Numerical simulation with finite differences of wave propagation in diffractive quadratic media

In this paper, we numerically solve a nonlinear Schrodinger-like system occuring in nonlinear optics with a new method, based on finite differences both in longitudinal and orthogonal space. Whereas various procedures have been written with the use of a split-step algorithm, we do not separate the diffractive and nonlinear part in the numerical resolution. The problem of the numerical treatment of the boundary is overcome with the theory of absorbing conditions. Several numerical experiments are presented.