Absorption and Gain for Lasers

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Homework Help Overview

The discussion revolves around calculating the net gain coefficient for a laser based on the round trip gain in a specified cavity length. The original poster presents a problem involving the relationship between gain and absorption in laser physics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive the net gain coefficient using the round trip power gain formula and questions the validity of their assumptions regarding reflectivity. They express uncertainty about the interpretation of their calculated value.
  • Another participant suggests an alternative interpretation of the round trip gain, proposing a different calculation method.
  • Further discussion includes questioning the definition of gain and its implications in the context of the problem.

Discussion Status

Contextual Notes

Participants are working with specific values and assumptions, such as the reflectivity of the mirrors and the interpretation of gain, which may influence their calculations. There is an acknowledgment of the complexity of the topic and the need for further clarification from textbooks and other resources.

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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!

Google ebook link: http://books.google.ca/books?id=DlW...EUQ6AEwAw#v=onepage&q=round trip gain&f=false
 
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Would the round trip power gain be Gr = 1 + .0516 = 1.0516? (Instead of .0516)
 
Last edited:
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!
 
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##
 

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