 + d) = > 0 and F =>

1 effmaximum, i.e. R => maximum.

5 +d = m k and 5 = rn 7t + k / 2 2.3.211 1 2 2

mi and m2 are arbitrary integers and maximum Feff= 104. In Fig.2.3.4, the output power P as a function of optical frequency change from central frequency v , Av = v - v q is plotted. It shows that only when active cavity modes coincide with finesse peaks, i.e. Eq.2.3.21 is satisfied, are laser emissions obtained, and other active cavity modes are suppressed. Curve b and Curve c show that as the external cavity length 1 increases, the emission mode is transferred from mode 0 to mode 1 and then 2. Another interesting observation, comparing Curve a and b, is the small shift in mode 1 frequency. Examining Eq.2.3.18, we find that this continuous tuning is due to the interface reflection phase change d with 82< Even without regard to finesse change which makes the optical output power in an emission mode change with tuning, the continuous tuning range will be limited by the maximum change of d, because the emission frequency must satisfy Eq.2.3.21, and therefore,

Af = Ad2 n • n l

and Ad is limited by structural parameters.If there is an optical length change A1 in the external cavity giving a

mode shift Av, this can be accounted for using2 • K + ^ ( A v ,A1) =

Because VQis the optical frequency which satisfies Eq.2.3.21, this can be rewritten

2 • 71 1 Av = d(Av,Al)

C 1

p 2 (l - p ;) .s in(282)

P; (1 + p l ) + P M + p*)-cos(25j2.3.20

50


cn

CN

CN

o

<N

cno CN

Ooo

ooO

uno

cnoo o o

CO4—>o

1300<D

OS<4-1oW)G

<1>"73O

TfCO<Nbb♦ f-H

(pQZIJUUUOU) J3M 0J [B O qdo

51


Substituting the above equation for 0 in Eq.2.3.204 n p -(1 - p2)-sin(25 )

tan(— I* Av) 2 1 2P jd + P*) + p - ( l + pJ)-cos(252)

2.3.22

where4 • K

sin(252) = sin

Eq.2.3.21 also requires 2 • K 1 v = m n

(1 +Al)-(v-Av)

Ctherefore

2 o

sin(282) = sin'4 • K

and

= sin

c o s (2 5 2) as cos

C

4 • K

(12-4V

.(12.Av

v -A1 + Al-Av)o 7

vo Al)

4 • K(12Av v0-Al)

Eq.2.3.22 can then be rewritten 4 • Jt

Pj(l - P2)sin( lj-Av) - p2smc

4- K+ IVAv - vrt-Al 2 0

- P, P2sin'4 • Jt

[a ,- y - Av + v0 ai] = 0 2.3.23

This equation will be very useful in determining the capability of a tunable structure for continuous tuning. Consider extreme cases, If p ^ 0 the interface 1 disappears, the emission modes will be defined by interface 0 and interface 2, and the mode shift range has no limitation; If p ^ 1 and p2-» 0 the emission modes depend almost only on the internal cavity, the changes in external cavity length having only a very small influence on mode shifts. Fig.2.3.5 shows the maximum mode shifts calculated by Eq.2.3.23. Each curve represents p t = 0, 0.10, 0.15, 0.40, 0.70 that is reflectance 0, 1, 2.25, 16, 49% and the feedback from external cavity is 0.05 in amplitude or 0.25% in power and 1}= 1.08 mm 12= 15 mm for all the curves.

52


O n

OO

OOOO

oodCL

C lO

O

CL

OTfdCL

o

o CNdo

C l

o

odo o

in

ino

<NCL

es

ooo

or -d<ddinr“Hdo 'r-Hoo'o

(z r o ) X ou3nb3jj i^opdQ

cnVh<Dcnc$

hJ

& • rH>u13a>

X

W

ocnO• rH4->cn

• rHLh<D4—>oc3L-(

43ubi)C

CP

H

vncn<N

bX)• i-HPh

53


The calculation shows that for an external cavity system withoutanti-reflection coating of the laser, having p ^ .5 5 , the continuous tuning range is to 2-3 GHz. In contrast the same external cavity system with antireflection coating of residual reflectivity 1% ^ = 0 .1 ) would give acontinuous tuning range about 9 GHz, almost the entire mode spacing.

It must be noticed that in the above analysis, only phase change is taken into account. When the external cavity length is changed, not only phase ft but also modulus R will be changed. Due to this change the emissionmode may jump before the maximum mode shift is reached.

From Eq.2.3.23 we can expect that with decreasing pj5 the continuous tuning range will increase and the amplitude variation will decrease because the variation of R will decrease. The variation of R can be measured by contrast

R -max

Rmin _ P ,a

- p ’ >

R +max

Rmm p 2o

- p J >

when

andR -

maxR

mm _ P2d - P?>

R +max

Rmm P.O

- P l>

when

Pi

P2I < IP, 2.3.24

For a small output power change in continuous tuning, we expect the coupling-cavity induced frequency selecting effect be weak, that means a small contrast in R i.e. I-1 p I - 1 p I I as large as possible, while for a strong mode selecting capability in discontinuous tuning, a strong coupling-cavity induced frequency selecting effect i.e. a large R contrast is desired.

Combining Eq.2.3.23 and Eq.2.3.24 in continuous tuning experiments we expect a large p2 and small pt to obtain a large tuning range and a small output power change. In the other hand for mode selecting experiment a largeR contrast i.e. I pt | = selecting capability.

is preferable for providing a strong mode

2.4 ConclusionIn this Chapter, the static characteristics of both single and multiple

cavity tuning structures were discussed. From the analysis of single cavity structures, the relationship between refractive index changes and continuous

54


tuning ranges and the maximum continuous tuning range were given. These are the basic formulas to analyze ideal continuous tuning situations.

In the analysis of multiple cavity structures, the more general and practical cases were considered. Multiple cavity structures were considered as a single active cavity with composite mirrors at one or both sides. Theformula deduced from this model is similar in form to the single cavity one, except that a phase shift f t is introduced and the effective finessebecomes a function of optical frequency. These relations determine the optical frequency related characteristics of the structures; in particular f t determines the continuous tuning characteristics and F „ determines the

effmode selecting characteristics. It was also found that the single cavitystructures can be considered as a special case of the multiple cavitystructures and characterized using the same formula. A three interface multiple cavity structure was analyzed in detail. The continuous and discontinuous tuning characteristics were obtained by computer modelling.

55


REFERENCE

1. F.K. Reinhart and R.A. Logan, Integrated Electro- Optic IntracavityFrequency Modulation of Double- Heterostructure Injection Laser, Appl. Phys. Lett. 27, 532, 1975

2. D. Renner and J.E. Carroll, Simple System for Broad-band Single-mode Tuning of D.F. GaALAs Lasers, E l e c t r o n . L e t t . 15, 73

3. K.R. Peston, Simple Spectral Control Technique for External Cavity Laser Transmitters, Electron. Lett. 18, 1092, 1982

4. W.T. Tsang, N.A. Olsson and A. Logan, High-speed DirectSingle-frequency Modulation With Large Tuning Rate and Frequency Excursion in Cleaved-coupled-cavity Semiconductor Lasers A p p l . P h y s . L e t t . 42, 650

5. S. Ikeda, A. Shimizu, Y. Sekiguchi, M. Hasegawa, Wide- range Wavelength Tuning of an Asymmetric Dual Quantum Well Laser With Inhomogeneous Current Injection, Appl. Phys. Lett., 55, 2057, 1989

6. S. Murata, I. Mito and K. Kobayashi, Over 720 GHz (5.8 nm) FrequencyTuning by an 1.5 pm DBR Laser with Phase and Bragg Wavelength ControlRegions, Electron. Lett., 23, 403, 1987

7. Y. Tohmori, K. Komori, S. Arai, Y. Suematsu and H. Oohashi, Wavelength Tunable 1.5 pm GalnAsP/InP Bundle- integrated- guide Distributed Bragg Reflector (BIG-DBR) Lasers, Trans. IECE Japan, 48, 84, 1985

8. Y. Kotaki, M. Matsuda, M. Yano, H. Ishikawa and H. Imai, 1.55 pm Wavelength Tunable FBH- DBR Laser, Electron. Lett., 23, 325, 1987

9. M. Kuznetsov, Theory of Wavelength Tuning in Two- segment Distributed Feedback Lasers, IEEE J. Quantum Electron., QE-24, 1837, 1988

10. Y. Yoshikuni, K. Oe, G. Motosugi and T. Matsuoka, Broad Wavelength Tuning Under Single- mode Oscillation with a Multi- electrode distributed Feedback Laser, Electron. Lett., 22, 1153, 1986

11. Y. Nakano, Y. Itaya, M. Fukuda, Y. Noguchi, H. Yasaka and K. Oe, 1.55 pm Narrow- linewidth Multielectrode DFB Laser for Coherent FSK Transmission, Electron. Lett., 23, 826, 1987

56


12. S. Illek, W. Thulke, C. Schanen, H. Lang and M.C. Amann, Over 7 nm (875GHz) Continuous Wavelength Tuning by Tunable Twin- guide (TTG) LaserDiode, Electron. Lett., 26, 46, 1990

13. M. Bom and E. Wolf, Principles of Optics, Pergamon Press, FourthEdition, 1970

14. B.Cai, A.J. Seeds, A. Rivers and J.S. Roberts, Multiple Quantum Well-tuned GaAs/AlGaAs Laser, Electron. Lett., 25, 145, 1989

57

CHAPTER THREE

DYNAMIC THEORY OF TUNABLE SEMICONDUCTOR LASERS

3.1 The Limitation of Tuning SpeedIn previous tuning experiments1'3, the variation of the resonator

optical length, needed for producing frequency tuning could be provided by changing either the effective refractive index1,2 or the physical length of the resonator . The most commonly used approach was carrier density inducedeffective refractive index change achieved by changing the injectioncurrent1. The operating speed of FM lasers based on this effect was limited by carrier recombination time and the maximum FM modulating frequencies were a few of hundred megahertz. An alternative was temperature induced effective index change2 which, due to thermal delay time, limited the modulating speed to a few megahertz. The physical length change of the resonator could simply be achieved by mechanical means such as thermal extension and piezoelectric effects. The tuning speeds were then limited to at most a few kilohertz. The limitations of tuning speed imposed by these effects play such a dominant part that other possible speed limiting factors such as device capacitance and the so called round trip time effect in Fabry-Perot resonators were always ignored in previous analyses.

As new devices, such as reverse biased QW devices, emerge 4-6 a very high speed of resonator optical length change should be obtained. This new possibility made it necessary to carry out some analysis in this new modulation speed range. The optical length change speed was no longer a dominant limiting factor and other speed limiting factors have to be considered.

This chapter, based on the above considerations, is dedicated to dynamic aspect of QW tunable semiconductor lasers under extremely highspeed operation. The structure chosen for this analysis was the MQW tuned external cavity laser which, as used in subsequent experiments, consists of a reflection MQW phase modulator, lens and laser diode with antireflection

58

Chapter Three: Dynamic Theory of Tunable Semiconductor Lasers

coating on one of its facets.Based on this model, the investigations were divided into three parts.

In the first part, Section 3.2, the limitation of operating speed of the MQW phase modulators was investigated. Attention was given to the speed limitation imposed by device structures rather than the mechanism and dynamic characteristics of electric field induced refractive index change inMQW materials which are discussed in later chapters. In the second part,Section 3.3, the problems discussed are slightly different from those considered in the other parts of this chapter. The dynamic characteristics of mode selection is investigated. This, to parallel the previous chapter,forms the dynamic part of mode selection theory. Although this part, from the point of view of the speed involved seems out of the scope of this chapter, it was deliberately integrated into this chapter not only forcompleteness of the dynamic theory but also as a necessary preparation forSection 3.4, where the round trip time effect of the resonator on continuous tuning is considered. The problem is treated as a parametric oscillation one. Some cases of special interest are discussed. All analysis in this partwill be concentrated on high speed small range continuous tuning. Finally, in Section 3.5, conclusions are drawn from these analyses.

3.2 Operating Speed of Tuning ElementsOne of the significant advantages of using QW materials in tuning

elements is that QW materials provide large electric field induced8 10refractive index change ’ and because this change is induced by the

electric field, it can respond at high speed. In this section we do not discuss the dynamic characteristics of electric field induced refractive index change in QW but assume that it is fast enough to be excluded from the consideration of device operating speed. Rather, we consider the speed limitation imposed by tuning element structures.

A QW PIN type modulator under reverse bias can be considered as a parallel plate capacitor and the equivalent circuit is shown in Fig.3.2.1. It is clearly that the working frequency of the circuit will be limited by effective capacity C . The cut-off frequency is

59


MQWModulator

■II-Ceff

- © — •?Signal and Bias

Fig. 3.2.1 The Equivalent Circuit of A MQW Device

60


1f 3.2.1

The effective capacity can be determined by

C = eS/deit

3.2.2

and substituting Eq.3.2.2 into 3.2.1

3.2.3in

where £ is dielectric constant d the thickness of intrinsic layer and S the area of the device. In practice, the dielectric constant £ is determined by the QW materials chosen for the operating optical wavelength and d by the

are predetermined, both variables have little room for manoeuvre to reduce the effective capacity. The most realistic approach is by reducing device area S. Consider a typical AlGaAs/GaAs PIN phase modulator; the intrinsic

oamers. in tnis case, a = u.v pm, e = i z j -e o wnere e = o.oo^xiu i^ is me primary electric constant, vacuum, = 500 and S = ^D2 for a circular device with diameter D. The relationship between device size and cutoff frequency is shown in Fig.3.2.2. Using conventional device structures, it is possible to obtain devices with up to gigahertz operating frequency. Although for optical alignment the device window could be reduced to a few tens of micrometres which correspond to cut-off frequencies of up to a hundred gigahertz, the bond area is very difficult to reduce. For even higher operating frequencies, some measures have to be taken toovercome this problem. One of the proposed device structures9 is sketched in Fig.3.2.3. By removing the bond pad from the active region, the device area which generates effective capacitance was reduced to just a little larger than the optical window area.

bias voltage and the optical phase change required. Once the specifications

o olayer consists of 75 periods of 60 A GaAs wells and 60 A A1 Ga As

61

Devi

ce

Cuto

ff Fr

eque

ncy

(GH

z)


1000

100-

Device Diameter (jam)

AlGaAs/GaAs PIN Device, Thickness of i Layer = 0.9 \xm

Fig.3.2.2 Cutoff Frquency as A Function of Device Size

62

C hapter Three: Dynamic Theory of Tunable Semiconductor Lasers

a

T3<DO ho

T3

05Vho4—>

3"T3

O '

C/5a3

Hx

£<DVh

O

0 0

<cn<Ncnb b• r—i

P h


3.3 Dynamic Characteristics of Mode SelectionMode selection can be achieved by weakly coupling an external cavity

with a laser resonator and changing the optical length of the external cavity. Although the optical length of the external cavity can be changed very quickly, the mode switch time is severely limited by the round trip time effect of the laser resonator. In this section, after some necessary preparation, the Fabry-Perot filter model will be used to introduce the round trip time effect. The investigation of the mode switch time will be based on coupled cavity structures and the Fabry-Perot filter model used.

3.3.1 The Fabry-Perot Resonator With Gain MediumThe Fabry-Perot resonator incorporating a gain medium was investigated

in the last chapter and was equivalent to a high Q Fabry-Perot resonator. Now we attempt to make some justifications for using this result in dynamic analysis. The key issue of this problem is whether at the speed we are interested in, the gain can be considered as constant.

The behaviour of the semiconductor gain medium has usually been studiedin two situations. In the first situation, direct intensity modulation of a

* 1112 semiconductor laser was investigated ’ ; the injection current wasmodulated and the gain-current relation was studied dynamically. As a resultof the gain change, the output optical intensity is modulated. In the secondcase, the laser amplifier was analyzed13,14; the intensity of the opticalsignal input to the gain medium was modulated and the relation betweenoptical intensity and gain was the key part of the investigation. The gainchange with optical intensity produced waveform distortion and non-uniformfrequency response.

Our problem can be simplified to that of a frequency modulated optical signal passing through the gain medium pumped at a given level. Unlike direct intensity modulation and the laser amplifier, neither the injection current i.e. pumping level nor input optical intensity is changed. There then are two possible sources of gain changes. One of them is the gain curve hole burning phenomenon. Compared with the bandwidth of the gain curve, the laser emission has a much narrower linewidth and is located at a position, determined by the cavity resonance, on the gain curve and, therefore consumes inverted population at a certain position of the conduction and

64


valence bands. At this position, the carrier population will become lower than at adjacent parts and form a gain hole. The width of the hole will mainly be determined by linewidth of the emission, while the depth will be determined by the ratio between the inter-band and intra-band relaxation time. In semiconductor materials, this ratio is normally quite large, about

3 1410" s , and therefore the hole is very shallow. More important, because the intra-band relaxation time is about 10’12s14, much shorter than the period of the optical FM signal we shall discuss in this chapter, there is enough time to form the hole when frequency changes. In the other words, the hole in the gain curve can move fast enough to follow the frequency change of an optical FM signal and the depth of the gain hole will not cause a frequency shift induced gain change. Moving away from the local carrier population problem, the shape of gain curve itself may be the other source of gain changes. If, as mentioned above, the relaxation time for intra-band transitions can be ignored, the gain can be expressed as

g(co)=

3 i21 2m m 2 f E 1C V CO-----------

hK J2xn 2co2 h (m + m )^ v V c J

[ f (CO) - f (CO)] 3.3.1

where n is refractive index of gain medium, % the inter-band relaxation time, m and m are the effective masses of an electron in the conduction

C V

band and a hole in the valence band respectively, Eg is the energy gap between the two bands, and f and f are Fermi-Dirac distribution functions

C V

for conduction and valence band. The quasi-Fermi level is predetermined by pumping level and optical signal intensity and will remain constant. Calculation15 shows that for semiconductor materials, the gain curve is very wide. Within the tuning range which of interest, the corresponding gain change is extremely small. Even with the reinforcement by the resonator, this change is negligible. This situation is equivalent to that of a very shallowly modulated optical signal passing through a laser amplifier. When the modulation is shallow enough, the amplifier can be considered as a ideal one.

Based on the above arguments in this chapter, it is assumed that the gain in the gain medium is constant, therefore, the Fabry-Perot resonator with gain medium will be treated as a high Q resonator (Q approaches

65


infinity when the laser oscillates). In the rest of this chapter, when we mention the reflection ratio in a resonator with gain, we mean the effective ratio, equal to the actual reflection ratio multiplied by the square root of the single trip gain.

3.3.2 The Round Trip Effect in a Fabry-Perot FilterLet us consider a Fabry-Perot resonator used as a filter. As an energy

storage system, a delay is expected for any signal passing through a Fabry-Perot resonator.

Imagine the case when a step optical input u ^ t) with optical frequency co and input rising at t = 0, giving an output u (t) at the other side of the Fabry-Perot resonator, u (t) and u (t) can be expressed as

in out

{a exp(jcot) when t > 03.3.2

0 when t < 0and

1 - p 2kexp(j2kcoL/c)u (t) = a exp[jco(t-L/c)](l-p )----------—------------------- 3.3.30111 1 - p exp(j2coL/c)

t . c lwhere k, a function of t, is the largest integer less than (-j— - - j - ) and pis the reflection ratio of both interfaces of the resonator. If the filter was designed for frequency co, e.g. exp(jcoL/c) = 1, then

u (t) = aexp(jcot)(l-p2k) 3.3.4out

This shows, from the energy storage view, that the input energy would need a transition time to charge the resonator before passing through. One obvious conclusion is that the higher the Q factor, the longer the transition time.

To obtain more general and quantitative results, consider the above filter problem not in the time domain as we did in the last paragraph by using light beam theory but in the optical frequency domain. Let U Cco) be the spectrum of u. (t)

m oo

U. (CD) = F (u .) = f u. (t) exp(jcot) dt 3.3.5in in J in* — OO

The transmission function of a Fabry-Perot resonator can be written as( l - p 2) exp(j coL/c)

T (co) = -------- 3.3.61 - p exp(jco2L/c)

66


+

ICN

g w

Vi •*-*

i—H V' oa

II/•— \ 1

M§

3w

o oA V

<Dd O

Q_

Q _

l-l<D

c uIPL,

.s3

3

C/3

C/3c3C/3O03GOC/3<D4-*0u<o

CLh1

X)03

CLi

c nc n

bb(X

67

Chapter Three; Dynamic Theory of Tunable Semiconductor Lasers

and the output spectrum can be expressed as

UJ “ ) = Tpp(“ )'UJ “ ) 3.3.7

Clearly Eq.3.3.6 and 3.3.7 are more general expressions for Fabry-Perot filter problems and u. (t) is not necessarily a step function. The delay

intime can be determined by the linewidth of the filter. The time for the output to half of the final power can be calculated by

2 n x p2x = ------------------------------------------------- 3.3.8

1/2 i - p2where x = 2L/c, the round trip time.o r

3.3.3 Mode Switch TimeExperience from the last chapter suggests that even static analysis of

multiple cavity problems is quite complicated. It is necessary to make some approximations to simplify the problem in dynamic analysis.

theBecause we are only interested in, \mode selection problem, assume that the feedback from the external cavity is so weak that it is just able toturn over the balance between two competing modes and realize mode selection but not strong enough to carry out any continuous tuning. This assumptionimplies: 1) An optical length change in the external cavity will not producean optical .'-■■■ phase change in laser resonator which causes continuous tuning; 2) The stored energy in the external cavity is negligible comparedwith the total stored energy in the laser resonator, therefore modulation of the stored energy is also negligible; 3) Because of 2), the Q factor of the system is mainly determined by the laser resonator and the linewidth reduction function of the coupled cavity is not obvious; and finally 4) Because the change of Q factor with coupled cavity modulation is small, the laser gain change caused by Q change is negligible. The other assumption is that the laser system can only operate in a single mode, or that theoptical length change needed for mode selection takes a very short time,therefore the multiple mode operation period is negligible, For instance,the external cavity is modulated by a step signal and takes no time tochange from one optical length to another.

When the laser system is switched from one mode to another by changing

68


the coupled cavity, because the total stored energy change is very small, the rise time of the new mode will be almost equal to the fall time of the old mode and therefore only one of them needs to be studied. For convenience, we choose to study the situation of the new mode rising. The problem can be very easily transferred to a Fabry- Perot filter one. Theinitial input signal is spontaneous emission u. and the rise time for the output to reach half of the final power can be calculated by Eq.3.3.8, or in frequency domain terms the maximum modulation frequency for mode selection is limited by the linewidth of the laser system. In some laser system this frequency can be as low as hundreds of kilohertz.

3.4 Dynamic Characteristics of Continuous TuningThe availability of very fast cavity length modulating means makes it

possible to carry out intra cavity modulation with speeds comparable to theresonator round trip time. As discussed in the last chapter from static analysis, this modulation, will produce continuous tuning for tunable laser structures. But because of the speed of the modulation, this raised concern about the influence of the so called round trip time effect which had, as indicated in the last section an obvious delay effect on mode selection with the Fabry-Perot resonator working as a filter.

3.4.1 The Parametric Resonators for Frequency TuningAn intra-cavity modulation problem can be studied as a parametric

resonator problem. There is a significant difference with the situation discussed in the last section: in intra-cavity modulation, the parameters ofthe filter i.e. parameters related to energy storage are changed, in other words the stored energy is modulated. This situation is different from either external modulation which is irrelevant to the laser resonator itself or the case of a modulated signal passing through a Fabry-Perot filter,which is simply determined by the finesse of the resonator.

As discussed in the last chapter, the tuning of semiconductor lasers isa procedure of modulating the optical length of the laser resonators. The simplest model of a tuning system consists of two opposite mirrors and one of them is moving toward or away from the other. During this movement, work has to be performed to move the mirror against light pressure. The energy

69


consumed or generated in this movement will contribute to the stored energy change.

The problem is also different from that faced in parametric circuitsbecause the sizes of the optical resonators are normally much larger thanthe optical wavelength. That means that the energy distribution in the resonator has to be considered. When the energy in the resonator is modulated non-uniformly, it needs some time to reach equilibrium and a delay is expected. The delay will be determined by the modulation method and the resonator size.

3.4.2 Oscillation in a Parametric ResonatorAssume the resonator of a tuning system can be simplified as shown in

Fig.3.4.1. The internal reflection caused by the non-uniform distribution of refractive index is negligible for example by antireflection coating, see Appendix A.

Without modulation, the field in the resonator can be written as

u(t,x) = u+(t - x) + u‘(t + x) 3.4.1

Notice that u+(t - x) and u'(t + x) represent forward and backwardtravelling waves and, because without modulation, n(x,t) can be simplified as n(x),

where the position measured by light travel time. For an ideal loss-free oscillator assume p => 1. At the boundary x = 0

Eq.3.4.3 and 3.4.4 indicate that at time t, oscillation in the resonator should have an instantaneous time period x q, or in frequency, an

o3.4.2

u+(t) = u*(t) = u(t)

At the other boundary x = 1

3.4.3

u(t + % J 2 ) = u(t - x J 2 ) 3.4.4

where

3.4.5

70


2 n kinstantaneous frequency co = where k is an integer. Because withouto

parametric modulation, n is time independent and thus so is the oscillation frequency co. The tq here represents the round trip time of the resonator. The result was expected and well-known in Fabry-Perot etalon analysis.

With refractive index modulation, the refractive index in the resonator is no longer only a function of position x but also of time t. The position related delay T can no longer simply be obtained from Eq.3.4.2. and the delays for the forward and backward waves, x+ and x are normally different.

To calculate x + and x \ let V(x,t) represent light velocity at position x and time t and we have

V(x,t) = c/n(x,t)

ordx _ c dT n(x,t)

for the forward wave, we have boundary and initial conditions

3.4.6

x ( t ) = 0 3.4.7v o7

x(tQ- x+) = 1 3.4.8

and for the backward wave

x ( t ) = 0 3.4.9v o'

x(tQ+ T) = 1 3.4.10

Solving the above equations, we obtain

x+= T+(tQ) and x — T (tQ) 3.4.11

Following Eq.3.4.3 and 3.4.4, we have

u(tQ- *+) = u(t0+ x ) 3.4.12

The instantaneous optical frequency at time t and position x = 0 should be 27tk 0

co(t) = --------- 3.4.13T+ + T‘

and the optical phase .t_

3.4.145 (0 = f 0 co(t) dt o J0

71


U+( t ) + U ^ t + T^u^ U ^ C*

► |

P n( x, t ) P

u ( t ) ^ ------------- u ( t - x ' )

»

Fig.3.4.1 General Model for Tunable Lasers

to tO + Tl tO +T +

12, Il2(t)

Section 1 Section 2

tO - T l tO - T

Fig.3.4.2 Model for Tunable External Cavity Lasers

72


3.4.3 FM Response for a Sinuous Modulated ResonatorTo simplify the problem further, assume that the resonator can be

separated into two uniform sections and that the refractive index modulation is only performed uniformly in one section, say section 2, by

n2(t) = n2+ Ansin(Qt+d)

when the modulation is very small, An « n2, the first order approximation is

n (t) =n2* An-sin(Qt+d)

From Fig.3.4.2, w e have

3.4.15

t +x

V Ti

andV x,

V T'

3.4.16

Where x = n l / c is the transit time in section 1. Substituting fromEq.3.4.15, Eq.3.4.16 can be rew ritten as

x+= x + d+ andow h ere XQ= (1 n l2n2)/c the average ro u n d trip tim e and

x = x + d'o 3.4.17

d+= |2 (x +- x^sinc [Q —j - 1] s in jil + d |x++x.

2

d =|n(x-- x ^ s i n c [n—2- i ] s i n j a [t„—3- -] + d |

Noticing that

I sinc(x) | < 1

we have

d+ < Ax and d* < Ax

3.4.18

3.4.19

3.4.20

where Ax = An-l2/c is the maximum variation of single trip time due to the modulation. Assume the tuning range is much smaller than optical frequency, e.g. Ax « x . and make the approximation x += x '= XQ in Eq.3.4.18 and 3.4.19

73


T +Td+=ATsinc(Qi2/2 ) s in |n |y - —— - J + d j 3.4.20

T +Td'=ATsinc(£2i2/2)sin |n^t0- —— - J + t f j 3.4.21

andx +x

x++x’=2xo+2 Ax- sinc(Qx 2/2) • cos(£2- —— -) sin(^tQ+,d) 3.4.22

Finally, after the first order approximation, the instantaneous oscillationfrequency at time t is

co(tQ) sc cok+ Aco-sin(QtQ+d) 3.4.23

7 tkwhere ©k = — , the oscillation frequency of the k th mode m the statico

resonator andx +x

Aco = ^ - s in c ( n t /2 ) cos(fi—— -) 3.4.24x o 2 2

the frequency deviation for the modulation. Notice through our wholederivation, no special conditions were imposed on the time tQ, so we canreplace it with t.

3.4.4 Three Special CasesTo make the meaning of this result more clear, consider some special

cases.First, when the modulation frequency C l is very low

x +x1 im sinc(f2-x /2) = 1 and 1 im cos(Q ) = 1

2 Q-> 0 2

therefore1 im Aco = ^

O>0 x oThis agrees with our results in static tuning experiments, Chapter 6.

Second, if the refractive index modulation is imposed uniformly throughout the resonator, i.e. 1 = x = 0, x2= xq then we have

Aco = ^-sinc(Q xQ) o

74


when £2 => 7c/tq, Aco =» 0, and there is no FM output. This is because starting at any moment and at any position in the resonator, a light beam travelling a round trip in the resonator should experience a whole modulation period,during which the average optical length change is zero therefore, a constantoscillation frequency results.

We are specially interested in the case when the modulation section ismuch shorter than the other, thus T2« Making appropriateapproximations, we obtain

Aco = | i c o s ( £ i t 0) 3.4.250

This is the basic formula to consider the round trip effect in later experiments.

To assess the impact of the result on tuning speed, consider a typicalexternal cavity system. Suppose the optical length of the resonator is 15 mm, the modulation frequency for the frequency deviation to fall to one fall of the value at low frequencies is f^ = = 6GHz. It is clearly a

serious limitation.

3.5 ConclusionIn conclusion, the continuous tuning speed of a MQW tunable laser will

be limited by the capacitance of the MQW device and by the delay effect caused by finite resonator size. The former can be improved by reducing the device area and a modulation frequency up to a hundred gigahertz is possible while the latter however, requires a compromise between the emission linewidth and the modulation speed, since both are determined by resonator size. For the derivation of this conclusion, the gain is assumed to be constant.

On the other hand, the speed of mode selection is simply limited by the emission linewidth of the laser system. In most situations, it is much slower than what can be reached for continuous tuning. This result is obtained under conditions of very weak coupling between the laser resonator and the external cavity.

Combined with previous chapter, these theoretical analyses form the foundation for designing and explaining later experiments.

75

Rela

tive

Mod

ulat

ion

Eff

icie

ncy


1 . 0

Uniform Wodulation

o . oLocalized Modulation

- 1.0

1.00.6 0.80.2 0.40 . 0

FM Frequency (/mode spacing)

Fig.3.4.3 Modulation Efficiency as a Function of FM Frequency

76

Chapter Three; Dynamic Theory of Tunable Semiconductor Lasers

References

1. S. Saito, O. Nilsson, and Y. Yamamoto, Oscillation Center Frequency Tuning, Quantum FM Noise, and Direct Frequency Modulation Characteristics in External Grating Loaded Semiconductor Lasers, IEEE J. Quantum Electron. QE-18, 961, 1982

2. N.K. Dutta, T. Wessel, T. Celia, and R.L. Brown, Continuously Tuning Distributed Feedback Laser Diode, Appl. Phys. Lett. 47, 981, 1985

3. D. Renner, and J.E. Carroll, Simple System For Broad-band Single-mode Tuning of D.H GaAlAs Lasers, Electron. Lett. 15, 73, 1979

4. P. B arnes, P. Pouganeli, A. Rivers, M. Whitehead, and G. Parry, GaAs/ALAs Multiple Quantum Well Optical Modulator Using Multilayer Reflector Stack Grown on Si Substrate, Electron. Lett. 25, 995, 1989

5. J.B.D. Soole, H.K. Tsang, I.H. WTiite, H.P. Leblanc, R. Bhat, and M.A. Koza, High Performance QCSE Phase Modulator for the 1.5-1.55 (im Fibre Band, Electron. Lett. 26, 1421, 1990

6. J.E. Zucher, and T.L. Hendrickson, Electro-optic Phase Modulation in GaAs/AlGaAs Quantum Well Waveguides, Appl. Phys. Lett. 52, 945, 1988

7. B. Cai, A.J. Seeds, J.S. A. Rivers, and J. Roberts, Multiple Quantum Well-tuned GaAs/AlGaAs Laser, Electron. Lett. 25, 145, 1989

8. H. Yamamoto, M. Asada, and Y. Suematsu, Electric- Field- Induced Refractive Index Variation in Quantum-well Structure, Electron. Lett. 21, pp. 579, 1985

9. H. N agai, Y. Kan, M. Yamanishi, and I. Suemune, Electroreflectance Spectra and Field- Induced Variation in Refractive Index of a GaAs/ALAs Quantum Well Structure at Room Temperature, Japanese J. Appl. Phys. 25, pp. L640, 1986

10. M. G lick, D. Pavuna, and F.K. Reinhart, Electro-optic Effects and Electroabsorption in a GaAs/AlGaAs Multiplequantum- Well Heterostructure Near the Bandgap, Electron. Lett. 23, 1235, 1987

11. A.J. Seeds, a n d J .R . Forrest, High-rate Amplitude and Frequency Modulation of Semiconductor Lasers, IEE Proc., 129, p. 275, 1982

77


12. G. S ch ie llerup , RJ.S. Pedersen, H. Olesen, and Tromborg, Center Frequency Shift and Reduction of Feedback in Directly Modulated External Cavity Lasers, IEEE Photon. Tech. lett. 1, 288, 1989

13. C.D. Zaglanikis, and A.J. Seeds, The Use of Semiconductor Laser Amplifiers in Optically Controlled Phased Array Antennas, XXIII General Assembly of the International Union of Radio Science, Prague, 1990

14. A.J. Lowery, A Study of the Static and Multigigabit Dynamic Effects of Gain Spectra Carrier Dependance in Semiconductor Lasers Using a Transmission Line Laser Model, IEEE J. Quantum Electron. 24, 2376, 1988

15. M.G. Bernard, and G. Duraffourg, Laser Conditions in Semiconductor, Phys. Status Solidi, 1, 699, 1961

78

CHAPTER FOUR

REFRACTIVE INDEX CHANGE IN QUANTUM WELL MATERIALS

4.1 IntroductionIn recent years, the optical properties of quantum wells have been the

subject of increasing interest1*7. Among these various properties, most attention has been concentrated on applied electric field induced variationsin the absorption coefficient4*6 and refractive index7*11. QW have been

8 12 10 12 investigated experimentally ’ and theoretically ’ m both aspectsbecause of their unique nature as solid state physics systems and theirpotential applicability to a large variety of electronic and optoelectronicdevices. Up to present, high-speed modulators13 and optical logic devices14have been fabricated, based on the successful applications of the electricfield dependence of optical absorption and initial results have beenobtained in applications of electric field dependence of the refractiveindex.15

Extensive investigations of the properties of QW structures have beencarried out, most concentrating on the large electric field induced

12absorption changes in QW . The absorption change is caused by two effects:1) The applied electric field makes the particle energy eigenvalues

shift to lower levels, and2) The wave functions of electrons and holes are dispersed by the

applied electric field causing coupling of electrons and holes between different quantisation numbers of energy levels and a reduction in coupling between the same quantisation numbers.

Both of the above effects cause absorption changes in the form of shifting, broadening and decreasing of QW absorption peaks. The absorption change caused is unevenly distributed across the whole optical spectrum. According to the Kramers-Kronig relationship, a related applied electric field induced refractive index change should occur.

Based on this idea and previous work on applied field induced

79

Chapter Four: Refractive Index Change In Quantum Well Materials

O 1Aabsorption change, some theoretical work on refractive index changes * hasbeen carried out. Amongst these efforts, different considerations have beentaken in calculating the absorption coefficients. For instance, in Yamamotoet al’s calculation , only intersubband transitions have been taken intoaccount and his results give only a rough estimate of refractive index

8 10change. Nagai et al and Hiroshima considered more factors: the former’scalculation takes into account the excitonic effect, and the latter includesthe forbidden excitonic transition which comes to be allowed in the presence of an external electric field. All the above calculations show that a refractive index change as large as l%-2% should be expected. These resultshave been confirmed by electroreflectance measurements8.

There are considerable difficulties in measuring refractive index change directly at or very near excitonic gap energies where the refractive index has a large change. In waveguide structures, the heavy absorption near the gap makes this measurement impossible, while in normal incidence structures, the layer is too thin to provide sufficient optical phase change for observation. Most of the results have been obtained evaluated from absorption coefficient or electroreflectance measurements using the Kramers-Kronig relation8. HoweveT, in practice, this technique suffers a big drawback because it is impossible to obtain accurate absorption measurementsover the whole spectrum from a single sample due to the large variation of absorption coefficient over the spectrum, from of the order of 104/cm at the exciton peaks to 1/cm at low photon energies. In theoretical modelling,there are also considerable difficulties in following the above technique using calculated absorption coefficients; the previous work on absorptioncalculations emphasized the position of the absorption peaks and their shift and the values of absorption coefficient were only accurate over very narrow wavelength ranges near the peaks, while accurate data over much wider ranges are required to calculate the refractive index change by the Kramers-Kronig relation. On the other hand, there is also great interest in absorptioncharacteristics at low photon energies considerably away from exciton peaks,because of the potential of achieving pure phase modulation. Therefore,achieving accurate results for absorption calculations over a wide spectral range becomes the key point in refractive index calculations andphase/amplitude modulation analysis in QW devices.

80


The purpose of this chapter is to provide a theoretical model for the design of the MQW structures used in this project. In this chapter, some recently developed theoretical models12,16'19 were adapted to assess appliedfield induced absorption change. In order to obtain better agreement withexperimental results over a much wider spectrum, several adjustableparameters were introduced into this model. Since the model was required as a design tool, no attempt was made to explore the detailed physics of QW, and thereby justify the adjustments of the parameters quantitatively, although some qualitative theoretical explanations are given. Parametervalues were determined from an investigation of the experimental results.

In this model, it is assumed that the absorption is due to electron- light hole and electron- heavy hole absorption. Each of the absorption canbe further divided to the exciton and continuum transitions which produce exciton absorption peaks and continuum absorption bands respectively. Theexciton parts of the absorption are modeled using the effective mass approximation and the continuum parts are modeled by Sommerfeld factors. The absorption coefficient curve is finally obtained by broadening both exciton and continuum parts. With the absorption curves under different appliedelectric fields, the refractive index changes can be calculated using the Kramers-Kronig relation.

The structure of this chapter is as follows: after a standardtheoretical description of QW properties with the effective mass approximation in section 4.2, in order to calculate the exciton absorptionpeaks, the particle equations were solved by the Airy function-matrix approach. Finite barrier height, tunnelling effects, and stress were aretaken into account. From the solutions the exciton absorption peak positionand height are determined. The continuum band absorption, binding energies and broadening effect e.g. the broadening lineshape and linewidth, wereevaluated using existing theoretical and experimental work. Finally the Kramers-Kronig relation was applied to the calculated absorption data to obtain the refractive index results.

4.2 Effective Mass Approximation ModelTo determine the absorption coefficient of MQW material, its energy

system has to be considered. Within the effective-mass approximation, the

81


energy state in a solid state physics system involving an electron and hole are generally expressed as

H\j/ = E \ \ fwhere H is the effective-mass electron-hole Hamiltonian in the presence of electric fields; E the system energy, in this case the photon energy; \jr the wave function of electron and hole, with proper normalization, according to quantum mechanics, | \ | / |2 will be the probability of finding the electron and hole in the same unit cell and therefore will be proportional to optical absorption at photon energy E.

