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KramersKronig relations on a finite data set 
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#1
Aug2613, 03:46 AM

P: 1,863

Hi
Say I have a finite data set (frequency, absorption) and I would like to find the corresponding dispersion. For this I could use the KramersKronig (KK) relation on the absorption data. What I would do is to make a qubic spline and then perform the KKtransformation. However, the absorption data naturally doesn't run from ±∞, but what I would do is simply to use the extremes of my frequencydata instead  this will naturally introduce some numerical error. What do professional people do in this case, do they quantify the error? Or is there not a way to extract the dispersion from the absorption data? Thanks in advance. 


#2
Aug2613, 04:13 AM

P: 229

Hmm, if you have a data set, you probaby want to calculate the KramersKroning integrals numerically. I wouldn't recommend first building a spline because they are terribly inaccurate outside of the range where you have data points, and using that could lead to very uncontrolled errors.



#3
Aug2613, 04:33 AM

Sci Advisor
P: 3,564

I have no idea what professional packages do, but have some general information on how the dielectric constant should behave asymptotically. Namely ε1 should fall off like 1/ω at very high frequencies and should go to a constant in the limit ω→0. There are also lots of sum rules which provide further information on the relevant constants as far as you cannot infer them from your data.



#4
Aug2613, 05:01 AM

P: 1,863

KramersKronig relations on a finite data set



#5
Aug2713, 03:35 AM

Sci Advisor
P: 3,564

I meant that you could integrate over the corresponding asymptotic expressions in the range where you don't have data.



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