Analytical Description of Quadratic Parametric Solitons

Abstract

Abstract. We study quadratic solitons supported by two-wave parametric interaction in X(2) nonlinear media. We obtain very accurate explicit solutions for bright solitons with the help of a specially developed analytical approach.Nowdays, the study of the physics of spatial optical solitons is an active area of research. In particular, parametric solitons, i.e. beams composed of mutually trapped fundamental and harmonic waves that propagate with undistorted profiles, were observed in media with quadratic (i.e. X(2)) nonlinearity, and their unique features can be utilized for the creation of alloptical information processing devices [1] . Many studies have been devoted to the theoretical analysis of quadratic solitons [2]. It was demonstrated that even in the simplest case of "type I" interaction between the fundamental frequency (FF) and second-harmonic (SH) waves in a planar waveguide, the soliton profiles depend on both the linear phase mismatch parameter, characterizing the nonlinear medium, and the propagation constant, related to the soliton wave number modified by nonlinear self-action. However, the governing equations are not integrable, and exact analytical expressions for the soliton profiles are known only for particular parameter values. If the parameters are close to these special values, approximate solutions can be obtained by asymptotic or variational techniques [3,4]. On the other hand, a variational approach, with Gaussian trial functions, can be used to find approximate soliton envelopes in the whole parameter range, but then the soliton tails (or far-field asymptotics) are not described corre ctly [3,5]. In this paper we introduce a different approach to find very accurate approximate solutions which (i) are valid for any values of the soliton parameters, and (ii) reduce to the exact solutions for the special cases.The parametric interaction between the FF and SH beams in a slab waveguide can be described by the following set of coupled equations [6] III A.D. Boardman and A.P. Sukhorukov (eds.) ,