Propagation of coupled super-Gaussian beam pairs in strong nonlocal media

The propagation of two mutually incoherent coupled super-Gaussian (SG) beam pairs in strong nonlocal media was studied by variational approach and numerical simulation. For forming a SG vector solitary wave, the total initial power must be equal to the critical power and the ratio of the two beam widths should be equal to a certain value. The numerical results show that the normalized critical power is a monotonically increase function of the order of SG solitary wave. Therefore, the phase shift, which is effectively determined by the critical power, will increase quickly with the order of SG solitary wave increasing. Since the phase shift is large for the low-order SG solitary wave and SG beam has some characteristics different with Gaussian beam, this theoretical result maybe has some potential applications value.