Vectorial solitary waves in optical media with a quadratic nonlinearity

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Abstract
We search for self-trapped beams due to the vectorial interaction of two orthogonally polarized components of a fundamental harmonic and a single component of the second harmonic in a quadratically nonlinear medium. The basic set of equations for both the temporal and the spatial case is derived. The resulting two-parameter family of solitary waves is investigated by means of a variational approximation and by direct numerical methods. Several limiting cases and differences to the scalar interaction in quadratic media are discussed. The propagation of stable solitary waves and mutual collisions are simulated and the decay of unstable solitary waves is demonstrated. We predict an internal boundary in the soliton parameter space which separates stable and unstable domains.