Electromagnetic Propagation in Multi-mode Random Media

235 Pages·1999·1.286 MB·English

by  Harrison E. Rowe

ElectromagneticPropagationinMulti-ModeRandomMedia.HarrisonE.Rowe
Copyright©1999JohnWiley&Sons,Inc.
PrintISBN0-471-11003-5;ElectronicISBN0-471-20070-0
Electromagnetic Propagation
in Multi-Mode Random Media
Electromagnetic
Propagation
in Multi-Mode
Random Media
HARRISON E. ROWE
AWILEY-INTERSCIENCE PUBLICATION
JOHNWILEY & SONS, INC.
NEWYORK/CHICHESTER/WEINHEIM/BRISBANE/SINGAPORE/TORONTO
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To Alicia,
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and to the memory of
Stephen O. Rice
Contents
1 Introduction 1
References 3
2 Coupled Line Equations 5
2.1 Introduction 5
2.2 Two-Mode Coupled Line Equations 6
2.3 Exact Solutions 8
2.4 Discrete Approximation 11
2.5 Perturbation Theory 13
2.6 Multi-Mode Coupled Line Equations 15
References 19
3 Guides with White Random Coupling 21
3.1 Introduction 21
3.2 Notation—Two-Mode Case 23
3.3 Average Transfer Functions 25
3.4 Coupled Power Equations 30
3.5 Power Fluctuations 35
3.6 Transfer Function Statistics 39
3.7 Impulse Response Statistics 43
3.8 Discussion 46
References 47
4 Examples—White Coupling 49
4.1 Introduction 49
vii
viii CONTENTS
4.1.1 Single-Mode Input 50
4.1.2 Multi-Mode Coherent Input 51
4.1.3 Multi-Mode Incoherent Input 51
4.2 Coupled Power Equations—Two-Mode Case 52
4.2.1 Single-Mode Input 52
4.2.2 Two-Mode Coherent Input 55
4.2.3 Two-Mode Incoherent Input 58
4.3 Power Fluctuations—Two-Mode Guide 58
4.3.1 Single-Mode Input 60
4.3.2 Two-Mode Coherent Input 60
4.3.3 Two-Mode Incoherent Input 61
4.3.4 Discussion 62
4.4 Impulse Response—Two-Mode Case 64
4.5 Coupled Power Equations—Four-Mode Case 67
4.5.1 Single-Mode Input 69
4.5.2 Multi-Mode Coherent Input 72
4.5.3 Multi-Mode Incoherent Input 72
4.6 Nondegenerate Case—Approximate Results 74
4.6.1 Average Transfer Functions 75
4.6.2 Coupled Power Equations 77
4.6.3 Power Fluctuations 81
4.6.4 Discussion 84
4.7 Discussion 84
References 85
5 Directional Coupler with White Propagation
Parameters 87
5.1 Introduction 87
5.2 Statistical Model 88
5.3 Average Transfer Functions 91
5.4 Coupled Power Equations 93
5.5 Discussion 95
References 97
6 Guides with General Coupling Spectra 99
6.1 Introduction 99
6.2 Almost-White Coupling Spectra 100
6.2.1 Two Modes 101
CONTENTS ix
6.2.2 N Modes 104
6.3 General Coupling Spectra—Lossless Case 106
6.3.1 Two Modes 109
6.3.2 N Modes 110
6.4 General Coupling Spectra—Lossy Case 115
6.4.1 Two Modes 116
6.4.2 N Modes 118
6.5 Discussion 121
References 122
7 Four-Mode Guide with Exponential Coupling
Covariance 123
7.1 Introduction 123
7.2 Average Transfer Functions 126
7.3 Coupled Power Equations 127
7.4 Discussion 127
8 Random Square-Wave Coupling 129
8.1 Introduction 129
8.2 Two Modes—Binary Independent Sections 132
8.3 Two Modes—Binary Markov Sections 135
8.4 Four Modes—Multi-Level Markov Sections 138
8.5 Discussion 143
9 Multi-Layer Coatings with Random OpticalThickness 145
9.1 Introduction 145
9.2 Matrix Analysis 147
9.3 Kronecker Products 150
9.4 Example: 13-Layer Filter 152
9.4.1 Statistical Model 153
9.4.2 Transmittance 155
9.4.3 Two-Frequency Transmission Statistics 155
9.5 Discussion 158
References 159
10 Conclusion 161
References 162
x CONTENTS
AppendixA Series Solution for the Coupled Line
Equations 163
References 168
AppendixB General Transmission Properties of
Two-Mode Guide 169
References 173
AppendixC Kronecker Products 175
References 177
AppendixD ExpectedValues of Matrix Products 179
D.1 Independent Matrices 179
D.2 Markov Matrices 183
D.2.1 Markov Chains 183
D.2.2 Scalar Variables 184
D.2.3 Markov Matrix Products 186
References 190
AppendixE Time- and Frequency-Domain Statistics 191
E.1 Second-Order Impulse Response
Statistics 191
E.2 Time-Domain Analysis 195
References 196
AppendixF Symmetric Slab Waveguide—LosslessTE
Modes 197
F.1 General Results 197
F.2 Example 200
References 202
AppendixG Equal Propagation Constants 203
AppendixH Asymptotic Form of Coupled Power Equations 209
AppendixI Differential Equations Corresponding to
Matrix Equations 211
I.1 Scalar Case 211
I.2 Matrix Case 212
CONTENTS xi
References 214
AppendixJ Random Square-Wave Coupling Statistics 215
J.1 Introduction 215
J.2 Binary Sections 217
J.2.1 Independent 218
J.2.2 Markov 218
J.3 Multi-Level Markov Sections 219
J.3.1 Low-Pass—Six Levels 219
J.3.2 Band-Pass—Five Levels 224
References 226
AppendixK Matrix for a Multi-Layer Structure 227
Index 231
Electromagnetic Propagation
in Multi-Mode Random Media