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I Derivation of phase change parameter in dispersive medium

  1. Mar 8, 2017 #1
    Hi, I'm trying to evaluate the derivates of first, second and third order of the phase change parameter in a dispersive medium.
    In such medium the refractive index is a function of the wavelength.
    In my case it depends on the wavelength in vacuum.

    \begin{equation*} n(\lambda_0 )\end{equation*} and it has a known expression that I can easy derivate in terms of the wavelength in vacuum.

    \begin{equation*}
    \beta =\frac{\omega } cn(\lambda_0 )
    \end{equation*}
    \begin{equation*}
    \frac{\partial \beta }{\partial \omega }=\frac{\partial }{\partial \omega }[\frac{\omega } cn(\lambda_0 )]=\frac 1 cn(\lambda_0 )+\frac{\omega } c\frac{\partial }{\partial \omega }[n(\lambda_0 )]
    \end{equation*}

    Before I could write this:
    \begin{equation*}
    \lambda_0 =\frac{2\pi c}{\omega }
    \end{equation*}
    but in general:
    \begin{equation*}
    \lambda =\frac{2\pi c}{\omega n}
    \end{equation*}
    or even maybe in this case:
    \begin{equation*}
    \lambda =\frac{2\pi c}{\omega n(\lambda_0 )}
    \end{equation*}
    Which one of the last three equation do I have to differentiate in order to proceed with derivatives?
     
  2. jcsd
  3. Mar 8, 2017 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    Remember, ##\lambda_0## is the wavelength in vacuum.
     
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