Comprehensive finite-difference time-dependent beam propagation model of counterpropagating picosecond pulses in a semiconductor optical amplifier

In this paper, we present a numerical model to study counter pulse propagation in semiconductor optical amplifiers. An improved finite-difference beam propagation method for solving the modified nonlinear Schrödinger equation is applied for the first time in the counterpropagation regime. In our model, group velocity dispersion, two-photon absorption, ultrafast nonlinear refraction, and the change in the gain peak wavelength with carrier density are included, which have not been considered simultaneously in previous counterpropagation models. The model is applied to demonstrate how a subpicosecond and picosecond probe pulse shape and spectrum can be modified by a counterpropagating pump pulse. Based on the results obtained by this model, while subpicosecond probe pulses can be compressed by in this scheme, their time-bandwidth product are also improved significantly. Furthermore, the effects of several parameters are analyzed to obtain the proper probe spectral peak shift using counterpropagating probe pulses. The accuracy and computational efficiency of the new scheme are assessed through numerical examples and are shown to be superior to previously published approaches.