12In a QW system, the Hamiltonian can be further expressed as:

H = H + V (Z ) electronke e e

+ H + V (Z ) holekh h h

+ H + V (r, Z + Z J binding 4.2.1kb b e h

where

- h 2 a 2 - h 2 a 2 -h2 a2H = ------- H = -------- -— H -----— 4.2.2

k' 2m . 3Z2 kh 2m . aZ kb 2|X 8r2e_L e h X

are the kinetic energy operators for electron, hole perpendicular to the QWlayer (Z direction) and the relative motion of electron and hole in the plane of the layers respectively, and and r n ^ are the effective massesof electron and hole in Z direction,

m „ ■ m ..= — — !l!1 4.2.3^ m ,,+m „

ell hit

is the reduced effective mass of electron and hole in the plane of the layers; m „ and m „ are the effective masses of electron and hole,

ell hllrespectively, in the plane of the layers; Zg and Zh the coordinatesperpendicular to the plane of the layer; r the relative position of electronand hole in the plane of the layer, q and F± here represent the value ofelectron charge and applied field.

V ( Z ), V (Z ) and V (r, Z +Z ) are the potential energies. With electrice e h h b e h

field only in the Z direction,

82


V(r, Z-Z) = 4.2.4

is the Coulomb potential energy of electron and hole relative to each other. To obtain the solution of Eq.4.2.1, set a separable trial function,

E and E are the energies of the individual electrons and holes. They aree h

related to the trial function by

All the above equations have to be solved numerically and with properly normalized \i/ ( Z ), w (ZJ and w(r), the absorption coefficient of the

e e h h bexciton is expressed as:

where B is a constant.In order to make the calculated results comparable with those of

experiments, more factors have to be considered. As the influence of these factors can not be quantitatively described by purely theoretical means, several experimentally fitted parameters are introduced. In introducing the parameters, their dependence upon QW structure is minimized, the determining factors being material growth.

4.3 Exciton AbsorptionBoth exciton energy and absorption intensity can be determined by

\|/(r, Z Z ) = w(Z)-w (Z)-w(r)6 n 6 6 A n D

4.2.5

This implies the photon energy is divided into three parts:

E = E + E - Ee h b

4.2.6

{H J- V (Z ) - qF± Z }Vc(Z ) = E .Vc(Z ) 4.2.7

and

E is the binding energy and evaluated by the variational methodb

4.2.8

V < v lH kb+ Vb(r, Z + Z ) l v > 4.2.9

E=E +E -E4.2.10

83


solving the one-dimensional Schrodinger equations (Eq.4.2.9 and 10)described as a particle- in- a- box problem in finite wells.

In MQW, the problem can be further specified as a particle p in an nregion structure as shown in Fig.4.3.1, where p represents either electronor holes, L. is the width of the region i, V , m , and

i pi _L.pi

_Lpi pare the potential energy, the effective mass and the kinetic energy operator of the particle p in the region i.

4.3.1 Solutions Under Zero FieldWithout applied field, the particle wave function in region i is

determined by

Hpi 2m . . a Z 2

4.3.1

The general solution is

where

4.3.2

pi h 2

2m. .(E - V .)-Lpi______ pi

We define vectors

4.3.3

and matrix4.3.4

cos(|3 Z) j-sin(P ,Z)/npi pi pij sin(P ,Z) n . cos(P .Z)pi pi pi

4.3.5

the relation between them is

4.3.6

84


V

a) o

ZO Zl Z2 Zi Zn-1

Z

V i k

c)

ZO Zl Z2 Zi

Fig. 4.3.1 An n Region Systema) Built-in Potential Structureb) Applied Electric Fieldc) Built-in Potential Under Electric Field

85

______ Chapter Four: Refractive Index Change In Quantum Well Materials

The boundary conditions at the interface between the region i and i+1 can be expressed by

The eigen energy is obtained by searching for the minimum o f '

4.3.2. Solutions Under Applied FieldWith applied field Fx- the Schrodinger function is

{H .+ q_F, Z + V - E}w (Z) = 0 4.3.12pi p pi pi

by setting pp.= -(2m^.q^Fj^/h2)1/3 and £p.= (E - V^Vq^F^, the general solution for Eq.4.3.12 is

4.3.7

it gives

4.3.8

or

4.3.9

where

4.3.10

The solution can also be expressed in forward and backward wavesv .(Z-Z. ) = c+-exp[-j|3 (Z - Z. )]

1 pi l- i pi pi i*i

+ c’. exp[+jp .(Z - Z )]pi pi i-i

4.3.11

and can be linked to Eq.4.3.2 by

A c A*+ _ pi pi A c. A*.c .= — ------- -pl 2 2n

_ p i pj_ and c =pi

pi , pi

v (Z - C .) = c+.Ai[p (Z - ? . ) ] + c‘ Bi[P .(Z - c .)]Tpi pi pl p i p i pi pi pi

where Ai( ) and Bi( ) are Airy functions defined by1 OO 1

Ai(Z) = i j cos(yt3+ Zt)dt

4.3.13

1 1 1

Bi(Z) = [exp(-^t3+ Zt) + sin(yt3+ Zt)dt

Following the Zero electric field,

86


D .(Z) = Z .(Z)'C .pi pi pi

whererAi(J3 Z) Bi(p Z)pi pi2 .(Z) =

P1

andn A i’ (B Z) n Bi’ (p Z)

>- pi V pi ' p i

4.3.14

C = [c+., c'.] 4.3.15Pi pi Piwhere ID . and n have the same definition as in Zero field. The boundarypi Piconditions give

thusID rz - C ,. J =D .(Z.- c ) 4.3.16

p(l+l) 1 p(l+l) pi 1 pi

C .= l ) . ( Z - ; . )*Z .(Z ; ,)'C . 4.3.17pi P(l+1) » p(l+l) pi 1 pi pi

With the initial conditions for electron (q^= -q) and holes (q^= q)CeQ= [0, 1] and [1, 0] 4.3.18

C can be calculated using the recurrence formula, and the eigen energy is obtained when c’ or c+ reach their minimum.

en l,hnDepending on the thickness of the wells, both with and without applied

field, more than one eigen value, representing higher exciton orders, may exist for each particle, However, only the exciton of lowest order is taken into account as the higher orders have much weaker oscillation strengths and are hardly distinguishable at room temperature.

Fig.4.3.2 shows the numerical modelling results of electron, light ando

heavy hole eigen energy for 100A well under different applied fields. They12are in good agreement with published results .

4.3.3 Light Hole Absorption Peak Red ShiftCompared with theoretical modelling results, the measured light hole

absorption peak is always found to have a red shift. This red shift has been12attributed to stress existing in QW structures . The lattice constants ofO 0

GaAs and ALAs, 5.654A and 5.660A, are slightly different at room temperature. During growth, differential thermal expansion coefficients (6.86X10"6/ C for GaAs and 5.20X10"6/ C for ALAs), permit lattice matching at higher temperature. The stress at the interface of different material regions will appear after cooling down to room temperature. At room temperature, the stress is proportional to the difference of the thermal

87


expansion coefficients, and therefore to the difference of the A1 molefractions in different regions. As the energy shift and stress are linearly

20related , the light hole shift caused by stress h proportional to the A1mole fraction difference.

Another design parameter, well thickness, may also contribute to QW stress and related red shift behaviours. In a wider well, the stressaffected boundary region has relatively smaller weight in the well’s overall performance than in a narrower one, therefore a smaller shift is expected. For the well thicknesses interest (5 to 15 nm), the red shift change isapproximately inversely proportional to well thickness. Based on the aboveconsideration, the stress caused light hole shift can be written as

8E = 8E*Ax — 4.3.1St St T.Lw

where Ax is the A1 mole fraction difference between well and barrier and5E1 is the stress-related energy shift in a 10 nm thick well for GaAs/ALAs

Stinterface (Ax = 1), to be determined from experimental data and is the well thickness.

With allowance for this shift, the modelling results for the light holeabsorption peak energy shown in Fig.4.3.2 are in good agreement withpublished results12.

4.3.4. Oscillation StrengthWith c+ and c" obtained from recurrence equations, Eq.4.3.8 or 17,Pi Pi

the wave functions are determined. In order to evaluate oscillation strength, they need to be normalized. It is noticed that with applied field, the integration for normalization

<V(Z)|v(Z)>p pdoes not exist. The normalization is realized by assuming y (Z) = 0 when it

pis significantly smaller than its peak value. The oscillation strength is proportional to

m,uT <ve(Z)IVZ)> 4-3-20where subscript e,l and h represent electron, light and heavy holes. Fig.4.3.3 shows the modelling results for | M 12 under different applied fields.

88

Ove

rlap

(Rel

ativ

e)

Eige

n En

ergy

(m

eV)


electron

light hole

-10

heavy hole-20

-30

-40100 120 140 160 180 200

Applied Field (kV/cm)

Fig.4.3.2 Eigen Energies of Electron, Light and Heavy Holes Under Applied Field

0.9

light hole

0.7

heavy hole0.6

0.5

0.4

0.30 20 40 60 80 180 200100 120 160140

Applied Field (kV/cm)

Fig.4.3.3 The Square of the Electron-hole Overlap

89


4.4 Continuum Band AbsorptionThe absorption due to the continuum of transitions between free states

can be described by Sommerfeld factors which take into account the Coulombinteraction produced enhancement of the absorption, even the above the bandedge where the excitons are ionized. The two- dimensional Sommerfeld factor

21is written as2

Kp(hCO) = ----------------------------------------- — 4.4.11 + exp{-27t[(hCO - Ep)/Ryp] }

wherep = 1, h and Ep= E + E 4.4.2

c e pare the continuous band edge of light and heavy holes, and

P 4U qRyp= — r-j 4.4.3

2 h ethe Rydberg constant (ip, defined in Eq 4.2.3, is the reduced effective mass of electron-light hole and electron-heavy hole for motion parallel to theplane of QW layers.

It is very difficult to determine absolute absorption at the excitonpeak and continuum theoretically with reasonable accuracy and therefore the continuum absorption at zero field was obtained from experimental data. As the ratio between light and heavy hole absorption intensity is 1:322,

a 1 = 0.25a and a h = 0.75a 4.4.4con con con con

Based on a two-dimensional model, the relation between exciton and continuum absorption is23

a p /a p =16 Ryp 4.4.5ex con

where a p and a p are exciton and continuum absorption values at zeroex con

applied field. However, because of the remaining three-dimensional behaviour in a real QW system, this ratio is actually smaller than the above value; in agreement with other authors19, it is found this ratio is only about 12Ryp. The dimensional behaviours of the QW can be clearly shown by the shape ofthe exciton. While the two- and three- dimensional excitons have a flat dishand spherical shapes respectively, the shape of the exciton in a real QW can be represented by an ellipsoid (shown in Fig.4.4.1). The effects of reduced dimensionality of a QW structure can be measured by dimensional coefficient T [ p = r? /rp ( 0 < T|p < 1). rp can be calculated from three dimensional

dim _L II dim II

90


Central Plane of Well

Fig.4.4.1 The Shape of Exciton in QW

91


model as it is in the well plane. For GaAs rp = 30nm. r£ can be calculated

Rep -<p |P e

Z 2 | (p (p >P e

1----- A -6 TJ -G n

| tp • <p >P e

« p -tp I z | ( p - 9 > 2‘,wp e p e

<(D • Cp I (p • (D > 2Tp T e T p T e

from the wavefunction (p (Z)p

'<cp -<p |zr ]= 3- — g— g --___ ‘ - p i -e , p e . 4.4.6

It is suggested thaty p, = a p /a p = 4Ryp-(4 - 3r| p ) 4.4.7

ex/con ex con dim

Fig.4.4.2 shows the relative change of tj p with well thickness under zerodim o

applied field. It shows that at a well thickness of about 40A, the y pex/con

reaches maximum. That is because when the well is too wide, the QW system will show more three-dimensional behaviour, whilst when the well is too narrow, the well confinement is reduced and again, the system shows more three- dimensional behaviour24.

In contrast to the predictions of the theoretical model, in the measured spectrum, the absorption in the continuum does not decline with the exciton peaks under applied field, but remains almost unchanged. This is caused by the reduction in carrier confinement in QW due to the applied field increase of continuum absorption. Based on this consideration, in this model, it is assumed that this effect cancels exciton oscillation strengths influence on continuum absorption.

4.5 Binding Energy12J25 28The binding energy has been calculated by several anthers . The

variational methods described in section 4.2 are the most widely used. It is found that the binding energy change plays only a small part in the total energy shift of a QW system under an applied field. For instance, according to Miller’s model12, which proposed a simple ls-like orbital for the in-plane radial motion, for a 25 meV total energy shift, the binding energyshift was less than 2.5 meV for both light and heavy holes at applied fields the above lOOkV/cm. Although this may not apply to some extreme cases, such as very wide wells, or very low or narrow barriers, in the structures ofinterest for this work which should show predominantly QCSE behaviour, the binding energy change remains relatively small. A very simple model to estimate binding energy can then be constructed. The binding energies inthree- and two- dimensional system are Ryp and 4R yp. The binding energy in

92

Bin

ding

En

ergy

(m

eV)

Dim

entio

nal

Coe

ffic

ient


0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25 light hole heavy hole

0.2

0.15

Well Thickness (nm)

Fig.4.4.2 Dimensional Coefficient Ti^im anc*

light hole

heavy hole

+ light hole

* heavy hole

0 20 40 60 12010080

A pplied Field (kV /cm )

Fig.4.5.1 Binding Energy (+, * from Reference 12)

93


a QW system must lie in this range as it is neither a pure three- nor two- dimensional system. The model proposed is

Eep= Ryp-(4 - 3rtP ) 4.5.1b dim

Fig.4.5.1 shows the numerical results for 100A well under different applied12fields. For comparison, Miller’s results are also plotted on the same

graph. In spite of much simpler model, they are remarkably similar.

4.6 Absorption Spectrum BroadeningIn a perfect crystal and at absolute temperature T = 0 K, the

absorption spectrum of both light and heavy holes can be expressed by aninfinitely narrow exciton peak at the exciton energy and a continuum the above the band edge, described by Sommerfeld factors. The energies and oscillation strengths of excitons were obtained by solving particle-in-a-boxproblems. The energy positions of light and heavy hole absorption peaks are

E = E + E - Ee_1 and E = E + E - E‘ h 4.6.1e-1 e 1 b e-h e h b

where Ee, and Eh are the eigen energies of electron, light and heavy holes obtained in section 4.3. With the absorption coefficient proportional to the square of the oscillation strength, the infinitely narrow excitonpeaks of light and heavy holes can be written as

a 1 M , S(hco - E ,) and a h M & ( h ( o - E )ex e -1 e-1 ex e-h e-h

and continuuma 1 K’(h(0) and a h Kh(hCD) 4.6.2

con con

When T > 0 or the crystal structure is not perfect, the absorption spectrum is expected to broaden by a broadening function, Ap(hCo).

From Section 4.3, the broadening effect and carrier life time can be obtained by considering particle tunnelling effects. This linewidth is much narrower than found experimentally and the Lorentzian lineshape which represents carrier life time related broadening, is too flat to match the steep low energy edge of exciton absorption peaks. Some authors suggest that

24Gaussian lineshapes may give better agreement . In the present measurements, the actual lineshape was found to be in between Lorentzian and Gaussian lineshapes, therefore, naturally a combined lineshape of these two is proposed. A physical justification is that the Gaussian lineshape is due

94


to the diversity of structure parameters. The dominant cause of such diversity for a single QW is the roughness of the interfaces between well and barrier. With this assumption, the whole sample can be considered as an assembly of a vast number of tiny wells in parallel (shown in Fig.4.6.1). Each well is independent of the others and only contributes a small fraction to the absorption spectrum, so that the Gaussian lineshape can be used to reflect their statistically summed effect. The relation between Gaussian linewidth and interface roughness is29

3EP (L )a = rj —----- — a

P d L4.6.3

where G and a are the standard deviations of the Gaussian broadeningp w

function and interface roughness, 0 < rj < 1 is a constant dependent upon the lateral extent of the two-dimensional islands describing interface roughness, and thus, the size of each individual tiny well. When the size is smaller than the three- dimensional exciton radius, the lateral coupling between adjacent tiny wells will reduce the spectrum broadening effect. This situation is represented by T| < 1. As both rj and G are to be determined experimentally, define G* = TVCTW as effective roughness. Then Eq.4.6.3 can be rewritten as

3Ep (L )e x w

aL4.6.4

In Eq.4.6.4, 3EP (L )/aLex w

described earlier inw

thiscan be calculated from numerical modelling section. However, in order to reduce the

calculation time, the infinite well model is used, instead, and we deduce an analytical formula

Under zero applied field

a =p m , L_Lp w

4.6.5

and with applied field

G =P

eF | a_L w

f r A i ( Z +) 1 ’^ T A i ( Z - ) l \Ibitz J + [BKZryJ

4.6.6TAi(Z+)r rAi(Z-)l ’

" IBI^J

95

Lin

ewid

th

(me

V)


vast num ber o f tiny wells w ith different thickness

Barrier

Fig.4.6.1 W ell T hickness Variation Due to Interface R oughness

4

3.5

ight hole

h e a v y h o l e

0 20 100 12040 60 80

A pplied Field (kV /cm )

Fig.4.6.2 Applied Field Induced Gaussian Broadening

96


where

z+=-’ 2m |

_Lwp1/3

(hCO - V + I-qF .L ) Z=-’ 2m |

JLwp

.(qhF ) p Z _L w .(qhF )

1/3•(hCO - V - T qF - L )

p L _L w

The broadening effect of each individual tiny well can, however, stillbe expressed by a Lorentzian lineshape, which forms the Lorentzian part of the combined lineshape.

The linewidth increase with applied field can also be divided into twoparts. The change in the Gaussian part, as shown in Fig.4.6.2, is determined by Eq.4.6.4 as aEp (L )/aL , a function of applied field. On the other hand,

ex w wthe applied field will also widen the individual tiny well’s linewidth, andthus the Lorentzian part of the combined lineshape. Furthermore, because itis caused by the weakened carrier confinement of the well with applied electric field, this part of the broadening should be somehow related to the degree of carrier confinement. In order to take into account the applied field broadening, the Lorentzian broadening linewidth is written as

r = r 0/ m 4.6.7P P e*P

where T0 is the Lorentzian linewidth at zero field for light and heavy hole absorption peaks. It is also supposed that as T is influenced by particle tunnelling behaviours, the light and heavy hole linewidths can be linked by

andu w r°= u w r°

1 1 h h

Uw = < v | \ i/>p p p in well

4.6.8

4.6.9

The heavy hole absorption peak linewidth r f , together with interfacenroughness can be obtained by fitting the low energy edge of the measured zero field heavy hole exciton absorption peaks.

Finally the broadening function can be written as:Ap(hco) = Lp(hco)*Gp(hco) 4.6.10

in this equation, the Lorentzian part is

Lp(hco) =n [ r '2+ (hCO - E )2]

P e 'Pand the Gaussian part

1Gp(hco) = ------ —-ex p

4.6.11

2 a np

1/2

(hCO - E )e-p

2n

4a4.6.12

97


The absorption of the exciton and continuum of both light and heavy holes can then be written as

a(hco) = Y aP -Ap(hco)*[M YP S(hco - E ) + Kp(hco)] 4.6.13Ld con e - p ex/con e-pp= 1 , h oThe numerical modelling results for 47A GaAs/AlQ3Gao7As QW are shown

in Fig.4.6.3. The parameters used in the modelling are listed inTable 4.6.1. The results give a good agreement with experimentally measured values.

Table 4.6.1 Parameters Used in the Model

V a l u e Un i t M e a n i n g Source

V g

1 4 2 4 + 1425X- 9 0 0 x 2 + 1 100x3 m e V

B a n d G a p of A 1 G a , AsX 1 - X R e f . 30

V e 5 7% Vg c o n d u c t i o n

b a n d R e f . 31

v i . h 4 3% Vg v a l e n c e

b a n d R e f . 31

mx« . 0 6 6 5 + . 0835x m oe 1 e c t r o n e f f . m a s s R e f . 31

m± i . 0 9 4 0 + . 0430x m 01 - h o 1 e e f f . m a s s R e f . 31

mi h . 3 4 0 0 + . 4200x m 0h - h o 1 e e f f . m a s s R e f . 31

“ II e ml ce - e f f . m a s s i n Q W p 1 ane R e f . 22

“ ll.4mXhmXi 3mX . + mx„

1 - e f f . m a s s i n Q W p 1 ane R e f . 22

m II h4mX imXh3mXh+ mx.

h - e f f . m a s s i n QW p 1 ane Ref. 22

8E1s t 1 5 m e V A 1A s / G a A s 1 - h o l e s h i f t m easured

e / e 0 1 3 . 0 We i 1 d i e 1 ect r ic c o n s t a n t R e f . 32

a 0c on 5 5 0 0 / cm h = U c o n t i nuum a b s o r p t i o n measured

a 1c on 2 5% a 0con f o r 1 - h o 1e R e f . 22

a hc on 7 5% a 0con f o r h - h o l e R e f .22*a r 1 . 5

uA S u r f a c e

r o u g h n e s s measured

r°h 1 me V h =0 h - h o l e L o r e n t z i an measured

98

Ref

ract

ive

Inde

x C

hang

e A

bsor

ptio

n (/

cm)


14000

12000

10000

8000

6000

4000

2000

0760 780 800 820 840 860 880

W avelength (nm)

Fig.4.6.3 Absorption Spectra of 47A Well

---------- ———,------------ -— , -------- r

A pplied Field

F - 0 kV /cm

F= 100 k V /c m ----------- _

1 ' VF -1 5 0 kV /cm ...............

