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Implemented phase dispersion in retarded time

  1. Apr 30, 2013 #1

    I am trying to implement phase dispersion in a retarded time frame.

    [tex]c_{phase}(ω) = c_{0} + c'(ω)[/tex]

    where [tex]c'(ω)[/tex] is a small deviation from the reference phase speed [tex]c_{0}[/tex].

    In the frequency domain, the propagation term appears as an exponent:

    [tex]e^{-(\alpha + iω/c_{phase}(ω))z}[/tex]

    where z is distance. I can re-write this as

    [tex]e^{-\alpha z}e^{-izωc_{0}^{-1} c_{0}/(c_{0} + c'(ω))}[/tex]

    Now this where I am confused...In my wave equation, I am using retarded time, so there is no [tex]ω/c_{0}[/tex]term. However, it seems I can't implement dispersion due to c'(ω) as it's coupled (multiplied) with a [tex]ω/c_{0}[/tex] term.

    Any input is appreciated.
  2. jcsd
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