I Laser gain and the saturation effects

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Summary
Explaining the notions of gain, small signal gain and saturated gain for a laser device.
Hello,

I study laser physics, using "Laser Physics" by Eberly and Milloni. I am confused regarding the notion of gain and the saturation effect. According to the book, the gain is defined as
## g(v) = \dfrac{g_o(v)}{1+I_v/I^{sat}_{v}} ##
where ## I^{sat}_{v}## is the saturation intensity and ##g_o(v)## is the small signal gain. The small signal gain and the saturation intensity are a function of the pump strength.

1) I have found in a lot of papers the claim, that with the increase in the pumping strength, we have an increase of the gain coefficient and subsequently the laser intensity. According to the book, when we have continuous wave lasing, the gain is equal to the cavity losses, namely ##g(v)=g_th##. Substituting the previous equation to this equality shows that
##I_v=I^{sat}(\dfrac{g_o(v)}{g_{th}}-1) ##

So, when bibliography states that the gain coefficient increases with pumping rate, do they mean the small signal gain ? In the end, the gain is always equal to the cavity losses. This gain equation describes all laser types according to the books, so it must well describe also semiconductor lasers, right?

2) Is ##g(v)##, what bibliography states as the saturated gain? I ask, because with stimulated emission and the rise of the optical intensity, the gain saturates until it reaches the cavity losses.

2) In light-current graphs, I see that the increase in current injection results in an increase of the output optical power in the stimulated emission regime. But for very high current graphs there is a saturation of the optical power in the output. Is this effect related to the gain saturation above? Because with respect to the previous equation, the increase of the pumping rate (current injection) results always in the increase of the light intensity. Is this phenomenon, related to different effects not described by the simple laser model above?
 

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