Preface ....................................................... xix
Author ........................................................ xxi
List of Abbreviations and Notations ......................... xxiii
1 Introduction ................................................. 1
1.1 Historical Overview of Integrated Optics and Photonics .. 1
1.2 Why Analysis of Optical Guided Wave Devices? ............ 4
1.3 Principal Objectives .................................... 5
1.1.4 Chapters Overview ................................ 6
References ................................................... 8
2 Single-Mode Planar Optical Waveguides ....................... 11
2.1 Introduction ........................................... 11
2.2 Formation of Planar Single-Mode Waveguide Problems ..... 13
2.2.1 Transverse Electric/Transverse Magnetic Wave
Equation ........................................ 13
2.2.1.1 Continuity Requirements and Boundary
Conditions ............................. 14
2.2.1.2 Index Profile Construction ............. 14
2.2.1.3 Normalization and Simplification ....... 15
2.2.1.4 Modal Parameters of Planar Optical
Waveguides ............................. 16
2.3 Approximate Analytical Methods of Solution ............. 19
2.3.1 Asymmetrical Waveguides ......................... 19
2.3.1.1 Variational Techniques ................. 19
2.3.1.2 Wentzel-Kramers-Brilluoin Method ....... 25
2.3.2 Symmetrical Waveguides .......................... 31
2.3.2.1 Wentzel-Kramers-Brilluoin Eigenvalue
Equation ............................... 32
2.3.2.2 Two-Parameter Profile-Moment Method .... 33
2.3.2.3 New Equivalence Relation for Planar
Optical Waveguides ..................... 40
2.3.3 Concluding Remarks .............................. 49
2.4 Appendix A: Maxwell Equations in Dielectric Media ...... 49
2.4.1 Maxwell Equations ............................... 49
2.4.2 Wave Equation ................................... 50
2.4.3 Boundary Conditions ............................. 50
2.4.4 Reciprocity Theorems ............................ 51
2.4.4.1 General Reciprocity Theorem ............ 51
2.4.4.2 Conjugate Reciprocity Theorem .......... 51
2.5 Appendix B: Exact Analysis of Clad-Linear Optical
Waveguides ............................................. 51
2.5.1 Asymmetrical Clad-Linear Profile ................ 52
2.5.1.1 Eigenvalue Equation .................... 52
2.5.1.2 Mode Cutoff ............................ 53
2.5.2 Symmetrical Waveguide ........................... 53
2.5.2.1 Eigenvalue Equation .................... 53
2.5.2.2 Mode Cutoff ............................ 53
2.6 Appendix C: Wentzel-Kramers-Brilluoin Method, Turning
Points and Connection Formulae ......................... 54
2.6.1 Introduction .................................... 54
2.6.2 Derivation of the Wentzel-Kramers-Brilluoin
Approximate Solutions ........................... 54
2.6.3 Turning Point Corrections ....................... 57
2.6.3.1 Langer's Approximate Solution Valid
at Turning Point ....................... 57
2.6.3.2 Behavior of Turning Point .............. 59
2.6.3.3 Error Bound for Φ Turning Point ........ 60
2.6.4 Correction Formulae ............................. 62
2.6.5 Application of Correction Formulae .............. 64
2.6.5.1 Ordinary Turning Point Problem ......... 64
2.6.5.2 Effect of an Index Discontinuity at
a Turning Point ........................ 66
2.6.5.3 Buried Modes near an Index
Discontinuity at a Turning Point ....... 66
2.7 Appendix D: Design and Simulation of Planar Optical
Waveguides ............................................. 67
2.7.1 Introduction .................................... 67
2.7.2 Theoretical Background .......................... 67
2.7.2.1 Structures and Index Profiles .......... 67
2.7.2.2 Optical Fields of the Guided
Transverse Electronic Modes ............ 68
2.7.2.3 Design of Optical Waveguide
Parameters: Preliminary Work ........... 70
2.7.3 Simulation of Optical Fields and Propagation
in Slab Optical Waveguide Structures ............ 70
2.7.3.1 Lightwaves Propagation in Guided
Straight Structures .................... 71
2.7.3.2 Lightwaves Propagation in Guided Bent
Structures ............................. 73
2.7.3.3 Lightwaves Propagation in Y-Junction
