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In Ng (the group index for a range of wavelengths), there is an index of refraction n used, but if the medium is dispersive, meaning n is a function of wavelength λ, which n is used? Is it some kind of an average? Or does n not change much over this range of wavelengths? if it doesn't change much, then
Ng = n - λ(dn/dλ)
would be approximately
Ng ~ n
So, it makes sense to me that dn/dλ must not be really small, because otherwise Ng ~ n and the concept of group index is redundant with the concept of the index of refraction. but if dn/dλ is not really small, then the choice of n (the first term in Ng) becomes crucial, does it not?
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Ng = n - λ(dn/dλ)
would be approximately
Ng ~ n
So, it makes sense to me that dn/dλ must not be really small, because otherwise Ng ~ n and the concept of group index is redundant with the concept of the index of refraction. but if dn/dλ is not really small, then the choice of n (the first term in Ng) becomes crucial, does it not?
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