BRIGHT AND DARK SOLITARY WAVES IN THE PRESENCE OF 3RD-HARMONIC GENERATION

We analyze the effect of phase-matched third-harmonic generation on th e existence and stability of (1 + 1)-dimensional bright and dark spati al solitary waves in optical media with a cubic (or Kerr) nonlinear re sponse. We demonstrate that parametric coupling of the fundamental bea m with the third harmonic leads to the existence of two-color solitary waves resembling those in a chi((2)) medium and that it can modify dr astically the properties of solitary waves due to effective non-Kerr n onlinearities. In particular, we find a power threshold for the existe nce of two-frequency parametric bright solitons and also reveal the so liton multistability in a Ken medium that becomes possible offing to a higher-order nonlinear phase shift caused by cascaded third-order pro cesses. We also analyze dark solitary waves and their stabilities. We show that, in a certain parameter domain, parametric chi((3)) dark sol itons may become unstable owing to the modulational instability of the supporting background or to other instability mechanisms caused by th e parametric coupling between the harmonics. (C) 1998 Optical Society of America [S0740-3224(98)02004-9].