information:extraction
Group index

Sometimes, a "group velocity refractive index", usually called the group index is defined: n g = c v g, {\displaystyle n_{\mathrm {g} }={\frac {\mathrm {c} }{v_{\mathrm {g} }}},} where v is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity. When the dispersion is small, the group velocity can be linked to the phase velocity by the relation v g = v − λ d v d λ, {\displaystyle v_{\mathrm {g} }=v-\lambda {\frac {\mathrm {d} v}{\mathrm {d} \lambda }},} where λ is the wavelength in the medium. In this case the group index can thus be written in terms of the wavelength dependence of the refractive index as n g = n 1 + λ n d n d λ. {\displaystyle n_{\mathrm {g} }={\frac {n}{1+{\frac {\lambda }{n}}{\frac {\mathrm {d} n}{\mathrm {d} \lambda }}}}.}

When the refractive index of a medium is known as a function of the vacuum wavelength (instead of the wavelength in the medium), the corresponding expressions for the group velocity and index are (for all values of dispersion) v g = c (n − λ 0 d n d λ 0) − 1, n g = n − λ 0 d n d λ 0, {\displaystyle {\begin{aligned}v_{\mathrm {g} }&=\mathrm {c} \!\left(n-\lambda _{0}{\frac {\mathrm {d} n}{\mathrm {d} \lambda _{0}}}\right)^{-1}\!,\\n_{\mathrm {g} }&=n-\lambda _{0}{\frac {\mathrm {d} n}{\mathrm {d} \lambda _{0}}},\end{aligned}}} where λ is the wavelength in vacuum.