/ / \ \ 1 jF=200 k V /c m -----------

* . * 1

-

1 ,

- 0.02 -

-0.04 -

-0.06 -

-0.08 -

- 0.1 -

760

Applied Field

F=100 kV /cm

F= 150 kV/cm

F=200 kV/cm

780 800 820 840 860 880

W avelength (nm)

Fig.4.7.1 Refractive Index Change in 47A Well

99


4.7 Refractive Index ChangeThe absorption of QW materials will change with applied field unevenly

over the optical spectrum. This change will introduce an additional refractive index change, due to the Kramers-Kronig relation. With absorption

33as a function of applied field, the Kramers-Kronig relation is written as

An(co,F± ) = -71

c r°°Aa(G)\F,)± dco’ 4.7.1

CO’ 2 - CO2oand

Aa(co’,F± ) = a(co’,F^) - a(co’,0)

For convenience of calculation and analysis, Eq.4.7.1 is changed to convolution form

An( | co I , F ,) = —_ .[co '* A a( | co I ,F .)] 4.7.2x 2 71 co x

or Fourier transform form

AndcoLF.) = [A a(|co |,F ,)]) 4.7.32 ttco

where * stands for convolution operation, ) and y’'( ) stand for Fourier and inverse Fourier transform operations. This is the formula actually used in the model.

Before proceeding to the numerical modelling, some interesting characteristics of the Kramers-Kronig relation result from Eq.4.7.3. If

AA(/) = 7[Aa( I co | ,FX)]

notice Aa(|a> l 'F±) is an even function and Ffco’1] =j sign(/), so thatoo

A a( |co | ,F , ) = F AA(/)cos(»/)d/' 4.7.4J 0

and- c oo

An( |co | ,F .) = ----- •[ AA^-sinCco^d/’ 4.7.52 tcco J o

As the relative variation of co is very small and AA * 0 over a limited region, we have approximately

^ A a d c o l^ ) ~ An(| co I, F± ) or 5 An(|co|,F± ) ~ A a(|co|,F± )

100


This indicates that the refractive index change peak is near the absorptionchange minimum. This is a profitable situation for tuning elements or phase modulators.

oNumerical results obtained from Eq.4.7.3 for 47A GaAs/Al Ga As QW

n 0.3 0.7are shown in Fig.4.7.1. Compared with Fig.4.6.3, there is clearly a peak- valley offset effect between absorption and refractive index changes.

4.8 SummaryIn conclusion, a computer model have been developed to assess the

electric field induced refractive index change in QW material. In thismodel, the refractive index change with applied electric field wascalculated from the calculated absorption spectrum by using the Kramers-Kronig transform. In order to obtain accurate absorption data over a wider spectrum and therefore, more accurate refractive index change data, both exciton and continuum transition were taken into account and additional parameters were introduced.

In the treatment of excitons, the effective mass approximation and Airy function- matrix approach were deployed. The use of the Airy function- matrix approach made this model potentially capable of handling MQW structures and the modelling speed was improved. To obtain accurate results near the exciton peak, the stress-induced light hole red shift was taken into account. For the lower energy part, where exciton lineshapes dictate the situation, a combined lineshape of Lorentzian and Gaussian was proposed for exciton absorption peaks. The roughness at the well/barrier interface was identified as the main cause of Gaussian broadening. The broadening of Lorentzian lineshape was connected with the recombined electron-hole density which roughly reflects the degree of exciton ionization and particle confinement.

In the continuum part, the Sommerfeld factor was used to reflect theabsorption caused by continuum transition and enhanced by Coulombinteraction. A simplified model for binding energy was used and the QWdimensional coefficient was introduced to describe QW behaviour between three- and two- dimensions. This coefficient was further used to assess theexciton/continuum absorption ratio.

In total four parameters in the model were obtained by fitting

101


experimental data. Among them, the interface roughness and heavy hole Lorentzian linewidth were obtained by fitting the measured lower energy edge of the heavy hole exciton peaks. The light hole stress- induced red shift was obtained by measuring the heavy and light hole absorption peak distance in the experimental spectrum and comparing it with the calculated one. The continuum band absorption was directly measured from the actual spectrum.All these parameters were determined under zero applied field.

The refractive index change was then calculated by the Kramers-Kronig transform. From its convolution form, it is found that theoretically, theKramers-Kronig transform gives a peak-valley offset relation between peak absorption and peak refractive index change. This property is useful fortuning elements.

Finally, the model was programmed, and the block diagram of the program is shown in Fig.4.8.1. It takes about 5 minutes to calculate for a single well structure on a standard IBM-PC or, equivalent by about 20 seconds on a SUN-3/260. The calculation results for two different structures are included

oin this chapter. One of them, with 100 A wells, was intended for comparison with results published in the literature for different modelling stages,owhile the otheT one, with 47A wells, was used to compare with our ownexperimental results. Both comparisons show very good agreement.

102


Structure Information Width of Wells lw Width of Barriers lb Number of Wells nw

Material Information Aluminum Concentration x

L,2i-l=lw L2i= lb Zi = Ln + Ln-1+"I+Li n = 2nw

fParticle in the Finite Wells F=0

rV=1.425x - 0 .9x2+1.1x 3

Light Hole Vh = 43%V m2i-i=.094 m2i=.094+.043x

IElectron

Vc = 57%V m2i-i=.0665 m2i=.0665+.0835x

Red Shift

L± U A

I

Heavy Hole Vi = 43 %V m2i-i=.34 m2i=.34+.42x 1-----

Particle in the FiniteWells F O

AppliedElectricField F

Binding Exciton ContinuumEnergy Absomtion Absorption

Broadenmg

AbsOTptionCoefficient

IRefractive

Index Change

Fig.4.8.1 Block Diagram of MQW Modelling

103


References

1. A. Harwit and J.S Harris, Observation of Stark Shifts in Quantum Well Intersubband Transitions, Appl. Phys. Lett.,50, 685, 1987

2. E.S. Koleles, B.S. Elman, C. Jagannath and Y.J. Chen, Temperature- dependent Optical Spectra of Single Quantum Well Fabricated Using Interrupted Molecular Beam Epilaxial Growth, Appl. Phys. Lett. ,49, 1465, 1986

3. M. Whitehead, G. Parry, J.S. Roberts, P. Misatry, P. Li Kam Wa and J.P.R. David, Quantum Confined Stark Shift in MOVPE-grown GaAs/AlGaAs Multiple Quantum Wells, Electron. Lett.,23, 1048, 1987

4. D.A.B. Miller, J.S. Weiner and D.S. Chemla, Electric-field Dependence of Linear Optical Properties in Quantum Well Structures: Waveguide Electroabsorption and Sum Rule, IEEE Quantum Electron., QE-22, 1816, 1986

5. G.D. Sanders and Y.C. Chang, Optical Properties in Modulation-doped GaAs/Gai ÂlÂs Quantum Wells,Phys. Rev., B31, 6892, 1985

6. W.T. Masselink, P.J. Pearah, J. Klem, C.K. Peng and H. Morkoc, Absorption Coefficients and Exciton Oscillator Strengths in AlGaAs/GaAs Superlattics, Phys. Rev., B32, 8027, 1985

7. H. Yamamoto, M. Asada and Y. Suematsu, Electric- field- induced Refractive Index Variation in Quantum Well Structures, Electron. Lett., 21, 579, 1985

8. H. Nagai, Y. Kan, M. Yamanishi and I. Suematsu, Electroreflectance Spectra and Field- induced Variation in Refractive Index of GaAs/ALAsGa Quantum Well Structures at Room Temperature, Jap. J. Appl. Phys. 25, L640, 1986

9. K.B. Kahen and J.P. Leburton, Exciton Effect in the Index of Refraction of Multiple Quantum Wells and Superlattics, Appl. Phys. Lett., 49, 734, 1986

10. T. Hiroshi m a, Electric Field Induced Refractive Index Change in GaAs/AH3ai Âs Quantum Wells, Appl. Phys. Lett., 50, 968, 1987

104


11. Y.C. Chang, Electro-optic Effect in Semiconductor Superlattics, J. Appl. Phys., 62, 4533, 1987

12. D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood and C.A. Burrus, Electric Field Dependence of Optical Absorption Near the Band Gap of Quantum Well Structures, Phys. Rev., B32, 1043, 1985

13. T.H. Wood, C.A. Burrus, D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard and W. Wiegmann, High-speed Optical Modulation with GaAs/GaAlAs Quantum Well in a p-i-n Diode Structure, Appl. Phys. Lett., 44, 16, 1984

14. P.J. Br a dley, P. Wheatly, G. Parry, J.E Midwinter, High- contrast Optoelectronic Logic Device Using A Waveguide Multiple Quantum Well Optical Modulator, Electron. Lett., 23, 213, 1987

15. B. Cai, A J. Seeds, A. Rivers and J.S. Roberts, Multiple Quantum Well-tuned GaAs/AlGaAs Laser, Electron. Lett., 25, 145, 1989

16. T. Hiroshima and R. Lang, Well Size Dependence of Stark Shift for Heavy Hole and Light Hole levels in GaAs/AlGaAs Quantum Wells, Appl. Phys. Lett. 49, 639, 1986

17. G.D. Sander, K.K. Bajaj, Electronic Properties and Optical- absorption Spectra of GaAs/Al^Gai ^As quantum wells in externally applied electric fields, Phys. Rev., B35, 2308, 1987

18. A.K. Ghatak, K. Thyagajan, and M.R. Shenoy, A Novel Numerical Technique for Solving the One-Dimensional Schrodinger Equation Using Matrix Approach - Application to Quantum Well Structures, IEEE J. Quantum Electron.,QE-24, 1524, 1988

19. P.J. Stevens, M. Whitehead, G. Parry, and K. Woodbridge, Computer Modelling of the Electric Field Dependent Absorption Spectrum of Multiple Quantum Well Material. IEEE J. Quantum Electron., QE-24, 2007, 1988

20. R.Dingle and W. Wiegmann, Optical Investigation of Stress in the Central GaAs Layer of Molecular- beam- grown A H ^ ^As- GaAs- A1 Ga As structures, J. Appl. Phys., 46, 4312, 1975

X 1-x21. M. Shinada and S. Sugano, Interband Optical Transition in Extremely

Anisotropic Semiconductor. I. Bound and Unbound Exciton Absorption, J. Phys. Soc. Japan, 21, 1936, 1966

105


22. D.S. Chemla, and D.A.B. Miller, Room- temperature Exciton Nonlinear-optical Effects in Semiconductor Quantum- well Structures, J. Opt. Soc.Am. B2, 1155, 1985

23. P. C. Klipstein and N. Apsley, A Theory for the Electroreflectance Spectra of Quantum Well Structures, J. Phys. C19, 6461, 1986

24. D.S. Chemla, D.A.B. Miller, P.W. Smith, A.C. Gossard and W. Wiegmann, Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures, IEEE J. Quantum Electron. QE-20, 265, 1984

25. R.C. Miller, D.A. Kleinman, W.T. Tsang and A.C. Gossard, Observation ofthe Excited Level of Exciton in GaAs Quantum Well, Phys. Rev. B24,1134, 1981

26. Y.E. Lozovik and V.N. Nishanov, Wannier- mott Excitons in Layer Structures and Near an Interface of Two Media Sov. Phys. Solid State, 18, 1905, 1976

27. G. Bastard, E.E. Mendez, L.L. Chang and L. Esaki, Exciton BindingEnergy in Quantum Well Phys. Rev., B26, 1974, 1982

28. Y.C. Lee and D.I. Lin, Wannier Excitons in a Thin Crystal Film Phys.Rev., B19, 1982, 1979

29. F.Y. Juan g , J. Singh, and P.K. Bhattacharya, Field- dependentLinewidths and Photoluminescence energies in GaAs/AlGaAs Multiplequantum Well Modulators, Appl. Phys. Lett., 48, 1246, 1986

30. D.A. Kleinman and R.C. Miller, Band- gap Renormalization in Semiconductor Quantum Well Phys. Rev., B32, 2266, 1985

31. R.C. Miller, D.A. Kleinman and A.C. Gossard, Energy-gap Discontinuities and Effective Masses for GaAs/Al Ga As Quantum Wells, Phys. Rev.,

X 1 -X

B29, 708532 J.S. Blackemore, Semiconducting and Other Major Properties of Gallium

Arsenide, Appl. Phys., 53, R123, 1982 33. F. Sterm, Dispersion of the Index of Refraction Near Absorption Edge of

Semiconductors, Phys. Rev., A 133, 1653

106

CHAPTER FIVE

COMPARISON OF VARIOUS TUNING MECHANISMS

5.1 IntroductionThe basic requirement for electronic tuning of semiconductor lasers, as

pointed out in previous, chapters is providing electronically controlled optical length change in laser resonators. This change can be achieved byvarious mechanisms1"5. In this chapter, some of these mechanisms arecompared with the quantum confined Stark effect in quantum well materials, based on their application to high speed tuning elements.

Some mechanisms, such as temperature4 and piezo-electrically controlled1 3mechanical tuning are clearly incapable of working at high speed. Some

others, such as tuning realized by birefringent crystals5, are alsounsuitable for our purpose because of material incompatibility with semiconductor lasers or detectors, high driving voltage and large physical size. By eliminating these mechanisms, efforts will be concentrated on the comparison in refractive index change produced by carrier injection effect (CIE), Franz-Keldysh effect (FKE), in bulk semiconductor materials, and quantum confined Stark effect (QCSE), in quantum well materials.

To compare these mechanisms, the discussion in this chapter is divided into five parts contained in Sections 5.2 to 5.6. In Section 5.2, a set ofstandards and parameters have been defined to form the common ground for comparison between physically different mechanisms. These standards and parameters best reflect the requirements of our specific application. In Section 5.3 the performance of QCSE is summarised. In Section 5.4 the performance of FKE is analysed and compared with QCSE.In Section 5.5 the performance of CIE is analysed and compared with QCSE. Finally in the last section, the most suitable solutions for tuning elements are discussed and conclusions given.

All discussions are restricted to the GaAs/AlGaAs material system,

107

Chapter Five: Comparison Of Various Tuning Mechanisms

although the conclusions can be easily extended to other semiconductor materials such as the InAlAs/InGaAs system. The discussions are also restricted to wavelengths close to the band gap, where different mechanisms show significant differences.

5.2 Application Requirements and Performance TargetsDifferent aspects of a given physical mechanism become important

depending on the intended application. Therefore comparison and performance6 7assessment have to be carried out for specific applications ’ . Before

embarking on the details of the comparison and performance assessment, the major requirements for tuning elements have to be analyzed and listed, then a set of targets and standards have to be set up to measure and compare the performances of different mechanisms.

The comparison will be made for two specific tunable semiconductorlaser structures shown in Fig.5.2.1 a and b. In the first structure, thelong path structure, the optical path inside the tuning element can be as long as several hundred microns, while in the second one, the short path structure, the length of the optical path is limited to a few microns.

In long path structures, the prime requirements for tuning elementsare

1. A k phase shift or, in optical length, a X I 2 optical length change so as to tune the laser through a complete mode space and achieve maximum continuous tuning;

2. Minimum insertion loss caused by material absorption to obtain enough feedback from the external cavity containing tuning elements andhence reasonable laser threshold current, More importantly, this will prevent photon current saturation in tuning elements.

3. Minimum insertion loss change with refractive index change to minimize laser output power variation and mode hopping during tuning.

4. Flat frequency response over a wide modulating signal bandwidth for potential application in wide band systems.

Although there are some other important factors, such as device driving voltage or power, operating wavelength, linearity, and thermal conditions, at this stage, the comparison will be carried out mainly upon the above four requirements.

108

lnse

nion

Lo

ss

& C

hang

e (i

lB)


Active Region Tuning Element Reflector

a) L ong Path Tuning Structures

Active Region Tuning Element Reflector

b) Short Path Tuning Structures

Fig.5.2.1 Long (a) and Short (b) Path Structures

101 200kV /cm 150kV /cm

r x_____ — aa. - * ' ' inI 1------------------------------- -t- ,_,____ .

1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 152010

Photon Energy (m eV)

Fig.5.3.1 Insertion Loss Ajn and its Change AAjn for QCSE

109


From the first three requirements, two coefficients are defined; the maximum insertion loss and AA , the change in insertion loss for a n

inphase shift in tuning elements. If, at wavelength X , the mechanism studied

fieldproduces a maximum refractive index change A n ^ and/ ^bsorption coefficient a , in order to obtain a k phase shift, the physical length of the optical

max

path in a tuning element must be designed as

2 An

The insertion loss measured in dB, then, is written as

A. = lOlog exp\ - a

m i x

An

X a= 4.3429-j------ ^

An

(dB)

5.2.1

Accordingly, Aa the maximum absorption coefficient change during thismax

process can be related to insertion loss change AA. by

A.- I A a I AA. = 4.3429— ; (dB) 5.2.2

An

These coefficients are more suitable for our application than the commonly used refractive index - absorption coefficient change ratio, which fails to represent the performance for large refractive index changes.

The fourth requirement can be characterized by two measures; the upper cutoff frequency and the flatness of the passband.

In the short path structures, the first requirement above has to be modified as with only a few micron long optical path, it is impossible to obtain 7t phase shift and the maximum continuous tuning range is not limited by the resonator free spectral range but by the maximum phase shift in the tuning element. In order to obtain the maximum continuous tuning range, maximum phase shift in the tuning element is required. The insertion loss and its change, become less important in this case, as the path is so short. Comparison on the basic of these two coefficients also becomes less relevant

110


as the maximum tuning ranges achieved by each mechanism are quite different.

5.3 Quantum Confined Stark EffectThe QCSE induced refractive index change in QW materials has been

modelled in Chapter 4. In this section, theoretical and experimental results are combined to assess its performance in phase shift and insertion loss.

The other aspect, the frequency response of QCSE, which was not discussed in Chapter 4, will also be discussed based on a simplepolarization model.

5.3.1 Phase Shift and Insertion LossFrom the literature and from our own modelling and experiments, QCSE

provides up to 3% refractive index change, undoubtedly the largest6,7 among the three effects to be compared. When the optical path lengths in tuning elements are very short, as in normal incidence PIN structures, QCSE is the effect which provides the largest tuning range. The compromise between tuning range, insertion loss and its change is hardly needed for such astructure.

As the optical path length is increased, the large refractive indexchange become unnecessary provided the total phase shift reaches 7t, and therefore the maximum refractive index change is no long a target inperformance assessment. On the other hand, for long paths, the insertion loss and its change become of critical importance.

Although, as pointed out in Chapter 4, the models of the refractive index change in QW materials can provide some important data with accuracy, such as exciton peak positions and maximum change, for device design, there is no theory providing satisfactory agreement with experiments, especially at photon energies far away from the exciton peaks. In this section, therefore, instead of theoretically calculated data, experimentally measured data are used for the comparison.

The difficulty in using measured data directly is that the variation in absorption coefficient across the spectrum is too large to be measured in a single sample. The MQW sample used in the experimental work of Chapter 6,o ofor example, consists of 75 periods of 47A wells and 60A barriers. With less than a 1 pm thick MQW layer, measurements at low photon energies become

111


unreliable. To overcome this difficulty, measured data are used to fit a pre-determined model which then provides the absorption coefficient data across the required spectrum. This procedure can be regarded as a kind of characterized interpolation. Following the modelling work in Chapter 4, it is proposed that the absorption of both heavy hole- electron and light hole- electron is due to exciton and continuum transitions described by broadened Dirac functions and Sommerfeld factors. The broadening lineshapes are the combination of Gaussian and Lorentzian functions.