(Splitter) and nterferometric
Structures ............................. 74
2.7 Problems ............................................... 74
References .................................................. 76
3 3D Integrated Optical Waveguides ............................ 79
3.1 Introduction ........................................... 79
3.2 Marcatili's Method ..................................... 80
3.2.1 Field and Modes Guided in Rectangular Optical
Waveguides ...................................... 81
3.2.1.1 Mode Fields of Hx Modes ................ 81
3.2.1.2 Boundary Conditions at the Interfaces .. 84
3.2.2 Mode Fields of Ey Modes ......................... 85
3.2.3 Dispersion Characteristics ...................... 86
3.3 Effective Index Method ................................. 86
3.3.1 General Considerations .......................... 86
3.3.2 A Pseudo-Waveguide .............................. 90
3.3.3 Finite Difference Numerical Techniques for 3D
Waveguides ...................................... 91
3.4 Non-Uniform Grid Semivectorial Polarized Finite
Difference Method for Optical Waveguides with
Arbitrary Index Profile ................................ 91
3.4.1 Propagation Equation ............................ 91
3.4.2 Formulation of Non-Uniform Grid Difference
Equation ........................................ 92
3.4.2.1 Quasi-Transverse Electronic Mode ....... 93
3.4.2.2 Inverse Power Method ................... 98
3.4.3 Ti:LiNbO3 Diffused Channel Waveguide ........... 100
3.4.3.1 Refractive Index Profile of the
Ti:LiNbO3 Waveguide ................... 100
3.4.3.2 Numerical Simulation and Discussion ... 104
3.5 Mode Modeling of Rib Waveguides ....................... 112
3.5.1 Choice of Grid Size ............................ 115
3.5.2 Numerical Results .............................. 118
3.5.3 Higher Order Modes ............................. 118
3.6 Conclusions ........................................... 121
3.7 Problems .............................................. 123
References ................................................. 123
4 Single-Mode Optical Fibers: Structures and Transmission
Properties ................................................. 127
4.1 Optical Fibers ........................................ 127
4.1.1 Brief History .................................. 127
4.1.2 Optical Fiber: General Properties .............. 128
4.1.2.1 Geometrical Structures and Index
Profile ............................... 128
4.1.3 Fundamental Mode of Weakly Guiding Fibers ...... 130
4.1.3.1 Solutions of the Wave Equation for
Step Index Fiber ...................... 130
4.1.3.2 Gaussian Approximation ................ 132
4.1.3.3 Cutoff Properties ..................... 135
4.1.3.4 Power Distribution .................... 136
4.1.3.5 Approximation of Spot Size r0 of a
Step Index Fiber ...................... 138
4.1.4 Equivalent Step Index (ESI) Description ........ 138
4.1.4.1 Definitions of Equivalent Step Index
Parameters ............................ 139
4.1.4.2 Accuracy and Limits ................... 140
4.1.4.3 Examples on Equivalent Step Index
Techniques ............................ 140
4.1.4.4 General Method ........................ 141
4.2 Nonlinear Optical Effects ............................. 141
4.2.1 Nonlinear Self Phase Modulation Effects ........ 142
4.2.2 Self Phase Modulation .......................... 142
4.2.3 Cross Phase Modulation ......................... 143
4.2.4 Stimulated Scattering Effects .................. 144
4.2.4.1 Stimulated Brillouin Scattering ....... 144
4.2.4.2 Stimulated Raman Scattering ........... 145
4.2.4.3 Four-Wave Mixing ...................... 146
4.3 Optical Fiber Manufacturing and Cabling ............... 147
4.4 Concluding Remarks .................................... 148
4.5 Signal Attenuation and Dispersion ..................... 148
4.5.1 Introductory Remarks ........................... 149
4.5.2 Signal Attenuation in Optical Fibers ........... 151
4.5.2.1 Intrinsic or Material Attenuation ..... 151
4.5.2.2 Absorption ............................ 151
4.5.2.3 Rayleigh Scattering ................... 151
4.5.2.4 Waveguide Loss ........................ 152
4.5.2.5 Bending Loss .......................... 152
