Phase modulations due to collisions of beam pairs in nonlocal nonlinear media

In this paper, discussed is the evolution of two co-propagating optical beams in parallel in nonlocal Kerr media, governed by the nonlocal nonlinear Schrödinger equation (NNLSE). A simplified model to the NNLSE is presented when the media is strongly nonlocal, which is a bridge between the Snyder–Mitchell model (Snyder and Mitchell Science 276 1538, 1997) and the strongly-nonlocal model (Guo, Luo, Yi, Chi, and Xie Phys. Rev. E. 69 016602, 2004). It is found that when one of the soliton beams is much stronger than the other, the weaker (probe beam) can experience $\pi $ nonlinear phase shift, which can be modulated by the stronger (pump beam), within a rather short propagation distance (about 40-m). The comparisons of analytical solutions of the model with numerical simulations of the NNLSE show that the model is of excellent accuracy in the case of strong nonlocality.