Comparisons of finite difference beam propagation methods for modeling second-order nonlinear effects

Three numerical methods, iterative finite difference (FD), split-step, and iterative split-step beam propagation methods (BPM's), for modeling second- order nonlinear effects are evaluated. All three methods are able to handle the depletion of the pump wave. The evaluation shows that both iterative m ethods are more accurate than the split-step method. In addition, the itera tive split-step method, even with its iterative nature, is more efficient t han the split-step one. Between the two iterative methods, further comparis ons indicate that, for a small stepsize, both have comparable accuracy. As the stepsize increases, the iterative split-step method is not as accurate as the iterative finite-difference one. However, the former method has a hi gher efficiency, suggesting that it is a better choice when the stepsize ha s to be small because of, for example, the quasiphase-matched geometrical c onfiguration.