Resonance and bright-dark solitons in group-velocity mismatched second-harmonic generation

Abstract

Waves interacting parametrically in quadratic media experience nonlinear phase changes which, under appropriate conditions, may be compensated for by dispersion or diffraction, resulting into mutually trapped (temporal or spatial) solitary envelopes or simultons. Although this trapping was predicted in the seventies [1], it was observed only recently for second-harmonic generation (SHG) in the 3D spatial case [2], motivating renewed interest for applications oriented to all-optical processing. Usually these solitons survive in the presence of moderate walkoff [3]. Here we investigate the opposite case for which the group-velocity difference or walk-off dominates over dispersion (or diffraction). This occurs whenever the beam widths are large enough so that the walkoff length zw is much shorter than dispersion length zd. The purpose of this communication is to show that, in this case, group-velocity difference may be offset by velocity-locking due to new types of solitons. We consider two specific cases of SHG. First, we show that type I bulk SHG, supports only dark-bright pairs whereas bright-bright solutions are not permitted. Conversely we show that when type II forward SHG occurs in a grating structure which couples the two fundamental polarization components, new types of stable solitons which fullflll the Bragg condition (i.e. resonance solitons) are supported.