Why Does Inhomogeneous Media Saturate More Slowly in Laser Technology?

[G01]

Hello All,

I'm going through some lecture notes from a course on Lasers, and have come across something that is confusing me.

In homogeneously broadened media, the gain coefficient depends on $(1-I/I_s)^{-1}$.

where $I_s$ is the saturation intensity.

However, in an homogeneously broadened media (doppler broadened in this case), the gain coefficient depends on $(1-I/I_s)^{-1/2}$.

Now, I can follow the math and see the square root appear when we integrate over individual distributions, but I'm confused as to the meaning of the square root factor.

Obviously, it means that inhomogeneous media saturate more slowly, but I'm not sure why that is?

Does anyone have any insight?

 

[Cthugha]

The reduction in the gain coefficient is mostly governed by the overlap of the linewidth of your resonator mode and the homogeneous linewidths of your transitions. For homogeneously broadened media the center frequency and linewidth is the same for every emitter of your medium. Therefore the gain per emitter will also be reduced equally for each emitter.

For inhomogeneously broadened media, the homogeneous linewidth will also be the same for each emitter, but the center frequency will differ for each emitter. As a consequence also the overlap between the resonator mode and the homogeneous linewidth will be different for each emitter. Therefore, the gain saturation will become frequency dependent. Those emitters which homogeneous linewidth shows large overlap with the resonator mode will saturate first, leading to a hole in the gain spectrum at this position. Those with a different center frequency and less overlap with the resonator mode will not saturate as fast, leading to the slower gain saturation of the ensemble of emitters.

 

[G01]

Ahh. That makes sense. Thanks a lot!