Numerical solutions of the Maxwell–Bloch equations for a fiber amplifier

Amplification of ultrashort pulses in fiber amplifiers is discussed within the context of the Maxwell–Bloch equations. The model includes the active medium nonlinear gain and absorption, dispersion and saturation effects through Bloch’s equations and the fiber group-velocity dispersion, higher-order group-velocity dispersion, self-steepening, and stimulated Raman scattering through the phenomenological Maxwell equation. We compare the complete model to the simplified models in the literature and show that a detailed quantitative analysis for femtosecond pulses requires the full Maxwell–Bloch treatment.