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Power of higher order mode beam

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Evaluate the ratio of the power contained within a circle of radius W(z) in the transverse plane to the total power in the Hermite-Gaussian beams of order (1,0)


    2. Relevant equations
    P=[itex]\int[/itex]IdA


    3. The attempt at a solution
    I have determined the ratio for the Gaussian beam but the higher order modes have a extra 'x' or 'y' in the integral but I am integrating w.r.t r (r2=x2+y2). So how can I evaluate the integral?
     
  2. jcsd
  3. Apr 14, 2012 #2
    Why don't you integrate in Decartes coordinates x and y? Because, if I understood correctly, then the integral is can be represented as
    [itex]\int^{W(z)}_{0} x*e^{-x^2}dx \int^{\sqrt{W(z)^2-x^2}}_{0}y*e^{-y^2}dy [/itex]
    this is only a quarter of the full energy of course.
     
    Last edited: Apr 15, 2012
  4. Apr 15, 2012 #3
    I don't understand what is Decartes coordinates but I managed to solve it. Its simply x=rcos[itex]\vartheta[/itex]. Have no idea why I didn't think of that when I posted this. Thanks
     
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