Analytical Studies on the Rate Equations Including Background Losses Applicable to Fiber Lasers Doped with Three-Energy-Level Ions

This paper derived an analytical expression of the threshold pump power of the fiber laser with three-energy level do pants from the rate equations including loss coefficients of the pump and laser radiations. And based on the implicit expression specifying the pump variation along the fiber and expressions of the position dependent population densities on the three energy levels in terms of the pump variation, the rate equations describing the threshold pumped fiber lasers was analytically solved out. The results show that the longer fiber length leads to the greater influence of the pump loss coefficient. Those results obtained in this paper are applicable to both single- and double-clad fiber lasers.