Absorption and Gain for Lasers

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SUMMARY

The discussion centers on calculating the net gain coefficient (g - α) for a laser with a round trip gain of 5.16% in a 56.8 cm cavity. The user correctly applies the formula Gr = R1 * R2 * exp[(g - α) * 2L] and simplifies it to ln(Gr)/2L = (g - α). By substituting Gr as 0.0516 and L as 56.8 cm, the user arrives at a value of approximately -0.0261 cm-1 for (g - α). Clarifications regarding the interpretation of round trip gain and the correct application of the gain formula are provided, emphasizing that the round trip gain should be expressed as Gr = 1 + 0.0516 = 1.0516.

PREREQUISITES
  • Understanding of laser physics concepts, specifically gain and absorption coefficients.
  • Familiarity with the round trip power gain formula: Gr = R1 * R2 * exp[(g - α) * 2L].
  • Basic logarithmic functions and their application in calculations.
  • Knowledge of laser cavity length and its impact on gain calculations.
NEXT STEPS
  • Study the derivation and implications of the round trip gain formula in laser systems.
  • Learn about the significance of the small signal gain coefficient (g) and absorption coefficient (α) in laser operation.
  • Explore advanced topics in laser physics through textbooks such as "Laser Physics" by Milonni and "Laser Fundamentals" by Silfvast.
  • Investigate practical applications of gain calculations in different types of lasers, including semiconductor and solid-state lasers.
USEFUL FOR

Students and professionals in laser physics, optical engineering, and anyone involved in the design and analysis of laser systems seeking to deepen their understanding of gain and absorption in lasers.

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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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