Threshold energy of vectorial spatial solitary waves in non-linear quadratic crystals

Excitation and propagation of spatial solitary waves due to three-wave mixi ng in quadratic non-linear media lead to a rich variety of interesting phen omena some of which have already experimental evidence. Analytical and nume rical modelling plays a key role in gaining insight in the experimental dat a, in completing the theoretical understanding of the process and in predic ting new possible applications. In this context, we present an extensive an alytical and numerical study on the multi-parameter family of vectorial spa tial solitary waves in bulk quadratic crystals. We focus our attention part icularly on the threshold energy necessary to drive solitary waves on avail able crystals exhibiting a second order non-linearity and in describing how this threshold depends on the crystal parameters.