Theoretical analysis on threshold pumped fiber lasers doped with quasi two-energy-level ions

The rate equations including loss coefficients describing threshold pumped fiber lasers doped with quasi two-energy-level rare-earth ions have been analytically and fully solved. An analytical expression of the threshold pump power has been deduced, a closed-form expression for the variation of the pump power along the fiber has also been obtained, together with analytical solutions to the laser power in terms of the pump power and the position dependent atom population density. A comparison has been made between the analytical result and the previously reported ones. It indicates that various approximations have underestimated the threshold pump powers after neglecting the loss coefficients of both the laser and pump waves, while our theoretical predication is the closest to the experimen