Nonlinear pulse propagation in a monomode dielectric guide

Abstract
We derive the nonlinear wave equation for an envelope of an electromagnetic wave in a monomode dielectric waveguide. Concrete examples are given for a single-mode optical fiber where the coefficients of resultant nonlinear Schrödinger equation with higher-order dispersion and dissipation (both linear and nonlinear) are given in terms of properties of the eigenfunction of the guided wave as well as of the material nonlinearity and dispersion. Using a newly-developed perturbation method, we show that the higher-order dispersions (linear and nonlinear) perserve the profile of a single soliton but to split up a bound N soliton ( N \geq 2 ) into individual solitons with different heights which propagate at different velocities. We also show that the higher-order nonlinear dissipation due to the induced Raman effect downshifts the carrier frequency of a single soliton in proportion to the distance of propagation and to the fourth power of the soliton amplitude.