Optical Network Theory

By: Yitzhak Weissman

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Hardcover | 31 March 1992

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Hardcover
292 Pages

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24.13 x 15.88 x 2.54

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This reference blends the concepts of optics and microwave theory. It is logically organized in two main parts, the first section deals with network analysis, while the second concentrates on signal analysis. As a whole, the text focuses on the fundamental aspects of optical networks. Methodology, rather than analysis, is the focus of the book. The discussion provides the tools you need to perform your own in-depth analysis of optical networks.

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Non-Fiction Engineering & Technology Other Technologies & Applied Sciences Applied Optics Computing & I.T.Computer Science Image Processing Electronics & Communications Engineering Communications Engineering & Telecommunications Electronics Engineering Microwave Technology Technology in General

Network Analysis	p. 1
Introduction	p. 3
Why Optical Networks Are Different From Microwave Networks	p. 3
To Whom This Book Is Addressed	p. 5
Book Overview	p. 6
Network Analysis	p. 6
Signal Analysis	p. 8
The Scope of the Book	p. 10
Mathematical Notations and Conventions	p. 11
List of Principal Symbols	p. 14
The Jones Calculus of Guided Fields	p. 17
The Jones Vectors for Guided Fields	p. 18
Jones Matrices	p. 20
The Jones Matrix as a Transfer Function of a Linear System	p. 22
The Fourier Representation of Cyclic Jones Matrices	p. 24
Examples of Cyclic Jones Matrices	p. 27
Summary	p. 31
S-Matrix Characterization of Optical Components	p. 33
The Jones Matrix and the S-Matrix (the Time-Independent Case)	p. 34
General Properties of the S-Matrix	p. 36
The S-Matrices of Some Common Optical Components	p. 38
One-Port Components	p. 38
Two-Port Components	p. 39
Directional Couplers	p. 40
Port Characterization of Time-Dependent Components	p. 42
Summary	p. 43
The Signal Flow Graphs in Network Analysis	p. 45
General Considerations	p. 46
Signal Flow Graphs	p. 48
The Signal Flow Graph as a Graphical Representation of Linear Algebraic Equations	p. 48
The Association of Algebraic Equations With a Given Signal Flow Graph	p. 50
The Network Algebra	p. 51
The Signal Flow Graphs of Optical Components	p. 53
Single-Port Components	p. 53
N-Port Components	p. 54
Two-Port Component	p. 55
Directional Couplers	p. 56
The Derivation of Signal Flow Graphs for Optical Networks	p. 57
Graphical Reduction Rules for the Optical Signal Flow Graphs	p. 60
Branches in Series	p. 61
Branches in Parallel	p. 62
Elimination of a Feedback Branch	p. 63
Expansion of Stars	p. 67
Summary	p. 67
The Analysis of Time-Independent Networks	p. 69
The Network Algebra Rules for the Time-Independent Case	p. 70
The Guided-Wave Fabry-Perot Interferometer	p. 71
The Recirculating Loop	p. 74
The Guided-Wave Mach-Zehnder Interferometer	p. 78
The Guided-Wave Michelson Interferometer	p. 80
The Algebraic Solution of the Time-Independent Network Problem	p. 82
Summary	p. 83
The Analysis of Networks That Are Periodic in Time	p. 85
Network Algebra Rules for Cyclic Transmissions With Identical Periods	p. 86
Preservation of the Periodic Time Dependence Upon Addition and Multiplication	p. 86
The Network Algebra Addition Operation in the Frequency Domain	p. 87
The Network Algebra Product Operation in the Frequency Domain	p. 88
Operations Between Time-Invariant and Cyclic Transmissions	p. 89
Serial Combination of Transmissions Representing Amplitude Modulators, Frequency Shifters, and Phase Modulators (Examples)	p. 90
The Transfer Matrix of an Instantaneous Modulator With Leads	p. 90
Two Amplitude Modulators in Series	p. 92
Combination of Frequency Shifters in Series	p. 93
Combination of Phase Modulators in Series	p. 94
The Modulated Mach-Zehnder Interferometer (Example)	p. 97
The Treatment of a Feedback Branch	p. 98
The General Procedure	p. 98
Feedback Branches Containing Instantaneous Modulators	p. 101
The Modulated Recirculating Loop	p. 102
The Combination of Two Transmissions with Commensurate Frequencies	p. 105
Summary	p. 105
Network Analysis of the Fiber-Optic Gyro	p. 109
The Sagnac Effect in the Rotating Fiber-Optic Ring	p. 110
A Basic Fiber-Optic Sagnac Interferometer	p. 112
Problems Arising From Birefringence and Mode Mixing	p. 114
Problems Arising From Coupler Losses	p. 119
A Practical Fiber-Optic Gyro	p. 120
The Introduction of Bias by Phase Modulation	p. 122
Summary	p. 124
Signal Analysis	p. 127
The Second-Order Statistics of Guided Fields	p. 129
Real Stochastic Processes	p. 130
The Characterization of a Real Stochastic Process	p. 130
