# Laser saturation and laser saturation intensity

Can someone explain what is laser saturation and laser saturation intensity? I don't find a proper definition and it seems to me similar to steady state intensity.

The saturation effect of the laser-active medium occurs especially in the case of optically pumped lasers. To understand what is happening here, we need to look a bit deeper into the mechanisms behind the laser process.

For simplification, consider a rod laser with cross sectional area $$A$$ and length $$L_L$$, the equations also work for disk and fiber lasers, as they are just extreme cases of rod lasers. The maximum power that we can extract from this laser rod is given by $$P_{max \ extract.}=g_{kl}(v)I_sAL_L$$ This equation can be derived from the equations describing the population inversion of the laser levels. For your question, the two remaining variables in the equation are important, $$g_{kl}(v)$$ is the small-signal gain coefficient and $$I_s$$ is the saturation intensity. The saturation intensity, again, is described by $$I_s = \frac{hv}{\sigma_{ou}\tau_o},$$ so it is a function of the energy of the emitted photon $$hv$$ (-> output wavelength of our laser), the cross section $$\sigma_{ou}$$ (-> probability that a photon is emitted) and the mean life time $$\tau_o$$ (-> average time until a particle in the upper laser level spontanously emits a photon) and thus depends on values that are inherent to the laser-active medium.

To return now to your question, there is a saturation mechanism in our laser-active medium that occurs when the intensity of the laser beam that gets amplified in the laser-active medium reaches the saturation intensity. In this case, the gain coefficient $$g$$ falls down to only half of the small-signal gain coefficient $$g_{kl}$$. What a small gain coefficient means, is, that the population inversion, an absolutely necessary condition for the laser process, gets less and we can not amplify our laser beam as much as we would like to. If the intensity increases even more, the gain coefficient gets even lower. At this point, we see an effect of lowered overall efficiency.

A graph to illustrate this behaviour is shown below:

Source: Graf, Thomas; Laser - Grundlagen der Laserstrahlerzeugung (Fundamentals of laser beam generation, title translation by me); Springer 2015

Essentially, the saturation effect occurs because at the described point, there is so much stimulated emission that despite pumping, the population inversion reduces. To say it very casually, the upper pumping level and upper laser level get sucked dry because we amplify the laser beam in an unsustainable fashion.

• What does $u$ stand for in $g_{kl}(u)$? Is it related to the wavelength? – NMech Oct 21 '20 at 7:07
• @NMech It's a greek nu, stands for the frequency of the light, so indeed related to the wavelength. – OpticalResonator Oct 21 '20 at 8:19
• Thank you for your answer, can you explain roughly the saturation mechanism? because even if your answer is very useful I think it would be better to explain the reason for which this is a saturation phenomena. – SimoBartz Oct 21 '20 at 8:49
• @SimoBartz I added some info as to how this effect causes saturation in the laser – OpticalResonator Oct 21 '20 at 9:31
• @SimoBartz level :) I edited it – OpticalResonator Oct 21 '20 at 13:37