Finite difference method to solve Maxwell's equations for soliton propagation

摘要

We present a finite-difference (FD) scheme for the nonlinear Maxwell's equations describing one-dimensional scalar optical soliton propagation in polarization-preserving nonlinear dispersive media. The existence of a discrete analog of the underlying continuous energy conservation law is shown to play a central role in the global accuracy of the scheme and a proof of its generalized nonlinear stability using energy methods is given. Numerical simulations of initial fundamental-, second- and third-order hyperbolic secant ultra-short soliton pulses of full width at half peak intensity equal to 25.7 fs (FWHM) containing as few as four and eight optical carrier cycles, confirm the stability, accuracy and efficiency of the algorithm. The decay of such solitons under the combined effects of higher-order dispersion and self-steepening is clearly evidenced.