Page 10 - Fiber Bragg Gratings

Contents ix

4.7 Radiation mode couplers 157
4.7.1 Counterpropagating radiation mode coupler:
The side-tap grating 157
4.7.2 Copropagating radiation mode coupling: Long-
period gratings 171
4.8 Grating simulation 178
4.8.1 Methods for simulating gratings 178
4.8.2 Transfer matrix method 179
4.9 Multilayer analysis 185
4.9.1 Rouard's method 185
4.9.2 The multiple thin-film stack 186
References 189

Chapter 5 Apodization of Fiber Gratings 195
5.1 Apodization shading functions 197
5.2 Basic principles and methodology 199
5.2.1 Self-apodization 200
5.2.2 The amplitude mask 203
5.2.3 The variable diffraction efficiency phase mask 205
5.2.4 Multiple printing of in-fiber gratings applied to
apodization 206
5.2.5 Position-weighted fabrication of top-hat
reflection gratings 208
5.2.6 The moving fiber/phase mask technique 211
5.2.7 The symmetric stretch apodization method 216
5.3 Fabrication requirements for apodization and chirp 221
References 223

Chapter 6 Fiber Grating Band-pass Filters 227
6.1 Distributed feedback, Fabry-Perot, superstructures,
and moire gratings 229
6.1.1 The distributed feedback grating 229
6.1.2 Superstructure band-pass filter 239
6.2 The Fabry-Perot and moire band-pass filters 242
6.3 The Michelson interferometer band-pass filter 246
6.3.1 The asymmetric Michelson multiple-band-pass
filter 255
6.4 The Mach-Zehnder interferometer band-pass filter 260