The insertion loss and its variation, defined in section 5.2, are functions of wavelength and this dependency becomes very strong close to the band gap, which is the area of interest. The curves of insertion loss A

inand AA^, as a function of photon energy, obtained from fitted experimental data, are plotted in Fig.5.3.1. The measured data were obtained from a PINo osample with 75 period 47A GaAs/60A A l^G a^A s MQW layer I region. Although the measurements were carried out with light incident perpendicular to the plane of the wells, the results are also valid for TE modes in waveguide situations. As the TM modes have a different heavy/light hole oscillation ratio, results for TM modes may be slightly different. A reverse bias of 10V and 15V, which generates 150kV/cm and 200kV/cm electric fields, was applied to the device.

5.3.2 The Upper Cutoff FrequencySince the QCSE tuning element is normally operated in reverse bias,

current flow is limited to photo current and leakage current. With such low currents, the thermal effect caused is negligible. As the thermal effect is the major reason for the lower frequency limit of the device operation band, the QCSE tuning element should have a flat frequency response at low frequencies. The important limits on operating frequency are at high frequencies.

Although QCSE has the reputation of being a very fast phenomenon, there is little research to model its speed limit.

As pointed out in Chapter 4, the external field induced absorption change is caused by two effects, the wavefunction polarization of electron and hole in opposite directions in the well and the change in the particle energy eigenvalue. The first effect causes a reduction in coupling of

112


electron and hole wavefunctions between the same quantisation numbers ofenergy levels and coupling between different quantisation numbers. The second effect shifts the exciton to lower energy. The related transition time can be investigated in term of particle and energy redistributions in the polarization model.

It may be worth while to point out that the speed analysis for the QCSE device is different from that for photo current related devices such as the SEED device considered by Fox8 as the two devices undergo different physicalprocesses. In the former case, the applied field is modulated and there islittle photon- carrier interaction, the analysis is carried out by dealing with the electric field- carrier interaction, while in the latter case, the electric field is constant as a background condition and the incident photon density is modulated, the analysis being carried out by discussing photon- carrier interaction and the resulting photo current which, to a degree, shares some similarity with laser diode analysis.1. Wavefunction Polarization

Suppose the wavefunctions of a particle with and without applied fieldare and Vpf(Z). With proper normalization, the particle existenceprobability or particle density at position Z can be represented by | ^ ( Z ) 12 and | Vpf(Z) 12 shown in Fig.5.3.2. The change in particle

distribution due to polarization reflects an applied field induced movement of charged particles. The transition time of this redistribution is to be modelled.

In order to reach a new equilibrium under applied field, particles have to move an average distance AZ determined by

AZ = I ^ ( Z ) | ZI Vp0(Z)> - <Vpf(Z) IZI y pf(Z)> | 5.3.1

From initial equilibrium conditions, at the start of the movement, although the particle kinetic energy is not equal to zero, its average speed in the field direction is zero. The initial acceleration due to the applied field is

aQ= F±-q/mp 5.3.2

where q is the electron charge, The acceleration will gradually decrease and, at the end of the movement, the final acceleration should reach zero as

113

Abs

orpt

ion

Coe

ffic

ient

(/c

m)


Barrier Barrier

WithoutField

WithField

Well

Fig .5 .3 .2 Particle Redistribution Due to A pplied F ield

F = 200 150 100 50 0 kV/cm

1250 1300 1350 1400 1450

Photon Energy (m ev)

Fig.5.4.1 FKE Induced Absorption Coefficient Change

114


applied field, the new particle distribution and the potential reach a new equilibrium. In order to simplify the model, it is suggested that the acceleration decreases linearly with time in spite of the possibility of more complicated variations in the real situation. For the particle to move a distance AZ, the redistribution time is

t= j2 AZ m / (q F ±) 5.3.3

With this relation, the transition time of particle redistribution can beo

estimated. In a 100A QW under lOOkV/cm external field, particle redistribution times are 15, 20 and 40 fs for electron, light and heavyholes respectively.2.Eigen energy shift

The transition behavior can also be discussed from the point of view of eigen energy shift. In wave theory, a QW can be regarded as a resonator andthe particle in the well can be represented by an appropriate De Brogliewave. In this sense, a QW resonator is similar to an optical one in not only its form but its physical nature. In Table 5.3.1, a few parameters of both resonators are listed for comparison.

Table 5.3.1 Comparison Between Optical and QW Resonatorsp a r t i d e pho t on e l e c t r o n / h o l em a s s U m

pp a r t i d e e n e rgy E = h v0 E = m c

0 p

K l n e t i c e n e rgy K = /iv K = E -V ( Z ) - q F .Z

p p x

Group V e l o c i t y

c-l 2E K - K 2 V - 0 -c

c J 2 E K - K 2 ,V — “ 2K / m

E oT7 * P

0

Wa velengthh e c

x -h e h

X -I 2 E K - K 2 v0 I 2 E K - K2 J 2 m K0 P

115


The differences are originate from two factors; 1) the unique properties of the photon (m=0 and V=c), and 2) electrons and holes are charged particles.

When the applied field is modulated, it is clear that the resonator parameters are modulated. Recalling the discussion in Chapter 3, this situation should be treated as a parametric resonator not a filter problem. When the resonator parameters are changed by a modulated applied field, it is not necessary to wait for particles with the previous eigen energy to tunnel out and particles with new energy to accumulate, which is governed by particle tunnelling-out time or in-well life time, or equivalently the Q factor of the resonator. Instead, the particles with the previous eigen energy are pumped to a new energy level by the modulation source and the time associated with this process is an energy redistribution time which is related to the round trip time of the resonator. As discussed in Chapter 3, in the worst situation in which the modulation is localized in a small

ofraction of whole resonator, for an 100A GaAs QW with modulation efficiency reduction less than 20%, the energy redistribution for electron, light and heavy holes take about 50, 70 and 224 fs respectively. Although these data may not be very accurate as the analysis in Chapter 3 was based on small signal assumptions which can not be satisfied in the strong applied field situation, they do reveal that the time scale of this transition process is very short.

From the point of view of particle and energy redistributions, it can be concluded that the transition time of QCSE is in the sub-picosecond time scale which is much faster than required for this work.

In fact, the main speed limitations are raised from the device structure rather than the QCSE mechanism. For a PIN structure modulator, the RC time constant due to the junction depletion capacitance is a critical limit to the device operating speed. For a 50|im circular PIN modulator with 1 J i m thick I region and 50 Q load, for example, the RC cutoff frequency is 10 GHz and a 4x200 J i m PIN waveguide modulator with 0.2 J im thick I region will have a similar cutoff frequency. With improvements in device structures, a modulation speed up to 100 GHz is possible. Experimentally, modulation at up to 20 GHz modulations has been demonstrated911 using QCSE and yet the speed limitations were recognized as device structure related.

116


5.4 Franz-Keldysh Effect12 12The Franz-Keldysh effect ’ (FKE) is an electric field induced change

of complex dielectric constant of a direct band-gap semiconductor, occurring at photon energies close to the band-gap energy. The FKE has two parts, electroabsorption (EA) and electrorefraction (ER), which respectively change the absorption coefficient and the refractive index in response to an applied electric field. These two changes are linked by the Kramers-Kronig relation. Both theoretical calculations and direct measurements of the refractive index changes have been reported14,15. A refractive index change much larger than that induced by the Pockels effect at photon energies close to the band-gap energy is found16'18.

In this section, the theory of FKE will be reviewed and the results will be used to evaluate its phase modulation performance.

5.4.1 Theoretical Model of FKE Induced Band Gap Shift12 12The earlier model of FKE proposed by Franz and Keldysh shows poor

agreement with experiments, because their treatments ignore the electron-hole interaction in the absorption process. This problem was first realized by Rees19 and subsequently by other workers20,21. To overcome this problem, various efforts have been made to take into account the effect of the electron-hole interaction in improved models19’22. Those models give a better agreement with experiments23.

As pointed out by Miller et al , although there is much difference incharacter between QCSE in QW and FKE in bulk materials, these two effects are fundamentally related. In principle, FKE can be considered as a special case of QCSE where the well width is infinitely large. As shown in Chapter 4, the wavefunction equations including Coulomb interaction are impossible to solve without some necessary assumptions and omissions. In bulk materials, the assumptions and omissions to simplify the problem have to be different from those for QCSE, and it is these differences that result in asolution which reflects the character of FKE.

In QW materials, electric fields applied perpendicular to the wellresult in a large shift in the optical absorption to lower photon energy,with the exciton resonances remaining well resolved. The shifts in exciton energy can be as much as 4 times the exciton binding energy, with little or

117


no broadening so far resolved. The excitons are not field-ionized because,1. the electrons and holes do not tunnel rapidly out of the wells, and 2.even when the electrons and holes are pulled to opposite sides of the wells, there is still a strong Coulomb attraction between them because the layers are so thin. Because the confinement is strong, i.e. the exciton binding energy is small compared to the separation between the quantum-confinedsubbands, the perturbation from the electron-hole interaction on electron and hole wave functions in the confinement direction can be neglected.Therefore the problem can be separated.

In bulk materials with applied field, the exciton absorption peak willbroaden rapidly, together with a small shift of the exciton resonance to

21lower photon energies . That is because when the well becomes very wide, the effect due to field ionization which is limited by narrow well width in QW can no longer be ignored and the Stark shift which plays a dominant role in QW becomes relatively small compared with the exciton binding energy21.

In this section, the model developed by Rees19 is adopted. In Rees’ model, the coulomb interaction of the electron and hole as well as lattice interactions were taken into account by using scattering theory. FKE, in this model, was represented by spectral broadening which is dominant, as discussed earlier. The attraction of this model to our analysis is that this model is devoted to the field dependence of the absorption rather than details of the absorption spectrum itself. This emphasis enables the model to provide reasonable agreement with experiments with relatively simple formulae17,23.

According to Rees, the field induced broadening of the zero field absorption edge can be expressed by convolution of the zero field absorption

25 28coefficient, which is obtained from various publications " , and a field related Airy function. Translated to our formalism, it can be expressed as

ocCFj^hv) and a(0,hv) are the absorption coefficients with and without the applied electric field 11 the reduced electron-hole effective mass and

a(F±,hv) = P-a(0,hv)*Ai(-p-hv) 5.4.1where

p =

118


Ai(x) the Airy function. Clearly Eq.5.4.1 only represents field inducedabsorption broadening but does not include Stark shift. Stark shift can beincluded approximately by replacing Ai(-p-hv) with Ai[-p-(hv - Es)]; whereE is the Stark shift. Because E is normally very small compared with

21broadening effect (less than 10% exciton binding energy) , it is ignored in the treatment.Fig.5.4.1 shows the calculation results of band edge changes.

5.4.2 Comparison Between FKE and QCSEApplying the Kramers-Kronig relation to the above results, the

refractive index changes under different applied electric fields due to FKE were obtained and plotted in Fig.5.4.2. With these data, A. and AA. are

in incalculated and plotted in Fig.5.4.3.

Comparing Fig.5.4.3 and Fig.5.3.1, it is found that the insertion lossminimum for both A and AA of FKE are 3-5 dB higher than that of QCSE.

in inAnother feature is that the AA curve declines faster for QCSE than for

inFKE, which reflect the fact that QCSE produces a much sharper absorption coefficient change than FKE. For FKE, a pure phase change can only beachieved by operating the modulator at even lower photon energy with heavier insertion loss, although this can be improved by operating the device at lower electric field with a longer optical path when a very long path is possible.

The results can also be explained by the Kramers-Kronig relation. TheKramers-Kronig relation reveals that the refractive index change is not only determined by the magnitude of absorption change but also its distribution throughout the whole spectrum. From the Kramers-Kronig relation, the refractive index change spectrum can be obtained by broadening the absorption coefficient spectrum with broadening function l/hco. This fact makes the refractive index change depend on the uneven distribution of the absorption change spectrum, and the finite width of the broadening function means that the refractive index change spectrum will be wider than that of absorption change. All the benefits obtained by off-band gap phase modulators are based on this concept. As an extreme example, a Dirac function-like absorption spectrum induces a refractive index change with l/hco-like spectrum centered at the position where absorption changes occur

119

Inse

rtio

n Lo

ss

& C

hang

e (d

B)

Ref

ract

ive

Inde

x C

hang

e


x l O 3

F = 200 150 100 50 kV/cm

F=50,100,150,200 kv/cm

1250 1300 1350 1400 1450

Photon Energy (mev)

Fig.5.4.2 FKE Induced Refractive Index Change

in200kv/cm

150kv/cm

AA;

1300 1350 14501400

Photon Energy (mev)

Fig.5.4.3 Insertion Loss A. and its Change A A . for FKEin ° in

120


and any small shift from this position give pure phase modulation. On the other hand, if the absorption change is uniformly distributed across the spectrum, there will be no refractive index change and pure intensitymodulation occurs. Generally, due to the shift of the narrow exciton peaks, the QCSE produces a much sharper absorption change than FKE, and therefore is more favourable for phase modulators.

One thing Fig.5.4.3 and Fig.5.3.1 fail to show is the optical pathlength needed for producing n shift. In short optical path structures, the optical path length is limited, as in our experiment where a normal incidence reflective phase modulator with less than 1 p thickness was used, the operating wavelength is located at the refractive index change peakwhere both A and AA reach local minima and the refractive index change

in inreaches the maximum. From Fig.5.4.2, it is easy to find that the maximum refractive index change generated by FKE is much smaller than that of QCSE.

For the operating speed comparison, as the FKE can be regarded as a special case of QCSE in a very wide well, a similar time scale for FKEtransition time is expected.

5.5 Carrier Injection EffectInjected free carriers in semiconductors have several effects on the

material absorption coefficient and refractive index. The most obvious effect is injected free carrier induced absorption or gain change. Another effect is the plasma effect which is widely considered as the main cause of refractive index change in tuning element or phase modulator

29 3 1analysis .One less obvious effect is the so-called gain-linked band-edge contribution to the refractive index change which is, due to Kramers-Kronig

32relation, an inevitable result of spectrum dependent absorption change . This effect is normally ignored because to avoid large optical loss, most phase modulators are operated at far lower photon energies than the absorption band edge and, in this region, this effect is less significant.

When the photon- carrier interaction becomes significant, for example, under lasing condition, the change of carrier density with injection current becomes much more complicated. When the injection current increases beyond the lasing threshold, roughly speaking, this interaction will clamp the carrier density level and the excess current is converted to output optical

121


power efficiently. Therefore, tuning in this region is caused mainly by thermal, nonlinear and transient effects.

In this section, the change in the absorption coefficient andrefractive index in intrinsic semiconductor materials with carrier pumping level below and far above lasing threshold is investigated.

5.5.1 Plasma Effect33As discussed by E.Garmire , the carrier density N and refractive index

change An due to plasma effect obeys a simple linear relationship

2jtq2NAn = - — ------ 5.5.1

co m np

where co is the angular frequency of incident light, n the refractive index of unpumped materials, m and N the effective mass and carrier density ■ of

p pthe carriers. The total refractive index change is the sum of the effects of electron density N and hole density N .

c h

27tqAn = An + An = -

e h 2co n

fN N 1-5 + -5.m m

e h5.5.2

where m and m are the effective mass for electron and hole. For undopede hmaterials, N = N = N, and the reduced electron-hole effective mass

e h

m m n = » hm + m

e h

is used to rewrite Eq.5.5.2

2nq2An = N 5.5.3

co2p n

For GaAs the constant part of above equation is 2.388xl0'21 cm3.In real devices, the variation of the carrier density is limited. The

limitation is imposed not only by thermal dissipation but also by specific device operating conditions, for example, lasing threshold. The actual value of these limits varies from device to device, depending on their structures, but normally lies in the range from 1015 to 1018 cm'3 giving a maximum refractive index change of the order of 10'3.

122


5.5.2 Band Gap Shift with Injection Carrier DensityThe absorption coefficient at optical frequency v depends on the

density of the initial and final states pc(/*v), py(&v), their stateoccupation probabilities f ( h v ) , f ( h v ) and related Einstein coefficient

C V 3B ( h v ) . The relationship can be expressed as 2oo

a ( h v ) = - f B(E ) p (E ) p ( h v - E -E )J C C C V g c

[f (E )-f ( h v - E -E )]dE 5.5.4C C V g c c

where Eg, Ec and Ey are the band gap and energy level in conduction andvalence bands respectively. In Eq.5.5.4, the only part related to carrier density is f.(Bc) ■ fy(^v - E - Ec). Close to the band gap energyfc(Ec) - fy(/iv - Eg- Ec) changes only slowly with energy and, therefore, canbe moved outside the integral in Eq.5.5.4.

oo

oc(hv) = - [f (E ) - f (E )]• f B(E ).p (E )-p (hv - E - E )dEC C v v l c c c v g c cJ - oo 6

and in unpumped intrinsic materials f ( E ) - f ( E ) = -1 and the aboveC C V V

equation can be rewritten as

a (hv) = - [f (E ) - fv(Ev)].ao(/zv) 5.5.5

where a Q(hv) is the absorption coefficient for unpumped intrinsic materials.Eq.5.5.5 gives the relationship of absorption between materials with andwithout carrier injection and is the basic equation for further discussions.1. The Absorption Coefficient for Unpumped Materials, a (hv)

Following Moss’ treatment25,34, the absorption edge of unpumped material can be represented by an exponential rising part and a followingflat part.

exp[ (hv - E g) / E 0]a ( h v ) = a ------------------------------------------------------------------------------5.5.6

0 exp[(Av - E )/E 1 + 1g o

where a Q is the height of absorption peak and the absorption curve is characterized by band gap tail energy Eq. In the actual calculation, a Q and Eq as the variable parameters were obtained by fitting to measured

123


absorption coefficient curves. This expression is reasonably accurate near the band gap, but not at very low and high photon energies. At low energies, it fails to reflect a small but constant "background" absorption; while at high energies it is unable to represent the continuous rise in absorption with increasing photon energy. To improve the accuracy, Eq.5.5.6 is altered to

exp[(/iv - E ) /E - E / h v ]

a m = a , + Pr ° V 5.5.7exp[(/zv - Eg) /E 0] + 1

where three additional coefficients are introduced; a for the background absorption at low photon energy, (3r and Ef for the absorption rise at high energy. All coefficients in Eq.5.5.7 are determined by fitting the equation to material data available from various publications5.5.1

25-28 listed in Table

Table 5.4.1 F i t t e d C o e f f i c i e n t s for Unpumped GaAs

a ^ / c m ) Pr a Q( /cm) E (mev)gE Q(mev) E f ( mev)

1.56 1.39 3 x l0 6 1427 9 . 91 69 79

2. The Fermi Energy for pumped materials, andUnder fixed pumping level, the density of electrons in the conduction

band (or holes in the valence band) is constant, which is represented as Nc in the conduction band and N in valence band. If the relaxation time in the

V

band is much shorter than that between the bands and, therefore, negligible,35in the conduction band

OO

N = f p (E)-f (E)dEc I c c

2jf

( 2 m I3

c 2

. 2h .

1 / 2

exp[(E-F )/KTJ + 1'dE 5.5.8

and in the valence band

oo

N = f p (E>f (E)dEV J ' V V

124


1 f2m 13 o o

V 2

2 K2 h 2k J

0

E 1 / 2

eTpl(E-Fv7 /R T J '+ l -dE 5'5'9

where m and m are effective carrier masses in conduction and valenceC V

bands.3. Absorption coefficient under pumping condition, a(/zv)

If the strict conservation of k() applies in conduction-valence band relaxations, the energy in conduction and valence bands bears the relation

E mc _ c

E~ “ m~~V V

ism

E = cC m + m

C V

mE = V

V m + m

( h v - E ) 5.5.10g

•(/iv - E ) 5.5.11g

using Eq.5.5.6

a(/zv) = -[f(Ec) - fv(Ev) ] a o(/iv) 5.5.12

The Tesults for GaAs under different pumping levels are shown in Fig.5.5.1.4. Refractive Index Change

A spectrum dependent absorption coefficient change will induce an additional refractive index change. The relationship between those two changes can be calculated from the Kramers-Kronig transform. The calculation shows that the band gap shift induced refractive index change at a photon energy below but near the band gap takes the same sign as that induced by the Plasma effect but is somewhat greater in magnitude. The overall refractive index change caused by both effects is calculated for GaAs under different pumping levels and shown in Fig.5.5.2.

