# Absorption and Gain for Lasers

## Homework Statement

If a round trip gain in a 56.8 cm long laser is 5.16%, what is the net gain coefficient (g-$\alpha$).

g is the small signal gain coefficient
$\alpha$ is the absorption coefficient
L-length of cavity

## Homework Equations

The Round Trip Power Gain: Gr= R1*R2* exp[(g-$\alpha$)*2L]
where I have to solve for (g-$\alpha$)

## The Attempt at a Solution

I have set R1=R2=1 assuming high reflectivity but I am not sure if this is alright.
First, solve as follows: ln(Gr)/2L = (g-$\alpha$)
Then, substitute the values for L and Gr:
ln(0.0516)/(2*56.8 cm) = -0.0260936057 = (g-$\alpha$)

However, I am not sure what this represents in terms of laser net gain coefficient and if I have correctly solved this (assuming R1=R2=1 and where Gr=0.0516 instead of 5.16% form.
I would appreciate some revision and explanation. I have read the textbooks from Milonni (Laser Physics) and Silfvast (Laser Fundamentals) but they don't really explain the meaning of this in detail. I have searched on google and this ebook helped a bit but I really can't say I understand completely... Any help is appreciated! THANKS!

TSny
Homework Helper
Gold Member
Would the round trip power gain be Gr = 1 + .0516 = 1.0516? (Instead of .0516)

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Truthfully, I am not certain. I have read over the textbook again and the only possible explanation for adding a one is to have a net gain per round trip increase through the amplifier?
I have tried your suggestion and I obtained a value of 4.43x10^-4 cm^-1... at least it's not negative. Do you know if this is correct? Why? Thanks again!

TSny
Homework Helper
Gold Member
I'm not real certain. But "gain" is often defined as the ratio of the output power to the input power. See http://en.wikipedia.org/wiki/Amplifier.

So, in your case, I would think the round trip gain would be the power after one round trip divided by the power at the start of the round trip. So, if ##P_o## is the power at the start of the round trip and if the power increases by 5 % in one round trip, then the power after one round trip would be ##P_o + .05P_o = (1+.05)P_o = 1.05 P_o##. So the gain would be ##\frac{1.05P_o}{P_o} = 1.05##