Modelling of strongly nonlinear sinusoidal Bragg gratings by the Method of Single Expression

Abstract

The one-dimensional problem of plane EM wave interaction with strongly nonlinear sinusoidal Bragg gratings is exactly solved using the new Method of Single Expression (MSE). The basic point of the method is the presentation of the electrical field in the modulated medium (Bragg grating) in the form of a single expression, contrary to the traditional counter-propagating waves approach. The spectral characteristics of linear Bragg gratings of different length are presented. The influence of loss or gain on the spectral characteristics of Bragg gratings is considered. The electrical field amplitude distributions along a grating at the wavelengths corresponding to the minima and maxima of reflectivity in the vicinity of the Bragg resonance are illustrated. Bistable and multistable dependences of reflectivity on the incident electrical field amplitude are obtained for negative and positive nonlinearities.