Solving rate equations including backgroud losses applicable to threshold pumped fiber lasers with three-energy-level dopants

An analytical expression of the threshold pump power of the fiber laser with three-energy-level dopants has been obtained from rate equations including loss coefficients of the pump and laser radiations. And the rate equations describing the threshold pumped fiber lasers have been analytically solved, following the derivation of the implicit expression specifying the pump power variation along the fiber and explicit expressions of the position dependent population densities on the three energy levels in terms of the pump power variation. With these expressions, threshold characteristics of the fiber lasers have been studied. The threshold pump power grows monotonously with the increase of the loss coefficient of the pump radiation. The population density of the upper level decreases with t