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Homework Help: Absorption and Gain for Lasers

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data
    If a round trip gain in a 56.8 cm long laser is 5.16%, what is the net gain coefficient (g-[itex]\alpha[/itex]).

    g is the small signal gain coefficient
    [itex]\alpha[/itex] is the absorption coefficient
    L-length of cavity

    2. Relevant equations

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

    3. 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-[itex]\alpha[/itex])
    Then, substitute the values for L and Gr:
    ln(0.0516)/(2*56.8 cm) = -0.0260936057 = (g-[itex]\alpha[/itex])

    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
  2. jcsd
  3. Oct 28, 2012 #2


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    Would the round trip power gain be Gr = 1 + .0516 = 1.0516? (Instead of .0516)
    Last edited: Oct 28, 2012
  4. Oct 28, 2012 #3
    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!
  5. Oct 28, 2012 #4


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    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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