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At continuous-wave oscillation the gain is equal to the threshold gain, i.e. g = g_{threshold}. Now in my book, I have the following expression for the steady-state population-inversion for a three-level laser

N_{2, steady state}- N_{1, steady state}= (P-Γ_{12})/(P+Γ_{12})N_{T}

where N_{T}=N_{1, steady state}+N_{2, steady state}, P is the pump rate and Γ_{12}is the rate at which level 2 decays into level 1. Now my question is: If at CW-oscillation g=g_{t}, then why is it that we can change N_{2, steady state}- N_{1, steady state}(and thereby the gain) in a three-level laser at steady-state? Isn't this a contradiction?

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# Laser: CW-oscillation in a 3-level laser

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