Hi Monica,

Usually, companies who provide PCFs, also provide a graph of dispersion parameter D (ps/nm-km) vs wavelength. From D, you can calculate beta2 (GVD). You can find a derivative of beta2 to find beta3, derivative of beta3 to find beta4 and so on.

The easier way is just to use curve fitting tool in Matlab for the beta2 vs wavelength graph and compare the fitting polynomial coefficients to the Taylor expansion of beta and you can find the higher-order dispersion.

But in both cases, you will require the dispersion parameter of at least beta2 values.

Thank you ankita,

Dear Monika Kiroriwal ;

Do you have any idea about the AI programming? if Yes, I think by using the Genetic Algorithms you will get on optimum solution.

Regards;

Thanks for your answer, i don't have too much knowledge about AI programming. can you provide me link for it?

Ankita ma'am in your first solution i hv calculated beta2 values, but again stuck to differentiate it with respect to angular frequency, because beta2 is numeric value, and when i plot a graph and use matlab curve fitting tool but unable to fit polynomial to taylor series coefficients.

If you know the fiber geometry, you can use an effective step-index method to calculate the dispersion, which relates very well to the actual dispersion. See for example: K. Garay-Palmett et al, Optics Express Vol. 15, Issue 22, pp. 14870-14886 (2007)

thank you for your answer Raul sir, but sir, in my tool i have simulated dispersion profile and also GVD, but facing difficulty to calculate higher order dispersion parameter.

Hi Monika,

Will you please share your D (or beta) Vs lambda graph with me?

Thank you,

Ok ma’am please provide me your id so I will send you my dat.

please check it out and resolve my problem.

It's actually very easy through curve fitting tool. I have attached the curve fitting graph for your data and I really want you to try this on your own because it is just a 2-minute job. If you still cannot get it, I will share the polynomial coefficients along with a document.

Thank you ma’am , I have already done this and got this graph, and also get equation of polynomials from p1 to p9 coefficients, but how this equation relate with Taylor expansion series. Because in journals papers beta 2 is negative then beta3 is positive, and so on for beta 4 and beta 5....., can you please provide me how to relate with taylor series?

Ankita ma'am, i have tried as you said, but in your given graph wavelength range is only 400 to 1800 but my wavelength range is from 1 to 6 um. and your graph is different from my graph beta2 vs wavelength as i attached here.

check it out

Hi Monika Kiroriwal ,

1. I shared beta2 vs omega graph with you because the Taylor expansion of dispersion relation is in terms of omega. Refer to chapter 1 in Non-linear optics by Govind P. Agarwal.

2. I calculated omega in 1/ps.

w = (2*pi*c*1e3./(lambda.*(1e-9)))*(1e-12); where c was in nm/ps ans lambda is in nm.

3. Plot beta2 vs omega, use curve fitting tool and then it is very easy to compare coefficients. Your beta2 unit will be ps^2/m, beta3 will be in ps^3/m so on and so forth.

*** In case you don't have access to the polynomial, I have attached the equation. Remember the equation in the book is for beta(omega). You will need to differentiate it twice to get the equation given in the document.

I hope this helps,

Thank you ankita mam for your valuable reply

very useful