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Laser beam propagation

  1. Feb 8, 2016 #1
    Hi all,

    I am interested in finding the power of a laser diode as function of the distance z, assuming a free space propagation. I think to have enough information to work it out but I am stacked at the moment.
    Given:
    • the initial power, P0 = 1mW
    • beam width clip (e-2 = 13.5%), wx = 3μm, wy = 1μm
    • wavelength, λ = 650nm
    • divergence beam width (full angular), θ = 1mrad
    • M2 = 5
    What would be the power P(z) and the radius w(z) of the beam at a distance z?

    Thanks in advance for any help!
     
  2. jcsd
  3. Feb 8, 2016 #2

    blue_leaf77

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    The power is constant everywhere. There is no way the power will change unless the energy inside the laser changes, e.g. due to battery depletion.
     
  4. Feb 8, 2016 #3
    Thanks for your prompt reply. About the radius of the beam, how large would be the laser spot after, let's say, 1m or 50m?
     
  5. Feb 8, 2016 #4

    blue_leaf77

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    The information about the angular divergence which you already have there should be sufficient to determine the width at a given distance, assuming this distance is far enough from the beam waist.
     
  6. Feb 8, 2016 #5
    I have used the following equation (2.8) to simulate the width at a given distance, using the beam width clip as w0. How do I include the angular divergence in the simulation of w(z)?
    Thanks
    Screen Shot 2016-02-08 at 16.23.43.png
    Screen Shot 2016-02-08 at 16.23.55.png


    Source: Sun, Haiyin. Laser diode beam basics, manipulations and characterizations. Springer Science & Business Media, 2012.
     
  7. Feb 8, 2016 #6

    blue_leaf77

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    Isn't the beam divergence given already in equation (2.11)? You can plug in this into equation (2.8).
     
  8. Feb 9, 2016 #7
    I thought that the 2.11 is valid only far away from the beam waist. After which value do you think it's "sensible" to use the far field approximation?
    I have plotted the beam radii propagation for the X and Y axis and after a distance of about 4 meter the two curves are overlapping each other, i.e. same radius in the plane and the spot is not elliptical anymore. Is that an expected result for such a laser diode?
     
  9. Feb 9, 2016 #8

    blue_leaf77

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    ##\theta## is indeed derived by taking the limit of ##\frac{d w(z)}{dz}## for ##z\rightarrow \infty##, but it turns out that ##\theta## has such a form given in (2.11). Therefore you can regard this equation as an identity and you use it to replace any factor containing the RHS of (2.11) with ##\theta##.
    Well at least for a perfect Gaussian beam, the smaller beamwaist you have, the bigger the angular divergence is. So, the behavior of the beam you observed makes quite some sense.
     
  10. Feb 23, 2016 #9
    I had to refresh my memory about this topic, now it makes sense.

    Thanks a lot for your replies :)
     
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