Stationary and Cyclostationary Processes and Their Power Spectral Densities	p. 131
A Harmonic Process With a Random Amplitude (Example)	p. 134
Ensemble Averages, Time Averages, and Ergodicity	p. 136
Complex Stochastic Processes	p. 137
Characterization of a Complex Stochastic Process	p. 137
A Superposition of Pure Spectral Lines With Random Amplitudes (Example)	p. 138
The Second-Order Field Correlation Functions and the Optical Field Power Spectrum	p. 139
Statistical Description of Jones Vectors	p. 139
The Second-Order Statistics of Guided Fields	p. 140
Optical Field Intensity and Spectrum	p. 142
The Separable Field	p. 143
Representation of a Real Jones Vector by a Complex One	p. 144
The Real Jones Vector and Its Associated Complex Jones Vector	p. 144
The Relation Between Coherency Matrices and Power Spectra of Real and Complex Processes	p. 146
Statistical Model of an Amplitude-Stabilized Laser	p. 147
Summary	p. 153
The Fourth-Order Statistics and the Optical Intensity Power Spectrum	p. 155
The Fourth-Order Field Correlation Functions	p. 156
General Properties	p. 156
The Frequency-Domain Representation of a Function of Four Variables Which Is Independent of Their Sum	p. 158
The Auxiliary Correlation Functions	p. 159
The Frequency-Domain Representation of the Fourth-Order Correlation Functions	p. 160
Special Cases	p. 162
Polarized and Unpolarized Fields	p. 162
Separable Field	p. 162
Gaussian Field	p. 163
The Random-Phase Field	p. 164
The Optical Intensity Power Spectrum	p. 167
The Time-Domain Representation of the Optical Intensity Power Spectrum	p. 167
The Intensity Noise Power Spectrum and the Intensity Variance	p. 168
The Frequency-Domain Representation	p. 170
Special Cases	p. 172
The Optical Intensity Power Spectrum of a Real Field and Its Associated Complex Field	p. 173
The Relative Intensity Noise Power Spectrum	p. 176
A Comparison Between Field-Induced Noise and Shot Noise	p. 177
Summary	p. 181
The Output Intensity Power Spectrum of Time-Independent Networks	p. 183
The Power Spectrum of the Output Field	p. 184
The Power Spectrum of the Output Field Intensity	p. 185
The General Expression	p. 185
Simplifications of the General Case	p. 187
A Phase-Noise Source Coupled to a Dispersive Waveguide	p. 189
A Degenerate Dispersive Waveguide and Its H Function	p. 190
Computation of the First Term in the Output Noise Power Spectrum	p. 191
The Output Intensity Noise Power Spectrum	p. 192
Frequency-Periodic Networks and the Incoherent Limit	p. 196
Discrete and Frequency-Periodic Networks	p. 196
The Decomposition Theorem	p. 198
The Output Average Intensity in the Incoherent Limit Approximation	p. 199
The Power Spectrum of the Optical Intensity Noise in the Incoherent Limit Approximation	p. 200
Network Parameters for the Characterization of the Output Intensity Noise in the Incoherent Limit	p. 202
The Network Characteristic Matrices and Noise Factors	p. 202
The Output Intensity Variance	p. 204
Summary	p. 206
Analytic Methods for the Incoherent Limit	p. 209
Application of the Residue Calculus for the Calculation of the Averaging Integral	p. 210
Computation of the Network Characteristic Functions	p. 211
The K Characteristic Function	p. 211
The L Characteristic Function	p. 215
The Guided-Wave Fabry-Perot Interferometer (Example)	p. 216
The K Characteristic Function	p. 217
The L Characteristic Function	p. 218
The Fabry-Perot Noise Factors	p. 218
The Variance Coefficient for the Fabry-Perot Interferometer	p. 220
The Recirculating Loop (Example)	p. 222
The Characteristic Functions	p. 222
The Recirculating Loop Noise Factors	p. 223
The Recirculating Loop Variance Coefficient	p. 225
The Guided-Wave Mach-Zehnder Interferometer (Example)	p. 227
The Characteristic Functions	p. 227
The Mach-Zehnder Noise Factors	p. 229
Summary	p. 229
Signal Analysis in Networks That Are Periodic in Time	p. 233
The Output Field of Time-Periodic Networks	p. 234
The Power Spectrum of the Output Field	p. 236
The General Formulation	p. 236
Qualitative Features of the Output Field Power Spectrum	p. 238
The Average of the Output Intensity	p. 240
Instantaneous Modulators (Example)	p. 241
The Output Intensity Power Spectrum	p. 243
General Formulation	p. 243
Qualitative Features of the Output Intensity Power Spectrum	p. 247
Instantaneous Modulators (Example)	p. 249
Analysis of the Modulated Fiber-Optic Gyro	p. 251
Summary	p. 254
Optical Signal and Noise in a Coherent Laser Radar	p. 255
The Transfer Functions of the Lidar System	p. 256
The Output Field Power Spectrum	p. 257
The Output Intensity Noise Power Spectrum	p. 258
The Output Intensity Power Spectrum	p. 261
The Signal-to-Noise Ratio in a Coherent Lidar	p. 262
Summary	p. 265
Index	p. 267
Table of Contents provided by Syndetics. All Rights Reserved.

Optical Network Theory

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