Average inversion level, modeling, and physics of erbium-doped fiber amplifiers

We present a detailed study of a set of models for characterizing the gain, the input and output powers of single erbium-doped fiber amplifiers (EDFAs) and networks of EDFAs. The time dependent gain is described by a single ordinary differential equation for the average inversion level of an EDFA with arbitrary number of signal channels with arbitrary power levels and propagation directions. In steady state, this ordinary differential equation becomes a transcendental equation from which many important parameters are derived. Through perturbation analysis of the time dependent model, the output perturbation can be expressed explicitly in terms of the input perturbations, which is useful for tone calculations. Therefore, this set of models can be applied to the steady state, and to large- and small-signal transient states in wavelength-division multiplexed (WDM) optical communication networks with EDFAs. The models are applied to analyze fast power transients in networks of EDFAs