Induced modulational instability in EDFAs in the presence of higher-order nonlinear and dispersive effects

We derive the dispersion equation for erbium doped fiber amplifiers (EDFAs), assuming the supplementary effects of time-derivative nonlinearities including intrapulse Raman scattering and self-steepening incorporated with third order dispersion and product of gain and square of dipole relaxation time parameter, in the extended form of nonlinear Schrödinger equation and investigate their impacts on gain and cut-off frequency of modulational instability (MI) in EDFAs. Also, the influences of those effects on instability of steady-state amplitude, in the form of generation of terahertz pulse train of femtosecond solitons from a weak-modulated signal by induced MI, are numerically simulated and discussed within EDFAs in normalized form.