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

Let $x=I_0/I_s$ and $G={\alpha }_{0}L$. Applying the integrated amplifier law to each section givesEliminating $G$ givesAs a consistency check, both amplifiers have $G\simeq 26.1175$. The second section receives a larger intensity and adds $80I_0$, compared with $69I_0$ in the first, while its multiplicative optical gain is much smaller. This is the expected approach to constant extracted power in saturation.