Computationally-efficient FDTD modeling of supercontinuum generation in photonic crystal fibers

It is shown in this paper that a finite-difference time-domain method can be successfully applied to rigorous electromagnetic analysis of supercontinuum generation in photonic crystal fibers. Large computational requirements of the method are alleviated by the use of a hybrid procedure where, at first, vector two-dimensional simulation is applied in order to determine mode properties of the fiber. Subsequently, one-dimensional simulation of a pulse propagating in a transmission line filled with effective material is performed. The parameters of the line take into account nonlinear characteristics of the filling material as well as the previously computed mode dispersion. It is depicted that the proposed novel hybrid approach opens the way for rigorous, yet, computationally-efficient modeling of third order nonlinear processes in optically long fibers. The example investigated in this paper shows very promising results as compared with experiments and approximate numerical simulations of a nonlinear Schrodinger equation performed with the aid of the split-step Fourier method.