Spatial optical solitons governed by quadratic nonlinearity

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Abstract
We demonstrate that a dielectric medium with purely quadratic nonlinearity [the so-called chi((2)) material] can display self-focusing phenomena through a new type of modulational instability of the interacting fundamental and second-harmonic field components and therefore can support propagation of (two-wave) optical solitons. We prove the existence of a family of such solitons, which are found numerically and, in some particular cases, also analytically. The two-wave solitons are stable in the whole parameter region in which they exist.