Explore this thorough overview of integrable microcavity semiconductor lasers and their applications from two leading voices in the field
Attracting a great deal of attention over the last decades for their promising applications in photonic integration and optical interconnects, microcavity semiconductor lasers continue to develop via advances in fundamental physics, theoretical analysis, and numerical simulations. In a new work that will be of interest to researchers and practitioners alike, Microcavity Semiconductor Lasers: Principles, Design, and Applications delivers an application-oriented and highly relevant exploration of the theory, fabrication, and applications of these practical devices.
The book focuses on unidirectional emission microcavity lasers for photonic integrated circuits, including polygonal microresonators, microdisk, and microring lasers. After an introductory overview of optical microcavities for microlasers and detailed information of the lasers themselves, including mode structure control and characteristics, and lasing properties, the distinguished authors discuss fabrication and applications of different microcavity lasers. Prospects for future research and potential new applications round out the book.
Readers will also benefit from the inclusion of:- A thorough introduction to multilayer optical waveguides, the FDTD Method, and Padé Approximation, and deformed, chaos, and unidirectional emission microdisk lasers- An exploration of mode analysis for triangle and square microresonators similar as FP Cavity- Practical discussions of mode analysis and control for deformed square microlasers- An examination of hexagonal microcavity lasers and polygonal microcavities, along with vertical radiation loss for 3D microcavities
Perfect for laser specialists, semiconductor physicists, and solid-state physicists, Microcavity Semiconductor Lasers: Principles, Design, and Applications will also earn a place in the libraries of materials scientists and professionals working in the semiconductor and optical industries seeking a one-stop reference for integrable microcavity semiconductor lasers.
Table of Contents
Preface xi
1 Introduction 1
1.1 Whispering-Gallery-Mode Microcavities 1
1.2 Applications of Whispering-Gallery-Mode Microcavities 2
1.3 Ultra-High Q Whispering-Gallery-Mode Microcavities 5
1.4 Mode Q Factors for Semiconductor Microlasers 6
1.4.1 Output Efficiency and Mode Q Factor 6
1.4.2 Measurement of Mode Q Factor 7
1.5 Book Overview 10
References 11
2 Multilayer Dielectric Slab Waveguides 13
2.1 Introduction 13
2.2 TE and TM Modes in SlabWaveguides 14
2.3 Modes in Symmetric Three-Layer SlabWaveguides 15
2.3.1 TE Modes in Three-Layer SlabWaveguides 15
2.3.2 TM Modes in Three-Layer SlabWaveguides 17
2.3.3 Guided and Radiation Modes 17
2.4 Eigenvalue Equations for Multilayer Slab ComplexWaveguides 18
2.4.1 Eigenvalue Equation for TE Modes 19
2.4.2 Eigenvalue Equation for TM Modes 21
2.4.3 Phase Shift of Total Internal Reflection 21
2.5 Eigenvalue Equations for One-Dimensional MultilayerWaveguides 22
2.5.1 Eigenvalue Equation for Vertical-Cavity Surface-Emitting Lasers 22
2.5.2 Resonance Condition for the Fabry-Perot Cavity 24
2.5.3 Mode Selection for Distributed Feedback Lasers 26
2.6 Mode Gain and Optical Confinement Factor 28
2.6.1 Optical Confinement Factor Based on Power Flow 28
2.6.2 Mode Gain for TE Modes 29
2.6.3 Mode Gain for TM Modes 30
