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Homework Help: Deriving Irradiance Expression

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Electric field for a single pulse of a laser (operating at central wavelength of 800nm):
    Code (Text):

    E = E0e^(-(t^2/2a^2))e^(iwt)
    (the a is sigma and w is omega)

    Derive an expression for the spectral intensity (irradiance)

    3. The attempt at a solution
    One way I know to calculate irradiance is the time average of the poynting vector: (1/u0)*ExB
    But that would involve taking the time average of e^(-(t^2)) which is non-integrable.

    I've also seen the function E integrated over an area, then squared to give an irradiance formula, but then again I run into problems with that function that's difficult to integrate. Any suggestions?
  2. jcsd
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