Theory of grating superstructures

Abstract

We develop the theory of linear and nonlinear grating superstructures, gratings in which the parameters vary periodically with position on the scale of typically about 1 mm. Following earlier work in semiconductors, these have now been written in optical fibers. We develop the theory by introducing a set of superenvelopes: envelopes of the usual envelope functions of the grating structure. We show that under very general conditions these superenvelopes satisfy a set of supercoupled mode equations, and that these equations have solitary wave solutions.