Dear Mr. Kumar,

which program do you to analyze the data? I made a fast test with Origin 2015G and it worked very well and I get the same data for the parameter! I think that only wo is an constant whereas dwo was calculate out of the fit like q and gamma.

Hi Dennis,

Thank you for letting me know that you know it. I have Origin 8.5.1, I started by constructing a Fano equation in the function builder tab in Origin (in tools). I will try again according to your suggestion. I will write back to you once I find some progress! 

I did not understand Origin 2015G is this a new version of origin, which has BWG inbuilt functions?

Regards,

Dinesh

yes, making a user equation in the function builder is the way to go. Using Labtalk skript is slowest for fitting but easiest for writing (I find). You will then need the "y = .... [formula]" statement.

Dear Sir,

Actually, I am stuck with which parameters to choose as a parameter to be obtained from fitting and which parameters to be treated as constant.

Can you please help me out on it?

Sincerely

Dinesh

I would use the following expression (where y corresponds to I and x corresponds to omega0)

you can actually use two statements, I think, separated by a semicolon.

(Writing out the products rather than using " ^2 " - statements is usually faster in execution.)

eps= (x - w0 - Dw) / G;

y = C + (q+eps)*(q+eps)/(1+eps*eps)

so your function has the parameters w0, Dw, G, q, C. I have never used the option of using constants from the outset, rather I take them as parameters, assign values and set them to "fixed". But you may of course try to define w0 as a constant (with the number they give in their text).

Instead of using two statements, you can also write out the whole thing in one line, replacing "eps" by " (x - w0 - Dw) / G " everywhere. Dw, G, q, C shall flow out from the fit.

Using w0 and Dw makes only sense, of course, since in the paper the authors do have a reference energy (w0) from which the actual experiment is shifted away. In case you don't have that, you can use w0 as a parameter right away and drop Dw from your formula. When proceding to fitting it is helpful to initialize the parameters with reasonable starting values. With respect to Fig.3 of the paper you are referring to, this could be something like w0=1340 (in case of dropped Dw), G=20, q=1, C=800. If the fit does not converge right away, leave only one parameter free, keeping the others fixed to see what is wrong. Then successively relax the other parameters one by one. It should work fine (haven't tried, though, on this dataset).

Addionally if you only want see if the eqaution is working right for the diagram shown in the paper (fig.3) you can use the "digitizer" function of origin which you can find under "tools". With that tool you can get the data points of the fig.3 (first approximate adjustment) and you can try with the given value in the paper to first fit their data and afterwards adapt it for your current problem (data set).

Dear Mr. Kumar,

Similar asymmetrical peaks are the problem of the results interpretation of the microwave resonator measurements (the absolute value of the complex transmission coefficient). Mainly, asymmetrical peak can be fitted by complex Lorentzian+additional coefficients +background or so-called circular fit.  

In your case you can try to perform the fit using the Fano line shape equation (eqn(1)) +Fano line shape equation  with infinite q (Lorentzian) as a background contribution (with peak position far from the main peak).  This model becomes more complex but it can be simplified by placing  bounds on varied parameters.

Usually I use Python and Octave fitting modules. Another useful program is Fityk, which allows to simulate custom equation (it can be useful to determine the initial guess of the parameter value) and, also, to perform the fit using this custom equation.

Thanks a lot for this discussion so far! 

I have also tried to fit Fano resonances which show up at an excitonic feature in the absorption spectrum of a semiconductor material. I have fitted the absorption peak with the BWF Fano function origin provides:

http://www.originlab.de/doc/Origin-Help/BWF-PAFunc

The fitting works quite well, but I have trouble to interprete the parameters. It is my aim to find a measure for the oscillator strength of my exciton absorption. Is the amplitude H a good measure for this? Or do I have to multiply it with the width to get a good measure for the oscillator strength? Is the width FWHM or width at 1/e of the amplitude H? Also, my q is consistently about -1.1 to -1.2. Is there any useful information I can derive from this in the frame of absorption spectroscopy?

Thanks is advance!

Hello Nils,

in what sense do you use the term oscillator strength? I have linked the German wikipedia page for reference, maybe this is exactly whatyou're thinking of.

Do you know how you would determine the o.s. in case there was no Kondo feature? If yes, would you also be able to determine the dipole matrix element?

I ask this, since, loosely speaking, the "coupling parameter" q actually does contain the ratio of the two matrix elements of the two interfering paths yielding the Fano profile (I know this is a simplification, though). This is, where I would go looking for oscillator strength.

I made my acquaintance with the Fano profile in a text written by K.O. Almbladh and L. Hedin in the Handbook of Synchrotron Radiation, Vol. 1b (1983). I found (and still find) this text very good. Since you're located in Würzburg, know that the book is available in the "library" at EP7. You won't probably be able to lend it but you could copy the relevant passage(s).

https://de.wikipedia.org/wiki/Oszillatorstärke

Hello Kai,

Thank you very much for your quick answer! The definition of oscillator strength given by the wikipedia article is exactly what I have in mind: coupling strength between light and exciton excitation. 