5.5.3 C arrier Density ModulationIt is clear from Sections 5.5.1 and 2 that, in order to obtain

refractive index modulation, the carrier density has to be modulated. In real devices, the carrier modulation is realized by injection current modulation. The relationship between injection current and carrier density can be determined by rate equations under different pumping conditions.

125


ucOJG

8 102 uccc-

<1 0 '

1250 1300 1350 1400 1450


Fig.5.5.1 C1E Induced Absorption Coeficient Change

- 0.002

-0.004

-0.006

c -0.008

- 0.01

- 0.012

-0.014 N = 4 ,6 ,8 ,10 E l 7 /cm a 3

-0.0161250 145014001300 1350


Fig.5.5.2 CIE Induced Refractive Index Change

126


1.Pumping Level Below Lasing Threshold LevelIn this situation, the photon- carrier interaction can be ignored as

the photon density is very low. The relation between injection current and carrier density can be easily determined. The carrier rate equation for undoped semiconductor is written

^ = J(t) - N2(t)/t 5.5.13

Under the small signal assumption, Eq.5.5.13 can be solved as

AJ • exp(jQt)AN = N - N = ------------------ 5.5.14

0 j Q + 2/twhere C l is the modulation angular frequency and x the carrier lifetime. The CIE induced refractive index change is proportional to AN and the linear coefficient can be determined from Sections 5.5.1 and 5.5.2. The maximum AN achievable in a real device is of the order of 1018/cm3 which produces about0.5% refractive index change.

Eq.5.5.14 also shows a strong dependency between the carrier density change and the modulation frequency. As x = 3 to 5 ns for GaAs the upper 3dB cutoff frequency is about a few hundred megahertz.2.Pumping Level Far Above Threshold Level

In this situation, the carrier density no longer bears the simple relation with injection current because of the present of dense photon population. The relation has to be determined by the rate equations of both carrier and photon.

In a laser system, the rate equations for photon and carrier can be written as

d<j>_ 1G - —

mq-jua - <j> d t mq a

qy

- 8 = £ 5.5.15mq mq

dN N— + _ + y ( j ) G = J 5.5.16d t x q mq mq

where <|> and N are photon and carrier density, a and x the photon and carrierlifetime, £ and J the input photon and carrier density, 5 spontaneous

mqemission rate per unit volume, subscript m and q represent longitudinal and transverse mode numbers, and

127


c

r is the confinement factor and V the volume of active region. Under theq a

assumptions of single mode operation and small signal modulation, with appropriate approximations, Eq.5.5.15 and 16 can be solved as

where Nq and <|>o are average carrier and photon densities, AJ the amplitude of current density modulation, and the resonance angular frequency coq and damping time constant xQ are given by

where % is the relative pumping level, JQ, and the particle current densities of the average injection current, the lasing threshold and material positive gain. Under the small signal assumption, the refractiveindex change caused is proportional to AN and the linear coefficient can be determined from Sections 5.5.1 and 5.5.2. The maximum AN achievable in a

17 3real device is of the order of 10 /cm which produces less than 0.05% refractive index change.

Eq.5.5.17 also reveals a strong relationship between the carrier density and the modulation frequency. In real devices, the value of theresonance frequency COJ 2 tz is from 6 to 20GHz and the damping time constant xq from 0.2 to Ins.

5.5.4 Thermal EffectOnly part of the pump power is converted to light emission for both the

spontaneous and stimulated emission situations. The rest of the power isreleased in the form of heat. When this power changes, the device temperature will follow in order to keep thermal equilibrium. The speed of

jQ AJ exp(jcot)AN = N - N 5.5.17

0 ( c o ^ Q 2+ j O / T o )

co2= (% - l) /(a x ) 5.5.18

5.5.19

X = 5.5.20

128


this response depends on the thermal structure of the device, and is normally complicated. For a small device, like a semiconductor laser chip, mounted on a perfect heat sink, the device temperature response to the change of thermally dissipated power is determined by

C-lr-AT = P + ATy 5.5.21t St t 1

where AT and y are the temperature difference and heat conducting constant between the device and the heat sink, C thermal capacity of the device and P thermally dissipated power of the device, which is proportional to carrier recombination rate and thermal efficiency. Solving the above equation

AT(t) = AT(0)-exp(-t/x) + P (t)*exp(-t/x )/C 5.5.22

where x = C/y is the thermal time constant for the device- heat sink system and represents the delay effect. The cutoff frequency f ■= 3/xt, typically in the range from a few kilohertz to a few megahertz. Because, in the small signal situation, the optical length change in the device is proportional to temperature change, f is also the cutoff frequency for the optical length modulation.

Temperature influences on device optical length are complicated.0 4Experimentally, about 1%/ C optical length change is observed . Normally, at

low frequency, the thermal effect produces a much larger optical length change than CIE. As the optical length change produced by these two effects is of opposite sign, they cause a very nonuniformed modulation response at low frequency. A typical response spectrum is plotted in Fig.5.5.3

5.5.5 Comparison Between CIE and QCSEInsertion loss A and its change AA , defined in Section 5.2 are

in inplotted in Fig.5.5.4 for carrier density below threshold level. From the point of view of insertion loss and its change, the CIE phase modulator is only marginally worse than QCSE one (notice both Fig.5.3.1 and Fig.5.5.4 are plotted in semi- logarithmic scale). If all the uncertainties in theoretical modelling and experimental measurements are taken into account, it is hard to V x determine which effect would be more suitable for phase modulators

129


B e lo w T h re sh o ld

10 1

<uCOaoQ«co<D* IQ2

Above Threshold

10°10-1M o d u la tio n F re q u e n c y (G H z )

Fig.5.5.3 Typical Modulation Frequency Response of CIE

0.2E18

1.0E18

145014003501300250


Fig.5.5.4 Insertion Loss A. and its Change AA . for CIE° in & in

130


merely based on insertion loss and its change. When, however, their maximum refractive index changes are compared, it is clear that QCSE provides much a larger change than CIE, a factor of vital importance in short pathstructures. The more serious drawback of CIE in both long and short path structures is its frequency response as shown in Fig.5.5.3. At the upper end, it is limited by carrier life time, and at the lower end, by thermaleffects. When the carrier density is far above threshold, because of theclamping effect, the refractive index change becomes very small. The output optical power change will also increase not only because of the increasinginsertion loss change but also because of the enhancement effect of theresonator. Furthermore, although the operating frequency band is shifted to higher frequency, the bandwidth of uniform modulation response increases little..

In conclusion, CIE’s potential in very wide band applications isseverely limited by its non-uniform frequency response and applications in the short path structures are also limited by its relatively smallrefractive index change.

5.6 ConclusionsThe QCSE in QW materials shows significant advantages over FKE in bulk

materials in term of lower insertion loss and less insertion loss change, it is concluded that, from the Kramers-Kronig relation, these advantages are associated with the sharp spectrum distribution of absorption change inQCSE. Comparing with the CIE, QCSE shows higher operating speed and more uniform frequency response. Some other advantages, such as higher modulation sensitivity, have been reported by other researchers .

For QCSE, two favourable positions in the spectrum for phase modulation were found. At the position near the exciton peaks, although only local minimums were obtained for both insertion loss and its change, a large refractive index change was observed and large optical length change can be achieved within short optical paths. At the other position, the phase modulation can be achieved with much lower insertion loss and less insertion loss change, although longer optical paths are needed. The insertion loss appears to have its minimum point while its change declines constantly with decreasing photon energy. The penalties of decreasing insertion loss change

131


are higher insertion loss and longer optical path. It seems that the primary consideration for device design should be the insertion loss. The operating position should be around the valley of the insertion loss curve because at even lower photon energies, reduction of the insertion loss change is less significant, however, insertion losses itself increase substantially. As an example, k phase shift can be achieved with less than 0.5 dB loss and 0.2 dBoloss change in a 250 Jim length device with 47A thick well at the operating wavelength about 840nm.

132


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17. D.R. Wight, J.M. Heaton, J.C.H. Birbeck, D.J. Taylor, G.J. Pryce, andK.P. Hilton, The Electrooptic Effect Due to GaAs Band Edge Electroabsorption in GaAs/GaALAs Optical Waveguides, Electron. Lett., 1987

18. M. Suzuki, Y. Noda, Y. Kushiro and S. Akiba, Characterization of aDynamic Spectral Width of an InGaAsP/InP Electro- absorption LightModulator Electron. Lett. 22, 312, 1986

19. H.D. Rees, Representation of the Franz-Keldysh Effect by Spectral Broadening, J. Phys. Chem. Sol, 29, 143-53, 1968

20. I.A. Merkulov and V.I. Perel, Effects of Electron-hole Interaction on Electroabsorption in Semiconductors, Phys. Lett., 45A, 83-4, 1973

21. J.D. Dow and D. Redfield, Electroabsorption in Semiconductor: the Exciton Absorption Edge, Phys. Rev. B l, 3358, 1970

22. D.F. Blossey, Wannier Exciton in an Electric Field: I. OpticalAbsorption by Bound and Continuum States, Phys. Rev., B2, 3976, 1970

23. D.R. Wight, J.M. Heaton, A.M. Keir, R.J. Norcross, G.J. Pryce, P.J.Wright, J.C.H. Birbeck, Limits of Electro-absorption in high purityGaAs, and the Optimisation of Waveguide Devices, IEE Proc. 135, Pt.J, 39-44, 1988

24. D.A.B. Miller and D.S. Chemla, Relation Between Electroabsorption inBulk Semiconductor and in Quantum Wells: the Quantum-confinedFranz-Keldysh Effect, Phys. Rev. B33, 6976-82, 1986

134


25. T.S. Moss, Optical Properties of Semiconductors, P40, Butterworth, London, 1961

26. M. D. Sturge, Optical Absorption of Gallium Arsenide Between 0.6 and 2.75 eV, Phys. Rev, 127, 768-73, 1962

27. J.S. Blackemore, Semiconducting and Other Major Properties of Gallium Arsenide, Appl. Phys., 53, R123-81, 1982

28. S. Adachi, GaAs, ALAs, and A1 Ga As: Material Parameters for Use inX 1-x

Research and Device Applications, J. Appl. Phys. 58, Rl-29, 198529. J.M. Liu, Y.C. Chen, and M. Newkirk, Carrier-induced Phase Shift and

Absorption in a Semiconductor Laser Waveguide under Current Injection, Appl. Phys. Lett. 50, 947-9, 1987

30. S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, Direct Frequency Modulation in AlGaAs Semiconductor Lasers, IEEE J. Quantum Electron. QE-18, 582-95, 1982

31. W.T. Tsang, N.A. Olsson, and A. Logan, High-speed Direct Single-frequency Modulation with Large Tuning Rate and Frequency Excursion in Cleaved-coupled-cavity Semiconductor Lasers, Appl. Phys. Lett. 42, 650-2, 1983

32. G.H.B. Thompsom, A Theory for Filamentation in Semiconductor Lasers Including the Dependence of Dielectric Constant on Injection Carrier Density, Opto-electronics, 4, 257-310, 1972

33. E. Garmire, Integrated Optics, P244, Springer, New York, 1975 (edited by T. Tamir)

34. T.S. Moss, Optical Absorption Edge in GaAs and Its Dependence on Electric Field, J. Appl. Phys. 32, 2136-9, 1961

35. A. Yariv, Optical Electronics, P473, CBS College Publishing, New York, 1985

135

CHAPTER SIX

MOW TUNED EXTERNAL CAVITY LASER EXPERIMENTS

6.1 IntroductionIn this chapter, an external cavity configuration is chosen to explore

the great potential ability of MQW materials as tuning elements in tunablesemiconductor lasers. Section 6.2, is devoted to mode selection experiments and gave the first experimental verification of the use of MQW devices asexternal cavity tuning elements. The experimental arrangement is describedin considerable detail, as this arrangement was also used in later experiments to ensure the best use of the electric field induced refractive index variation in MQW materials and mechanical stability. Section 6.3 andSection 6.4 concentrate on continuous tuning and its dynamiccharacteristics. The experimental setup, results and analyses are given. The design and processing details of the MQW tuning devices are also described briefly; full details can be found in the appendices. The conclusions are drawn and possible improvements are discussed in the last section.

6.2 Discontinuous Tuning ExperimentsWith an external cavity laser structure in which no efforts are made to

weaken internal modes defined by the solitary laser diode cavity, modeselection is relatively easy to observe. Although, according to the analysisin Chapter 2, there will be a small range of continuous tuning accompanied by intensity changes, the mode selecting mechanism is the dominant one.

6.2.1 Experimental ArrangementTo make best use of the electric field induced refractive index

variation in MQW materials, several points have to be considered in theoptimization of the experimental arrangement. First, the working wavelengthmust be carefully chosen to ensure that the laser emission is at thewavelength where the MQW material provides maximum refractive index change and minimum absorption change, this region is normally very narrow as shown in later experiments. The rough alignment relied on choosing suitable laser

136

Chapter Six: MQW Tuned External Cavity Laser Experiments

diodes and MQW well width. The further fine adjustment relies on optimizing laser injection current, MQW bias variation range and the temperatures oflaser diode and MQW device. Second, the external cavity should be as shortas possible to utilize the limited refractive index variation in MQW device and achieve larger tuning. From Chapter 2, it is clear that for a given change in cavity length, the tuning range is inversely proportional to the cavity length. Finally, as external cavity experiments are among the mostdelicate optical experiments, some special optical and mechanical techniques have to be used to make the experimental environment requirements less harsh and the experimental procedure easier.

The MQW tuning element, shown in Fig.6.2.1, designed based on the principle described in Chapter 4, was a GaAs/AlGaAs PIN structure withquantum wells occupying the intrinsic region, so that an electric field can be applied across the wells by reverse biassing the device. For working at a

owavelength of about 830 nm, the MQW region consisted of 75 47A thick wells

oseparated by 60A thick barriers. The details have been described byWhitehead et al (wafer MV246)4. From the measured results, it was found that the first heavy hole induced absorption peak was at a wavelength of about 828 nm and the first heavy hole induced refractive index variation peak was at about 822 nm with -16V bias (see Fig.6.2.2). From all the measuredresults, the characteristics of those two wavelength of special interest were deduced from measured data and plotted in Fig.6.2.3. In Fig.6.2.3a, the absorption coefficient and refractive index variation as a function of biasvoltage at wavelength 822 nm is plotted. It gives a clear view that with relatively small absorption changes, large refractive index variation can beachieved. This encourages us to make a tuning element with high tuning efficiency and speed and an acceptably small intensity modulation. On the other hand, Fig.6.2.3b shows a situation which is favourable to intensity modulation.

Fig.6.2.4 shows the experimental arrangement used. The laser was a GaAs/AlGaAs CSP device (Hitachi HLP 1400)5 emitting at about 822 nm at room temperature. The MQW tuning element was as described above. Devices were defined by mesa etching, and 400 (im x 400 Jim windows were etched through the GaAs substrate so that the structure could be illuminated perpendicularly to the junction plane (see Fig.6.2.1). At a wavelength of 822 nm, the change in

137


400 Jim Metallic ohmic contacts

AlGaAs P i - MQW

AlGaAs i f

2-3 lim

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GaAs substrate n

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Fig. 6.2.1 MQW Device Structure

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transmission of the completed devices was less than 2 % over the reverse bias range 0 - 12V. Devices were mounted on glass slides with a plane mirror behind the devices to complete the optical cavity.

One facet of the laser diode was coupled to the tuning element through a GRIN-rod lens(2 mm diameter, 0.25 pitch), giving a short optical cavity length of 15 mm. The object-image conjugate relation between the laser facet and MQW device made the system less sensitive to mechanical vibration. The other facet was coupled to a scanning Fabry-Perot interferometer through a xl0/0.17 NA microscope objective, care being taken to minimize optical feedback to the laser diode, although no optical isolator was used in the path.

A Peltier thermal pump and temperature controller was used to adjusto olaser diode temperature from 5 C to 50 C. Apart from injection current, this gave an additional means to align the laser emission at the optimized MQW wavelength. No attempt was made to assess the temperature accuracy and stability as they were not very critical in this experiment.

Neither facet of the laser diode was anti-reflection coated. The system can therefore be analyzed as a multiple cavity system with emission occurring at the wavelength where the two cavity resonances coincide. Because the coupling of the external cavity to the laser diode is weak, its main effect is to select laser internal cavity modes. From Chapter 2, the change in the optical length of the external cavity required to produce a wavelength increase of k modes is

X.A1 =

r k ie n

16 .2.1

where 1 is the optical length of the semiconductor laser cavity, 1 that ofo e

the external cavity for k = 0 (1 > 1 ), X the emission wavelength fore o o

k = 0, and n the largest integer less than k-1 / 1 . Optimum tuningsensitivity occurs when le is close to an integral multiple of 1q, theminimum value being set by the onset of multimode operation. In theexperiment, 1 was optimized by placing the tuning element on a

epizo-electric controlled micropositioning stage.

Since it is hard to measure the ratio 1 / 1 with accuracy, A1 waso e

roughly estimated by first adjusting 1 to give low mode selection sensitivity and biassing the laser close to threshold so that the laser

142


cavity modes were broadened, A1 could then be determined from the optical frequency shift Af produced by tuning the external cavity by an amount insufficient to produce a laser cavity mode change:

Af-1 XA1 = ------^ 6.2.2

c

where c is the velocity of light in vacuo.

6.2.2 Experimental ResultsFig.6.2.5 is a multiple-exposure photograph of laser spectra taken as

the MQW device reverse bias was varied between 8 and 14V. The laserinjection current was maintained constant at 53 mA. Stable operation on five different single modes was found to be possible. For the HLP 1400 laser, the optical length of the internal cavity is about 1 mm which gives a modespacing of 150 GHz. Therefore, the total tuning range was about 600 GHz or, in wavelength, 1.4 nm. Output power variation over this range was less than0.6 dB. The tuning range was not limited by refractive index change in theMQW device as further increase in bias made the oscillation return to the first mode again. However the mechanical instability of the arrangement andthe laser spectral linewidth prevented further adjustment leading to ahigher mode selection sensitivity, and therefore, limited the tuning range. In this experiment the observation of larger tuning range was also limited by the free spectral range of Fabry-Perot interferometer whose minimummirror spacing was about 0.2 mm, corresponding to a free spectral range of 750 GHz.

To evaluate the refractive index change in the MQW device, the external cavity length and laser injection current were adjusted,as discussed earlier to obtain a low mode selection sensitivity and the spacing of theFabry-Perot interferometer was increased to obtain higher spectral resolution. Continuous tuning over a frequency range of 1.5 GHz was observed as the reverse bias on the MQW device was increased from 0 to 13.5V. Over the bias range 5-10V linear tuning over a range of 0.6GHz was observed.Substituting this value in Eq.6.1.2 gives an optical length change inrefractive index A1 = 25 nm in the external cavity. This is related to thechange in refractive index An by An = Al/1 , where 1 is the physical

143


thickness of the MQW layer and refractive index change in the other layers is neglected. For the device used 1 = 0.80 pm, giving a refractive index change of 1%. It must be observed that this calculation was only a rough estimation of the minimum values, the actual refractive index change could be larger as the single cavity equations are not very suitable for this weak feedback situation. More accurate values can be obtain from a multiplecavity formulation when coupling conditions between internal and external cavities are clearly known.

6.2.3 DiscussionIn this experiment, the MQW device used was initially designed for

other purposes; it was thus not optimized as a tuning element for the exact wavelength range used. Although the MQW device and laser could be matched to each other in wavelength by adjusting the MQW device bias range and laser injection current, better performance can be expected by optimizing thedevices.

Without anti-reflection coating on the facets of the laser diode, the continuous tuning, in this experiment, was limited by the laser diode internal modes. Although low injection current made the linewidth much wider and thus it was possible to observe limited continuous tuning, the accompanying output power change was obvious (shown in Fig.6.2.6). This situation was modelled using the formulas given in Chapter 2. Fig.6.2.7 gives the modelling results for different reflection coefficients at the interface between laser internal cavity and external cavity. For comparison the laser internal mode linewidth for the same bias conditions but withoutthe external cavity were drawn in the figures and becomes very wide because the laser was biased below the threshold of the diode itself. In the extremecase, when the reflection coefficient is zero, as can be achieved with a perfect anti-reflection coating on one of the laser diode facets, the interface vanishes and continuous tuning can be achieved without accompanying output power change (Fig.6.2.7d). In fact, this structure can be theoretically considered as the single cavity case discussed in Chapter2. Therefore, a small accompanying output power change depends on a high performance of the anti-reflection coating on the laser facet adjoining the external cavity.

