Numerical Simulation of the Nonlinear Propagation of Ultrashort Pulses in Fiber Amplifiers Using Time-Frequency Representations

To predict the behavior of high power pulsed lasers, fine numerical simulations of nonlinear propagation of short chirped pulses in fiber amplifiers are needed. In particular, the gain used in the nonlinear Schrödinger equation (NLSE) should take into account the simultaneous dependence of the gain with frequency (i.e. gain dispersion) and time (i.e. gain saturation). We propose here a method using a time-frequency representation (TFR) of the pulse to compute the gain that can be used in the NLSE. Basic TFRs can be computed by estimating the group delay or the instantaneous frequency of the pulse but the low numerical complexity of these methods introduce some limitations in term of cases that can be properly simulated. We show that the more time-consuming computation of the reassigned spectrogram (RS) of the pulse allows to obtain a gain more suitable for general cases than can be encountered in high energy ultrafast lasers.