I Introduction ................................................. 1
1 A Quick Survey ............................................... 3
II Physical Foundations ....................................... 13
2 Treatment with Ray Optics ................................... 15
2.1 Waveguiding by Total Internal Reflection ............... 15
2.2 Step Index Fiber ....................................... 17
2.3 Modal Dispersion ....................................... 20
2.4 Gradient Index Fibers .................................. 22
2.5 Mode Coupling .......................................... 23
2.6 Shortcomings of the Ray-Optical Treatment .............. 24
3 Treatment with Wave Optics .................................. 25
3.1 Maxwell's Equations .................................... 25
3.2 Wave Equation .......................................... 27
3.3 Linear and Nonlinear Refractive Index .................. 28
3.3.1 Linear Case ..................................... 28
3.3.2 Nonlinear Case .................................. 29
3.4 Separation of Coordinates .............................. 30
3.5 Modes .................................................. 32
3.6 Solutions for m = 0 .................................... 35
3.7 Solutions for m = 1 .................................... 37
3.8 Solutions for m > 1 .................................... 38
3.9 Field Amplitude Distribution of the Modes .............. 38
3.10 Numerical Example ...................................... 41
3.11 Number of Modes ........................................ 42
3.12 A Remark on Microwave Waveguides ....................... 43
3.13 Energy Transport ....................................... 43
4 Chromatic Dispersion ........................................ 47
4.1 Material Dispersion .................................... 48
4.1.1 Treatment with Derivatives to Wavelength ........ 50
4.1.2 Treatment with Derivatives to Frequency ......... 51
4.2 Waveguide and Profile Dispersion ....................... 53
4.3 Normal, Anomalous, and Zero Dispersion ................. 54
4.4 Impact of Dispersion ................................... 55
4.5 Optimized Dispersion: Alternative Refractive Index
Profiles ............................................... 58
4.5.1 Gradient Index Fibers ........................... 58
4.5.2 W Fibers ........................................ 59
4.5.3 T Fibers ........................................ 61
4.5.4 Quadruple-Clad Fibers ........................... 61
4.5.5 Dispersion-Shifted or Dispersion-Flattened? ..... 62
4.6 Polarization Mode Dispersion ........................... 64
4.6.1 Quantifying Polarization Mode Dispersion ........ 64
4.6.2 Avoiding Polarization Mode Dispersion ........... 65
4.7 Microstructured Fibers ................................. 67
4.7.1 Holey Fibers .................................... 69
4.7.2 Photonic Crystal Fibers ......................... 73
4.7.3 New Possibilities ............................... 74
5 Losses ...................................................... 75
5.1 Loss Mechanisms in Glass ............................... 75
5.2 Bend Loss .............................................. 77
5.3 Other Losses ........................................... 79
5.4 Ultimate Reach and Possible Alternative
Constructions .......................................... 80
5.4.1 Heavy Molecules ................................. 81
5.4.2 Hollow Core Fibers .............................. 82
5.4.3 Sapphire Fibers ................................. 83
5.4.4 Plastic Fibers .................................. 83
III Technical Conditions for Fiber Technology ................. 85
6 Manufacturing and Mechanical Properties ..................... 87
6.1 Glass as a Material .................................... 87
6.1.1 Historical Issues ............................... 87
6.1.2 Structure ....................................... 88
6.1.3 How Glass Breaks ................................ 91
6.2 Manufacturing of Fibers ................................ 93
6.2.1 Making a Preform ................................ 93
6.2.2 Pulling Fibers from the Preform ................. 96
6.3 Mechanical Properties of Fibers ........................ 98
6.3.1 Pristine Glass .................................. 98
6.3.2 Reduction of Structural Stability ............... 99
7 How to Measure Important Fiber Characteristics ............. 101
7.1 Loss .................................................. 101
7.2 Dispersion ............................................ 102
7.3 Geometry of Fiber Structure .......................... 106
7.4 Geometry of Amplitude Distribution .................... 108
7.4.1 Near-Field Methods ............................. 108
7.4.2 Far-Field Methods .............................. 110
7.5 Cutoff Wavelength ..................................... 112
7.6 Optical Time Domain Reflectometry (OTDR) .............. 114
8 Components for Fiber Technology ............................ 117
8.1 Cable Structure ....................................... 117
8.2 Preparation of Fiber Ends ............................. 119
8.3 Connections ........................................... 120
8.3.1 Nonpermanent Connections ....................... 120
8.3.2 Permanent Connections .......................... 123
8.4 Elements for Spectral Manipulation .................... 124
8.4.1 Fabry-Perot Filters ............................ 124
8.4.2 Fiber-Bragg Structures ......................... 124
8.5 Elements for Polarization Manipulation ................ 125
8.5.1 Polarization Adjusters ......................... 125
8.5.2 Polarizers ..................................... 127
8.6 Direction-Dependent Devices ........................... 128
8.6.1 Isolators ...................................... 128
8.6.2 Circulators .................................... 130
8.7 Couplers .............................................. 131
8.7.1 Power Splitting/Combining Couplers ............. 131
8.7.2 Wavelength-Dependent Couplers .................. 133
8.8 Optical Amplifiers .................................... 134
8.8.1 Amplifiers Involving Active Fibers ............. 135
8.8.2 Amplifiers Involving Semiconductor Devices ..... 138
8.9 Light Sources ......................................... 139
8.9.1 Light from Semiconductors ...................... 139
8.9.2 Luminescent Diodes ............................. 140
8.9.3 Laser Diodes ................................... 140
8.9.4 Fiber Lasers ................................... 145
8.10 Optical Receivers ..................................... 145
