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Let's consider a ring laser where the laser must pass through the gain material before it is sent toward a partially reflective surface $\ R=1-T $. The other mirrors are perfect reflectors with $\ R_1=R_2=1 $. Furthermore the output irradiance of the setup is give as $\ I_{out} = I_{sat}(\gamma - \gamma_{th})L$ where $I_{sat}$ is the saturation irradiance, $\gamma_{th} $ is the threshold gain coefficient, and $\gamma $ is the small-signal gain coefficient. Now I am trying to understand what needs to happen in order to have the scenario when every pump event results in an output photon. That is to say a theoretical one to one correspondence, every photon I put in I will get right back. (Neglect spontaneous emission). Does this happen when $\gamma > \gamma_{th}$ ? or when they are equal?

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thanks for the edit! I wasn't sure how to subscript them. –  kuantumbro Dec 17 '12 at 20:46
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