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 methods are more accurate than the split-step method. In addition, the iterative split-step method, even with its iterative nature, is more efficient than the split-step one. Between the two iterative methods, further comparisons 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 higher efficiency, suggesting that it is a better choice when the stepsize has to be small because of, for example, the quasiphase-matched geometrical configuration.