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I'm studying the laser input-output power relation. In particular I'm studying the laser slope efficiency $\eta_s$ ($\eta_s=\frac {dp_{out}} {dp_{in}})$. However, my textbook tells that $\eta_s$ can be divided in 4 factors: $\eta_s=\eta_p \eta_c \eta_q \eta_t$. I'm having difficulties in understanding $\eta_c$ that it is called "output coupling efficiency". On my textbook, principle of lasers by O. Svelto, it is written that it represents the fraction of generated photons coupled out of the cavity, which one can call the output coupling efficiency.

Can you explain me $\eta_c$ in other words? What does it mean "coupled out" in this context?

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In a way, from the laser resonators point of view, we can consider two kinds of losses. The actual wasted losses (for example heat dissipation) and "useful losses", that is, the actual laser beam that leaves the resonator. While this laser beam is of course the reason to do the whole ordeal, it still means that we take a part of the laser beam that bounces through the resonator.

The output coupling efficiency relates these two kinds of losses, the wasted loss ($loss$) and the "useful" loss, to each other. $$\eta_{c} = \frac{T_{oc}}{T_{oc}+{loss}}$$

In context of a laser resonator, "coupling out" describes the concept of taking a part of the laser beam that gets amplified in the resonator and letting it leave the resonator through a mirror (the outcoupling or OC mirror) with a transmission of up to 5 % or even more (there are probably higher ones, but I have only ever worked with up to 5 %). While you usually want a mirror to reflect as much as possible, the outcoupling mirror is designed to let a certain exact amount of light pass. This transmission degree, $T_{oc}$ in the equation, is therefore also called outcoupling degree. When developing a laser, picking the outcoupling degree is an interesting parameter to play with, putting it too low makes your actually usable laser power too low, too high and your losses and with it the laser threshold increase too much.

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