4.5.2.6 Microbending Loss ..................... 152
4.5.2.7 Joint or Splice Loss .................. 153
4.5.2.8 Attenuation Coefficient ............... 154
4.6 Signal Distortion in Optical Fibers ................... 154
4.6.1 Basics on Group Velocity ....................... 154
4.6.2 Group Velocity Dispersion ...................... 156
4.6.2.1 Material Dispersion ................... 156
4.6.2.2 Waveguide Dispersion .................. 159
4.6.2.3 Alternative Expression for Waveguide
Dispersion Parameter .................. 162
4.6.2.4 Higher Order Dispersion ............... 162
4.6.2.5 Polarization Mode Dispersion .......... 163
4.7 Transfer Function of Single Mode Fibers ............... 165
4.7.1 Linear Transfer Function ....................... 165
4.7.2 Nonlinear Fiber Transfer Function .............. 170
4.7.3 Transmission Bit Rate and the Dispersion
Factor ......................................... 175
4.8 Fiber Nonlinearity .................................... 175
4.8.1 SPM, XPM Effects ............................... 176
4.8.2 Modulation Instability ......................... 178
4.8.3 Effects of Mode Hopping ........................ 178
4.9 Advanced Optical Fibers: Dispersion-Shifted,
Flattened and Compensated Optical Fibers .............. 178
4.10 Numerical Solution: Split Step Fourier Method ......... 180
4.10.1 Symmetrical Split Step Fourier Method (SSFM) ... 180
4.10.2 MATLAB® Program and MATLAB Simulink Models of
the SSFM ....................................... 181
4.10.2.1 MATLAB Program ........................ 181
4.10.2.2 MATLAB Simulink Model ................. 185
4.10.2.3 Modeling of Polarization Mode
Dispersion ............................ 185
4.10.2.4 Optimization of Symmetrical SSFM ...... 186
4.10.3 Remarks ........................................ 186
4.11 Appendix: MATLAB Program for the Design of Optical
Fibers ................................................ 187
4.12 Program Listings of the Split Step Fourier Method
with Self Phase Modulation and Raman Gain
Distribution .......................................... 193
4.13 Program Listings of an Initialization File (Linked
with Split Step Fourier Method of Section 4.12) ....... 196
4.14 Problems .............................................. 199
Some Questions ............................................. 206
References ................................................. 207
5 Design of Single-Mode Optical Fiber Waveguides ............. 209
5.1 Introduction .......................................... 209
5.2 Unified Formulation of Optical Fiber Waveguide
Problems .............................................. 210
5.2.1 First Order Scalar Wave Equation ............... 211
5.2.2 Eigenvalue Equation ............................ 214
5.2.3 Polarization Correction to b ................... 215
5.2.4 Waveguide Characteristics Parameters ........... 216
5.2.4.1 Chromatic Fiber Dispersion ............ 216
5.2.4.2 Spot Size ............................. 219
5.2.4.3 Fiber Extinct Loss Formulae ........... 221
5.2.4.4 Generalized Mode Cutoffs .............. 223
5.3 Simplified Approach to the Design of Single-Mode
Optical Fibers ........................................ 223
5.3.1 Introductory Remarks ........................... 223
5.3.2 Classification Scheme for Single-Mode Optical
Fibers ......................................... 224
5.3.2.1 Fiber with Small Waveguide
Dispersion ............................ 225
5.3.2.2 Fibers with Large Uniform Waveguide
Dispersion ............................ 225
5.3.2.3 Fibers with Very Large Steep
Waveguide Dispersion .................. 226
5.3.2.4 Fiber with Ultra-Large Waveguide
Dispersion ............................ 226
5.3.3 Practical Limit of Single-Mode Optical Fiber
Design ......................................... 226
5.3.4 Fiber Design Methodology ....................... 227
5.3.5 Design Parameters and Equations ................ 228
5.3.5.1 Group Velocity Dispersion (GVD) ....... 228
5.3.5.2 Dispersion Slope ...................... 230
5.3.6 Triple-Clad Profile ............................ 230
5.3.6.1 Profile Construction .................. 230
5.3.6.2 Waveguide Guiding Parameters of
Triple-Clad Profile Fiber ............. 232
5.4 Dispersion Flattening and Compensating ................ 233