2.7 Numerical Results of Optical Confinement Factors 31
2.7.1 Edge-Emitting Semiconductor Lasers 31
2.7.2 Si-on-SiO2 SlabWaveguide 32
2.7.3 Vertical-Cavity Surface-Emitting Lasers 33
2.8 Effective Index Method 35
References 36
3 FDTD Method and Padé Approximation 37
3.1 Introduction 37
3.2 Basic Principle of FDTD Method 38
3.2.1 Maxwell’s Equation 38
3.2.2 2D FDTD Method in Cartesian Coordinate System 38
3.2.3 3D FDTD Method in Cartesian Coordinate System 41
3.2.4 3D FDTD Method in Cylindrical Coordinate System 43
3.2.5 Numerical Stability Condition 45
3.2.6 Absorption Boundary Condition 46
3.2.7 FDTD Simulation of Microcavities 48
3.3 Padé Approximation for Time-Domain Signal Processing 50
3.3.1 Padé Approximation with Baker’s Algorithm 50
3.3.2 Calculation of Intensity Spectra for Oscillators 52
3.4 Examples of FDTD Technique and Padé Approximation 53
3.4.1 Simulation for Coupled Microdisks 53
3.4.2 Simulation for Microring Channel Drop Filters 54
3.4.3 Light Delay Simulation for Coupled Microring Resonators 57
3.4.4 Calculation of Propagation Loss in Photonic CrystalWaveguides 59
3.5 Summary 62
References 62
4 Deformed and Chaotic Microcavity Lasers 65
4.1 Introduction 65
4.2 Nondeformed Circular Microdisk Lasers 65
4.2.1 Whispering-Gallery Modes in Circular Microdisks 65
4.2.2 Circular Microdisk Semiconductor Lasers 70
4.3 Deformed Microcavity Lasers with Discontinuous Boundary 70
4.3.1 Microdisk Lasers with a Local Boundary Defect 70
4.3.2 Spiral-Shaped Microcavity Lasers 72
4.3.3 Waveguide-Connected Spiral Microcavity Lasers 75
4.4 Chaotic Microcavity Lasers with Smoothly Deformed Boundary 75
4.4.1 Quadrupolar-Shaped Microcavity Lasers with Directional Emission 76
4.4.2 Limaçon Microcavity Lasers with Unidirectional Emission 79
4.4.3 Wavelength-Scale Microcavity Lasers with Unidirectional Emission 82
4.4.4 Waveguide-Coupled Chaotic Microcavity Lasers 86
4.5 Summary 87
References 88
5 Unidirectional Emission Microdisk Lasers 91
5.1 Introduction 91
5.2 Mode Coupling inWaveguide-Connected Microdisks 92
5.2.1 Whispering-Gallery Modes in Circular Microdisks 92
5.2.2 Mode Coupling inWaveguide-Connected Microdisks 94
5.3 Waveguide-Connected Unidirectional Emission Microdisk Lasers 100
5.3.1 Lasing Characteristics of Unidirectional Emission Microdisk Lasers 100
5.3.2 Direct Modulation Characteristics of Unidirectional Emission Microdisk Lasers 103
5.4 Unidirectional Emission Microring Lasers 107
5.5 Unidirectional Emission Hybrid Deformed-Microring Lasers 111
5.6 Wide-Angle Emission and Multiport Microdisk Lasers 113
5.6.1 Wide-Angle Emission-Deformed Microdisk Lasers 113
5.6.2 Multiport Output Microdisk Lasers 117
5.7 Summary 119
References 119
6 Equilateral-Triangle-Resonator Microlasers 123
6.1 Introduction 123
6.2 Mode Analysis Based on the ETR Symmetry 123
6.2.1 Wave Equations for TE and TM Modes 123
6.2.2 Transverse Modes by Unfolding Light Ray in the ETR 124
6.2.3 Evanescent Fields in External Regions 125
6.2.4 Eigenvalue Equation 127
6.3 Mode-Field Distributions 128
6.3.1 Mode Degeneracy and Classify 128
6.3.2 Comparisons of Analytical Solutions with Simulated Results 129
6.3.3 Size Limit for ETR 129
6.4 Far-Field Emission andWaveguide-Output Coupling 131
6.4.1 Mode Q-Factor Calculated by Far-Field Emission 131
6.4.2 Output Coupling by Connecting aWaveguide 133
6.5 Mode Analysis Using Reflected Phase Shift of PlaneWave 135
6.5.1 Mode Analysis Using Mode Light Ray Approximation 135
6.5.2 Comparison of Mode Q Factors 138
