Photonic technology promises much faster computing, massive parallel processing, and an evolutionary step in the digital age. The search continues for devices that will enable this paradigm, and these devices will be based on photonic crystals. Modeling is a key process in developing crystals with the desired characteristics and performance, and Electromagnetic Theory and Applications for Photonic Crystals provides the electromagnetic-theoretical models that can be effectively applied to modeling photonic crystals and related optical devices. The book supplies eight self-contained chapters that detail various analytical, numerical, and computational approaches to the modeling of scattering and guiding problems. For each model, the chapter begins with a brief introduction, detailed formulations of periodic structures and photonic crystals, and practical applications to photonic crystal devices. Expert contributors discuss the scattering matrix method, multipole theory of scattering and propagation, model of layered periodic arrays for photonic crystals, the multiple multipole program, the mode-matching method for periodic metallic structures, the method of lines, the finite-difference frequency-domain technique, and the finite-difference time-domain technique. Based on original research and application efforts, Electromagnetic Theory and Applications for Photonic Crystals supplies a broad array of practical tools for analyzing and designing devices that will form the basis for a new age in computing.
Author(s): Kiyotoshi Yasumoto
Series: Optical science and engineering 102
Edition: 1
Publisher: Taylor & Francis
Year: 2006
Language: English
Pages: 459
City: Boca Raton, FL
dk5845fm.pdf......Page 2
Electromagnetic Theory and Applications for Photonic Crystals......Page 8
Preface......Page 10
The Editor......Page 12
Contributors......Page 13
Table of Contents......Page 15
CONTENTS......Page 16
Table of Contents......Page 0
1.1 INTRODUCTION......Page 17
1.2.1 PRESENTATION OF THE PROBLEM AND NOTATION......Page 18
1.2.2 FOURIER–BESSEL EXPANSIONS OF THE FIELD INSIDE THE CYLINDERS......Page 20
1.2.3 FOURIER–BESSEL EXPANSIONS OF THE FIELD OUTSIDE THE CYLINDERS......Page 22
1.2.4 FIRST SET OF EQUATIONS: CAUSALITY PROPERTY FOR EACH CYLINDER......Page 26
1.2.5 SECOND SET OF EQUATIONS: INTRODUCING THE COUPLING BETWEEN CYLINDERS......Page 27
1.2.6 FINAL EQUATION......Page 30
1.3.1 INTRODUCTION......Page 31
1.3.2 SETTING OF THE PROBLEM......Page 32
1.3.3 THE METHOD OF FICTITIOUS SOURCES (MFS)......Page 33
1.3.4 IMPLEMENTATION OF THE SCATTERING MATRIX METHOD (SMM)......Page 37
1.3.5 HYBRID METHOD USING MFS AND SMM......Page 38
1.3.6 NUMERICAL EXAMPLE......Page 39
