Past exam of the atomic and laser physics course of the University of Oxford / 2022 / 4 / b / Solution

In a uniform steady amplifier, with no extra propagation losses, the local optical gain law givesIntegrate between the two faces of length $L$ to obtainFor $I\ll I_s$, this reduces to exponential amplification. In deep saturation, the intensity increment approaches ${\alpha }_0{I}_{s}L$: finite pumping limits the extracted power.