ON THE ACCURACY OF THE FINITE-DIFFERENCE METHOD FOR APPLICATIONS IN BEAM PROPAGATING TECHNIQUES

In this paper it is shown that the inaccuracy in the beam propagation method based on the finite difference scheme, introduced by the use of the slowly varying envelope approximation, can be overcome in an effective way. By the introduction of a perturbation expansion the accuracy can be improved as much as wanted, often nearly without any increase of the computation time. An error analysis is given and the method is illustrated by an example.