Laser gain and the saturation effects

[Ulver48]

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?

 

[eljose79]

Hello,

Thank you for bringing up this interesting topic. As a fellow laser physicist, I can understand your confusion regarding the notion of gain and the saturation effect. Let me try to address your questions one by one.

1) You are correct in your understanding that the gain coefficient increases with the pumping rate, which is also known as the small signal gain. This is because as we increase the pumping strength, we are essentially increasing the number of excited atoms or electrons in the gain medium, which leads to a higher probability of stimulated emission and therefore an increase in gain. However, as you have correctly pointed out, in the case of continuous wave lasing, the gain eventually reaches a steady state where it is equal to the cavity losses, which is known as the threshold gain. This is why the gain is always equal to the cavity losses in a laser system.

2) The gain coefficient $g(v)$ is indeed what is referred to as the saturated gain in the bibliography. This is because as the optical intensity increases, the gain eventually reaches a maximum value and cannot increase any further, which is known as gain saturation. This is a result of the stimulated emission process, where the number of excited atoms or electrons in the gain medium becomes depleted and cannot sustain any further amplification.

3) The saturation of the output optical power at high current injection is indeed related to the gain saturation effect discussed above. As the current injection increases, the gain also increases and leads to an increase in the output optical power. However, as the gain reaches its maximum value, any further increase in current injection does not result in a corresponding increase in gain, leading to a saturation in the output optical power. This effect is also influenced by other factors such as the optical cavity design and the properties of the gain medium.

In conclusion, the simple laser model described in the book does capture the fundamental principles of laser operation, including gain and saturation effects. However, there are other factors that can influence the behavior of a laser, such as the optical cavity design, gain medium properties, and external factors such as temperature and current injection. I hope this clarifies your doubts and helps you in your studies. Keep exploring the fascinating world of laser physics!