Abstract

Self-trapping and soliton-like propagation due to interplay of dispersion and nonlinearity-induced phase shift due to cascaded nonlinearities [1] has attracted a great deal of interest [2-6]. Soliton propagation may occur either in the form of strongly coupled symbiotic pairs for the fundamental-frequency (FF) and the second-harmonic (SII) fields [2-6], or in the limit of nonzero mismatch, for which the propagation is governed by an equivalent nonlinear Schrödinger (NLS) equation for the FF field, obtained by means of asymptotic techniques [7]. However, in χ⁽²⁾ materials there always exist cubic nonlinearities which might become also important and even compete with quadratic nonlinearities. Here we analyze the effect of such competing nonlinearities on properties of solitary waves. As we will show, self-phase (SPM) and cross-phase (CPM) modulation induced by a cubic nonlinearity can strongly perturb solitary waves of a purely quadratic medium, and they may eventually destroy them. Nevertheless, we show that, even for such competing nonlinearities, stable solitary waves do exist.

© 1995 Optical Society of America