5.4.1 Approximation of Waveguide Dispersion
Parameter Curves ............................... 234
5.4.2 Effect of Core and Cladding Radius on the
Total Dispersion ............................... 237
5.4.3 Effects of Refractive Indices of the Cladding
Layers on the Total Dispersion Parameter ....... 239
5.4.4 Effect of Doping Concentration on the Total
Dispersion ..................................... 242
5.5 Design Algorithm ...................................... 242
5.5.1 Design Algorithm for DFF ....................... 242
5.5.2 Design Algorithm for DCF ....................... 242
5.6 Design Cases .......................................... 244
5.6.1 Design Case 1 .................................. 244
5.6.2 Design Case 2 .................................. 245
5.6.3 Design Summary ................................. 247
5.7 Concluding Remarks .................................... 247
5.8 Problems .............................................. 249
Appendix A: Derivatives of the RI with Respect to
Wavelength ............................................ 252
Appendix B: Higher Order Derivatives of the Propagation
Constant .............................................. 253
6 Scalar Coupled-Mode Analysis ............................... 291
6.1 Introduction .......................................... 291
6.2 Coupler Configurations ................................ 291
6.2.1 Overview ....................................... 291
6.2.1.1 Two-Mode Couplers ..................... 291
6.2.1.2 Fiber-Slab Couplers ................... 292
6.2.1.3 Grating-Assisted Couplers ............. 292
6.2.2 Configurations ................................. 292
6.2.3 Two-Mode Couplers .............................. 293
6.2.4 Multimode Couplers ............................. 293
6.2.5 Fiber-Slab Couplers ............................ 293
6.3 Two-Mode Couplers ..................................... 294
6.3.1 Coupled-Mode Equations ......................... 294
6.3.2 Power Parameters ............................... 295
6.3.3 Symmetric Two-Mode Coupler ..................... 296
6.3.3.1 Coupled-Mode Equations ................ 296
6.3.3.2 Analytical Solutions .................. 297
6.3.4 Asymmetric Two-Mode Coupler .................... 300
6.3.4.1 Coupled-Mode Equations ................ 300
6.3.4.2 Analytical Solutions .................. 301
6.4 Fiber-Slab Couplers ................................... 304
6.4.1 Coupled-Mode Equations ......................... 304
6.4.2 Compound-Mode Equations ........................ 307
6.4.3 Coupling Coefficients .......................... 308
6.4.4 Attenuation Coefficients ....................... 309
6.5 Fiber Bending ......................................... 310
6.5.1 Fiber Bend Expression .......................... 310
6.5.2 Effects on Coupling ............................ 311
6.6 Numerical Calculations ................................ 312
6.6.1 Optical and Structural Parameters .............. 312
6.6.1.1 Uniform Fiber-Slab Couplers ........... 312
6.6.1.2 Couplers with Bend Fibers ............. 313
6.7 Results and Discussion ................................ 315
6.7.1 Characteristics of Mode Coupling ............... 317
6.7.2 Characteristics of Ridge Modes ................. 318
6.7.3 Effects of Other Waveguide Parameters .......... 319
6.7.3.1 Effect of Light Wavelength ............ 320
6.7.3.2 Effect of Guide-Layer Size ............ 322
6.7.3.3 Effect of the Refractive Index of
the Cladding .......................... 324
6.7.4 Distributed Coupling ........................... 324
6.7.4.1 Fixing n0 Each Time while Varying
nƒ, with Respect to ns ................ 324
6.7.4.2 Fixing nƒ Each Time while Varying n0 .. 327
6.8 Concluding Remarks .................................... 328
6.8.1 Symmetric and Asymmetric Two-Mode Coupling
Systems ........................................ 328
6.8.2 Uniform Fiber-Slab Coupling Systems ............ 329
6.8.3 Distributed Fiber-Slab Coupling Systems ........ 329
6.9 Problems .............................................. 330
References ................................................. 330
7 Full Coupled-Mode Theory ................................... 333
7.1 Full Coupled-Mode Analysis ............................ 333
