Hybrid solitary waves in quadratic nonlinear media

Considering nondegenerate, backward quasi-phase-matched parametric interact ion, we show that quadratic media support two dimensional ''hybrid'' solita ry waves. Their structure results from the combination of two distinct mech anisms which, in isolation, are at the origin of the two classes of quadrat ic solitary waves considered in nonlinear optics. In the transverse dimensi on the structure results from a balance between diffraction and quadratic n onlinearity while the longitudinal structure results from net energy exchan ges between the three interacting velocity-mismatched waves. The hybrid sol itary waves can propagate at arbitrarily small velocity, a feature that sho uld make them easy to observe experimentally. [S1063-651X(99)05803-1].