Practical Applications of Microresonators in Optics and Photonics (Optical Science and Engineering)

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PRACTICAL APPLICATIONS OF MICRORESONATORS IN OPTICS AND PHOTONICS......Page 8
Contents......Page 10
Preface......Page 12
Editor......Page 15
Contributors......Page 16
CONTENTS......Page 20
Table of Contents......Page 0
1.1 Introduction......Page 21
1.2.1 2D and 3D Photonic Crystals......Page 22
1.2.2 Ultrasmall Cavity: Photonic Crystal Nanocavity......Page 25
1.3.1 Design of High-Q Photonic Crystal Nanocavity......Page 26
1.3.2 Waveguide-Coupled High-Q Photonic Crystal Nanocavity......Page 27
1.3.3.1 Line Defect Cavities with Modulated End-Holes......Page 28
1.3.3.2 Point Defect Hexapole Cavity with Rotational Symmetry Confinement......Page 31
1.3.3.3 Width-Modulated Line Defect Cavity with Mode-Gap Confinement......Page 35
1.3.3.4 Other Photonic Crystal Nanocavities......Page 36
1.3.4 Discussion of Structural Error and Q......Page 38
1.4.1 Spectral Domain Measurement......Page 39
1.4.1.2 Spectrum Measurement using Electro-Optic Frequency Shifter......Page 40
1.4.2 Time Domain Measurement......Page 42
1.4.3 Technical Issues Related to Obtaining Accurate Q......Page 44
1.5.1.2 Slow Light with Photonic Crystal Nanocavity......Page 45
1.5.2 Compact Optical Add-Drop Filter......Page 49
1.5.3 All-Optical Switching......Page 50
1.5.3.1 Switching by Thermo-Optic Effect......Page 51
1.5.3.2 Switching by Carrier Plasma Dispersion Effect......Page 53
1.5.3.3 Numerical Study of Carrier Dynamics in Silicon Photonic Crystal......Page 54
1.5.3.4 5-GHz Return-to-Zero Pulse Train Modulation......Page 57
1.5.3.5 Accelerating the Speed of All-Optical Switches using Ion-Implantation Technology......Page 58
1.5.4 Ultra-Low Power Bistable Memory......Page 60
1.5.5.1 Optical Flip-Flop......Page 64
1.5.5.2 Pulse Retiming Circuit......Page 66
References......Page 67
CONTENTS......Page 72
2.1 Introduction......Page 73
2.2 Design and Fabrication......Page 77
2.2.1 Design of Pillar Microcavities......Page 78
2.2.2 Growth of QDs......Page 84
2.2.3.1 First Generation......Page 87
2.2.3.2 Second Generation......Page 88
2.3 Device Characterization......Page 91
2.3.1 Modifying Single QD Spontaneous Emission......Page 92
2.3.1.1 First and Second Generation......Page 93
2.3.1.2 Third Generation......Page 98
2.3.2 Photon Statistics......Page 99
2.3.2.1 Mechanism for Single-Photon Generation in QDs......Page 100
2.3.2.2 Experimental Results with Pillar DBR Devices......Page 102
2.3.3 Efficiency......Page 105
2.3.4 Photon Indistinguishability......Page 108
2.3.5 Strong Coupling......Page 114
2.4 Applications......Page 117
2.4.1 BB84 Quantum Key Distribution......Page 118
2.4.2 Entanglement Generation without a “True” Interaction......Page 121
2.4.3 Single-Mode Teleportation......Page 127
2.4.4 Coherent Single-Photon Emission and Trapping......Page 133
2.4.4.1 Coherent Photon Generation in Ideal Systems......Page 134
2.4.4.2 Performance of Practical Systems......Page 138
2.4.4.4 Mathematical Details of the Theory......Page 139
2.5 Conclusions......Page 144
References......Page 145
CONTENTS......Page 152
3.1 Introduction......Page 153
3.2 Fabrication Technique......Page 154
3.3.1 Critical Coupling......Page 156
3.3.2 Prism......Page 158
3.3.4 Fiber Taper......Page 161
3.3.5 Planar Coupling......Page 162
3.4 Modal Structure and Spectrum Engineering......Page 163
