Interactions of Type II vectorial spatial solitary waves in materials with quadratic non-linearity

We present analytical, numerical and experimental results of the interactions between Type II vectorial spatial solitary waves (QSSW) in second-order non-linear media. We show that the outcome of the interaction can be changed from beam coalescence to steering, crossing or repulsion through a non-coherent control (i.e. the control does not rely on the relative phase between the interacting QSSW). We also provide experimental evidence that both quasi-elastic and inelastic collision between QSSW are feasible in second order non-linear media, depending on the relative velocity of the interacting QSSW. We determine (analytically, numerically and experimentally) the critical transverse velocity for elastic collision to be observed, when the fundamental frequency component of the two interacting beams are orthogonally polarized at the input face of the non-linear crystal.