Abstract

Recently, it was demonstrated experimentally that nonlinearity-induced phase shifts may be achieved in χ⁽²⁾ materials by means of cascaded nonlinearities.¹ This opens new perspectives for analyzing well-known nonlinear effects in cubic materials, such as self-focusing and (spatial or temporal) optical solitons, that exist solely because of X⁽²⁾. As shown in Ref. 2, bright solitons can exist in χ⁽²⁾ materials in the form of two- wave symbiotic (i.e., strongly coupled) localized modes of the fundamental and the second-harmonic fields. The explicit analytical forms² of such solitons are only a particular case of a family of localized solutions of an effective dynamical system.³ However, in χ⁽²⁾ materials there always exist next-order (i.e., cubic nonlinearities, which might become very important and even strongly compete with quadratic nonlinearities (see, e.g., Ref. 4). In this paper we discuss the effects of the competing nonlinearities on the existence and stability properties of bright optical solitons. Using analytical and numerical (shooting) methods, we find families of the simplest localized soliton solutions and their bifurcations to more complicated ones. Some of these solutions resemble the familiar solitons known for either pure χ⁽²⁾ or χ^,3) media, but we also find other solitons that reflect the effect of the competing nonlinearities. We consider the coupled equations obeyed by the envelope amplitudes £, and E₂ of the first (ω₂ = ω) and second (ω₂ = 2ω) harmonics in a χ⁽²⁾ + χ⁽³⁾ medium,

© 1995 Optical Society of America