When we talk about a medium with dispersion, we can define the phase velocity $v_\phi = \omega/k$ and the group velocity $v_g = d\omega/dk$. Likewise the phase index $n = c/v_\phi$ and the group index $n_g = c/v_g$.
The group velocity dispersion (GVD) in s$^2$/m is the frequency derivative of the inverse group velocity. However, I've also heard the wavelength derivative of the group index, $-\lambda\frac{d^2 n}{d\lambda^2}$, in m$^{-1}$, referred to as the group velocity dispersion.
And there is also a "dispersion parameter," $D=-(2\pi c/\lambda^2) \times GVD$, in s/m$^2$ or ps/(nm km).
My questions:
- Which expression is properly called "group velocity dispersion"? Or are both?
- Does $D$ have a name other than the unspecific "dispersion parameter"?
