As i know the dispersion equation related to beta2 value, means if i have dispersion value at particular wavelength, then i can calculate beta2. We use this beta2 value to generate higher order dispersion coefficient like beta3, beta4 and so on..... by differentiating this beta2 value with respect to wavelength. and all these betas are used to generate supercontinuum spectrum. My doubt is while calculating higher order through curve fitting tool in MATLAB, all the values of betas are same as betas values which are calculated through differentiation ????
Curve fitting is not a reliable way to determine higher-order dispersion. It may work well for \beta_2 and \beta_3, but not for \beta_6 and \beta_7 anymore. The best way is symbolic differentiation with a computer algebra program like Mathematica. If you only have Matlab, you can try numerical differentiation. This is definitely better than curve fitting and may prove sufficient for your problem. Some more details on how to do that are here: http://www2.math.umd.edu/~dlevy/classes/amsc466/lecture-notes/differentiation-chap.pdf
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