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The group velocity of a wave is the velocity with which the overall shape of the wave's amplitude (known as the envelope of the wave)
progagates through space. The group velocity is defined in terms of the wave's angular frequency ω and wave vector k
by
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It is often thought of as the velocity at which energy or information is conveyed along a wave. In most cases this is accurate, and the group
velocity can be thought of as the signal velocity of the waveform.
It is however possible to design experiments where the group velocity of laser light
pulses sent through specially prepared materials significantly exceeds the signal velocity, and even exceeds the speed of light. It is also possible to stop the laser pulse.
The dispersion in the group velocity with wavelength leads to a distortion in the envelope of the light as it propagates. This
group velocity dispersion (GVD) is an important
effect in the propagation of signals through optical fibers and in the
design of short pulse lasers.
See dispersion for a full discussion of wave
velocities.
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