Few-cycle optical solitons in dispersive media beyond the envelope approximation

Abstract

We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our theory extends beyond the slowly varying envelope approximation. The optical field is derived directly from the Maxwell equations under the assumption that generation of the third harmonic is a non-resonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using a modification of the spectral renormalisation method originally developed for the envelope solitons.