8.10.1 Principle of pn and pin Photodiodes ............ 146
8.10.2 Materials ...................................... 148
8.10.3 Speed .......................................... 148
8.10.4 Noise .......................................... 148
8.10.5 Avalanche Diodes ............................... 149
IV Nonlinear Phenomena in Fibers ............................. 151
9 Basics of Nonlinear Processes .............................. 153
9.1 Nonlinearity in Fibers vs. in Bulk .................... 153
9.2 Kerr Nonlinearity ..................................... 155
9.3 Nonlinear Wave Equation ............................... 156
9.3.1 Envelope Equation Without Dispersion ........... 156
9.3.2 Introducing Dispersion by a Fourier
Technique ...................................... 158
9.3.3 The Canonical Wave Equation: NLSE .............. 160
9.3.4 Discussion of Contributions to the Wave
Equation ....................................... 161
9.3.5 Dimensionless NLSE ............................. 162
9.4 Solutions of the NLSE ................................. 165
9.4.1 Modulational Instability ....................... 165
9.4.2 The Fundamental Soliton ........................ 165
9.4.3 How to Excite the Fundamental Soliton .......... 170
9.4.4 Collisions of Solitons ......................... 174
9.4.5 Higher-Order Solitons .......................... 174
9.4.6 Dark Solitons .................................. 176
9.5 Digression: Solitons in Other Fields of Physics ....... 178
9.6 More χ(3) Processes ................................... 180
9.7 Inelastic Scattering Processes ........................ 182
9.7.1 Stimulated Brillouin Scattering ................ 183
9.7.2 Stimulated Raman Scattering .................... 188
10 A Survey of Nonlinear Processes ............................ 193
10.1 Normal Dispersion ..................................... 193
10.1.1 Spectral Broadening ............................ 193
10.1.2 Pulse Compression .............................. 195
10.1.3 Chirped Amplification .......................... 195
10.1.4 Optical Wave Breaking .......................... 197
10.2 Anomalous Dispersion .................................. 199
10.2.1 Modulational Instability ....................... 199
10.2.2 Fundamental Solitons ........................... 200
10.2.3 Soliton Compression ............................ 201
10.2.4 The Soliton Laser and Additive Pulse Mode
Locking ........................................ 202
10.2.5 Pulse Interaction .............................. 203
10.2.6 Self-Frequency Shift ........................... 205
10.2.7 Long-Haul Data Transmission with Solitons ...... 207
V Technological Applications of Optical Fibers ............... 209
11 Applications in Telecommunications ......................... 211
11.1 Fundamentals of Radio Systems Engineering ............. 211
11.1.1 Signals ........................................ 211
11.1.2 Modulation ..................................... 212
11.1.3 Sampling ....................................... 216
11.1.4 Coding ......................................... 218
11.1.5 Multiplexing in Time and Frequency: TDM and
WDM ............................................ 218
11.1.6 On and Off: RZ and NRZ ......................... 220
11.1.7 Noise .......................................... 221
11.1.8 Transmission and Channel Capacity .............. 224
11.2 Nonlinear Transmission ................................ 225
11.2.1 A Single Wavelength Channel .................... 226
11.2.2 Several Wavelength Channels .................... 229
11.2.3 Alternating Dispersion ("Dispersion
Management") ................................... 231
11.3 Technical Issues ...................................... 234
11.3.1 Monitoring of Operations ....................... 234
11.3.2 Eye Diagrams ................................... 236
11.3.3 Filtering to Reduce Crosstalk .................. 236
11.4 Telecommunication: A Growth Industry .................. 238
11.4.1 Historical Development ......................... 238
11.4.2 The Limits to Growth ........................... 243
12 Fiber-Optic Sensors ........................................ 247
12.1 Why Sensors? Why Fiber-Optic? ......................... 247
12.2 Local Measurements .................................... 249
12.2.1 Pressure Gauge ................................. 249
12.2.2 Hydrophone ..................................... 249
12.2.3 Temperature Measurement ........................ 251
12.2.4 Dosimetry ...................................... 252
12.3 Distributed Measurements .............................. 253
12.4 The Status Today ...................................... 256
VI Appendices ................................................ 257
A Decibel Units .............................................. 259
A.l Definition ............................................ 259
A.2 Absolute Values ....................................... 260
A.3 Possible Irritations .................................. 260
A.4 Beer's Attenuation and dB Units ....................... 261
В Skin Effect ................................................ 263
С Bessel Functions ........................................... 265
C.l Terminology for the Various Functions ................. 265
C.2 Relations Between These Functions ..................... 266
C.3 Recursion Formulae .................................... 266
C.4 Properties of Jm and Km ............................... 266
C.5 Zeroes of J0, J1, and J2 ............................... 267
C.6 Graphs of the Most Frequently Used Functions .......... 267
D Optics with Gaussian Beams .................................. 269
D.l Why Gaussian Beams? ................................... 269
D.2 Formulae for Gaussian Beams ........................... 270
D.3 Gaussian Beams and Optical Fibers ..................... 271
E Relations for Secans Hyperbolicus .......................... 273
F Autocorrelation Measurement ................................ 275
F.l Measurement of Ultrashort Processes ................... 275
F.l.l Correlation .................................... 275
F.1.2 Autocorrelation ................................ 276
F.1.3 Autocorrelation Measurements ................... 277
F.1.4 A Catalogue of Autocorrelation Shapes .......... 278
Bibliography .................................................. 281
Glossary ...................................................... 293
Index ......................................................... 299
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