3.4.1 The Spectrum and the Shape of the Resonator......Page 164
3.4.2 White Light Resonators......Page 166
3.4.3 Single-Mode Resonators......Page 170
3.4.4 Elliptical Resonators......Page 174
3.5 Quality Factor and Finesse of Crystalline Resonators......Page 176
3.5.1 Fundamental Limits......Page 181
3.5.2 Technical Limits......Page 183
3.6 Filters and Their Applications......Page 185
3.6.1 First-Order Filters......Page 186
3.6.2 Periodical Poling and Reconfigurable Filters......Page 188
3.6.3 Third-Order Filters......Page 190
3.6.5 Sixth-Order Filters......Page 193
3.6.6 Tuning of the Multi-Resonator Filter......Page 194
3.6.8 Insertion Loss......Page 197
3.6.9 Vertically Coupled Resonators......Page 199
3.6.10.1 Opto-Electronic Oscillator......Page 203
3.6.10.2 Microwave Photonic Receivers......Page 204
3.7 Frequency Stability of WGM Resonators......Page 206
3.7.1.1 Thermorefractive Fluctuations: Steady State......Page 208
3.7.1.2 Thermorefractive Fluctuations: Spectrum......Page 209
3.7.1.4 Thermoelastic Fluctuations: Spectrum......Page 212
3.7.1.5 Thermal Expansion Fluctuations: Spectrum......Page 213
3.7.2.1 Photothermal Fluctuations......Page 215
3.7.2.2 Ponderomotive Fluctuations......Page 216
3.7.3 Stabilization Scheme: An Example......Page 217
3.7.4 Applications for Laser Stabilization......Page 218
3.8 Conclusion......Page 219
References......Page 220
CONTENTS......Page 229
4.1 Introduction......Page 230
4.2.1 Overview of Polygonal-Shaped Microresonators......Page 232
4.2.2 N-Bounce Orbits in Polygonal-Shaped Microresonators......Page 234
4.2.3 Modes in Square-Shaped Microdisk Resonators......Page 235
4.2.4 Directional Coupling via Polygonal-Shaped Microdisk Flat Sidewalls......Page 240
4.2.5 Sharp Corner Radiative Loss and Corner Rounding......Page 243
4.2.6 Experimental Demonstrations......Page 244
4.3.1 Overview of Spiral-Shaped Microresonators......Page 245
4.3.2 Numerical Simulations......Page 248
4.3.3 Experimental Demonstrations......Page 251
4.3.4 Tilted Notch-Coupled Waveguide Design for Mode Matching......Page 254
4.4.1 Overview of Silicon Electro-Optic Modulators......Page 256
4.4.2 Principle of Microresonator-Based Modulators......Page 257
4.4.3 Microdisk Resonator-Based Modulators......Page 258
4.4.3.2 Toward GHz-Speed Microdisk Resonator-Based Modulators......Page 259
4.5.1 Overview of Coherent Interference in Photonic Resonators......Page 262
4.5.2 Reconfigurable Microring Resonator-Based Add-Drop Filters Using Fano Resonances......Page 263
4.5.3.1 Coherent Feedback-Coupled Filters......Page 266
4.5.3.2 Coherent Feedback-Coupled Modulators and Logic Devices......Page 271
4.5.3.2.1 Modulators with Tunable Operating Wavelengths and Extinction Ratios......Page 272
4.5.3.2.2 Demonstration of OR-logic Functionality......Page 273
4.6 Summary and Outlook......Page 274
References......Page 275
CONTENTS......Page 282
5.1 Introduction......Page 283
5.2.1 Ring Resonator Basics......Page 284
5.2.2 Electro-Optic Ring Modulators......Page 287
5.2.3 Bandwidth of Ring Resonant Modulators......Page 288
5.2.3.2 Traveling Wave Electrode......Page 289
5.2.4.2 Optical and Electro-Optical Properties......Page 294
5.2.4.3 Traveling Wave Electrode Properties......Page 295
5.2.4.4 Modulation at the First FSR Spacing of 28 GHz......Page 297
5.2.4.5 Modulation at Multiples of the FSR......Page 300
5.3.1.1 Fundamentals of OSP......Page 303
5.3.1.2 Representations of OSP......Page 305
5.3.1.3 Operations of OSP......Page 306
