1. Introduction to Optical Microsystems ......................... 1
1.1. Scaling of Optics ....................................... 1
1.2. Design of miniaturized optics ........................... 3
1.3. Roadmap ................................................. 4
References ................................................... 8
2. Electromagnetic Fields ands Energy .......................... 10
2.1. Introduction to Fields and Energy ...................... 10
2.2. From Maxwell's Equations to the Wave Equation .......... 11
2.3. Plane Waves ............................................ 14
2.4. Phasor Notation ........................................ 18
2.4.1. Michelson Interferometer-Phasor notation ........ 20
2.5. The Poynting Theorem ................................... 23
2.6. Combination of Optical Fields from Separate Sources .... 26
2.7. Analysis Based on Energy Conservation - Examples ....... 28
2.7.1. "Collimated optical beam" ....................... 28
2.7.2. Combination of optical beams - Fan-in ........... 29
2.7.3. Optical devices with two inputs and two
outputs - General Case .......................... 30
2.7.4. Dielectric interface ............................ 31
2.7.5. Y-coupler ....................................... 32
2.7.6. Fan-in loss ..................................... 33
2.7.7. Practical beam combiner ......................... 34
2.7.8. Wavelength Division Multiplexing ................ 34
2.8. Summary of Fields and Waves ............................ 36
Further Reading ............................................. 38
Exercises ................................................... 38
3. Plane Waves at Interfaces ................................... 42
3.1. Introduction to Plane Waves ............................ 42
3.2. Plane Waves at a Dielectric Interface - Fresnel
Reflections ............................................ 43
3.2.1. Laws of Reflection and Refraction
(Geometrical Optics) ............................ 43
3.2.2. Fresnel Equations ............................... 45
3.2.3. Numerical Evaluation of the Fresnel Equations ... 48
3.2.3. Reflectance and Transmittance ................... 50
3.2.4. Brewster Angle .................................. 51
3.3. Wave description of Total Internal Reflection (TIR) .... 52
3.3.1. Evanescent Fields ............................... 53
3.3.2. Goos-Hanchen Shift .............................. 55
3.3.3. Optical Devices Based on TIR .................... 55
3.4. Multilayer Stacks ...................................... 57
3.5. Applications of Layered Structures ..................... 60
3.5.1. Anti-Reflection Coatings ........................ 61
3.5.2. Bragg reflectors ................................ 62
3.5.3. Photon Tunneling ................................ 63
3.5.4. Surface Plasmons ................................ 65
3.6. Summary of Plane Waves ................................. 67
Exercises ................................................... 69
References .................................................. 75
4. Diffraction and Gaussian Beams .............................. 76
4.1. Introduction to Diffraction and Gaussian Beams ......... 76
4.2. Paraxial Wave Equation ................................. 77
4.2.1. The Fundamental Gaussian Profile ................ 78
4.2.2. Beam Waist ...................................... 79
4.2.3. Higher Order Gaussian Modes ..................... 81
4.3. Gaussian Beam Transformation in Lenses ................. 84
4.4. Resolution of a Lens ................................... 89
4.4.1. Focusing into high-index media .................. 91
4.5. Projecting Gaussian Beams .............................. 95
4.6. Gaussian Beam "Imaging" ................................ 96
4.6.1. Graphical Description of Gaussian Beam
"Imaging" ....................................... 98
4.7. Truncation of Gaussian Beams ........................... 99
4.7.1. Energy loss due to Truncation of Gaussian
Beams .......................................... 100
4.7.2. Far-field of Truncated Gaussian Beams -
Frauenhofer Diffraction ........................ 103
4.8. Summary of Gaussian Beams ............................. 107
Further Reading ............................................ 110
Exercises .................................................. 1ll
References ................................................. 114
5. Optical Fibers and Waveguides .............................. 116
5.1. Introduction to Fibers and Waveguides ................. 116
5.2. Geometrical optics description of waveguides .......... 116
