Analytical method for few-mode erbium doped fiber amplifiers

An analytical method for few-mode erbium doped fiber amplifiers (EDFAs) is proposed by introducing the uniformity coefficient of population inversion. The validity of the derivation process of the analytical method is identified by the numerical method. It is shown that the more uniform the transverse distribution of erbium ion population density at the metastable level, the closer the analytical solution is to the numerical result. The optimized uniformity coefficient is also applied to the case of varying pump power to some extent. The analytical method is especially suitable for the design of the gain-saturated EDFAs. (letter)