Chapter 4 – Theory of Fiber Bragg Gratings

Publisher Summary This chapter reviews the theory of fiber Bragg gratings. A fiber Bragg grating of a constant refractive index modulation and period therefore has an analytical solution. A complex grating is considered to be a concatenation of several small sections, each of constant period and unique refractive index modulation. The modeling of the transfer characteristics of fiber Bragg gratings becomes a relatively simple matter, and the application of the transfer matrix method provides a clear and fast technique for analyzing more complex structures. The modes of an optical fiber can be described as a summation of transverse guided mode amplitudes along with a continuum of radiation modes with corresponding propagation constant. The waveguide modes satisfy the unperturbed wave equation. In order to derive the coupled mode equations, effects of perturbation have to be included, assuming that the modes of the unperturbed waveguide remain unchanged. The spatially periodic refractive index modulation is also elaborated in the chapter.

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