Gap solitons in a medium with third-harmonic generation

Abstract

We find two-component optical solitons in a nonlinear waveguide with a Bragg grating, including Kerr effects and third-harmonic generation (THG). The model may be realized in temporal and in spatial domains. Two species of fundamental gap solitons (GSs) are found. The first (``THG-gap soliton'') has the bulk of its energy at the fundamental frequency (FF) and a lesser part in the third-harmonic (TH) band. The FF part of the soliton is always single humped; the TH part may be single or double humped. Stability domains for quiescent and moving THG-gap solitons strongly shrink with increase of velocity. The second species is the usual (``simple'') GS, sitting entirely in the TH band. More complex solutions are also found, in the form of a bound state of a THG-gap soliton and two simple GSs, with a finite binding energy. When a THG-gap soliton is unstable, the instability is oscillatory. It may ultimately cause the THG-gap soliton to throw off some radiation and evolve into a localized structure with the FF and TH components out of phase, with or without internal oscillations. Stable solitons feature an excited state (i.e., they support a localized eigenmode).