Theory of Nonlinear Pulse Propagation in Periodic Structures

Abstract

We consider here the propagation of intense light in a periodic structure. The models that we discuss are one-dimensional; this means that only a sin­gle spatial direction, that in which the light propagates, is relevant, and that the refractive index only depends on this spatial coordinate. Of course such a geometry is highly idealized, and, strictly speaking, only applies to a plane wave propagating through a periodically stratified medium, in a direction orthogonal to the layers. However, it is a very good approximation for light propagating through an optical fiber with a grating written in the core, or for a ridge waveguide with a periodic variation in its thickness. The reason for this is that the light is in a mode of the guided-wave structure and that the perturbation is so weak that coupling into other modes, including radiation modes, can often be neglected. A one-dimensional treatment is thus an excellent approximation, provided that the relevant mode is sufficiently far from cut-off. In practice the geometries are designed such that this is always true.