145

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tive

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erChapter Six: MQW Tuned External Cavity Laser Experiments

600MHz

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0.5

1500MHz

External Cavity Length = 15mm

Fig.6.2.6 Continuous Tuning Results

146

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a. R = 30% at the interface

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Fig.6.2.7 Continuous Tuning Modeling

147

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1.0

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d. R = 1% at the interface

Fig.6.2.7 Continuous Tuning Modeling

148


The continuous tuning range largely depends on the optical length of the external cavity and the change in length achieved. In the earlier experiments, a microscope objective was used to couple light from the external cavity into the laser diode. The external cavity length was 65 mm and only0.2 GHz continuous tuning was observed. Use of a GRIN-rod lens made a shorter external cavity possible but further shortening was limited by the difficulties in aligning the system and finding suitable high performance lenses. Therefore the best solution for an even larger continuous tuning range seems to be the integration of the laser diode and MQW tuning device.

One of the advantages of the MQW tuning elements is that it is a reverse biased device. As discussed in Chapter 3, there is thus the potential of high speed operation. In this experiment, the large device area resulted in a large RC time constant, therefore, the low cutoff frequency (about 250 MHz) prevents this potential from being realized.

Finally, comparing Fig.6.2.3 and the peak height changes of emission modes in Fig.6.2.5, we can see that the carefully chosen working wavelength made the output power change minimal over the tuning range, since the change in output power, first decreasing and then increasing again gives a clear evidence that the tuning bias range crossed the absorption peak where the largest refractive index change occurs as shown in Fig.6.2.3a.

6.3 Continuous Tuning ExperimentsAs explored theoretically in Chapter 2 and experimentally in the last

section, a large continuous tuning range can be obtained by weakening the laser diode internal modes and increasing the feedback from the external cavity. This also brings another important benefit: emission linewidthnarrowing. In practice, this was realized by depositing an anti-reflection coating on the interface between the internal and external cavities6. Due to the increase of the feedback from the external cavity, the experiment was expected to be more sensitive to the operating environment.

6.3.1 Experimental ArrangementThe setup, with 15 mm long external cavity, was almost identical with

that for the discontinuous tuning experiments described in the last section. There were three major modifications required to obtain and observe continuous tuning:

149


First, the laser diode was replaced by an anti-reflection coated laser diode. One of the facets was coated with a single A/4 SiO layer which could reduce reflectance of the coated surface to 0.1% (Appendix A). In this experiment, due to the variation of the refractive index of SiO material with evaporating conditions and thickness error of A/4 layer, a residual reflectance of about 1-3% was estimated from the performances of the lasers coated using direct emission monitoring. Both direct and indirect reflectance monitoring, which are more effective for antireflection coating, could not be implemented for such extremely small coating areas. Relevant technical details are given in Appendix A.

Second, the mirror spacing of Fabry-Perot interferometer had to be increased to 50 mm in order to obtain finer spectral resolution. In this case, a free spectrum range of 3 GHz and, with a finesse of 50, a resolution of 60 MHz were obtained.

Finally, the large mirror spacing of Fabry-Perot interferometer made it impossible to decouple feedback from measuring path by slightly misaligning the Fabry-Perot interferometer. To avoid feedback, a quarter wavelength retarder at 45° angle had to be inserted between the external cavity laser and the Fabry-Perot interferometer. The polarizing direction of the light reflected from Fabry-Perot interferometer was rotated by 90° and could not then interfere with the external cavity laser system. It should be pointed out that this method could only be applied to isolate the feedback without changes in polarization state, otherwise, as in an optical fibre system, magneto-optical isolators have to be used. To reduce the feedback further, a neutral density filter was also used. This method reduced the unwanted feedback efficiently.

6.3.2 Experimental ResultsTwo of the experimental results are shown by multiple exposure

photographs in Fig.6.3.1 and 6.3.2. 1.4 GHz and 2.3 GHz continuous tuning range were obtained respectively. In the first result, the laser injection current was just above the threshold current of the external cavity laser, far below the laser diode threshold, and there was no visible output power change over the whole tuning range. As the bias applied to the MQW device changed from 0 to 8.9v, the corresponding optical frequency changes were

150


Optical Frequency (0.5GHz/div.)

F-P Interferometer: Mirror Space 50mmFSR 3 GHz

Laser Diode: Optical length 1 mmInjection current 46mATemperature 9 °C

Cavity: Optical length 15 mmFSR 10GHz

MQW device: Optical Thickness 3 pmTemperature 20 °CBias 11.6-8.9V

Fig.6.3.1 Continuous Tuning Result 1

151


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Optical Frequency (0.5GHz/div.)

F-P Interferometer: Mirror Space 50mmFSR 3 GHz

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Cavity: Optical length 15mmFSR 10GHz

MQW device: Optical Thickness 3 (imTemperature 20 °CBias 9 .2 - 0V

Fig.6.3.2 Continuous Tuning Result 2

152


very small and had a nonlinear relationship with bias changes. Details of this nonlinear relationship, although they could be very interesting in understanding MQW device behaviours, could not be resolved because of the small frequency change (less than 100 MHz). The optical frequency changes corresponding to bias 8.9v, 9.8v, 10.8v, 11.6v were less than 0.1GHz,0.5GHz, 1GHz and 1.5GHz. Further increase in bias was not tried because of the risk of MQW device breakdown. In the second result, the laser injection current was increased and the output power changed substantially with frequency changes. The optical frequency changes were 0.75GHz, 1.60GHz, 2.30GHz at bias voltage of 5v, 7v, 9.2v. At a bias voltage of 9.2v the frequency change reached its peak and began to turn back when the bias wasincreased further. The bias voltage-frequency shift relationships of bothresults are plotted in Fig.6.3.3.

6.3.3 DiscussionsIt was noticed from the experimental results that the refractive index

changes in the MQW device were very sensitive to working wavelength. The difference in emission wavelengths due to different injection currents in these two experiments resulted in different MQW bias ranges being required. This indicated that the peaks of refractive index change were very narrowand their position moved as electric field changed. That could be the reason why it is so difficult to observe large refractive index change experimentally in MQW material.

The second result gave more information. The selection of operatingbias range as a wavelength aligning method was clearly demonstrated. The larger injection current shifted the laser gain peak to a shorterwavelength, therefore the external cavity system emitted at shorter wavelength, closer to the refractive index change peak making it possible to approach maximum frequency shift before MQW device breakdown. The lower operating bias voltages also means less QW exciton peak decline andtherefore larger refractive index change at the peak. This is the reason forobtaining a larger frequency shift. The optical length change related to2.3GHz frequency shift in the external cavity was 95nm and a refractive index change as large as 3.2% was obtained without large absorption change although the basic absorption could be high.

153


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In the experiments, besides the operating bias range, the laser diodeoand MQW device temperatures, which were individually controlled and had 9 C difference, were also employed as a means of wavelength alignment. It was found that the position of the MQW refractive index change peak was also very sensitive to temperature.

6.4. Measurements of the Dynamic Tuning CharacteristicsOne of the major attractions of MQW tuned lasers is their wide

modulation bandwidth. As pointed out in Chapter 5, at low modulation frequencies, the modulation should have a flat frequency response because there is no thermal tuning effect in a reverse biased MQW tuning element and, there is a potential for a very high cutoff frequency because of the short response time of the QCSE induced refractive index change in QW.

7 9There are various methods for optical FM signal measurements' . Themeasurements can be done in either microwave frequency domain or the optical

7 8frequency domain. They can be achieved, by self homodyne , heterodyne or frequency discriminator9 in the microwave frequency domain and, by directly measuring the FM sidebands of the optical spectrum in the optical frequency domain.

In this work, the FM frequency response is evaluated in both microwave and optical frequency domain. In the microwave frequency domain, the measurement is carried out using an optical frequency discriminator formedby a 60 metre length of high birefringence fibre and some polarization components. In the optical frequency domain, the measurement is carried out using a high resolution scanning Fabry- Perot interferometer.

6.4.1 Fast Tuning ElementsAs discussed in Chapter 3, the operating speed of a tuning element is

mainly determined by its effective the capacitance. To reduce capacitance, small area PIN devices with integrated MQW and Bragg reflector were designed and fabricated. These devices were of area l.SxlO^cm, giving a predicted 3 dB cutoff frequency (for 50Q source) of about 2 GHz. With packageparasitic capacitance and inductance, the response is limited to about 1 GHz. The measured breakdown voltages of these devices were in excess of 17 V. The devices were antireflection coated with a single SiO quarterwavelength layer. The device structure is illustrated in Fig.6.4.1 and the

155


processing steps in Fig.6.4.2.

6.4.2 Fabry- Perot Interferometer Method1. Mechanism

A frequency modulated optical signal can be expressed as A = exp{j[cot + (Aco/£2)sin(£2t + <j))]} 6.4.1

where A is the complex amplitude, co the angular optical frequency, Aco the frequency modulation deviation, £2 and (|) the frequency and initial phase of the modulation. To carry out spectrum analysis, Eq.6.4.1 can be expanded in Fourier series10.

ooA = y JJAco/Q)exp{j[(co + kn)t + <>]} 6.4.2

k=-o°where Jk() is the k th order Bessel function. The above equation indicates that, in the optical spectrum of the FM optical signal, sidebands willappear at optical frequency co ± 12, co ± 2£2, ... with normalized peak height

2 2J (Aco/£2), J (Aco/£2), ..., and the normalized power at carrier frequency co will be reduced to JQ(Aco/f2). This change can be best illustrated in Fig.6.4.3 where the output power at the first two side frequencies peaks are plotted as a function of the modulation index Aco/£2. The spectrum is in theoptical domain because £2 « co and can be observed optically if theobservation instruments have high enough resolution to distinguish peaks £2/27t apart.2. Measurement

The spectral resolution of ordinary scanning Fabry- Perot interferometer is limited to about 100 MHz, and is thus not suitable for usein this kind of measurement. To obtain higher resolution, in this work, ahigh resolution spherical mirror scanning Fabry- Perot interferometer wasused. The structure of the interferometer is given in Fig.6.4.4. Its full

1112technical and theoretical details can be found from references ’ . In Fig.6.4.5, spectra for the MQW tuned laser as function of modulating frequency £2 are shown. In this particular case, a spectral resolution of 30 MHz was obtained. A set of theoretical modelling results of FM spectra and their comparison with experimental results are plotted in Fig.6.4.6 and 7. Both figures indicate a frequency response of the frequency modulated MQW tuned semiconductor laser that is uniform over the frequency range 0-300 MHz.

156

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158

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Fig.6.4.5 FM Optical Spectra (Frequency Deviation Av = 100 M Hz)

161

Opt

ical

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er

(Lin

ear

Scal

e)Chapter Six: MQW Tuned External Cavity Laser Experiments

444 4 4 4

Optical Frequency (75MHz/Div.)

Fig.6.4.6 Theoretical Modelling of FM Optical Spectra (Frequency Deviation Av = 100 MHz)

162

Relat

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ht (

100%

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Zero & First Order Peak Height100

90x experimental

80Zero Order- Theoretical

70

60

50

40

30

20 First Order -----10

020018016014060 80 100 120

Modulation Frequency (MHz)

Fig.6.4.7 Comparison Between Experimental and Theoretical FM Spectra

163


Fig.6.4.3 shows that the zero order peak will disappear when modulation index reaches about 2.41. In experiments, this property provides a simple and reliable method to determine frequency deviation Aol>/27L It also provides a convenient method to evaluate the parasitic intensity modulation signal. In this experiment, the frequency deviation was about 100 MHz and, within the sensitivity of the testing system (about 5 % IM), no parasitic IM was observed.

When the modulation frequency Q was increased beyond 300MHz, the side peak would become too low to recognize. The frequency deviation Aco had to be increased to match the modulation frequency £2. In this experiment, because of an offset of the laser and tuning device optimized operating wavelengths, the frequency deviation was limited to about 100 MHz, preventing higher frequency measurements. On the other hand, when the modulation frequency £2 becomes too low (Below 50 MHz), the sidebands can no longer be resolved because of the limits of the Fabry- Perot interferometer.

6.4.3 Birefringent Filter Method1. Mechanism

A Birefringent filter system can be used as a frequency discriminator to convert optical FM to an IM signal which is relatively easy to process.

An ordinary birefringent filter is shown in Fig.6.4.8. The problem faced by such kinds of systems is that their initial phase will change with the FM carrier frequency and can not be controlled independently. This results an uncontrollable FM-IM conversion efficiency. As the carrier frequency drifts, the efficiency will drift from maximum to 0. This is clearly unacceptable in FM measurements.

In this experiment, a phase adjusting mechanism was introduced into the birefringent filter system by adding a single quarter wavelength retarder between the birefringent material mid the second polarizer. The modified system is shown in Fig. 6.4.9. The matrix related to each component characterises its polarization properties. For the FM input defined in Eq.6.4.1, the normalized system power output is

I(t) = sin2[JS + 4 ? cos(flt-H)>) - fl - 5] 6.4.3J 0 ■' 0

where / is the free frequency range of the birefringent filter and ri the

164

= co/

/ o

+ A

co//

0 co

s(Q

t +

<|))


FM D

etec

tion

Syst

em

(<t> +

J y)S

03 o //(O

V

+ o

//(i) =


CO

C D

.s'c/aS 'c/aOO

CD

c/aOO

CMw.s'c/a

CM

wc/aOo

o

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sc/aOosc/a

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0

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vi OX)

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166


polarization angle of the polarizer defined in Fig.6.4.9. When is•'o

reasonably smaller than k , Eq.6.4.3 can simplified to

I(t) = siiA -S - d - 5) - cos(“ - 2 i 3 ) ^ cos(nt-Hj>) 6.4.4J o j o J 0

It is clear that the maximum conversion efficiency can always be maintained by adjusting polarization angle f>.2. Measurement

In this experiment, the birefringent path was formed by about 60 metre of high birefringence fibre. The free frequency range of the system was about 10 GHz. As the polarizer was rotated, the output changed between 0 and maximum. The maximum FM-IM conversion efficiency was obtained at the position where output reached its half maximum. Results for low modulation frequencies are shown in Fig.6.4.10. The frequency response appeared to be flat from DC to 20MHz.

The conversion efficiency of this testing system, although it could be calculated theoretically, was obtained by calibrating the system at modulation index value 2.41 which was determined by Fabry- Perot interferometer method.

6.5. ConclusionsAn MQW tuned external cavity laser was constructed. Over 600 GHz

discontinuous and 2 GHz continuous tuning range were realised experimentally with large area MQW devices. The dynamic measurements of the MQW tuned external cavity laser were carried out using an integrated small area MQW- Bragg reflector phase modulator. Two different testing systems; a high resolution Fabry- Perot interferometer system and a birefringent filter frequency discriminator system, were constructed for these measurements. Experimental results showed a uniform FM frequency response from DC to 300 MHz. Further higher modulation frequencies were not measured due to the sensitivity of the detection systems.

167

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d

B


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DC

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po • oap

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CDns

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rd“VO6 b• rH

P h

168


REFERENCE

1. D. Renner and J.E. Carroll, Simple System for Broad-band Single-mode Tuning of DH GaAlAs Lasers, Electron. Lett., 15, 73-74

2. R. Wyatt and W J. Devlin, 10kHz Linewidth 1.5 pm InGaAsP External Cavity Laser with 55nm Tuning Range, Electron. Lett., 19, 110-112

3. M.W. Flem ing, Spectral characteristics of External Cavity Controlled Semiconductor Lasers, IEEE J. Quantum Electron. QE-17, 44-59

4. M. Whitehead, P. Stevens, A. Rivers, G. Parry, J.S. Roberts, P. Mistry, M. Pate, and G. Hill, Effects of Well Width on Characteristics of GaAs/AlGaAs Multiple Quantum Well Electro-absorption Modulators, Appl. Phys. Lett. 53, 956

5. Hitachi Optoelectronic Semiconductor Products Data Book6. H.D. Edmonds, C. DePalma, and E.P. Harris, Preparation and Properties

of SiO Antireflection Coatings for GaAs Injection Laser with External Resonators, Appl. Opt. 10, 1591

7. D.M. Baney, P.B. Gallion and C. Chabran, Measurement of the Swept- frequency Carrier- induced FM Response of a Semiconductor Laser Using an Incoherent Interferometric Technique, IEEE Photonic. Techn. Lett., 2, 325, 1990

8. S. Saito, Y. Yamamoto and T. Kimura, Optical Heterodyne Detection of Directly Frequency Modulated Semiconductor Laser Signals, Electron. Lett., 16, 826, 1980

9. F.P. Vankwikelberge, F. Buytaet, A. Franchois, R. Baets, P.I. Kuindersma and W. Fredriksz, Analysis of the Carrier- induced FM Response of DFB Laser: Theoretical and Experimental Case Studies, IEEE J. Quantum Electron., QE-25, 2239, 1989

10. M. Abramowitz and I.A. Stegum, Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series, 1964

11. G.D. Boyd and H. Kogelnick, Generalized Confocal Resonator Theory, Bell Syst. Tech. J., 41, 1347, 1962

12. The User Manual and Tech Meno on High-Finesse Etalons(HIFASE) for Laser Diagnosics, Produced by Burleigh Instruments, Inc.

169

CHAPTER SEVEN

CONCLUSIONS

The work on MQW tuned semiconductor lasers in this thesis has been carried out in three major parts; the theoretical study of tuningstructures; a comparative study of tuning mechanisms and experiments on MQW tuned external cavity lasers.

7.1 Tunable Laser StructuresFabry- Perot cavity tunable laser structures were studied statically

and dynamically. The study is essential for Fabry- Perot cavity tunable laser structure design and performance analysis.

In the static study, the relations between the continuous tuning rangeand parameters of the structure were derived. Without a mode selection mechanism, the continuous tuning range is limited by the both free spectral range of the laser resonator and residual reflection from the surfaces dividing the resonator. In single cavity structures, where all the surfaces dividing the resonator are perfectly antireflection coated, the maximum continuous tuning range will be equal to the free spectral range of the resonator for a corresponding optical length change in the resonator of a half wavelength. In multiple cavity structures where surfaces with considerable reflection divide the resonator into an active laser cavity and external cavities, changing the optical length of the external cavity causes it to select modes defined by the active cavity.

In the dynamic study, the limits to tuning speed were investigated from two aspects; the tuning element structure and, more fundamentally, the resonator round trip time effect. The tuning speed limits related to the tuning element structures are mainly caused by the PIN junction capacitanceof the tuning element and the resonator round trip time related tuning speedlimits are due to the finite distribution time of the energy disturbance induced by frequency modulation. The FM response to modulation frequencies has been derived for different tuning element and external cavity

170

Chapter Seven: Conclusions

structures.

7.2 Tuning MechanismsVarious tuning mechanisms which produce refractive index change have

been investigated and compared. The refractive index change induced by the QCSE in QW has been studied intensively and a computer model has been developed. In this model, the effective mass approximation and Airy function- matrix approach were deployed to calculate exciton absorption. The Gaussian linewidth broadening caused by interface roughness, the binding energy change due to the reduced dimensionality of the QW, continuum band absorption due to continuum band transitions and light hole eigen energy red shift due to interface stress have been taken into account. Four measured parameters were introduced into this model to give a better agreement between modelling and experimental results. These parameters were selected in such a way that they have very weak, if any, dependence on QW structures but strong dependence on QW growth conditions.

Comparisons between the quantum confined Stark effect (QCSE), the Franz-Keldysh effect (FKE) and the forward biased carrier injection effect (CIE) were carried out in term of insertion loss and operating bandwidth. To compare the insertion loss, two parameters were defined according to the requirements of tuning elements. To compare the operating bandwidth, a polarization model concerning particle and energy redistribution times and a rate equation model concerning carrier density change with injection current were established for QCSE and CIE respectively. The results shows an obvious superiority of QCSE over the other two effects.

