Analytical solutions to rate equations of fiber lasers containing three-energy-level ions

A 980-nm wave pumped erbium-doped single-clad fiber laser has been studied by using rate equations for three-energy-level ions. A closed-form expression for the output laser power has been deduced and the output characteristics of the fiber laser have been analytically quantified. The effects of the input pump power and the fiber length on the ratio of the exit pump power to the input pump power have been discussed. In addition, the variations of the averaged population densities on each energy-level with the fiber length have been studied.