- #1
enc08
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Hi,
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.
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.