7.1.1 Introduction ................................... 333
7.1.2 Two-Mode Couplers .............................. 333
7.1.2.1 Full Coupled-Mode Equations ........... 333
7.1.2.2 Analytical Solutions .................. 334
7.1.3 Fiber-Slab Couplers ............................ 338
7.1.3.1 Full Coupled-Mode Equations ........... 338
7.1.4 Full Compound-Mode Equations ................... 342
7.1.5 Power Conservation ............................. 343
7.1.5.1 Power Conservation Law ................ 343
7.1.5.2 Full Scalar Coupled-Mode Expression ... 344
7.1.6 Numerical Results and Discussion ............... 344
7.1.6.1 Parameters and Computer Programs ...... 345
7.1.6.2 Effects of Higher-Order Terms ......... 345
7.1.6.3 Characteristics of Mode Coupling ...... 350
7.1.6.4 Characteristics of Ridge Modes ........ 350
7.1.7 Concluding Remarks ............................. 354
7.1.7.1 Full CMT of Two-Mode Coupling
Systems ............................... 354
7.1.7.2 Full CMT of Fiber-Slab Coupling
Systems ............................... 355
7.2 Scalar CMT with Vectorial Corrections ................. 355
7.2.1 Introduction ................................... 355
7.2.2 Formulations for Fiber-Slab Couplers ........... 356
7.2.2.1 Field Expression and Index Profile .... 356
7.2.2.2 Coupled-Mode Equations ................ 357
7.2.2.3 Vector-Correcting Coupling
Coefficients .......................... 358
7.2.3 Numerical Results and Discussion ............... 359
7.2.3.1 Effects on Mode Coupling .............. 359
7.2.3.2 Effect of Slab Thickness .............. 360
7.2.3.3 Effects on Coupling Coefficients ...... 362
7.2.3.4 Effects on Compound Modes ............. 363
7.2.4 Concluding Remarks ............................. 364
7.3 Grating-Assisted Fiber-Slab Couplers .................. 365
7.3.1 Introduction ................................... 365
7.3.2 Analytical Formulation ......................... 365
7.3.2.1 Coupled-Mode Equations ................ 365
7.3.2.2 Additional Coupling Coefficients ...... 367
7.3.3 Numerical Results and Discussion ............... 368
7.3.3.1 Effects on Mode Coupling .............. 368
7.3.3.2 Effects of Grating Parameters ......... 369
7.3.4 Conclusions .................................... 372
7.4 Analysis of Nonlinear Waveguide Couplers .............. 373
7.4.1 Nonlinear Two-Mode Couplers .................... 373
7.4.1.1 Power Parameters ...................... 373
7.4.1.2 Simplified CMT ........................ 374
7.4.1.3 Generalized Full CMT .................. 375
7.4.2 Nonlinear Fiber-Slab Couplers .................. 382
7.4.2.1 Simplified Scalar CMT ................. 382
7.4.2.2 Coupling Coefficients ................. 383
7.4.2.3 Power Tuning Effects .................. 384
7.4.3 Concluding Remarks ............................. 386
7.4.3.1 Nonlinear Two-Mode Couplers ........... 386
7.4.3.2 Nonlinear Fiber-Slab Couplers .......... 387
7.5 Coupling in Dual-Core Microstructure Fibers ........... 387
7.5.1 Introduction ................................... 387
7.5.2 Coupling Characteristics ....................... 388
7.5.3 Dual-Core MOF Design without Loss .............. 391
7.5.4 Remarks ........................................ 392
7.6 Problems .............................................. 393
References ................................................. 393
8 Nonlinear Optical Waveguides: Switching, Parametric
Conversion and Systems Applications ........................ 395
8.1 Introduction .......................................... 395
8.2 Formulation of Electromagnetic Wave Equations for
Nonlinear Optical Waveguides .......................... 396
8.2.1 Introductory Remarks ........................... 396
8.2.2 Nonlinear Wave Equations and Constitutive
Relations ...................................... 397
8.2.3 Extended Operator and Penalty Function Method .. 398
8.2.4 Eigenvalues and Methods of Moments ............. 400
8.2.5 Solution Methods for Nonlinear Generalized
Eigenvalue Problems ............................ 403
8.2.5.1 Successive over Relaxation and
Rayleigh Quotient ..................... 403
8.2.5.2 Vector Iteration ...................... 404
8.2.5.3 Posteri Error Estimate ................ 405
