Analytical characterization of an end pumped rare-earth-doped double-clad fiber laser

Few steps of derivations on the rate equations have made it clear that the key issue of obtaining an analytical expression for the output laser power, from a double-clad Yb3+-doped fiber laser, is how to integrate the products between the radiation power and its respective loss coefficient for both the pump and laser waves. After examining the approximations adopted in previous studies, instead of nullifying the population density of the upper-level atom, we used its average value in the pump equation, so that the cavity length range, that the analytical result can be applied, is extended. Consequently, we have shown that the output laser power can be expressed as η(Pp−Pth) when pumped by a power of Pp. And the analytical expressions for the differential pump efficiency η and the threshold pump power Pth have also been derived.