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Spectrum of plane EM wave

  1. Aug 19, 2009 #1

    Let E(r,t) = E(r)exp(-ikz)exp(iwt)
    be a plane wave in time domain, propagating along Z direction.

    I wonder how to find the spectral representation of it (i.e. E(r,w))??

    I know, for a finite intensity field (i.e. |E(r,t)|^2 < infinity), we can give the spectral representation of the signal by,

    E(r,w) = Fourier Transform of [E(r,t)].

    But when I do the intergration in Fourier Transform between the + infinity and - infinity, I can't get a solution for above.

    Can any one help me with this???

  2. jcsd
  3. Aug 19, 2009 #2


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    Science Advisor

    The spectrum is a Dirac delta function in omega [tex]\delta(\omega-\omega_0)[/tex]
    if E(t)~[tex]e^-i\omega_0 t[/tex].
  4. Aug 20, 2009 #3
    Thanks Clem.
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