5.3. Three-layered Slab Waveguide .......................... 118
5.3.1. Numerical Solutions to Eigenvalue Equations .... 121
5.3.2. TM Solutions ................................... 122
5.3.3. Nature of the Solutions ........................ 122
5.3.4. Number of Modes ................................ 123
5.3.5. Energy carried by a mode ....................... 125
5.3.6. Properties of Modes ............................ 126
5.3.7. Normalized propagation parameters .............. 127
5.4. Optical Fibers ........................................ 129
5.4.1. Modes in Step-Index Optical Fibers ............. 130
5.4.2. Linearly Polarized Modes ....................... 131
5.4.3. The Fundamental Mode of a Cylindrical
Waveguide ...................................... 135
5.4.4. Power Confinement .............................. 136
5.5. Dispersion ............................................ 137
5.5.1. Material Dispersion ............................ 138
5.5.1.1. Frequency Dependent Dielectric
Constant .............................. 140
5.5.1.2. Group Delay Caused by Material
Dispersion ............................ 142
5.5.2. Waveguide Dispersion ........................... 143
5.5.3. Modal Dispersion ............................... 144
5.5.4. Total dispersion - Simultaneous Material,
Modal and Waveguide Dispersion ................. 146
5.6. Pulse Spreading on Fibers ............................. 148
5.6.1. Pulse Broadening ............................... 150
5.6.2. Frequency Chirp ................................ 152
5.6.3. Dispersion Compensation ........................ 153
5.6.4. Dispersion Expressed in Normalized Propagation
Parameters ..................................... 154
5.6.5. Single-Mode Dispersion Expressed in
Normalized Parameters .......................... 157
5.6.6. Single Mode Fiber Design ....................... 158
5.7. Fiber Calculation Example ............................. 159
5.8. Summary of Fibers and Waveguides ...................... 160
Further Reading ............................................ 165
Exercises .................................................. 166
References ................................................. 172
6. Fiber and Waveguide Devices ................................ 174
6.1. Introduction to Fiber and Waveguide Devices ........... 174
6.2. Coupling to Fibers and Waveguides ..................... 175
6.2.1. Loss in Single Mode Fiber Splices .............. 177
6.2.2. Coupling Coefficients .......................... 179
6.2.3. Laser to Single-Mode-Fiber Coupling ............ 181
6.2.4. Laser-Mode Size Measurements Using the Knife-
Edge Method .................................... 182
6.2.5. Coupling from Spatially Incoherent Sources
to Multi Mode Fibers ........................... 184
6.2.6. Coupling between Spatially Coherent Sources
and Multimode Fibers ........................... 185
6.2.7. Coupling from Spatially Incoherent Sources
to Single Mode Fibers .......................... 185
6.2.8. Prism Coupling ................................. 185
6.2.9. Grating Coupling ............................... 187
6.3. Coupled Optical Modes ................................. 189
6.4. Directional Couplers .................................. 193
6.4.1. Coupled Mode Description of Directional
Couplers ....................................... 195
6.4.2. Eigenmodes of the Coupled System ............... 200
6.4.3. Conceptual Description of Directional
Couplers based on Eigen Modes .................. 203
6.5. Optical Devices Based on Directional Couplers ......... 204
6.5.1. Modulators and Switches based on Directional
Couplers ....................................... 205
6.5.2. Power Combiners and Filters based on
Directional Couplers ........................... 207
6.6. Periodic Waveguides - Bragg Filters. 208
6.6.1. Energy Conservation in Counter Propagating
Waves .......................................... 210
6.6.2. Modes of the Bragg Grating ..................... 211
6.6.3. One-Dimensional Photonic Bandgaps .............. 212
6.6.4. Bragg Filters .................................. 213
6.7. Waveguide Modulators .................................. 215
6.7.1. Mach-Zender modulators ......................... 215
6.7.2. Figures of Merit for Optical Modulators ........ 217
6.7.3. Phase Modulation ............................... 218
6.7.4. Acoustooptic Modulators ........................ 221
6.7.5. Modified Mach-Zender Modulators ................ 221
6.7.6. Directional Coupler Switches ................... 222
6.7.7. Fabry-Perot Modulator .......................... 223
6.7.8. Resonant Waveguide Coupling .................... 224
