The signal gain of an amplifier pumped by a laser can be calculated from ${\displaystyle g_{0}={\frac {J_{\rm {sto}}}{J_{\rm {sat}}}}}$

The propagation in a regenerative amplifier can be simulated using a Frantz-Nodvick model:^[1]

${\displaystyle E_{\rm {out}}=E_{\rm {sat}}\ln \left\{1+\exp(g_{0})\left[\exp \left({\frac {E_{\rm {in}}}{E_{\rm {sat}}}}\right)-1\right]\right\}\,,}$

where ${\displaystyle E_{\rm {out}}}$ is the output energy and ${\displaystyle E_{\rm {in}}}$ the input energy. ${\displaystyle g_{0}}$, the small-signal gain of the amplifier can be calculated if we assume that the lifetime of the excited-state of the amplifier medium is longer than any time involved in the process:

${\displaystyle g_{0}={\frac {(E_{p}\alpha \lambda _{p})/(S\lambda _{L})}{E_{\rm {sat}}/S}}}$

Here ${\displaystyle \alpha }$ is the total absorption of the radiation pump, ${\displaystyle S}$ is the cross-section of the pump beam, while ${\displaystyle \lambda _{p}}$ and ${\displaystyle \lambda _{L}}$ are the pump and the laser wavelength, respectively.