It can easily be shown that the intensity of a laser is $$I = I_0e^{z\gamma} \,, \tag{1}$$ where $\gamma$ is the gain coefficient.

It can also be shown that $$\gamma = \frac{\gamma_0}{1+I/I_{\text{sat}}} \,, \tag{2}$$ where $I_{\text{sat}}$ is the saturation intensity.

Seeing as though equation 1 suggests that as the gain coefficient increases the intensity increases whilst the second equation suggests that as intensity increases the gain coefficient decreases I am unsure how to reconcile equations 1 and 2.


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