Computer simulations of nonlinear propagation of an optical pulse using a finite-difference in the frequency-domain method

To simulate propagation of an optical pulse in a nonlinear medium, a finite-difference in frequency-domain (FDFD) method was developed. In this method, Maxwell's equations were solved rigorously without introducing an electric-field envelope function commonly used in conventional methods. This method was used to calculate the propagation of an optical soliton in a fused-silica-like material, and results were compared with those of a finite-difference in time-domain (FDTD) method. It was found that the FDFD method was efficient and more robust than the FDTD method. Another advantage of the FDFD method is the case of incorporating arbitrary linear dispersion relations into the calculations.