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Kramers-Kronig Analysis of Spectral Data

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Kramers Kronig Transform

> 

restart; with(plots); with(ExcelTools); with(ArrayTools); with(CurveFitting)

Import and plot data

> 

data := Import("data.xls", "Sheet2")
> 

data := FlipDimension(data, 1):
> 

lambda := data[() .. (), 1]:
> 

alpha := data[() .. (), 2]:
> 

p1 := plot(lambda, alpha):
> 

display(p1);


Reverse x-axis of plot

Kramers-Kronig Transform

> 

R := proc (omega) options operator, arrow; Spline(lambda, alpha, omega) end proc:
> 

theta := proc (omega) options operator, arrow; omega*evalf(Int(ln(R(Omega)/R(omega))/(Omega^2-omega^2), Omega = min(lambda) .. max(lambda), method = _d01ajc, epsilon = 0.1e-4))/3.141592 end proc:

Evaluate and plot transform

> 

theta(456)

-0.1459121574e-1

 (3.1)
> 

p2 := plot(('theta')(x), x = 400 .. 4000, adaptive = false, numpoints = 1000):
> 

p2


Reverse x-axis of plot

Both Plots

x-axis reversed

> 

pArray := array([[p1flip], [p2flip]]):
> 

display(pArray)