Time-Domain Modeling of Nonlinear Optical Structures With Extended Stability FDTD Schemes

Abstract—Two numerical methodologies based on the finite-dif-ference time-domain (FDTD) technique are formulated and applied to model optical structures with Raman and Kerr type nonlinearities. The first scheme is based on the alternating-direc-tion implicit finite-difference time-domain (ADI-FDTD), while the second one is based on a recently introduced spatially filtered FDTD method. Both methods are able to extend FDTD time steps beyond the conventional Courant-Friedrichs-Lewy stability limit. It is demonstrated that both methods are significantly faster than the standard nonlinear FDTD, while maintaining its level of accuracy. Their potential as design and analysis tools for nonlinear periodic structures is demonstrated with the study of a 1-D problem involving a nonlinear Bragg reflector. Index Terms—Finite-difference time-domain (FDTD) methods, numerical stability, optical propagation in nonlinear media, peri-odic structures. I