# Group Index dependence on refractive index

1. Oct 23, 2014

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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2. Oct 24, 2014

### DrDu

$N_g$ is a function of $\lambda$ too: $N_g(\lambda)$, so you should use the respective value $n(\lambda)$ in the formulas you gave.
Take in mind that the group index refers to a wavepacket which is very broad, so that the spread of $\lambda$ in Fourier space is arbitrary small. If n depends strongly on $\lambda$, the wavepacket will deform while travelling through the medium and it will be difficult to define a group velocity, or, you have to regard it as a superposition of broader wavepackets which travel with slightly different group velocities.

3. Oct 24, 2014