8.2.5.4 Nonlinear Acceleration Techniques ..... 406
8.3 Numerical Examples of Nonlinear Optical Waveguides .... 407
8.3.1 Waveguides of Non-Saturation Nonlinear
Permittivity ................................... 407
8.3.1.1 Embedded Channel ...................... 407
8.3.1.2 Overlay Nonlinear Film and Linear
Embedded Channel ...................... 412
8.3.1.3 Waveguides of Nonlinear Permittivity
with Saturation ....................... 415
8.3.1.4 Bistability Phenomena in Nonlinear
Optical Waveguide ..................... 418
8.4 Nonlinear Optical Waveguide for Optical Transmission
Systems ............................................... 421
8.4.1 Introduction ................................... 421
8.4.2 Third-Order Nonlinearity and Propagation
Equation ....................................... 423
8.4.3 Simulation Model ............................... 425
8.4.3.1 Parametric Amplification .............. 425
8.4.3.2 Demultiplexing of the Optical Time
Division Multiplexed Signal ........... 429
8.4.3.3 Triple Correlation Simulation Model ... 432
8.4.3.4 Concluding Remarks .................... 434
8.5 Demultiplexing 320 Gb/s Optical Time Division
Multiplexed-Differential Quadrature Phase Shift
Keying Signals Using Parametric Conversion in
Nonlinear Optical Waveguides .......................... 435
8.5.1 Introduction ................................... 437
8.5.2 Operational Principles ......................... 440
8.5.2.1 Conventional Demultiplexing
Technique ............................. 444
8.5.2.2 Optical Coherent Demultiplexing and
Demodulation .......................... 445
8.5.3 Simulation Models .............................. 446
8.5.3.1 Optical Time Division Multiplexed-
Differential Quadrature Phase Shift
Keying Transmitter .................... 446
8.5.3.2 Fiber Link ............................ 446
8.5.3.3 Demultiplexer and Receiver ............ 446
8.5.3.4 Performance of Optical Time Division
Multiplexed-Differential Quadrature
Phase Shift Keying Receivers: A
Comparison ............................ 448
8.5.4 Influence of Synchronization ................... 448
8.6 Concluding Remarks .................................... 450
8.7 Problems .............................................. 454
References ................................................. 454
9 Integrated Guided-Wave Photonic Transmitters ............... 457
9.1 Introduction .......................................... 457
9.2 Optical Modulators .................................... 458
9.2.1 Phase Modulators ............................... 458
9.2.2 Intensity Modulators ........................... 460
9.2.2.1 Phasor Representation and Transfer
Characteristics ....................... 460
9.2.2.2 Bias Control .......................... 462
9.2.2.3 Chirp Free Optical Modulators ......... 462
9.2.2.4 Structures of Photonic Modulators ..... 464
9.2.2.5 Typical Operational Parameters ........ 464
9.3 Traveling Wave Electrodes for Integrated Modulators ... 465
9.3.1 Introduction ................................... 466
9.3.2 Numerical Formulation .......................... 467
9.3.2.1 Discrete Fields and Potentials ........ 467
9.3.2.2 Electrode Line Capacitance,
Characteristic Impedance and
Microwave Effective Index ............. 469
9.3.2.3 Electric Fields Ex and Ey and the
Overlap Integral ...................... 471
9.3.3 Electrode Simulation and Discussions ........... 471
9.3.3.1 Grid Allocation and Modeling
Performance ........................... 471
9.3.3.2 Model Accuracy ........................ 474
9.3.4 Electro-Optic Overlap Integral ................. 476
9.3.5 Tilted Wall Electrode .......................... 478
9.3.6 Frequency Responses of Phase Modulation by
Single Electrode ............................... 481
9.3.7 Remarks ........................................ 484
9.4 Lithium Niobate Optical Modulators: Devices and
Applications .......................................... 485
9.4.1 Mach-Zehnder Interferometric Modulator and
Ultra-High Speed Advanced Modulation Formats ... 485
9.4.1.1 Amplitude Modulation .................. 486
9.4.1.2 Phase Modulation ...................... 486
9.4.1.3 Frequency Modulation .................. 486
9.4.2 LiNbO3 MZIM Fabrication ........................ 487
