"Fourier-Direct Method" for the Analysis of Monocycle Optical Pulses Propagating in Nonlinear Media.

Abstract

We analyzed the nonlinear propagation of monocycle optical pulses under intense dispersion and nonlinear effects in glass fibers. We applied bi-directional propagation equations, as fundamental as Maxwell's equations, without approximations to derive the nonlinear Schrödinger equation (NLS equation) including the slowly varying envelop approximation (SVEA). We were able to incorporate the delayed Raman response, the self-steepening and the core-dispersion as well as the full linear dispersion. We solved them by the split-step Fourier method (SSF), which was extended and improved for multi-dimensional integro-differential equations, instead of the finite-difference time-domain numerical method (FDTD). We call this approach the Fourier-direct method (FDM). We compared the obtained results with those by the NLS equation and calculated the compressed pulses after complete chirp compensation.