For a given optical fiber profile, I can simulate effective index (neff) or a given mode as function of wavelength λ. Using numerical differentiation, I can then estimate group index (ng) or group velocity (vg). However, if I calculate ng for the vector modes of a given group (for instance TE0,1, TM0,1, and HE2,1), and if I do the same for the corresponding LP modes (e.g. LP1,1), the value for ng I obtain for the LP mode is not the the average of ng of constituting vector modes. In some cases, I even can obtain a value for LP mode that is lower than each constituting vector modes. Is it normal?
In other words, if I launch a pulse of a LP1,1 mode in a fiber, and that I measure the time of flight in a long enough fiber, should I see three distinct peaks for each of the constituting vector modes, or should I see only one peak, as if the LP pulse was only one mode?
Does the simulated ng value I get for LP modes means anything?
This is a very detailed and pertinent question. You are right about the fact that the values of ng for LP modes and vector modes can be considerably different, especially near their cutoff. However, it is often a good enough approximation when one is in the "weakly guiding" regime. To answer your question about observing those peaks for a long-enough piece of fiber, in theory you should be able to. However, you will have to plan the measurement to be able to resolve the differences, and this can be tricky as what you will likely see is a broadened peak due in part to the distribution of dispersion along the fiber length as it is not strictly constant for a real fiber. Distributed coupling can also broaden the peak.
Reading on S2 (s-squared, see Nicholson, 2008 and later publications) might be a good starting point to see the the different effects and help plan your measurement to be able to resolve what you are trying to see.
I agree with Mr. Benoit Sévigny. In the theory point of view if you have a long-enough piece of fiber you would observe 3 peak as you know LP11 is included by 1 mode of TE01, 1 mode of TM01, and 2 modes of HE21(I mean 4 linearly polarized modes). Each one them has different Ng (because: Ng=n - lambda(dn/dlambda and n=neff for that mode.) From the attached figures we could see this difference.
but in the practical point of view as you know there are different kinds of dispersion such as modal, waveguid, and material dispersion.all of them have terms of wavelength-dependence and they may affect your measurement!
Ng which you've simulated has a straight meaning. It is the index group of a bunch frequency of three modes:TE01, TM01, and HE21.
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