9.4.3 Effects of Angled-Wall Structure on RF
Electrodes ..................................... 488
9.4.4 Integrated Modulators and Modulation Formats ... 490
9.4.5 Remarks ........................................ 492
9.5 Generation and Modulation of Optical Pulse Sequences .. 492
9.5.1 Return-to-Zero Optical Pulses .................. 492
9.5.1.1 Generation ............................ 492
9.5.1.2 Phasor Representation ................. 493
9.5.2 Differential Phase Shift Keying ................ 498
9.5.2.1 Background ............................ 498
9.5.2.2 Optical Differential Phase Shift
Keying Transmitter .................... 499
9.6 Generation of Modulation Formats ...................... 500
9.6.1 Amplitude Shift Keying ......................... 500
9.6.1.1 Amplitude-Modulation Amplitude Shift
Keying-Non-Return-to-Zero and
Amplitude Shift Keying-Return-to-
Zero .................................. 500
9.6.1.2 Amplitude-Modulation on-off Keying
Return-to-Zero Formats ................ 501
9.6.1.3 Amplitude-Modulation Carrier-
Suppressed Return-to-Zero Formats ..... 501
9.6.2 Discrete Phase-Modulation Non-Return-to-Zero
Formats ........................................ 503
9.6.2.1 Differential Phase Shift Keying ....... 503
9.6.2.2 Differential Quadrature Phase Shift
Keying ................................ 504
9.6.2.3 M-Ary Amplitude Differential Phase
Shift Keying .......................... 505
9.6.3 Continuous Phase-Modulation (PM)-Non-Return-
to-Zero Formats ................................ 506
9.6.3.1 Linear and Nonlinear Minimum Shift
Keying ................................ 509
9.6.3.2 Minimum Shift Keying as a Special
Case of Continuous Phase Frequency
Shift Keying .......................... 511
9.6.3.3 Minimum Shift Keying as Offset
Differential Quadrature Phase Shift
Keying ................................ 512
9.6.3.4 Configuration of Photonic Minimum
Shift Keying Transmitter Using Two
Cascaded Electro-Optic Phase
Modulators ............................ 512
9.6.3.5 Configuration of Optical Minimum
Shift Keying Transmitter Using Mach-
Zehnder Intensity Modulators: I-Q
Approach .............................. 514
9.6.4 Single Side Band (SSB) Optical Modulators ...... 514
9.7 Problems .............................................. 515
References ................................................. 518
10 Nonlinearity in Guided Wave Devices ........................ 521
10.1 Nonlinear Effects in Integrated Optical Waveguides
for Photonic Signal Processing ........................ 521
10.1.1 Introductory Remarks ........................... 521
10.1.2 Third-Order Nonlinearity and Parametric
Four-Wave Mixing Process ....................... 522
10.1.2.1 Nonlinear Wave Equation ............... 522
10.1.2.2 Four-Wave Mixing Coupled-Wave
Equations ............................. 523
10.1.2.3 Phase Matching ........................ 524
10.1.3 Transmission Models and Nonlinear Guided Wave
Devices ........................................ 525
10.1.4 System Applications of Third-Order Parametric
Nonlinearity in Optical Signal Processing ...... 526
10.1.4.1 Parametric Amplifiers ................. 526
10.1.4.2 Wavelength Conversion and Nonlinear
Phase Conjugation ..................... 530
10.1.4.3 High-Speed Optical Switching .......... 533
10.1.4.4 Triple Correlation .................... 537
10.1.5 Application of Nonlinear Photonics in
Advanced Telecommunications .................... 542
10.1.6 Remarks ........................................ 548
10.2 Nonlinear Effects in Actively Mode-locked Fiber
Lasers ................................................ 549
10.2.1 Introductory Remarks ........................... 549
10.2.2 Laser Model .................................... 549
10.2.2.1 Modeling of the Fiber ................. 550
10.2.2.2 Modeling of the Er:Doped Fiber
Amplifiers ............................ 550
10.2.2.3 Modeling of the Optical Modulator ..... 550
10.2.2.4 Modeling of the Optical Filter ........ 551
10.2.3 Nonlinear Effects in Actively Mode-Locked
Fiber Lasers ................................... 551
10.2.3.1 Zero Detuning ......................... 551
10.2.3.2 Detuning in Actively Mode-Locked
Fiber Laser with Nonlinearity Effect .. 553
10.2.3.3 Pulse Amplitude Equalization in