6.8. Summary of Fiber and Waveguide Devices ................ 231
Exercises .................................................. 232
References ................................................. 245
7. Otical MEMS Scanners ....................................... 246
7.1. Introduction to MEMS Scanners ......................... 246
7.2. Scanner Resolution .................................... 248
7.2.1. Resolution of an Ideal Scanner ................. 249
7.2.2. Optimum Resolution of a Scanned Gaussian Beam .. 251
7.2.3. Scanner Aperture ............................... 253
7.2.4. Surface Roughness, Curvature, and Bending
of Micro Mirrors ............................... 255
7.3. Reflectivity of Metal Coated Micromirrors ............. 265
7.4. Lens Scanners ......................................... 268
7.5. Mechanical Scanner Design - One Dimensional Scanners .. 270
7.5.1. Transformation from Linear Motion to Rotation .. 270
7.5.2. Torsional Spring Design ........................ 272
7.5.3. Mechanical Resonances .......................... 275
7.5.4. Higher-Order Mechanical Resonances ............. 278
7.6. Two Dimensional Scanners .............................. 281
7.7. High Resolution 2-D Scanners - Design Examples ........ 284
7.7.1. Gimbaled Scanner ............................... 284
7.7.2. Universal Joint Microscanner with "Terraced-
Plate" Actuators ............................... 287
7.7.3. Universal Joint Microscanner with Combdrive
Actuators ...................................... 288
7.8. Summary of MEMS scanners .............................. 289
Exercises .................................................. 291
References ................................................. 293
8. Optical MEMS Fiber Switches ................................ 296
8.1. Introduction to MEMS Fiber Switches ................... 296
8.2. Fiber Optical Switches and Cross Connects ............. 297
8.3. MEMS Switch Architectures ............................. 299
8.4. 2 by 2 Matrix Switch .................................. 304
8.4.1. Fiber Separation in 2 by 2 MEMS Switches ....... 304
8.4.2. Mirror Thickness in 2 by 2 Matrix Switches ..... 306
8.4.3. Low-loss 2 by 2 Matrix Switches ................ 308
8.4.4. MEMS Implementation of 2 by 2 Fiber Switch ..... 309
8.5. N by N Matrix Switches ................................ 311
8.5.1. Scaling of N by N Matrix Switch ................ 313
8.5.2. MEMS Implementations of N by N Matrix Switch ... 316
8.6. N by N Beam Steering Switches ......................... 317
8.6.1. Scaling of the Beam Steering Switch ............ 318
8.6.2. MEMS Implementations of the N by N Beam
Steering Switch ................................ 325
8.7. Summary of MEMS Fiber Switches ........................ 327
Exercises .................................................. 329
References ................................................. 331
9. Micromirror Arrays - Amplitude and Phase Modulation ........ 332
9.1. Introduction to Micromirror Arrays .................... 332
9.2. Amplitude Modulating Mirror Arrays .................... 333
9.2.1. Projection Display ............................ 334
9.3. Projection of Micromirror Arrays ...................... 338
9.3.1. The Point Spread Function ...................... 339
9.3.2. Image formation with finite Point Spread
Functions ...................................... 344
9.3.3. Projection of a Gaussian Source ................ 345
9.3.4. Projection of a Gaussian Micromirror ........... 347
9.3.5. Projection of a 1-D Gaussian Source ............ 349
9.4. Micromirrors with Phase Modulation .................... 349
9.4.1. Projection of a Phase Step .................... 350
9.4.2. Projection of a Phase Modulated Line ........... 353
9.4.3. Sub-Pixel Shifts in Phase-Modulated
Micromirror arrays ............................. 356
9.5. Projection of Micromirrors through Hard Apertures ..... 356
9.6. Adaptive Optics ....................................... 358
9.6.1. Micromirror Arrays for Adaptive Optics ......... 360
9.7. Phase vs. Amplitude Modulation ........................ 362
9.7.1. Diffractive Optical MEMS ....................... 364
9.8. Summary of Micromirror Arrays ......................... 368
Exercises .................................................. 369
References ................................................. 371
10.Grating Light Modulators ................................... 374
10.1.Introduction to Grating Light Modulators .............. 374
10.2.Phenomenological Description of MEMS Grating
Modulators ............................................ 374
