A reference/text that introduces a variety of spectral computational techniques, including k-space theory, Floquet theory, and beam propagation. Contents include mathematical principles, spectral state variable formulation for planar systems, planar diffraction gratings, and more.
Author(s): Partha P. Banerjee, John M. Jarem
Series: Optical engineering 69
Edition: 1
Publisher: Marcel Dekker
Year: 2000
Language: English
Pages: 437
City: New York
Table of Contents......Page 13
1.1 INTRODUCTION......Page 14
1.2 THE FOURIER SERIES AND ITS PROPERTIES......Page 15
1.3 THE FOURIER TRANSFORM......Page 18
1.4 THE DISCRETE FOURIER TRANSFORM......Page 19
1.5 REVIEW OF EIGENANALYSIS......Page 20
REFERENCES......Page 26
2.1 INTRODUCTION......Page 27
2.2.2 Analysis......Page 32
2.2.3 Complex Poynting Theorem......Page 37
2.2.4 State Variable Analysis of an Isotropic in Free Space......Page 40
2.2.5 State Variable Analysis of a Radar Absorbing Layer (RAM)......Page 45
2.2.6 State Variable Analysis of a Source in Isotropic Layered Media......Page 48
2.3.1 Introduction......Page 54
2.3.2 Basic Equations......Page 55
2.3.3 Numerical Results......Page 60
2.4.1 Introduction......Page 65
2.4.2 General Bi-Anisotropic State Variable Formulation......Page 66
2.4.3 Incident, Reflected, and Transmitted Plane Wave Solutions......Page 70
2.4.4 Numerical Example......Page 75
2.5.1 Introduction......Page 77
2.5.2 K-Space Formulation......Page 78
2.5.3 Ground-Plane Slot-Waveguide System......Page 79
2.5.4 Ground-Plane Slot-Waveguide System, Numerical Results......Page 88
2.6.1 Introduction......Page 91
2.6.2 The Field Inside the Anisotropic Layer......Page 92
2.6.3 Solution of the Boundary Value Problem......Page 94
2.6.4 Numerical Results and Discussion......Page 96
2.6.5 Conclusion......Page 100
2.7.2 Variable Transformation in the Matrix Exponential Method......Page 101
2.7.3 An Example: Scattering from a Biased Ferrite Layer......Page 105
PROBLEMS......Page 106
REFERENCES......Page 108
3.1 INTRODUCTION......Page 110
3.2 H-MODE PLANAR DIFFRACTION GRATING ANALYSIS......Page 115
3.2.1 Full Field Formulation......Page 116
3.2.2 RCWA Wave Equation Method......Page 124
3.2.3 Numerical Results......Page 131
3.2.4 Diffraction Grating-Mirror......Page 140
3.3 APPLICATION OF RCWA AND THE COMPLEX POYNTING THEOREM TO E-MODE PLANAR DIFFRACTION GRATING ANALYSIS......Page 142
3.3.1 E-Mode RCWA Formulation......Page 145
3.3.2 Complex Poynting Theorem......Page 148
Sample Calculation of Puwe......Page 149
Other Poynting Theorem Integrals......Page 151
Simplification of Results and Normalization......Page 152
3.3.3 Numerical Results......Page 157
3.4.1 Formulation......Page 166
Slanted Gratings (0=)......Page 177
Pure Reflection Gratings (=0)......Page 178
3.5 MULTILAYER ANALYSIS OF E-MODE DIFFRACTION GRATINGS......Page 183
3.5.1 E-Mode Formulation......Page 187
3.5.3 Numerical Results......Page 193
3.6.1 Crossed-Diffraction Grating Formulation......Page 196
3.6.2 Numerical Results......Page 214
3.7 STABLE IMPLEMENTATION OF RCWA FOR MULTILAYER DIFFRACTION GRATINGS: AN ENHANCED TRANSMITTANCE APPROACH......Page 225
