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Kramers-Kronig Mathematica code

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm trying to write Mathematica code to use Kramers-Kronig on a csv file with 2 columns. Column 1 is h(eV). It goes from 0 to 6, in increments of 0.1. Column 2 is alpha (cm^-1).
    In the equation below, I'm guessing column 1 is Ω. But what should I put in for ω?


    2. Relevant equations

    kk_n.gif

    (Source: http://www.rp-photonics.com/kramers_kronig_relations.html)
    3. The attempt at a solution

    Code (Text):
    c = 300000000;



    data = Import[
       "kk.csv", "CSV"];
    column1 = data[[All, 1]];
    column2 = data[[All, 2]];


    output :=
     1 + (c )/(pi) NIntegrate[
        column2/(column1^2 - omega^2), {column1, 0.1, 0, infinity},
        Method -> "PrincipalValue", Exclusions -> Automatic]

    Plot[output, {column1, 0, 6}, AxesOrigin -> {0, 0}]
     
  2. jcsd
  3. Apr 17, 2013 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    It's been a while so I've forgotten most about this stuff, but I noticed that [itex]\Omega[/itex] is your integration variable. Also column1 is a defined list and your integration variable is supposed to be a dummy, I think, so I'm not sure what you have written will actually work.

    Since [itex]\omega[/itex] (lower-case omega) is the variable on the left hand side, I would expect that you get a function, i.e.
    Code (Text):

    output := Function[\[omega], (* NIntegrate expression *)]
    Plot[output, {\[omega], ..., ...}]
     
     
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