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Question regarding Helmoltz equation

  1. Mar 19, 2009 #1

    I have the following question regarding the Helmoltz equation in the context of a Transverse Magnetic wave in a waveguide:

    [tex]\nabla_{t}^{2}E_z + h^2E_z = 0[/tex]

    Question: Is [itex]h[/itex] always real?

    ([itex]\nabla^{2}_{t}[/itex] denotes the transverse Laplacian operator)

  2. jcsd
  3. Mar 19, 2009 #2


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    Science Advisor

    In a wave guide h is almost always real. It must be real for a wave to propagate.
    If the frequency is below the critical frequency, the wave is rapidly attenuated, as
    exp[-(Im h)x].
  4. Mar 20, 2009 #3
    Thanks clem.
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