6.5.3 Effect of Metal Layer on Mode Confinement 139
6.6 Mode Characteristics of ETR Microlasers 140
6.6.1 Device Fabrication 140
6.6.2 Lasing Characteristics 142
6.7 Summary 145
References 145
7 Square Microcavity Lasers 147
7.1 Introduction 147
7.2 Analytical Solution of Confined Modes 148
7.3 Symmetry Analysis and Mode Coupling 150
7.4 Mode Analysis for High Q Modes 154
7.5 Waveguide-Coupled Square Microcavities 157
7.6 Directional-Emission Square Semiconductor Lasers 163
7.7 Dual-Mode Lasing Square Lasers with a Tunable Interval 165
7.8 Application of Dual-Mode Square Microlasers 168
7.9 Lasing Spectra Controlled by Output Waveguides 171
7.10 Circular-Side Square Microcavity Lasers 174
7.11 Summary 180
References 181
8 Hexagonal Microcavity Lasers and Polygonal Microcavities 185
8.1 Introduction 185
8.2 Mode Characteristics of Regular Polygonal Microcavities 186
8.2.1 Symmetry Analyses Based on Group Theory 186
8.2.2 Numerical Simulations ofWGMs in Regular Polygonal Microcavities 190
8.2.3 Circular-Side Polygonal Microcavities 193
8.3 WGMS in Hexagonal Microcavities 197
8.3.1 Periodic Orbits in Hexagonal Microcavities 197
8.3.2 Symmetry Analyses and Mode Coupling 200
8.3.3 Numerical Simulation ofWGMs in Hexagonal Microcavities 201
8.3.4 WGMs inWavelength-Scale Hexagonal Microcavities 203
8.4 Unidirectional Emission Hexagonal Microcavity Lasers 205
8.4.1 Waveguide-Coupled Hexagonal Microcavity Lasers 206
8.4.2 Circular-Side Hexagonal Microcavity Lasers 209
8.5 Octagonal Resonator Microlasers 211
8.6 Summary 214
References 215
9 Vertical Loss for 3D Microcavities 219
9.1 Introduction 219
9.2 Numerical Method for the Simulation of 3D Microcavities 220
9.2.1 Effective Index Method 220
9.2.2 S-Matrix Method 222
9.3 Control of Vertical Radiation Loss for Circular Microcavities 225
9.3.1 Mode Coupling and Vertical Radiation Loss 225
9.3.2 Semiconductor Microcylinder Lasers with the Sizes Limited by Vertical Radiation Loss 230
9.3.3 Cancelation of Vertical Radiation Loss by Destructive Interference 236
9.4 Verical Radiation Loss for Polygonal Microcavities 245
9.4.1 3D Equilateral-Triangular Microcavity withWeak Vertical Waveguiding 245
9.4.2 3D Square Microcavity withWeak VerticalWaveguiding 246
9.5 Summary 247
References 249
10 Nonlinear Dynamics for Microcavity Lasers 251
10.1 Introduction 251
10.2 Rate Equation Model with Optical Injection 253
10.3 Dynamical States of Rate Equations with Optical Injection 255
10.4 Small Signal Analysis of Rate Equations 261
10.5 Experiments of Optical Injection Microdisk Lasers 263
10.5.1 Nonlinear Dynamics Under Optical Injection 263
10.5.2 Comparison Between Experiment and Simulated Results 268
10.5.3 Modulation Bandwidth Enhancement Under Optical Injection 269
10.6 Microwave Generation in Microlaser with Optical Injection 271
10.7 Integrated Twin-Microlaser with Mutually Optical Injection 275
10.8 Discussion and Conclusion 276
References 278
11 Hybrid-Cavity Lasers 283
11.1 Introduction 283
11.2 Reflectivity of aWGM Resonator 284
11.3 Mode Q-Factor Enhancement for Hybrid Modes 286
11.4 Hybrid Mode-Field Distributions 288
11.5 Fabrication of Hybrid Lasers 290
11.6 Q-Factor Enhancement and Lasing Characteristics 292
11.7 Robust Single-Mode Operation 295
11.8 Optical Bistability for HSRLS 297
11.9 All-Optical Switching 302
11.10 All-Optical Logic Gates 306
11.11 Hybrid Square/Rhombus-Rectangular Lasers (HSRRLS) 309
11.12 Summary 312
References 314
Index 317
