Consequences of a lower level population on the modeling of a homogeneously broadened injection laser

An exact, analytic solution has been found for the coupled, nonlinear differential equations which describe the amplification of mode intensities for propagation through a homogeneously broadened amplifier with negligible population in the lower level. It is shown in this letter that the predictions of an analytic laser model based on the solutions to these equations can be scaled in a straight forward and easy manner to include the effects of a constant, lower level population.