7.3 MQW Tuned External Cavity Laser ExperimentsMQW tuned external cavity laser experiments were carried out. The

measured absorption coefficient data and corresponding refractive index changes of MQW materials were analyzed. Based on these analyses, a suitable MQW structure was chosen to ensure that the MQW device and semiconductor laser diode match each other in wavelength. It was found both in theoretical modelling and experiments that for a given bias range, there was a certain wavelength where the maximum refractive index variation and minimum absorption coefficient variation could be obtained. This finding encouraged the use of MQW devices as tuning elements in tunable semiconductor laser

171


systems.Based on the above work, the first reverse biased MQW tunable

semiconductor laser was constructed and successfully operated. In static tuning experiments, a 400pmx400|im large area MQW device and a mirror were used as a tuning element to form an electronically controlled external cavity. Without antireflection coating on either of the laser diode facets, a discontinuous tuning range of over 600 GHz or, in wavelength, 1.4 nm was achieved, with less than 0.6 dB output power change. A continuous tuning range of 0.6 GHz was also observed, although a large intensity variation was also present. With one of the laser diode facets antireflection coated, the continuous tuning range was increased to as much as 3.2 GHz with no significant output power change. This continuous tuning range implied a refractive index change of 3.2% in the MQW material which is in good agreement with predicted data from measured absorption coefficient data.

FM dynamic properties of MQW tuned semiconductor lasers were measured in dynamic experiments. In order to achieve higher operating speed, a newtuning device was designed and fabricated. In the new device, the MQW layer was integrated with a multilayer Bragg reflector. This arrangement enables the device to have a small PIN area and, therefore, higher operating speed. To carry out the measurements, two optical FM detection systems were constructed. In the Fabry- Perot interferometer FM detection system, a non-confocal high resolution spherical mirror scanning Fabry- Perot interferometer was used to observe optical FM spectra directly. In thebirefringent filter FM detection system, a phase adjustable fibrebirefringent filter was introduced as an optical frequency discriminator to convert the optical FM to optical IM which could be easily detected. Bothsystems operated successfully and showed the FM response to be uniform over the frequency range 0 to 300MHz.

Although these experiments were mainly designed to prove the feasibility of MQW tuned semiconductor lasers, it seems that with a little further development the MQW tuned external cavity laser should be applicable to systems where a light source with small but uniform frequency modulation response is required.

172


7.4 Proposed WorkThis work has proved that the QCSE induced refractive index change in

QW materials has great potential in high speed tunable semiconductor laser applications. Although the experiments were carried out for a bulk component external cavity, most of the conclusions of this work can be extended to integrated tunable laser structures and much information can be obtained for designing such structures to achieve larger tuning range and more practical source design. Theoretically, the QCSE induced refractive index change in QW can be deployed in almost any existing integrated tunable semiconductor laser structures. As an example, its application in QW DBR laser is given. Fig.7.1 shows a proposed structure. When the lengths of active section land

aphase adjusting section lp have the relationship

1p

= TV 7.11 + 1 a p

where r \ is the coupling coefficient between the Bragg grating and waveguide layers, the structure can provide single electrode controlled continuous tuning over more than one mode spacing. That is because Eq.7.1 ensures that under the same applied electric field, the mode selecting section(Bragg reflector section) and phase adjusting section provide the same amount of frequency change. The continuous tuning range can be determined by

AnA X = — — T| X 1 . 2

e ff b

where n and An „ are the effective refractive index and its change foreff eff

the waveguide layer and X is the operating wavelength. For a typical DBR laser structure, where T| = 30% and X = 1.55jxm, 2% refractive index change

bin the waveguide will generate a continuous tuning of over 10 nm (or 1200 GHz). As this structure has a QW active section and an additional passive section(phase control section), a narrower emission linewidth is also expected.

7.5 SummaryIn summary, the continuous tuning range and speed of external cavity

lasers have been modelled; it is concluded that large tuning range and high

173


tuning speed can be achieved by reducing intra resonator reflection and resonator length. The QCSE induced refractive index change in QW material as a tuning mechanism has been modelled and compared with that induced by FKE and CIE; it is concluded that QW material provides larger refractive index change, smaller absorption change and more uniform modulation frequency response than the competing techniques. A reverse biased MQW tuned external cavity laser has been constructed and a discontinuous tuning range of over 600GHz, a continuous tuning range of over 2 GHz and uniform modulation response from 0 to 300MHz have been achieved. The upper frequency limit was dictated by the measurement technique used and it is expected that multi-GHz rate tuning should be possible. This uniform modulation response marks a distinct advantage over previously developed tunable sources.From these theoretical analysis and experimental results, it is concluded that QW devices deploying the QCSE have good potential for application in wide band tunable semiconductor lasers.

174


l i t

W M M -Substrate

Waveguide

QW layer

Active Phase ControlSection Section

Laser Pump Tuning Bias

Bragg Reflector Section

Fig.7.4.1 Proposed MQW Tuned DBR Laser

175

Appendix A

SiO Anti-reflection Coating on GaAs/AlGaAs Laser Facets

The first trial was carried out using a vacuum evaporator with a conventional optical monitoring system. The deposited layer thickness was measured by measuring light reflection from a silicon sample placed beside the laser and assuming that there was the same deposition rate and therefore the same optical thickness at the laser facet. After an unsuccessful trial, it was realized that because of the different surface conditions between laser facet and monitoring slice, there was a big difference in deposited thickness even though they were very close to each other.

The solution to this problem was to monitor directly the facet to be coated.

A.I. Experimental SetupThe experimental setup was similar to that of Edmonds’1 except there

was no water cooling system because a Peltier effect semiconductor heat pump was used (shown in Fig.A.l). In fact there was such a small change in

otemperature (less than 2 C), that this temperature controlling system was not really needed. A photo detector was mounted opposite the facet to becoated. An offset was given between the laser and detector to allow the evaporated material access to the facet (shown in Fig.A.2). The laser diodewas biased at current below lasing threshold so as to produce only spontaneous emission. Although this made the emission linewidth much wider and the wavelength slightly longer than for lasing, considering thebandwidth of a single layer anti-reflection coating, this would not affect the performance of the coating at the laser working wavelength. The laser bias was also modulated at a frequency of 15 KHz. After pre-amplification, the signal from the photodetecter was processed in a lock-in amplifier. The output signal was observed using a chart recorder.

176

Appendix A: SiO Anti-reflection Coating on GaAs/AlGaAs Laser Facets

Laser-Detector

\Bell JarAperture

Tungsten Boat With SiO

Shutteri) cd

TemperatureController

© oOscilloscope

Modu Source

Pre-amplifier

Lock-inAmplifier

Chart Recorder

Fig.A. 1 Setup for SiO Anti-reflection Coating

177


Peltier Cooler Mount

Heat Sink

Laser Facet

Detector

Fig.A.2 Laser-detector Sub-mount

178

Appendix A; SiO Anti-reflection Coating on GaAs/AlGaAs Laser Facets

A.2. ExperimentThe material used to coat the laser facet was SiO. Its refractive index

is about 2 which is nearly ideal to satisfy the anti-reflection coating requirement n = n n where n , n and n are refractive index of air,

c a s a c scoating material and laser chip. SiO can be evaporated by resistive heating in a tungsten boat.

Before evaporating, preheating of the material was needed to release moisture and impurities contained in the material. When the vacuum had recovered sufficiently (less than 5x1 O’5 Torr) the evaporating process was begun.

The evaporating was kept slow in order to control the deposited thickness precisely. When the output signal reached turning point (see Fig.A.3), the shutter was turned to shadow the evaporating source and the heating current was turned off. The whole procedure lasted about two minutes.

3. ResultsBefore antireflection coating, the threshold current of the laser diode

at Toom temperature was 48 mA which increased to 58 mA after coating. The optical power - current curves are plotted in Fig.A.4. There was also a significant improvement in coupling efficiency between laser diode and external cavity. After coupling, the threshold current decreased to 44 mA compared with 47mA for the external cavity system without antireflection coating.

179


cn

oo

o v*(N <D

VO

O 0 . 0Ov 00 t"-

UOISSIUISTOJX

o

cdP

cotoQp

• VhO+-»• rHPO

too. 3cdO

UPo

♦

0<u

<DVh1• fHp

<cn

oi)PH

180

Outp

ut O

ptica

l Po

wer

(mW

)

Appendix A: SiO Anti-reflection Coating on GaAs/AIGaAs Laser Facets

7

2after

Laser Injection Current (mA)

Fig.A.4. Optical power-current curves for HLP-1400 laser before and after antireflection coating

181

Appendix A; SiO Anti-reflection Coating on GaAs/AlGaAs Laser Facets

References

1. H.D. Edmonds, C. DePalma, and E.P. Harris, "Preparation and Properties of SiO Antireflection Coatings for GaAs Injection Laser with External Resonators", Appl. Opt., 10., 1591, 1971

182

Elec

trod

e

Appendix B

Data on HLP-1400 Semiconductor Lasers

J-l<DCD

hJo oT—lIP h

S3M-ho<D

5u 3Jh-4->CD

CO .bb• I—(

P h

183

Outp

ut O

ptica

l Po

wer

(mW

)

Appendix B: Data on HLP-1400 Semiconductor Laser

8

7

6

5

4

3

2

1

0

Laser Injection Current (mA)

Fig.B.2. Optical power-current curves for HLP-1400

184

Appendix C

Design of Semiconductor Bragg Reflectors

matrix:The optical properties of a dielectric layer can be characterised by a

1

IM =cos (8) jsin(8)/n'

jsin (8 )-n cos(5)C.l

where n is the refractive index and

2jiLnC.2

For a multilayer structure, the optical properties can be expressed by multiplication of each layer’s property matrix.

M =m 11 m

12

m21

m.22J

mC.3

where m is the number of layers, stands for the property matrix of layer

M =icos (8 .) jsin(8.)/ni i ijs in (8 .)n . cos(8.)

C.4

8, n have the same meanings as above and i denotes layer i.The reflectance of such structure can be easily obtained from the

elements of matrix M.

Appendix C: Design of Semiconductor Bragg Reflectors

where n and n are the refractive index of the incident medium and0 ssubstrate.

For the Bragg reflectors, each layer has the same optical thickness, a quarter of the centre wavelength, so we have

8 = 5 =......= 5 C.61 2 mfrom the above general discussion some useful results can be obtained.

C.l. The Peak Reflectivity at the Centre WavelengthAt the central wavelength A. , 5 = 8 = ....... = 8 = 2-0 1 2 m Z

M =i■0 j/n.

j n 0C.7

If the film is made of two materials whose refractive indices are n^nd n2 respectively,

M =2i

0 j/n)

j n l 0

0 j/n2

j n2 0

C.8

C.9

when m is even

M =

m /2 r \ n.x 0m /2

0 (-K)m/ 2C.10

where K = nyn2

R(V=fn - n K.0 s

oa + n KmsC.11

when m is odd

186


M = C.12

R(V =f 'XT' ni \I n n - K n-n 1Os 12

n n + Kmn nOs 1 2C.13

Obviously, the peak reflectivity of the Bragg reflector stronglydepends on the ratio of the refractive index between the two materials usedand the number of layers.

C.2. The Reflection BandwidthThe reflection band width can be evaluated for the so-called

high-reflectance zone. For the two medium Bragg reflectors,

W2M= %’ W2i= M2

M = (M M )n 2= 1 2m m

11 12

m21 m22J

m/2

C.14

whenm + m

11 22 > 1

the reflectance increases steadily with increasing number of layers. Therefore the boundaries of the high-reflectance zone are given by

m + m 11 22 = 1 C.15

From Eq.C.4 and C.14 we have

m + m i11 2 2 - 1 2 cos 5 - - j - — + — n n2 1

sin2S C.16

Let g = - j - , therefore 8 = - j - g = -2~(l+Ag), where Ag is the relative half width of the high-reflectance zone.

187


Ag = K sin'1n - n 1 2n + n2 1

C.17

the boundary on the long wavelength side is given bya.

i _ °f TTAg"

and on the short wavelength side

X ni - 0

. T+Ag~

C.18

C.19

Obviously, the high-reflection zone is asymmetric in wavelength about XQ.

C.3. Design of A ^ G a ^ A s and AlAs Bragg ReflectorsC.3.1 Evaluating the Refractive Index of AlxGai-xAs and AlAs.

The refractive index of both materials can be found in references2. ForA1 Ga As, it is related to Aluminium content x:

X 1 - X

AiGaAs

e0(a» = A0(/(O+4-[Ey(E0+Ao)]3*/(yJ)+B0where

/(C) = c 2[2 - (i+C)‘“- (1-C)‘M1

c = hw/E0,

y „ - hw/(Eo+ V -

1/2 . 1/2-1

andAQ(x) = 6.3 + 19.0x

Bq(x) = 9.4 - 10.2x

= 1.425 + 1.155x + 0.37x2

C.20

C.21

E + A = 1.765 = 1.115x + 0.37xo owhere x is A1 content, hco the photo energy.

For AlQiGa09As at a wavelength of 830nm,

x = 0.1, hco = 1.50

no.r 3 61 1 = 576 Ao.iFor AlAs at the same wavelength,

188


x = 1n =3.00 1.0 1 = 692 A

1.0

C.3.2. Determining the Number of Layers.The choice of material used for the first material to be grown

immediately upon the substrate is made for purely technical reasons. Once?decided, we can name the refractive indices n and n ^ . Following Eq.C .ll and C.13, the number of layers m can be easily worked out for a required reflectivity, Rq For an even number of layers

In r v i - n r o>i

mn (1+TET) s v C.22

ln(K)m should take the nearest even number. For an odd number of layers

In

m =

V . d - ^ o ) ’

■ nin2<1+'n r 0) • C.23ln(K)

m should take the nearest odd number.For A1 Ga As/AlAs, the AlGaAs as the first layer and

0.1 0.9 Jn = n = 3.5 and R = 95%

s 0 0m = 23 or 24

C.3.3. Checking the BandwidthThe bandwidth can be estimated by Eq.C.18 and C.19. If the bandwidth

does not satisfy the application, a change of materials or a relocation of the centre wavelength has to be considered.

For A1 Ga As/AlAs the band width is0.1 0.9

Ag = 14.5%X - 724.8 nm

sX = 970.9 nm

189


C.3.4. Calculation of Reflection SpectrumIn the above design procedure, the materials used were considered as

ideal dielectric media, that means the absorption in real materials was neglected. In fact the weak absorption in semiconductor materials may reduce the reflection and narrow the bandwidth. With absorption, the media refractive index will no longer be real numbers.

n. = n. - ja . C.241 1 J 1

Substituting Eq.C.24 into Eq.C.3 and Eq.C.5 at each wavelength, the spectrum for this structure were finally obtained and plotted out in Fig.C.l.. The effect of 5% layer thickness error is also illustrated in this figure.

190

Ref

lect

ance

(%

)


0.9

0.7

0.6

0.5

0.4

0.3

0.2

700 750 800 850 900 950 1050 11001000

Wavelength (nm)-5% 1-5% Correct

Fig.C. 1 Spectra of Semiconductor Bragg Reflectors

191


References

1. H.A. Macleod, "Thin-film Optical Filters", Second Edition, Adam Hilger Ltd.

2. S. Adachi, "GaAs, AlAs, and AlGaAs: Material Parameters for Use in Research and Device Applications", J.Appl. Phys.,58, R l, 1985

192

Appendix D

The Measurement of Semiconductor Bragg Reflectors

The reflection measurement of the semiconductor Bragg reflectors was carried out using a conventional scanning optical spectrophotometer. In order to measure the reflectance using this kind of equipment which is usually used for absorption and transmission measurements, specially designed accessory was used to convert the reflectance to transmission measurement. Fig.D.l shows the optical scheme of this accessory and its function in the sample path of the scanning optical spectrophotometer. The measured results are shown in Fig.D.2. Analysis of results is a little complicated for three reasons; First, from Fig.D.2 it is clear that it is impossible to measure reflectance at normal incidence. The minimum incident

oangle is 20 in this measurement. Fortunately, the large refractive index of semiconductor materials makes the angle much smaller in the material by the formula:

n sin# = n sin#0 0 1 1

where Nq and are the refractive index of incident medium (air, Nq = 1)and refractive medium (AlGaAs/ALAs Ni = 3 to 3.6); and # the incident

0 1 oand refractive angles, # as revealed from the above formula is about 5 . Such a small angle only produces a reflectance spectrum shift towards short wavelength of about 3nm. Second, the existence of relatively thick MQWo olayers (30 period 60 A GaAs/ 60 A AlQ3Gao7As) on top of the Bragg reflector causes a Fabry-Perot resonator related spectrum which is mixed with the Bragg reflection band spectrum and produces fluctuations in the observed spectrum. Finally, the wavelength dependent absorption in AlAs, AlGaAS and MQW make the reflection band narrower than an ideal dielectric Bragg structure. The heavy and light hole related absorption peaks even produce a valley in the reflection band.

In conclusion, in spite of the narrowing in reflection band caused by absorption and some fluctuations caused by the Fabry-Perot resonator effect

193

Appendix D: Measurements of Semiconductor Bragg Reflectors

and absorption peak of MQW layer, the central wavelength of the reflection band was well in agreement with the design and the bandwidth was sufficiently wide for proposed application. Therefore the same Braggstructure is expected in later processing.

194


Sample to be measured

Optical Window

Normal Sample Path for Transmission Measurement

Sample to be measured

Optical Window

Sample Path for Reflection Measurement

Fig.D. 1 Sample Path Change for Reflectance Measurement

Refle

ctan

ce

(%)


0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

700 750 800 850 900 950 1000 1050 1100Wavelength (nm)

Fig.D.2 Measured Spectrum of Semiconductor Bragg Reflectors

196

Appendix E

Small Area Device Processing

Small area devices are processed from an MQW-Bragg stack wafer. The wafer structure is shown in Fig.E.l. The processing steps are as follows:

clean waferplace in heated stripper for about 5 mins rinse in methanol blow dry in N2

form top electrodeo

place in oven at 85 C for about 10 mins to drive off all solventremove from oven and allow to coolcoat with S1499-31 resist at 4000 revs for 20 secs

osoft bake for 20 mins at 85 C remove from oven and allow to coolalign mask 1 (shown in Fig.E.2a) for the top electrode parallel to cleaved edgeexpose to UV lamp for 8 secs immerse in chlorobenzene for 5 mins blow dry in N2 obake for 5 mins at 85 C and then allow to coolimmerse in 1:2 (351 developer:DI water) until pattern developedrinse in DI waterdip in HCkFHD (1:1) for 30 secs to remove oxides rinse in DI water blow dry in N2mount samples on suitable support and place in vacuum chamber pump down to P < 4x10^ mbar deposit 100A Cr deposit 2000A Au

197

Appendix E: Device Processing

remove samples from vacuum chamber place in acetone to remove the resist and excess metal blow dry in N2

define mesao


osoft bake for 20 mins at 85 C remove from oven and allow to coolalign mask 2 (shown in Fig.E.2b) for definition of the mesa over

deposited contact expose to UV lamp for 8 secsimmerse in 1:2 (351 developer:DI water) until pattern developed rinse in DI water blow dry in N2place in H PO :H O :H O (3:3:1) for 15 secs to define mesar 3 4 2 2 2

(etch down 6 pm) rinse in DI water blow dry in N2remove resist layer with acetone blow dry in N2

form lower electrodeo


osoft bake for 20 mins at 85 C remove from oven and allow to coolalign mask 3 (shown in Fig.E.2c) for definition of the mesa over

deposited contact expose to UV lamp for 8 secsimmerse in 1:2 (351 developer:DI water) until pattern developed rinse in DI waterdip in HC1:H20 (1:1) for 30 secs to remove oxides rinse in DI water blow dry in N2

198


mount samples on suitable support and place in vacuum chamber pump down to P < 4x1 O'6 mbardeposit 100A Cr0deposit 2000A Auremove samples from vacuum chamber place in acetone to remove the resist and excess metal blow dry in N2

alloy electrodesplace samples on spade in alloying furnace allow furnace to re-stablise push spade into the furnace

ostop spade at 440 C for 120 secsremove spade from the furnace so the samples cool rapidly

package devicestest I-V trace on each device cleave to separate individual device mount devices on suitable mounts bond electrodes

199


n - G a A s C a p p i n g Layer

0 . 1 pm

n-A1 Q 3 G a Q ? A s Layer

0 . 57 p m

i - MQW S t r u c t u r e

75x(6nm A1 G a A s + 6nm G a A s )v 0 . 3 0 . 7

p - B r a g g St r u e ture

12x(57.6nm A 1 (jra QA ^ + 6 9 . 2 n m A 1 As)

p - G a A s L a y e r

S u b s t r a t e

Fig.E.l MQW-Bragg Wafer Structure

200


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