Spontaneous X waves: numerical experiments

This study presents a detailed analysis based on numerical experiments devoted to the characterization of the non-linear spatio-temporal dynamics of an initially separable (gaussian-like, spherical, short and focused) wave-packet, encompassing second-harmonic generation (SHG) in a conventional, bulk, X⁽²⁾ material. The initial self focusing of the fundamental wave is supported by the chosen positive phase mismatch. As to the temporal broadening, the authors addressed both the case of dominant group-velocity mismatch and the case dominated by positive group-velocity dispersion.