Harmonic Mode-Locked Fiber Laser ...... 555
10.2.4 Experiments .................................... 556
10.2.4.1 Experimental Setup .................... 556
10.2.4.2 Mode-Locked Pulse Train with 10 GHz
Repetition Rate ....................... 557
10.2.4.3 Pulse Shortening and Spectrum
Broadening under Nonlinearity Effect .. 559
10.2.5 Remarks ............................................. 559
10.3 Nonlinear Photonic Pre-Processing for Bispectrum
Optical Receivers ..................................... 560
10.3.1 Introductory Remarks ........................... 560
10.3.2 Bispectrum Optical Receiver .................... 561
10.3.3 Triple Correlation and Bispectra ............... 561
10.3.3.1 Definition ............................ 561
10.3.3.2 Gaussian Noise Rejection .............. 562
10.3.3.3 Encoding of Phase Information ......... 562
10.3.3.4 Eliminating Gaussian Noise ............ 562
10.3.4 Bispectral Optical Structures .................. 563
10.3.4.1 Principles ............................ 564
10.3.4.2 Technological Implementation .......... 564
10.3.5 Four-Wave Mixing in Highly Nonlinear Media ..... 565
10.3.6 Third Harmonic Conversion ...................... 565
10.3.7 Conservation of Momentum ....................... 565
10.3.8 Estimate of Optical Power Required for Four-
Wave Mixing .................................... 565
10.3.9 Mathematical Principles of Four-Wave Mixing
and the Wave Equations ......................... 566
10.3.9.1 Phenomena of Four-Wave Mixing ......... 566
10.3.9.2 Coupled Equations and Conversion
Efficiency ............................ 567
10.3.9.3 Evolution of Four-Wave Mixing along
the Nonlinear Waveguide Section ....... 568
10.3.10 Transmission and Detection .................... 568
10.3.10.1 Optical Transmission Route and
Simulation Platform .................. 568
10.3.10.2 Four-Wave Mixing and Bispectrum
Receiving ............................ 569
10.3.10.3 Performance .......................... 569
10.3.11 Remarks ....................................... 572
10.4 Raman Effects in Microstructure Optical Fibers or
Photonic Crystal Fibers ............................... 573
10.4.1 Introductory Remarks ........................... 573
10.4.2 Raman Gain in Photonic Crystal Fibers .......... 575
10.4.2.1 Measurement of Raman Gain ............. 575
10.4.2.2 Effective Area and Raman Gain
Coefficient ........................... 576
10.4.3 Remarks ........................................ 582
10.5 Raman Gain of Segmented Core Profile Fibers ........... 582
10.5.1 Segmented-Core Fiber Design for Raman
Amplification .................................. 583
10.5.2 Advantages of Dispersion Compensating Fiber
as a Lumped/Discrete Raman Amplifier (DRA) ..... 583
10.5.3 Spectrum of Raman Amplification ................ 584
10.5.4 Key Equations for Deducing the Raman Gain of
Ge-Doped Silica ................................ 584
10.5.5 Design Methodology for Dispersion
Compensating Fiber - Discrete Raman
Amplifiers ..................................... 586
10.5.6 Design Steps ................................... 589
10.5.7 Sampled Profile Design ......................... 590
10.5.8 Remarks ........................................ 591
10.6 Summary ............................................... 592
References ................................................. 595
Appendix 1 Coordinate System Transformations .................. 601
Appendix 2 Models for Couplers in FORTRAN ..................... 607
Appendix 3 Overlap Integral ................................... 633
Appendix 4 Coupling Coefficients .............................. 637
Appendix 5 Additional Coupling Coefficients ................... 639
Appendix 6 Elliptic Integral .................................. 641
Appendix 7 Integrated Photonics: Fabrication Processes
for LiNbO3 Ultra-Broadband Optical Modulators .............. 643
Appendix 8 Planar Waveguides by Finite Difference Method -
FORTRAN PROGRAMS ........................................... 665
Appendix 9 Interdependence between Electric and Magnetic
Fields and Electromagnetic Waves ........................... 729
Index ......................................................... 743
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