Group velocity

When a signal is propagated without any great distortion, the group velocity is the speed at which the envelope of the signal travels.

More rigorously, group velocity is defined as the derivative of the pulse with respect to the wavenumber of the pulse.

Generally, the group velocity is the velocity at which energy is transported by the signal, but this is not always the case, particularly for dispersive materials with special properties. Thus, in certain materials laser pulses have been seen to be propagated at group velocities higher than the speed of light in a vacuum without the energy moving faster than the latter, and therefore without violating the principle of relativity.

Group velocity

For an illustration of this definition and of the difference with phase velocity see the following figure.

Click on the image to see the animation.