User:Sandafala

Amplification
The signal gain of an amplifier pumped by a laser can be calculated from $$ g_0=\frac{J_{\rm sto}}{J_{\rm sat}} $$

The propagation in a regenerative amplifier can be simulated using a Frantz-Nodvick model:

$$ E_{\rm out}=E_{\rm sat}\ln\left\{1+\exp(g_0)\left[\exp \left(\frac{E_{\rm in}}{E_{\rm sat}}\right)-1\right]\right\} \,, $$

where $$E_{\rm out}$$ is the output energy and $$E_{\rm in}$$ the input energy. $$g_0$$, 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:

$$ g_0= \frac{(E_p \alpha \lambda_p)/(S \lambda_L)}{E_{\rm sat}/S} $$

Here $$\alpha$$ is the total absorption of the radiation pump, $$S$$ is the cross-section of the pump beam, while $$\lambda_p$$ and $$\lambda_L$$ are the pump and the laser wavelength, respectively.