10.2.1.Mechanical design and actuation of Grating
Light Modulators ............................... 374
10.2.2.Optical Design and Operation of Grating Light
Modulators ..................................... 377
10.2.3.Schlieren Projection System .................... 379
10.3.Phasor Representation of Grating Modulator Operation .. 380
10.4.High Contrast Grating Light Modulator ................. 386
10.5.Diffraction gratings .................................. 389
10.6.Projection Displays Based on Grating Modulators ....... 403
10.6.1.Actuator Design ................................ 403
10.6.2.Ribbon Mechanics ............................... 407
10.6.3.Linear Display Architecture .................... 411
10.6.4.1-D Modulator Array Fabrication ................ 414
10.6.5.Light Sources for swept-line projection
displays ....................................... 418
10.7.Summary of Grating Light Modulators ................... 422
Exercises .................................................. 423
References ................................................. 425
11.Grating Light Modulators for Fiber Optics .................. 428
11.1.Fiber Optic Modulators ................................ 428
11.2.Low Dispersion Grating Light Modulators ............... 430
11.2.1.Three-level Grating Light Modulator ............ 430
11.2.2.Optimum Design of Three-Level Grating
Modulator ...................................... 433
11.2.3.Contrast in the Three-level Grating Modulator .. 435
11.2.4.Wavelength Dependence of Attenuation ........... 437
11.2.5.Alternative Modulator Architectures ............ 439
11.3.Polarization Independent Grating Light Modulators ..... 440
11.4.Summary of GLMS for Fiber Optics ...................... 444
Further Reading ............................................ 444
Exercises .................................................. 445
References ................................................. 446
12.Optical Displacement Sensors ............................... 448
12.1.Introduction to Optical Displacement Sensors .......... 448
12.2.Interferometers as Displacement Sensors ............... 451
12.2.1.The Michelson Interferometer ................... 451
12.2.2.Displacement Sensitivity ....................... 454
12.2.3.Implementations of Interferometric
Displacement Sensors ........................... 455
12.2.4.Improved Sensitivity of High-Finesse
Interferometers ................................ 460
12.2.5.Effect of Apertures in Interferometers .......... 466
12.3.Optical Lever ......................................... 469
12.3.1.Displacement and Angle Sensitivity of the
Optical Lever .................................. 471
12.3.2.Grating Optical Lever .......................... 472
12.4.Sources of Noise in Displacement Measurements ......... 473
12.4.1.Thermal Noise .................................. 474
12.4.2.Shot Noise ..................................... 475
12.4.3.Relative Intensity Noise ....................... 475
12.5.Signal-to-Noise Ratio ................................. 476
12.5.1.Noise Equivalent Power ......................... 478
12.6.Detection Limits in displacement measurements ......... 479
12.6.1.Resolution of Optical Interferometers .......... 479
12.6.2.Resolution of Optical Levers ................... 481
12.6.3.Resolution of Capacitive Sensors ............... 481
12.6.4.Resolution of Piezoresistive Sensors ........... 483
12.6.5.Comparison of Displacement Sensors ............. 485
12.7.Summary of Optical Displacement Sensors ............... 486
Exercises .................................................. 487
References ................................................. 489
13.Micro-Optical Filters ...................................... 490
13.1.Introduction to Micro-Optical Filters ................. 490
13.2.Amplitude Filters ..................................... 491
13.2.1.Fabry-Perot Filters ............................ 491
13.2.2.Bragg Filters .................................. 495
13.2.3.Microresonator Filters ......................... 495
13.3.Dispersion compensators ............................... 498
13.4.MEMS Spectrometers .................................... 500
13.4.1.Swept Pass Band Spectrometers .................. 501
13.4.2.Generalized Transform Spectrometers ............ 502
13.4.3.Fourier Transfer Spectrometers ................. 503
13.4.4.MEMS Implementations of Transform
Spectrometers .................................. 507
13.5.Diffractive Spectrometers ............................. 511
13.5.1.Spectral Synthesis ............................. 511