3.7.1 Second-Order RCWA......Page 227
3.7.2 Electromagnetic Fields in Regions 1 and 3......Page 232
3.7.3 Enhanced Transmittance Matrix Analysis......Page 234
3.7.4 Numerical Stability and Convergence [23]......Page 239
3.8 HIGHLY IMPROVED CONVERGENCE OF THE COUPLE WAVE METHOD FOR E-MODE INCIDENCE......Page 241
PROBLEMS......Page 247
REFERENCES......Page 249
4.1 TRANSFER FUNCTION FOR PROPAGATION......Page 256
4.2 SPLIT-STEP BEAM PROPAGATION ALGORITHM......Page 258
4.3.1 Linear Free-Space Propagation......Page 260
4.3.2 Propagation of Gaussian Beam Through a Graded Index Medium......Page 261
4.3.3 Beam Propagation Through Diffraction Gratings: Acousto-optic Diffraction......Page 262
4.4.1 Nonlinear Self-focusing and Defocusing of Beams......Page 266
4.4.2 Beam Fanning and Distortion in Photorefractive Materials......Page 268
4.4.3 Two-Beam Coupling in Photorefractive Materials [18]......Page 278
4.5 q-TRANSFORMATION OF GAUSSIAN BEAMS THROUGH NONLINEAR MATERIALS: z-SCAN AND P-SCAN TECHNIQUES......Page 280
4.5.1 Model for Beam Propagation Through a PR Linb03 Single Cystal......Page 282
4.5.2 z-SCAN: ANALYTICAL RESULTS, SIMULATIONS, AND COMPARISON WITH SAMPLE EXPERIMENTS......Page 285
4.5.3 P-SCAN SIMULATIONS AND COMPARISON OF THEORY WITH EXPERIMENT......Page 289
PROBLEMS......Page 291
REFERENCES......Page 293
5.1.1 Background......Page 295
5.2.1 Introduction......Page 299
5.2.2 Basic Equations......Page 300
5.2.3 NUMERICAL RESULTS [15]......Page 306
5.3.1 Introduction......Page 310
5.3.2 State Variable Analysis [23]......Page 312
5.3.3. Numerical Results [23]......Page 317
5.4.1 Introduction......Page 323
5.4.2 Rigorous Coupled Wave Analysis Formulation [26]......Page 325
5.4.3 Numerical Results [26]......Page 337
PROBLEMS......Page 344
REFERENCES......Page 347
6.1.1 Introduction......Page 350
6.1.2 Waveguide Description......Page 351
6.1.3 Cross-Tensor Media......Page 352
6.1.4 Formulation......Page 353
6.1.5 Multilayer Analysis......Page 358
6.1.6 Comparison with Experimental Data......Page 361
6.1.7 Conclusion......Page 364
6.2.1 Introduction......Page 365
6.2.2 H-mode Formulation......Page 366
6.2.3 Coordinate Transformations......Page 372
6.2.5 Numerical Results......Page 373
PROBLEMS......Page 374
REFERENCES......Page 378
7.1 INTRODUCTION TO PHOTOREFRACTIVE MATERIALS......Page 380
7.2 DYNAMIC NONLINEAR MODEL FOR DIFFUSIN-CONTROLLED PR MATERIALS......Page 383
7.3 APPROXIMATE ANALYSIS [29,30]......Page 384
7.3.1 Numerical Algorithm......Page 388
7.3.2 TE Numerical Simulation Results......Page 389
7.3.3 TM Numerical Simulation Results......Page 400
7.3.4. Discussion of Results from Approximate Analysis......Page 404
7.4 EXACT ANALYSIS [34]......Page 405
7.4.1 Finite Difference Kukhtarev Analysis......Page 408
7.4.2 TM Numerical Simulation Results......Page 411
7.5.1 RCWA Optical Field Analysis......Page 421
7.5.2 Material Analysis......Page 424
7.5.3 Numerical Results......Page 428
7.5.4 Conclusion......Page 431
PROBLEMS......Page 433
REFERENCES......Page 435