In fact, I do not need to an absolute value of the o.s., but am looking for a relative measure to see how the o.s. evolves as function of another parameter such as temperature. So I have taken absorption spectra of my sample (a 2D semiconductor, MoS2). Normally for most semiconductor quantum wells (most compareable to a 2D semiconductor), the absorption spectra show a Lorentzian shaped features that can be easily fitted. In this case, the integrated peak intensity (peak area) is taken as a measure for the absorption strength, which in turn is proportional to the os.

However, I can not simply integrate the fano type resonance, because it has very long tails that don't converge within the fitting range. Just taking the amplitude as a measure for the absorption (or o.s.) might not be acceptable either as this approach does not consider the broadening of the fano resonance at higher temperatures. So I though of the product of amplitude and width.

Unfortunately, I still have not identified the origin of the continuum of states that interfer with the discrete exciton resonance. It would be good to know if the q factor is directly proportional to ratio of the dipole matrix elements. Is a q factor of 1.2 telling me that the dipole matrix element of my discrete resonance to the one of the continious resonance is 1.2 to 1?

I will try and see, if can get access to the book you pointed out. Thank you so much so this advice! The main library of the chair for x-ray technology might also have it.

I have fitted my data using the BWF function given in Origin 8.5. However, I am unable to view the parameters of the fitted data. I need to access the value of q. what is the procedure for it? 

You can "tell" the fitting module to output a "results table" at the end of the fitting procedure. (With me that was the default setting and I never had to bother about it...)

Alternatively, you can just call the fitter again and it should restart with the previous parameters - then you can look and take note.

Finally, (no sure about that with O8.5) there should be a results sheet added to the worksheet holding the fitted data. In there, too, you should be able to find the final parameters of the fit.

If you'ree not getting anwhere, post your question at the originlab forum linked below. I am seeking their help at times and usually get some.

http://originlab.com/forum/default.asp

Probably this has been resolved since... Origin appends a new sheet (two, actually, one as a report, and the other with the fitted data) to the workbool of the data that have been fitted. All the details on the fit can be found there.

i have tried to fit fano for my ZnO raman peak. i have added the fano function but i dint get the fit. it shows that fit did not converge. i had some problems with parameter. how should fix parameters for fitting fano?

There is more than one reason why a fit might not converge. It is difficult to give advice without having the data at hand.

But then - what is the physics in ZnO that makes you think that Raman peaks should be fitted by Fano functions?

In raman spectra of my ZnO samples E2H mode shows asymmetric nature. so i want to calculate the asymmetric factor by fitting it with  fano function. i have used this equation y=A*[((qg+(x-wc))^2)/((x-wc)^2+(g^2))]. here g is my FWHM, wc is centre. in this equation how should i fix x value? i have attached the data. how should i initialize paramaters?

Somehow, the link to the data does not work. (edit: sorry, I hadn't regognized the file format initially).

In your function, "x" would actually be the the frequency (i.e. Raman loss energy), so it is not a value but the "independent variable".

But again, the sole observation of an asymmetric peak is not really a physical justification for using a Fano lineshape. The Fano profile results from quantum mechanical interference of two interaction channels with identical final states (one having a slow change of the phase in the matrix element, the other one a rapid one [typically the resonance, which here would be the Raman loss]). It would be good to show that in the Raman spectrum, a Fano lineshape is indeed expected to occur (sorry, I can't help with that). In absence of an underlying physical picture, a sheer numerical q-parameter provides little if any insight imho.

Here you go with a simple Fano fit with nearly your formula. I have added a constant "BG" (constant background) removed "[" and "]" (not sure origin understands them) and replaced "qg" by "q*g", which is what makes sense formula-wise.

The Fano parameter q comes out negative, which is related to the "more flat" part of the asymmetric line shape being on the low frequency side.

So technically you can get it to work but (repeating myself) you should strive for a physical picture underlying such an analysis. Especially, I would find it important to find a reason for the asymmetry having the skewedness the data show (i.e. negative q). In those cases I have so far been dealing with Fano line shapes, it always was the other way around.

As to physical reasoning concerning Fano line shapes, there is an old paper by Cerdeira et al. (on heavily doped Si) :

Solid State Commun. 13, 325 (1973)

More recent work mentioning Fano line shape at least includes the Paper of Racu et al. on single crystal silicides:

Phys. Rev. B 76, 115103 (2007)

Both papers have been cited a fair number of times, so that following the leads of what they cite and whom they are cited by might provide you with further insight. I am not an expert with Raman spectroscopy and therefore cannot be of great more specific help.

http://www.sciencedirect.com/science/article/pii/0038109873906029?via%3Dihub

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.76.115103

thank you sir. i tried. i got that fit. i will go through the articles u sent.

Hey,

I am trying to fit fano dip in my data . Can you suggest me which function will get fitted in my data.

My Job is done on Fano.. Finally paper is published..titled.. Effect of boron doping on first-order Raman scattering in superconducting boron doped diamond films

Dear All,

You might also be interested in our recent work "Determination of atomic boron concentration in heavily boron-doped diamond by Raman spectroscopy" published in Diamond & Related Materials 93 (2019) 54–58

DOI: 10.1016/j.diamond.2019.01.028