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Inaccuracy of the solution from Lorentzian dielectric function

Posted 4 years ago
POSTED BY: Phoebe Perez
4 Replies
Posted 4 years ago

Thank you very much, Dr. Lichtblau!

POSTED BY: Phoebe Perez

One issue is the formula. There are squares missing in the numerator. Check the section "Extension to multiple oscillators" here. Plots will look better if you change the model as below.

model1[x_] := 
 Sqrt[n + ((c1*a1^2)/((a1*a1) - (x*x) + I*b1*x)) + ((c2*
       a2^2)/((a2*a2) - (x*x) + (I*b2*x))) + ((c3*
       a3^2)/((a3*a3) - (x*x) + (I*b3*x))) + ((c4*
       a4^2)/((a4*a4) - (x*x) + (I*b4*x)))]

I do not know how to account for the sign of the imaginary part. But you can get the expected plots like so:

ResourceFunction["MultipleAxesPlot"][
 Evaluate[{1, -1}*ReIm[model1[x]], {x, 0.60, 3.50}, 
  PlotLabel -> "n and k vs. energy", PlotRange -> All, 
  PlotPoints -> 150]]

enter image description here

POSTED BY: Daniel Lichtblau
Posted 4 years ago

Hi, Dr. Lichtblau.

I have edited my post to include the images of the plots and the reference. Thanks!

POSTED BY: Phoebe Perez

There is neither plot nor a set of reference values to contrast with. Please provide some values that are off, along with the expected values and some reason for why they are correct.

POSTED BY: Daniel Lichtblau
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