Output saturation in fiber lasers

An analytical theory is developed for a four-level cw fiber laser which accounts for saturation of the output due to bleaching of the pump transition. A simple closed form expression is obtained which relates the pump power and output power. Output saturation is most important for systems having at least one long lived excited state other than the upper laser level. The model is used to optimize the fiber length, core radius, and mirror reflectivities for an Er(3+) doped fluorozirconate fiber laser operating at 2.7 microm. The optimized efficiency is found to be independent of pump power. Maximum efficiencies of 9.8 and 12.9% are calculated for fibers with attenuation coefficients of 100 and 10 dB/km, respectively.