1.4 DISPERSION RELATIONS OF BLOCH MODES......Page 40
1.4.1 INFINITE STRUCTURE......Page 41
1.4.2 FINITE-SIZE PHOTONIC CRYSTALS......Page 45
1.5.1 ULTRAREFRACTION WITH DIELECTRIC PHOTONIC CRYSTALS......Page 50
1.5.2 ULTRAREFRACTION WITH METALLIC PHOTONIC CRYSTALS......Page 51
1.5.3 NEGATIVE REFRACTION BY A DIELECTRIC SLAB RIDDLED WITH GALLERIES......Page 54
1.6 CONCLUSION......Page 57
REFERENCES......Page 58
CONTENTS......Page 61
2.1 INTRODUCTION......Page 62
2.2.1 GENERAL FRAMEWORK......Page 65
2.2.2 FIELD REPRESENTATION......Page 66
2.2.3 RAYLEIGH FIELD IDENTITY......Page 69
2.2.4 FIELD COUPLING AND CONTINUITY CONDITIONS......Page 72
2.2.5 FIELD PROBLEM OF MICROSTRUCTURED OPTICAL FIBERS......Page 74
2.2.6 INFINITE PERIODIC STRUCTURES......Page 76
2.2.7 GRATINGS......Page 82
2.3.2 GUIDING MECHANISMS AND THE “FINGER DIAGRAM”......Page 87
2.3.3 IMPLEMENTATION OF THE MULTIPOLE METHOD......Page 89
2.3.4.1 Number of Modes......Page 90
2.3.4.2 Properties of the Fundamental Mode......Page 92
2.3.5 AIR-GUIDED MODES......Page 94
2.4.1 BACKGROUND......Page 96
2.4.2 2D GREEN TENSOR AND LDOS......Page 97
2.4.3 2.5D GREEN TENSOR AND LDOS......Page 100
2.5.1 BACKGROUND AND NOMENCLATURE......Page 106
2.5.2 FORMULATION OF THE EIGENVALUE PROBLEM......Page 109
2.5.3 CALCULATION OF BAND DIAGRAMS AND BAND SURFACES......Page 111
2.5.4 CLASSIFICATION OF THE EIGENVALUES......Page 114
2.5.4.1 Formal Properties of Bloch Modes......Page 116
2.5.5 DEFECT MODE MODELING OF EXTENDED PHOTONIC CRYSTAL DEVICES......Page 118
2.5.6 INTERFACING PHOTONIC CRYSTAL MEDIA AND FRESNEL COEFFICIENTS......Page 119
2.5.7 RECURSIVELY COMBINING PC STACK SEGMENTS......Page 121
2.6.1 BACKGROUND......Page 122
2.6.2 STRAIGHT PC WAVEGUIDES......Page 123
2.6.3 RESONANT FILTERS AND JUNCTIONS......Page 124
2.6.4 MACH–ZEHNDER INTERFEROMETER......Page 128
2.7 DISCUSSION AND CONCLUSIONS......Page 130
REFERENCES......Page 133
CONTENTS......Page 137
3.1 INTRODUCTION......Page 138
3.2.1 TWO-DIMENSIONAL SCATTERING......Page 140
3.2.2 TWO-DIMENSIONAL T-MATRIX OF A CIRCULAR CYLINDER......Page 142
3.2.3 THREE-DIMENSIONAL SCATTERING......Page 143
3.2.4 THREE-DIMENSIONAL T-MATRIX OF A CIRCULAR CYLINDER......Page 144
3.3.1 TWO-DIMENSIONAL SCATTERING......Page 145
3.3.2 LATTICE SUMS AND T-MATRIX......Page 150
3.3.3 THREE-DIMENSIONAL SCATTERING......Page 153
3.4.1 REFLECTION AND TRANSMISSION MATRICES......Page 156
3.4.3 FLOQUET-MODE APPROACH FOR LAYERED IDENTICAL ARRAYS......Page 159
3.4.4 LAYERED ARRAYS EMBEDDED IN A SLAB......Page 163
3.5 THREE-DIMENSIONAL SCATTERING FROM LAYERED CROSSED-ARRAYS......Page 165
3.5.1 SCATTERING FROM A PARALLEL ARRAY OF CIRCULAR CYLINDERS......Page 166
3.5.2 UNIT CELL OF A CROSSED-ARRAY OF CIRCULAR CYLINDERS......Page 171
