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

PRACTICAL APPLICATIONS OF MICRORESONATORS IN OPTICS AND PHOTONICS......Page 7
Contents......Page 9
Preface......Page 11
Editor......Page 14
Contributors......Page 15
Table of Contents......Page 0
CONTENTS......Page 19
1.1 Introduction......Page 20
1.2.1 2D and 3D Photonic Crystals......Page 21
1.2.2 Ultrasmall Cavity: Photonic Crystal Nanocavity......Page 24
1.3.1 Design of High-Q Photonic Crystal Nanocavity......Page 25
1.3.2 Waveguide-Coupled High-Q Photonic Crystal Nanocavity......Page 26
1.3.3.1 Line Defect Cavities with Modulated End-Holes......Page 27
1.3.3.2 Point Defect Hexapole Cavity with Rotational Symmetry Confinement......Page 30
1.3.3.3 Width-Modulated Line Defect Cavity with Mode-Gap Confinement......Page 34
1.3.3.4 Other Photonic Crystal Nanocavities......Page 35
1.3.4 Discussion of Structural Error and Q......Page 37
1.4.1 Spectral Domain Measurement......Page 38
1.4.1.2 Spectrum Measurement using Electro-Optic Frequency Shifter......Page 39
1.4.2 Time Domain Measurement......Page 41
1.4.3 Technical Issues Related to Obtaining Accurate Q......Page 43
1.5.1.2 Slow Light with Photonic Crystal Nanocavity......Page 44
1.5.2 Compact Optical Add-Drop Filter......Page 48
1.5.3 All-Optical Switching......Page 49
1.5.3.1 Switching by Thermo-Optic Effect......Page 50
1.5.3.2 Switching by Carrier Plasma Dispersion Effect......Page 52
1.5.3.3 Numerical Study of Carrier Dynamics in Silicon Photonic Crystal......Page 53
1.5.3.4 5-GHz Return-to-Zero Pulse Train Modulation......Page 56
1.5.3.5 Accelerating the Speed of All-Optical Switches using Ion-Implantation Technology......Page 57
1.5.4 Ultra-Low Power Bistable Memory......Page 59
1.5.5.1 Optical Flip-Flop......Page 63
1.5.5.2 Pulse Retiming Circuit......Page 65
References......Page 66
CONTENTS......Page 71
2.1 Introduction......Page 72
2.2 Design and Fabrication......Page 76
2.2.1 Design of Pillar Microcavities......Page 77
2.2.2 Growth of QDs......Page 83
2.2.3.1 First Generation......Page 86
2.2.3.2 Second Generation......Page 87
2.3 Device Characterization......Page 90
2.3.1 Modifying Single QD Spontaneous Emission......Page 91
2.3.1.1 First and Second Generation......Page 92
2.3.1.2 Third Generation......Page 97
2.3.2 Photon Statistics......Page 98
2.3.2.1 Mechanism for Single-Photon Generation in QDs......Page 99
2.3.2.2 Experimental Results with Pillar DBR Devices......Page 101
2.3.3 Efficiency......Page 104
2.3.4 Photon Indistinguishability......Page 107
2.3.5 Strong Coupling......Page 113
2.4 Applications......Page 116
2.4.1 BB84 Quantum Key Distribution......Page 117
2.4.2 Entanglement Generation without a “True” Interaction......Page 120
2.4.3 Single-Mode Teleportation......Page 126
2.4.4 Coherent Single-Photon Emission and Trapping......Page 132
2.4.4.1 Coherent Photon Generation in Ideal Systems......Page 133
2.4.4.2 Performance of Practical Systems......Page 137
2.4.4.4 Mathematical Details of the Theory......Page 138
2.5 Conclusions......Page 143
References......Page 144
CONTENTS......Page 151
3.1 Introduction......Page 152
3.2 Fabrication Technique......Page 153
3.3.1 Critical Coupling......Page 155
3.3.2 Prism......Page 157
3.3.4 Fiber Taper......Page 160
3.3.5 Planar Coupling......Page 161
3.4 Modal Structure and Spectrum Engineering......Page 162
3.4.1 The Spectrum and the Shape of the Resonator......Page 163
3.4.2 White Light Resonators......Page 165
