Laser: CW-oscillation in a 3-level laser

[Niles]

Hi

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-Γ₁₂)/(P+Γ₁₂)N_T

where N_T=N_{1, steady state}+N_{2, steady state}, P is the pump rate and Γ₁₂ 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?

 

[Cthugha]

What happens if you increase the pumping power further after laser oscillation sets in, is called gain clamping or upper population clamping. Any atoms you pump into the upper level will be almost immediately converted into laser light as fast as you pump them up (well - on statistical average, of course not necessarily the same atoms you just pumped up). Therefore the decay rate will also momentarily increase. If you do not increase the pump power constantly but just add short pulses of high pump power, you might also see the population numbers and the intracavity photon number undergo relaxation oscillations according to the fluctuation-dissipation theorem.