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Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion

We model the propagation and interaction of few-cycle pulses using a variant of the finite-difference time-domain (FDTD) method that incorporates a novel pseudospectral technique. Our pseudospectral spatial-domain (PSSD) method offers significant advantages over the standard FDTD approach. Run time is comparable to the analogous FDTD and pseudospectral time-domain (PSTD) methods, but our technique is far more flexible. Representative results are presented for self-phase modulation, second and third harmonic generation and parametric generation, in both real and designer media. We also include results that illustrate the interplay of third harmonic generation and self-phase modulation in the formation of carrier shocks.