How does anomalous dispersion give a negative refractive index?

[n0_3sc]

Anomalous Dispersion?

All I know about anomalous dispersion is that it has a negative second order propagation vector.
That would mean the refractive index is negative...how?

How do you also "achieve" or get "into" the anomalous dispersion regime?

 

[Meir Achuz]

The group velocity of a wave is given by
$$v_g=\frac{c}{n}\left(1+\frac{\lambda}{n}\frac{dn}{d\lambda}\right)$$.
This means when $$dn/d\lambda$$ is positive, the group velocity could be greater than c. The refractive spectrum would also be reversed. For these reasons, $$dn/d\lambda>0$$ is called "anomalous dispersion".
n is still usually positive, but the lambda derivative is positive.
Anomalous dispersion usually occurs near a resonant frequency of the material, where n varies rapidly with wavelength. Because of this rapid variation, $$v_g$$ does not represent the propagation velocity of a pulse, so that relativity is not violated.