The effect of an inhomogeneous cladding of a gradient optical waveguide on the mode and envelope characteristics of a soliton pulse

Abstract

The nonlinear dynamics of a short pulse in a gradient waveguide layer is studied analytically taking into account the occurrence of a cladding layer and the longitudinal inhomogeneity of the two layers. The class of functions is presented in terms of which the transverse profiles of the refractive indices of both the gradient and the cladding layers can be represented, and, at the same time, the mode structure of the pulse can be explicitly described in terms of a hypergeometric equation. Expressions are presented that describe the variations of the propagation constant and transverse distribution of the wave field under the action of the longitudinal inhomogeneities of the gradient and cladding layers. It is shown that the envelope of the pulse satisfies the generalized nonlinear Schrodinger equation the coefficients of which are functions of the longitudinal coordinate and are expressed via the refractive indices of the waveguide layer and cladding.