3.5.3 LAYERED CROSSED-ARRAYS OF CIRCULAR CYLINDERS......Page 174
3.6.1 DISPERSION EQUATION......Page 175
3.6.2 MODE FIELD ANALYSIS......Page 178
3.7.1 TWO-DIMENSIONAL SCATTERING FROM LAYERED PARALLEL ARRAYS......Page 181
3.7.2 THREE-DIMENSIONAL SCATTERING FROM LAYERED CROSSED-ARRAYS......Page 188
3.7.3 GUIDED MODES OF TWO-DIMENSIONAL PHOTONIC CRYSTAL WAVEGUIDES......Page 195
REFERENCES......Page 201
4.1 INTRODUCTION AND OVERVIEW......Page 205
4.2 INTRODUCTION TO PHOTONIC CRYSTAL SIMULATION......Page 207
4.3 BASICS OF THE MULTIPLE MULTIPOLE PROGRAM......Page 208
4.4 HANDLING PERIODIC SYMMETRIES WHILE USING PERIODIC BOUNDARY CONDITIONS......Page 212
4.5 ADVANCED MMP AND MAS EIGENVALUE SOLVERS......Page 214
4.6 COMPUTATION OF WAVEGUIDE MODES IN PHOTONIC CRYSTALS......Page 220
4.7 COMPUTATION OF WAVEGUIDE DISCONTINUITIES......Page 224
4.8 SENSITIVITY ANALYSIS OF PHOTONIC CRYSTAL DEVICES......Page 226
4.9 OPTIMIZATION BASED ON THE SENSITIVITY ANALYSIS......Page 230
4.10 ACHROMATIC 90° BEND......Page 231
4.11 FILTERING T-JUNCTION......Page 232
4.12 CONCLUSIONS AND OUTLOOK......Page 236
REFERENCES......Page 237
CONTENTS......Page 239
5.1 INTRODUCTION......Page 240
5.2.1 TM POLARIZED CASE......Page 241
5.2.2 TE POLARIZED CASE......Page 244
5.2.3 NUMERICAL EXAMPLES AND DISCUSSION......Page 245
5.3 ANALYSIS OF PHOTONIC CRYSTALS CONSISTING OF METALLIC CYLINDERS WITH ARBITRARY CROSS SECTION......Page 247
5.3.1 A SCATTERING MATRIX OF ONE SLICED LAYER WITH TM POLARIZED INCIDENCE......Page 248
5.3.2 A GLOBAL MATRIX OF THE ORIGINAL ARRAY WITH ARBITRARY CROSS SECTION......Page 250
5.3.4 S-MATRIX SOLUTION FOR TE POLARIZED INCIDENCE......Page 251
5.3.5 A MULTILAYERED STRUCTURE PROBLEM......Page 252
5.3.6 2D PHOTONIC CRYSTAL WAVEGUIDES CONSISTING OF METALLIC CYLINDERS WITH ARBITRARY CROSS SECTION......Page 253
5.3.7 NUMERICAL EXAMPLES......Page 256
5.4.1 FORMULATION......Page 269
5.5 SCATTERING ANALYSIS OF CROSSED PHOTONIC CRYSTALS CONSISTING OF ARBITRARILY SHAPED CYLINDERS......Page 274
5.5.1 REFLECTION AND TRANSMISSION MATRICES OF ONE Z-ARRAY LAYER......Page 276
5.5.2 S-MATRIX OF ONE X-ARRAY LAYER......Page 279
5.5.3 NUMERICAL EXAMPLES......Page 283
5.6 DIFFRACTION FROM A CONDUCTIVE SLAB CUT PERIODICALLY BY RECTANGULAR HOLES......Page 286
5.6.1 FORMULATION......Page 287
5.6.2 NUMERICAL EXAMPLES......Page 293
5.7 SCATTERING ANALYSIS OF A CONDUCTIVE SLAB CUT PERIODICALLY BY RECTANGULAR HOLES IN AN ARBITRARY DIRECTION......Page 297
5.8 CONCLUSION......Page 305
REFERENCES......Page 306
CONTENTS......Page 309
6.1 INTRODUCTION......Page 310
6.2 BASIC THEORY......Page 312
6.2.2 MAXWELL’S EQUATIONS IN MATRIX NOTATION......Page 313
6.2.3 GENERALIZED TRANSMISSION LINE EQUATIONS IN GENERAL ORTHOGONAL COORDINATES......Page 314
