Dispersive time-delay dynamical systems

Abstract

We present a theoretical approach to model the dynamics of a dispersive nonlinear system using a set of delay differential equations with distributed delay term. We illustrate the use of this approach by considering a frequency swept laser comprising a semiconductor optical amplifier (SOA), a tunable bandpass filter and a long dispersive fiber delay line. We demonstrate that this system exhibits a rich spectrum of dynamical behaviors which are in agreement with the experimental observations. In particular, the multimode modulational instability observed experimentally in the laser in the anomalous dispersion regime and leading to a turbulent laser output was found analytically in the limit of large delay time.