Hybrid solitary waves in quadratic nonlinear media

Considering nondegenerate, backward quasi-phase-matched parametric interaction, we show that quadratic media support two dimensional ''hybrid'' solitary waves. Their structure results from the combination of two distinct mechanisms which, in isolation, are at the origin of the two classes of quadratic solitary waves considered in nonlinear optics. In the transverse dimension the structure results from a balance between diffraction and quadratic nonlinearity while the longitudinal structure results from net energy exchanges between the three interacting velocity-mismatched waves. The hybrid solitary waves can propagate at arbitrarily small velocity, a feature that should make them easy to observe experimentally. [S1063-651X(99)05803-1].