6.2.4 DISCRETIZATION......Page 315
6.2.5 ABSORBING BOUNDARY CONDITIONS......Page 321
6.2.7 EIGENVALUE AND MODAL MATRICES......Page 322
6.3.1 TRANSFORMATION THROUGH WAVEGUIDE SECTIONS......Page 323
6.3.3 TRANSFORMATION AT METALIZED WAVEGUIDE INTERFACES......Page 324
6.3.4 STEPS OF THE ANALYSIS PROCEDURE......Page 325
6.4.1 INTRODUCTION......Page 326
6.4.2 SYMMETRIC PERIODIC STRUCTURES......Page 327
6.4.3 PROPAGATION CONSTANTS OF FLOQUET MODES......Page 328
6.4.4 WAVE IMPEDANCE/ADMITTANCE OF FLOQUET MODES......Page 329
6.4.5 EFFICIENT CALCULATION OF THE FLOQUET MODE PARAMETERS......Page 330
6.4.6 CONCATENATION OF N PERIODS......Page 332
6.5.1 PROPAGATION ALGORITHM......Page 333
6.5.2 EIGENMODE ALGORITHM......Page 337
6.5.3 LINES OF VARYING LENGTH......Page 339
6.6.1 PORT RELATIONS......Page 342
6.6.2 MAIN DIAGONAL SUBMATRICES......Page 344
6.6.3 OFF-DIAGONAL SUBMATRICES: COUPLING TO OTHER PORTS......Page 346
6.7.1 BAND STRUCTURE CALCULATIONS......Page 350
6.7.2 PC WAVEGUIDE DEVICES......Page 353
6.7.3 BRAGG GRATINGS......Page 356
6.8 CONCLUSION......Page 361
REFERENCES......Page 362
CONTENTS......Page 365
7.1 INTRODUCTION......Page 366
7.2.1 FORMULAE FOR 2D WAVEGUIDE PROBLEMS......Page 369
7.2.2 THE FDFD METHOD WITH PMLS......Page 372
7.2.3 NUMERICAL TREATMENT AT THE DIELECTRIC INTERFACE......Page 377
7.3 MODAL ANALYSIS OF PHOTONIC CRYSTAL FIBERS......Page 379
7.3.1 HOLEY FIBERS......Page 380
7.3.2 TWO-CORE PCFS......Page 386
7.3.3 HONEYCOMB PCFS......Page 387
7.3.4 HOLLOW PCFS......Page 390
7.4.1 THE FDFD FORMULAE......Page 393
7.4.1.1 The TE Mode......Page 394
7.4.1.2 The TM Mode......Page 396
7.4.2 PERIODIC BOUNDARY CONDITIONS FOR 2D PCS......Page 397
7.5.1 PCS WITH SQUARE LATTICES......Page 399
7.5.2 PCS WITH TRIANGULAR LATTICES......Page 400
7.5.3 FINGER PLOTS OF 2D PCS......Page 402
7.6 MODAL ANALYSIS OF PLANAR PC WAVEGUIDES......Page 405
7.7 CONCLUSION......Page 409
REFERENCES......Page 411
8.1 INTRODUCTION......Page 415
8.2.1 FORMULATION OF PROBLEM......Page 416
8.2.1.1 Transformation of Maxwell’s Equations......Page 417
8.2.1.2 An FDTD Method Based on MD-WDFs......Page 420
8.2.2 NUMERICAL DISPERSION AND NUMERICAL ERRORS......Page 425
8.3 PHOTONIC CRYSTAL STRAIGHT WAVEGUIDE......Page 429
8.3.1 NUMERICAL RESULTS......Page 430
8.3.2 FLOQUET MODE......Page 431
8.3.3 DISPERSION RELATION......Page 434
8.4.1 DIRECTIONAL COUPLER......Page 437
8.4.2.1 Pillar Type Photonic Crystal Bent Waveguide......Page 441
8.4.2.2 Air-Hole Type Photonic Crystal Bent Waveguide......Page 450
8.5 WAVELENGTH MULTI/DEMULTIPLEXER......Page 452
8.5.1 DESIGN PARAMETERS......Page 453
8.5.2 NUMERICAL RESULTS......Page 454
8.6 CONCLUSION......Page 455
REFERENCES......Page 457