5.3.2 Structure......Page 307
5.3.3 Analysis......Page 308
5.3.3.2 Racetrack......Page 309
5.3.3.4 One-Block OSP......Page 310
5.3.4 Verification and Operation......Page 312
5.3.4.1 Racetrack......Page 313
5.3.4.2 Configurable Couplers......Page 314
5.3.4.3 MZ Phase Shifter......Page 315
5.3.4.4 Summary of One-Block OSP......Page 316
5.3.4.5 Pole/Zero Locations Using One-Block OSP......Page 317
5.3.4.6 DC Operation......Page 318
5.3.5.1 Arbitrary Waveform Generator......Page 321
5.3.5.2 Linearized Modulator......Page 323
5.3.5.3 True-Time-Delay Element......Page 324
5.3.5.4 Discrete-Time Applications of OSP......Page 327
References......Page 330
CONTENTS......Page 333
6.2.1 Context......Page 334
6.2.2 Basic Elements......Page 336
6.3 Polymer-Based Technology and Process......Page 340
6.3.1 Materials......Page 341
6.3.2 Etching Methods......Page 342
6.4.1 Background......Page 343
6.4.2 Various Set-Up......Page 344
6.4.3 Spectra......Page 345
6.5 Theoretical Approaches......Page 349
6.5.1 General Methodology......Page 350
6.5.2 Spectrum......Page 351
6.5.3 Directions of Emission......Page 356
6.5.4.1 Benefit of “Scarring”......Page 360
6.5.4.2 Perturbation Approach......Page 362
6.6 Conclusion......Page 364
Appendix A: Lyapounov Coefficient for Unstable Periodic Orbits......Page 365
References......Page 366
7.1 Introduction......Page 370
7.2 Microfiber Photonics......Page 371
7.3.1 Theory of an MLR......Page 374
7.3.1.1 Transmission Amplitude......Page 375
7.3.1.2 Q-Factor, Extinction Ratio, and Finesse......Page 376
7.3.1.3 Models of Directional Coupling......Page 377
7.3.2.1 MLR Fabricated by Macro-Manipulation......Page 378
7.3.2.1.1 Transmission Spectrum......Page 379
7.3.2.1.2 Ultra-Fast Direct Contact Gas Temperature Sensor......Page 381
7.3.2.2.1 Transmission Spectrum......Page 383
7.4 Microfiber Coil Resonator (MCR)......Page 385
7.4.1 Theory of an MCR......Page 386
7.4.1.2 Uniform MCR......Page 387
7.4.1.3 MCR Transmission Line......Page 388
7.4.2.1 MCR in Air......Page 390
7.4.2.2 MCR in Low-Index Polymer......Page 392
7.4.2.3 MCR Microfluidic Sensor......Page 393
7.5 Conclusion......Page 395
References......Page 396
CONTENTS......Page 399
8.1.2 Optical Ring Resonator Biosensors......Page 400
8.1.3 Opto-Fluidic Ring Resonator (OFRR) Biosensors......Page 402
8.2.1 Model......Page 403
8.2.2 Bulk Refractive Index Sensitivity (BRIS)......Page 404
8.2.2.2 Mode Number Dependence......Page 405
8.2.3.1 Thermally Induced Noise......Page 407
8.2.3.2 Amplitude Noise......Page 408
8.2.3.3 Pressure Induced Noise......Page 409
8.2.3 Relation between BRIS and the Sensitivity to Molecule Binding......Page 410
8.2.4 Detection Limit......Page 411
8.3.1 OFRR Fabrication......Page 412
8.3.2 Experimental Setup......Page 413
8.3.3 Q-Factor of the OFRR......Page 414
8.3.5 Characterization of Thermally-Induced Noise......Page 415
8.3.6 Surface Activation......Page 416
8.3.7.1 Protein Detection......Page 417
8.3.7.2 DNA Detection......Page 419
8.3.7.4 Bacterium and Whole Cell Detection......Page 421
8.3.8 Integration with Microfluidics......Page 423
8.3.9.1 Integration with Antiresonant Reflecting Optical Waveguide (ARROW)......Page 425
8.3.9.2 Integration with Metal-Clad Waveguide......Page 426
Acknowledgments......Page 427
References......Page 428
CONTENTS......Page 435
9.1 Introduction......Page 436
9.2 The ADNERF Concept......Page 437
9.3 Immunity to High EM Fields......Page 439
9.4 Thermal Consideration......Page 440