3.4.3 Single-Mode Resonators......Page 169
3.4.4 Elliptical Resonators......Page 173
3.5 Quality Factor and Finesse of Crystalline Resonators......Page 175
3.5.1 Fundamental Limits......Page 180
3.5.2 Technical Limits......Page 182
3.6 Filters and Their Applications......Page 184
3.6.1 First-Order Filters......Page 185
3.6.2 Periodical Poling and Reconfigurable Filters......Page 187
3.6.3 Third-Order Filters......Page 189
3.6.5 Sixth-Order Filters......Page 192
3.6.6 Tuning of the Multi-Resonator Filter......Page 193
3.6.8 Insertion Loss......Page 196
3.6.9 Vertically Coupled Resonators......Page 198
3.6.10.1 Opto-Electronic Oscillator......Page 202
3.6.10.2 Microwave Photonic Receivers......Page 203
3.7 Frequency Stability of WGM Resonators......Page 205
3.7.1.1 Thermorefractive Fluctuations: Steady State......Page 207
3.7.1.2 Thermorefractive Fluctuations: Spectrum......Page 208
3.7.1.4 Thermoelastic Fluctuations: Spectrum......Page 211
3.7.1.5 Thermal Expansion Fluctuations: Spectrum......Page 212
3.7.2.1 Photothermal Fluctuations......Page 214
3.7.2.2 Ponderomotive Fluctuations......Page 215
3.7.3 Stabilization Scheme: An Example......Page 216
3.7.4 Applications for Laser Stabilization......Page 217
3.8 Conclusion......Page 218
References......Page 219
CONTENTS......Page 228
4.1 Introduction......Page 229
4.2.1 Overview of Polygonal-Shaped Microresonators......Page 231
4.2.2 N-Bounce Orbits in Polygonal-Shaped Microresonators......Page 233
4.2.3 Modes in Square-Shaped Microdisk Resonators......Page 234
4.2.4 Directional Coupling via Polygonal-Shaped Microdisk Flat Sidewalls......Page 239
4.2.5 Sharp Corner Radiative Loss and Corner Rounding......Page 242
4.2.6 Experimental Demonstrations......Page 243
4.3.1 Overview of Spiral-Shaped Microresonators......Page 244
4.3.2 Numerical Simulations......Page 247
4.3.3 Experimental Demonstrations......Page 250
4.3.4 Tilted Notch-Coupled Waveguide Design for Mode Matching......Page 253
4.4.1 Overview of Silicon Electro-Optic Modulators......Page 255
4.4.2 Principle of Microresonator-Based Modulators......Page 256
4.4.3 Microdisk Resonator-Based Modulators......Page 257
4.4.3.2 Toward GHz-Speed Microdisk Resonator-Based Modulators......Page 258
4.5.1 Overview of Coherent Interference in Photonic Resonators......Page 261
4.5.2 Reconfigurable Microring Resonator-Based Add-Drop Filters Using Fano Resonances......Page 262
4.5.3.1 Coherent Feedback-Coupled Filters......Page 265
4.5.3.2 Coherent Feedback-Coupled Modulators and Logic Devices......Page 270
4.5.3.2.1 Modulators with Tunable Operating Wavelengths and Extinction Ratios......Page 271
4.5.3.2.2 Demonstration of OR-logic Functionality......Page 272
4.6 Summary and Outlook......Page 273
References......Page 274
CONTENTS......Page 281
5.1 Introduction......Page 282
5.2.1 Ring Resonator Basics......Page 283
5.2.2 Electro-Optic Ring Modulators......Page 286
5.2.3 Bandwidth of Ring Resonant Modulators......Page 287
5.2.3.2 Traveling Wave Electrode......Page 288
5.2.4.2 Optical and Electro-Optical Properties......Page 293
5.2.4.3 Traveling Wave Electrode Properties......Page 294
5.2.4.4 Modulation at the First FSR Spacing of 28 GHz......Page 296
5.2.4.5 Modulation at Multiples of the FSR......Page 299
5.3.1.1 Fundamentals of OSP......Page 302
5.3.1.2 Representations of OSP......Page 304
5.3.1.3 Operations of OSP......Page 305
5.3.2 Structure......Page 306
5.3.3 Analysis......Page 307
