# Implemented phase dispersion in retarded time

1. Apr 30, 2013

### enc08

Hi,

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

$$c_{phase}(ω) = c_{0} + c'(ω)$$

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

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

$$e^{-(\alpha + iω/c_{phase}(ω))z}$$

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

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

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

Any input is appreciated.