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

Excitation and propagation of spatial solitary waves due to three-wave mixing in quadratic non-linear media lead to a rich variety of interesting phenomena some of which have already experimental evidence. Analytical and numerical modelling plays a key role in gaining insight in the experimental data, in completing the theoretical understanding of the process and in predicting new possible applications. In this context, we present an extensive analytical and numerical study on the multi-parameter family of vectorial spatial solitary waves in bulk quadratic crystals. We focus our attention particularly on the threshold energy necessary to drive solitary waves on available crystals exhibiting a second order non-linearity and in describing how this threshold depends on the crystal parameters.