5.3.3.2 Racetrack......Page 308
5.3.3.4 One-Block OSP......Page 309
5.3.4 Verification and Operation......Page 311
5.3.4.1 Racetrack......Page 312
5.3.4.2 Configurable Couplers......Page 313
5.3.4.3 MZ Phase Shifter......Page 314
5.3.4.4 Summary of One-Block OSP......Page 315
5.3.4.5 Pole/Zero Locations Using One-Block OSP......Page 316
5.3.4.6 DC Operation......Page 317
5.3.5.1 Arbitrary Waveform Generator......Page 320
5.3.5.2 Linearized Modulator......Page 322
5.3.5.3 True-Time-Delay Element......Page 323
5.3.5.4 Discrete-Time Applications of OSP......Page 326
References......Page 329
CONTENTS......Page 332
6.2.1 Context......Page 333
6.2.2 Basic Elements......Page 335
6.3 Polymer-Based Technology and Process......Page 339
6.3.1 Materials......Page 340
6.3.2 Etching Methods......Page 341
6.4.1 Background......Page 342
6.4.2 Various Set-Up......Page 343
6.4.3 Spectra......Page 344
6.5 Theoretical Approaches......Page 348
6.5.1 General Methodology......Page 349
6.5.2 Spectrum......Page 350
6.5.3 Directions of Emission......Page 355
6.5.4.1 Benefit of “Scarring”......Page 359
6.5.4.2 Perturbation Approach......Page 361
6.6 Conclusion......Page 363
Appendix A: Lyapounov Coefficient for Unstable Periodic Orbits......Page 364
References......Page 365
7.1 Introduction......Page 369
7.2 Microfiber Photonics......Page 370
7.3.1 Theory of an MLR......Page 373
7.3.1.1 Transmission Amplitude......Page 374
7.3.1.2 Q-Factor, Extinction Ratio, and Finesse......Page 375
7.3.1.3 Models of Directional Coupling......Page 376
7.3.2.1 MLR Fabricated by Macro-Manipulation......Page 377
7.3.2.1.1 Transmission Spectrum......Page 378
7.3.2.1.2 Ultra-Fast Direct Contact Gas Temperature Sensor......Page 380
7.3.2.2.1 Transmission Spectrum......Page 382
7.4 Microfiber Coil Resonator (MCR)......Page 384
7.4.1 Theory of an MCR......Page 385
7.4.1.2 Uniform MCR......Page 386
7.4.1.3 MCR Transmission Line......Page 387
7.4.2.1 MCR in Air......Page 389
7.4.2.2 MCR in Low-Index Polymer......Page 391
7.4.2.3 MCR Microfluidic Sensor......Page 392
7.5 Conclusion......Page 394
References......Page 395
CONTENTS......Page 398
8.1.2 Optical Ring Resonator Biosensors......Page 399
8.1.3 Opto-Fluidic Ring Resonator (OFRR) Biosensors......Page 401
8.2.1 Model......Page 402
8.2.2 Bulk Refractive Index Sensitivity (BRIS)......Page 403
8.2.2.2 Mode Number Dependence......Page 404
8.2.3.1 Thermally Induced Noise......Page 406
8.2.3.2 Amplitude Noise......Page 407
8.2.3.3 Pressure Induced Noise......Page 408
8.2.3 Relation between BRIS and the Sensitivity to Molecule Binding......Page 409
8.2.4 Detection Limit......Page 410
8.3.1 OFRR Fabrication......Page 411
8.3.2 Experimental Setup......Page 412
8.3.3 Q-Factor of the OFRR......Page 413
8.3.5 Characterization of Thermally-Induced Noise......Page 414
8.3.6 Surface Activation......Page 415
8.3.7.1 Protein Detection......Page 416
8.3.7.2 DNA Detection......Page 418
8.3.7.4 Bacterium and Whole Cell Detection......Page 420
8.3.8 Integration with Microfluidics......Page 422
8.3.9.1 Integration with Antiresonant Reflecting Optical Waveguide (ARROW)......Page 424
8.3.9.2 Integration with Metal-Clad Waveguide......Page 425
Acknowledgments......Page 426
References......Page 427
CONTENTS......Page 434
9.1 Introduction......Page 435
9.2 The ADNERF Concept......Page 436
9.3 Immunity to High EM Fields......Page 438
9.4 Thermal Consideration......Page 439
9.6 Receiver Sensitivity......Page 441
