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Homework Help: Gaussian Beam focused using a lens

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data

    Hello, I'm really confused about this one, =(
    Suppose I have a guassian beam that is colliminated (beam expanded) and then suppose i let it passed through a lens to focus it.

    Given an initial waist and focal length of the lens. How can i find the waist (or half width) at the focus?

    2. Relevant equations

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    a3a76eb12dd62a821aa8c00723c30cdc.png

    3. The attempt at a solution

    There's an approximation using the formula above

    w(z)=(lambda*z)/(pi*w0)

    where w0 is the waist at focus and z is the distance from it, so if i let z=f i can solve for w0
    but this only works if z >> pi(w0)/lambda

    how about for the case when z is small (or the focal length is small), i cant seem to solve it using the above equations.

    Thanks~ ^^;
     
  2. jcsd
  3. Dec 8, 2008 #2

    Redbelly98

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    Homework Helper

    Welcome to PF! :smile:

    Sorry about the late reply, don't know how I missed your question earlier.

    There's another equation for the angle of a Gaussian beam, given it's wavelength and waist size (at the focus). You can use that, as long as the focal length is much much longer than ZR -- and you can verify if that's true after you have found wo at the focus.

    EDIT: Oh, I see you want a more general result, one that does not assume f>>ZR . Hang on while I check in my old Lasers textbook ... I'll post back soon

    EDIT #2: Okay. What you want is to look up the "q parameter" for Gaussian beams, and how ABCD matrices can be used in calculating Gaussian beam propagation. Do you have a textbook that discusses these in detail?
     
    Last edited: Dec 8, 2008
  4. Dec 10, 2008 #3
    looked up the 'q parameter' and you're right~
    Just need the Matrix ABCD to calculate the beam parameters at any z.

    thank you! ^^
     
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