Numerical methods for accurate description of ultrashort pulses in optical fibers

We consider a one-dimensional first-order nonlinear wave equation, the so-called forward Maxwell equation (FME), which applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity and spatial homogeneity in the propagation direction. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization.