Accurate modeling of distributed Erbium-doped Fiber Amplifiers with bidirectional pump

In this paper, we present an analysis of unsaturated erbium-doped fiber amplifiers (EDFA) with fiber back-ground loss and bidirectional pumping. This analysis provides an exact closed-form expression for the amplifier gain as a function of input pump power. This model is useful to study distributed EDFA's [1,2] and to determine the optimal Er3+ concentration and pumping configuration that minimizes the required pump power, as shown in this paper. In the case of forward pumping, it is also shown that a simple relation exists between the input pump power required for EDFA transparency and pump threshold, which can be usefully applied to EDFA characterization.