Page 9 - Fiber Bragg Gratings

viii Contents

3.1.1 The bulk interferometer 55
3.1.2 The phase mask 57
3.1.3 The phase mask interferometer 62
3.1.4 Slanted grating 69
3.1.5 The scanned phase mask interferometer 71
3.1.6 The Lloyd mirror and prism interferometer 74
3.1.7 Higher spatial order masks 77
3.1.8 Point-by-point writing 80
3.1.9 Gratings for mode and polarization conversion 80
3.1.10 Single-shot writing of gratings 83
3.1.11 Long-period grating fabrication 84
3.1.12 Ultralong-fiber gratings 85
3.1.13 Tuning of the Bragg wavelength, moire,
Fabry-Perot, and superstructure gratings 88
3.1.14 Fabrication of continuously chirped gratings 93
3.1.15 Fabrication of step-chirped gratings 99
3.2 Type II gratings 101
3.3 Type IIA gratings 101
3.4 Sources for holographic writing of gratings 102
3.4.1 Low coherence sources 102
3.4.2 High coherence sources 104
References 108

Chapter 4 Theory of Fiber Bragg Gratings 119
4.1 Wave Propagation 121
4.1.1 Waveguides 122
4.2 Coupled-mode theory 125
4.2.1 Spatially periodic refractive index modulation 127
4.2.2 Phase matching 130
4.2.3 Mode symmetry and the overlap integral 131
4.2.4 Spatially periodic nonsinusoidal refractive index
modulation 133
4.2.5 Types of mode coupling 134
4.3 Coupling of counterpropagating guided modes 142
4.4 Codirectional coupling 145
4.5 Polarization couplers: Rocking filters 148
4.6 Properties of uniform Bragg gratings 152
4.6.1 Phase and group delay of uniform period
gratings 155