9.7 Choice of EO Material......Page 443
9.8 Receiver Dynamic Range......Page 444
9.9 RF Gain in the Optical Front-End......Page 445
9.10 Heterogeneous Dielectric Antenna for Wideband Operation......Page 446
9.12 EO Resonator Design: Whispering Gallery Versus Fabry–Perot......Page 447
9.14 Maximum Power in Disk and Ring Resonators......Page 449
9.17 Competing Technologies......Page 450
9.18 Summary......Page 453
A.1 Equivalent Epi of resonant Modulators......Page 454
A.2 Dynamic Range of Resonant EO Field Sensors......Page 455
A.4 Biasing for Minimum Distortion......Page 456
Appendix B: RF Gain in the Optical Front-End......Page 457
References......Page 458
10.1 Introduction......Page 460
10.2.1 Coupled Mode Equations......Page 463
10.2.2 Modifications due to Dynamic Back-action: Method of Retardation Expansion......Page 465
10.2.3 Sideband Formalism......Page 470
10.3.1 Mechanical Modes of Optical Microcavities......Page 475
10.3.2 Measuring the Opto-mechanical Response......Page 477
10.3.3 Displacement Sensitivity......Page 478
10.4.1 Threshold and Mode Selection Mechanisms......Page 479
10.4.2 Threshold Dependence on Optical Q and Mechanical Q......Page 480
10.5.1 Experimental Setup......Page 484
10.5.2 Experimental Observation of Cooling......Page 485
10.5.3 Quantum Limits of Radiation Pressure Back-action Cooling......Page 489
10.5.4 Physical Interpretation of the Quantum limits of Back-action Cooling......Page 490
10.6 Summary and Outlook......Page 491
References......Page 493
11.1 Introduction to Optical Frequency Combs......Page 496
11.2.1 Physics of the Comb Generation Process......Page 498
11.2.2.1 Multiheterodyne Spectroscopy......Page 501
11.2.2.2 Proving the Equidistance of the Mode Spacing at the mHz Level......Page 502
11.2.3 Dispersion in Toroidal Microresonators......Page 504
11.3 Stabilization of the Comb......Page 506
11.3.1 Principle......Page 507
11.3.2 Implementation......Page 508
11.3.3 Characterization of the Locking Mechanism......Page 509
11.3.4 Actuation Properties......Page 511
11.4 Generation of a Stabilized Microwave Repetition Rate Frequency Comb......Page 512
11.4.1 Monolithic Frequency Comb Generators with Microwave Repetition Rate......Page 513
11.4.2 Stabilization and Characterization of a Microwave Frequency Comb......Page 514
11.5 Conclusion......Page 516
References......Page 517
12.1 Introduction......Page 520
12.2 Single and Coupled Microresonators as Optical Delay Elements......Page 521
12.3 Single and Coupled Microresonators as Optical Switches......Page 526
12.4 Loss and GDD Limitations in CRS Delay Lines......Page 531
12.5 Mitigation of GDD......Page 537
12.6 Conclusions......Page 539
References......Page 540
13.1 Introduction......Page 542
13.2.2 Dispersion Relationship......Page 544
13.2.3 Tail of the Dispersion Relationship......Page 545
13.3 Localization in the Presence of Disorder......Page 547
13.4.1 Quadratic Dispersion at the Band Edge......Page 552
13.4.2 The Nonlinear Evolution Equation......Page 553
13.4.3 Time-Invariant Evolution......Page 554
13.4.4 The “Super-Resonant” Mode......Page 555
13.4.5 Nonlinear Anderson Localization......Page 557
13.5.1 Slow Light in Fabry–Perot and Gires–Tournois Resonators......Page 558
13.5.2 Slow Light in the Coupled Fabry–Perot Structure......Page 560
13.5.3 Advantages and Disadvantages of the Nested Architecture......Page 561
13.6 Summary......Page 563
References......Page 564