9.6 Receiver Sensitivity......Page 442
9.7 Choice of EO Material......Page 444
9.8 Receiver Dynamic Range......Page 445
9.9 RF Gain in the Optical Front-End......Page 446
9.10 Heterogeneous Dielectric Antenna for Wideband Operation......Page 447
9.12 EO Resonator Design: Whispering Gallery Versus Fabry–Perot......Page 448
9.14 Maximum Power in Disk and Ring Resonators......Page 450
9.17 Competing Technologies......Page 451
9.18 Summary......Page 454
A.1 Equivalent Epi of resonant Modulators......Page 455
A.2 Dynamic Range of Resonant EO Field Sensors......Page 456
A.4 Biasing for Minimum Distortion......Page 457
Appendix B: RF Gain in the Optical Front-End......Page 458
References......Page 459
10.1 Introduction......Page 461
10.2.1 Coupled Mode Equations......Page 464
10.2.2 Modifications due to Dynamic Back-action: Method of Retardation Expansion......Page 466
10.2.3 Sideband Formalism......Page 471
10.3.1 Mechanical Modes of Optical Microcavities......Page 476
10.3.2 Measuring the Opto-mechanical Response......Page 478
10.3.3 Displacement Sensitivity......Page 479
10.4.1 Threshold and Mode Selection Mechanisms......Page 480
10.4.2 Threshold Dependence on Optical Q and Mechanical Q......Page 481
10.5.1 Experimental Setup......Page 485
10.5.2 Experimental Observation of Cooling......Page 486
10.5.3 Quantum Limits of Radiation Pressure Back-action Cooling......Page 490
10.5.4 Physical Interpretation of the Quantum limits of Back-action Cooling......Page 491
10.6 Summary and Outlook......Page 492
References......Page 494
11.1 Introduction to Optical Frequency Combs......Page 497
11.2.1 Physics of the Comb Generation Process......Page 499
11.2.2.1 Multiheterodyne Spectroscopy......Page 502
11.2.2.2 Proving the Equidistance of the Mode Spacing at the mHz Level......Page 503
11.2.3 Dispersion in Toroidal Microresonators......Page 505
11.3 Stabilization of the Comb......Page 507
11.3.1 Principle......Page 508
11.3.2 Implementation......Page 509
11.3.3 Characterization of the Locking Mechanism......Page 510
11.3.4 Actuation Properties......Page 512
11.4 Generation of a Stabilized Microwave Repetition Rate Frequency Comb......Page 513
11.4.1 Monolithic Frequency Comb Generators with Microwave Repetition Rate......Page 514
11.4.2 Stabilization and Characterization of a Microwave Frequency Comb......Page 515
11.5 Conclusion......Page 517
References......Page 518
12.1 Introduction......Page 521
12.2 Single and Coupled Microresonators as Optical Delay Elements......Page 522
12.3 Single and Coupled Microresonators as Optical Switches......Page 527
12.4 Loss and GDD Limitations in CRS Delay Lines......Page 532
12.5 Mitigation of GDD......Page 538
12.6 Conclusions......Page 540
References......Page 541
13.1 Introduction......Page 543
13.2.2 Dispersion Relationship......Page 545
13.2.3 Tail of the Dispersion Relationship......Page 546
13.3 Localization in the Presence of Disorder......Page 548
13.4.1 Quadratic Dispersion at the Band Edge......Page 553
13.4.2 The Nonlinear Evolution Equation......Page 554
13.4.3 Time-Invariant Evolution......Page 555
13.4.4 The “Super-Resonant” Mode......Page 556
13.4.5 Nonlinear Anderson Localization......Page 558
13.5.1 Slow Light in Fabry–Perot and Gires–Tournois Resonators......Page 559
13.5.2 Slow Light in the Coupled Fabry–Perot Structure......Page 561
13.5.3 Advantages and Disadvantages of the Nested Architecture......Page 562
13.6 Summary......Page 564
References......Page 565