Accurate propagation of ultrashort pulses in nonlinear waveguides using propagation models for the analytic signal

Abstract

We present a numerical approach for the accurate simulation of the complex propagation dynamics of ultrashort optical pulses in nonlinear waveguides, especially valid for few-cycle pulses. The propagation models are derived for the analytical signal, which includes the real optical field, exempt from the commonly adopted slowly varying envelope approximation. As technical basis for the representation of the medium dispersion we use rational Pad´e approximants instead of commonly employed high-order polynomial expansions. The implementation of the propagation equation is based on the Runge-Kutta in the interaction picture method. In addition, our modular approach easily allows to incorporate a Raman response and dispersion in the nonlinear term. As exemplary use-cases we illustrate our numerical approach for the simulation of a few-cycle pulse at various center frequencies for an exemplary photonic crystal fiber and demonstrate the collision of a soliton and two different dispersive waves mediated by their group-velocity event horizon.