Group velocity (EM)
v_g = dω/dk. The speed at which a wave packet's envelope — and therefore its energy and information content — propagates. In a dispersive medium v_g differs from the phase velocity v_p = ω/k.
Definition
The group velocity v_g = dω/dk is the speed at which a narrow wave packet's envelope propagates through a dispersive medium. It differs from the phase velocity v_p = ω/k, which is the speed at which individual wavefronts move; in a non-dispersive medium (vacuum, or a medium where n is frequency-independent) the two are equal, but in general they are not. Group velocity carries the physical content of a pulse — its energy, its information, its ability to trigger a detector — while phase velocity is a mathematical property of the wave's phase surfaces.
In an optical material with refractive index n(ω), the group velocity is v_g = c/n_g where the group index n_g = n + ω(dn/dω). In regions of normal dispersion (dn/dω > 0, typical in the visible for transparent glasses) the group velocity is less than the phase velocity; in regions of anomalous dispersion near absorption resonances, dn/dω < 0 and v_g can even exceed c or become negative, without violating relativity because the signal velocity (the speed of the leading edge of an information-carrying pulse) remains ≤ c. Group velocity dispersion (GVD) — the variation of v_g with frequency — is what spreads short optical pulses as they travel through fibres; compensating for GVD with chirped mirrors or prism pairs is a core technique in femtosecond laser technology.