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Refractive index plasma mode

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Attached as pdf.


    2. Relevant equations

    Attached as pdf.

    3. The attempt at a solution

    I know that refractive index is given by [tex] n=\sqrt{\varepsilon} [/tex] normally. But is it still the case when asked for [tex] n( \omega) [/tex]?

    If so, I've tried rearranging equation 3 for [tex] \varepsilon [/tex]. Which gives [tex] \varepsilon = -k_m \varepsilon_0 / k_v [/tex], where the subscript v and m denote metal and vacuum. How does this help in finding [tex] n (\omega) = \sqrt{ \frac{\varepsilon( \omega)}{\varepsilon ( \omega) + \varepsilon_0}} [/tex]?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

    • ref.pdf
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  2. jcsd
  3. Oct 21, 2011 #2
    Please do suggest reading materials on this topic as I don't think I fully understand it from my lectures. Thank you.
     
  4. Oct 24, 2011 #3
    I went through the algebra and got this equation:

    [tex] \frac{c^2}{\omega^2}k_x^2=\frac{(1-\varepsilon_0^3/\varepsilon(\omega))}{(1-\varepsilon_0^4/\varepsilon(\omega)^2)} [/tex]

    And I know that:

    [tex] n(\omega)=\frac{c}{v_x}=\frac{ck_x}{\omega} [/tex]

    Is there a way in which I can arrange equation 1 into:

    [tex] \frac{\varepsilon(\omega)}{\varepsilon(\omega)+ \varepsilon_0} [/tex]

    ?
     
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