13.5.2.Diffractive MEMS Spectrometers ................. 514
13.6.Tunable lasers ........................................ 517
13.6.1.MEMS Vertical Cavity Surface Emitting Lasers ... 518
13.6.2.MEMS External Cavity Semiconductor Diode
Lasers ......................................... 519
13.6.3.Tunable External Cavity Semiconductor Diode
Lasers with Diffractive Filters ................ 522
13.7.Summary of Microoptical Filters ....................... 523
Exercises .................................................. 524
References ................................................. 527
14.Photonic Crystal Fundamentals .............................. 532
14.1.Introduction to Photonic Crystals ..................... 532
14.2.Photonic Crystal Basics ............................... 533
14.2.1.1-D Photonic Crystals .......................... 535
14.2.2.Bloch States ................................... 538
14.2.3.Band Structure of 2-D and 3-D Photonic
Crystals ....................................... 539
14.3.Guided Resonances ..................................... 543
14.3.1.Reflection and Transmission through 2-D
Photonic Crystals .............................. 544
14.3.2.Reflection and Transmission for a Mirror-
Symmetric 2-port with one Guided Resonance ..... 546
14.3.3.Reflection and Transmission for a Mirror-
Symmetric 2-port with two Guided Resonances .... 549
14.3.4.Coupling to Guided Resonances - Symmetry ....... 551
14.4.Comparison of Photonic and Electronic Crystals ........ 553
14.5.Summary of PC fundamentals ............................ 555
Exercises .................................................. 556
References ................................................. 557
15.Photonic Crystal Devices and Systems ....................... 560
15.1.Introduction to PC devices and systems ................ 560
15.2.1С Compatible Photonic Crystals ....................... 561
15.2.1.Silicon Compatible 2-D Photonic Crystals ....... 561
15.2.2.3-D Structuring of Photonic Crystals ........... 566
15.3.Photonic Crystal Optical Components ................... 567
15.3.1.Mirrors and Filters ............................ 568
15.3.2.Photonic Crystal Fabry-Perot Resonators ........ 569
15.3.3.PC Tunneling Sensors ........................... 570
15.3.4.PC Polarization Optics ......................... 571
15.3.5.PC Index Sensors ............................... 571
15.4.Tunable Photonic Crystals ............................. 573
15.4.1.Photonic Crystal MEMS Scanners ................. 574
15.4.2.Photonic Crystal Displacement Sensors .......... 577
15.5.Photonic Crystal Fiber Sensors ........................ 579
15.6.Summary of PC devices and systems ..................... 581
Exercises .................................................. 582
References ................................................. 583
Appendix A. Geometrical Optics ................................ 588
A.l. Introduction to Geometrical Optics .................... 588
A.2. Geometrical Optics Treatment of Lenses ................ 588
A.2.1.Lens - Ray Picture .............................. 588
A.2.2.Lenses-Wave Picture ............................. 589
A.2.3. Ray Tracing .................................... 590
A.3. ABCD matrices ......................................... 591
A.3.1. Free space ..................................... 592
A.3.2. Slab of Index n ................................ 592
A.3.3. Thin Lens ...................................... 593
A.3.4. Curved Mirror .................................. 594
A.3.5. Combinations of Elements ....................... 594
A.3.6. Reverse transmission ........................... 595
Appendix В.Electrostatic Actuation ............................ 596
B.l. The parallel Plate Capacitor .......................... 596
B.l.l. Energy Storage in Parallel-Plate Capacitors .... 597
B.2. The Parallel Plate Electrostatic Actuator ............. 599
B.2.1. Charge Control ................................. 600
B.2.2. Voltage Control ................................ 602
B.3.Energy Conservation in the Parallel Plate
Electrostatic Actuator ................................. 606
B.4. Electrostatic Spring .................................. 610
B.4.1. Sensors Based on the Electrostatic Spring ...... 613
B.5. Electrostatic Combdrives .............................. 614
B.6. Summary of Electrostatic Actuation .................... 620
References .................................................... 624
Index ......................................................... 626
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