Refractive index(n(ω)) calculation: Kramers-Kronig relations

In summary, the refractive index can be evaluated by using the Hilbert transform. However, this can be done by using MATLAB or Origin.
  • #1
ddhirhe
2
0
I try to calculate refractive index of experimental spectral data using Kramers-Kronig relations but didn’t succeed. I need your expert advice and help to solve this problem.
Data and expression for KK relation is give in worksheet, where alpha(omwga) is in cm-1. Solution through Matlab or Origin is more helpful for me since I am familiar with this two software.
 

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  • #2
ddhirhe said:
I try to calculate refractive index of experimental spectral data using Kramers-Kronig relations but didn’t succeed. I need your expert advice and help to solve this problem.
Data and expression for KK relation is give in worksheet, where alpha(omwga) is in cm-1. Solution through Matlab or Origin is more helpful for me since I am familiar with this two software.

You need to look at the Fourier transform method to evaluate hilbert transforms, as the Kronig Kramers transform is nothing but the Hilbert transform. Look it up. There's also a MATLAB function 'hilbert' for hilbert transform of discrete data.

I have used it myself and it works pretty well
 
  • #3
singhvi said:
You need to look at the Fourier transform method to evaluate hilbert transforms, as the Kronig Kramers transform is nothing but the Hilbert transform. Look it up. There's also a MATLAB function 'hilbert' for hilbert transform of discrete data.

I have used it myself and it works pretty well

Many Thanks for your reply Singhvi,

Yes, KK relation is the Hilbert transform and no need to write complected program for KK relation in Matlab.

Cheers

Devnath
 
  • #4
can you please give details of the steps you have taken to solve your problem. I am facing similar problem, I have n, k values and by using KK want to extrapolate to higher and especially lower energies.
thank
 
  • #5
I want to evaluate refractive index from experimental data using KKR relation. As the data is limited to a finite spectrum, it is difficult to reduce errors related to infinite spectrum integration in KKR.

The calculated hilbert transform directly on 'absorption coefficient' data but it did not make any sense. Can you please elaborate on Hilbert transform in MATLAB to solve KKR relations.

Thanks,
Amin
 
  • #6
That is the kind of stuff I get paid for. :) Can't just give out all the details of the program for free.
 
  • #7
I have Absortion data vs wavelength. I want to evaluate the refractive index using MATLAB or origin but I did not success..I use hilbert transform but after that I don't know how to manage the refractive index from these data. Please help!
 

1. What is the Kramers-Kronig relation?

The Kramers-Kronig relation is a mathematical relationship between the real and imaginary components of a complex function. It states that the real part of a function is related to its imaginary part through an integral transform.

2. What is the significance of the Kramers-Kronig relation in refractive index calculation?

The Kramers-Kronig relation is used in refractive index calculation to relate the real and imaginary parts of the complex refractive index. This allows for the determination of the refractive index at any given wavelength, even if only one component is known.

3. How is the Kramers-Kronig relation applied in refractive index calculation?

In refractive index calculation, the Kramers-Kronig relation is used to calculate the real part of the refractive index from the known imaginary part. This is done by taking the Hilbert transform of the imaginary part, which then gives the real part of the complex refractive index.

4. What are the limitations of the Kramers-Kronig relation in refractive index calculation?

The Kramers-Kronig relation assumes that the refractive index is a smooth function and does not take into account any discontinuities or sharp changes. It also assumes that the material is homogeneous and isotropic, which may not always be the case.

5. Are there any alternative methods for refractive index calculation?

Yes, there are alternative methods for refractive index calculation, such as the Sellmeier equation and the Cauchy equation. These methods use empirical data and are more suitable for materials with complex refractive index behaviors.

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