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In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency, [1] [2]
Phase and group velocity divided by √ gh as a function of h / λ . A: phase velocity, B: group velocity, C: phase and group velocity √ gh valid in shallow water. Drawn lines: based on dispersion relation valid in arbitrary depth. Dashed lines: based on dispersion relation valid in deep water.
The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
Animation: phase and group velocity of electrons This animation portrays the de Broglie phase and group velocities (in slow motion) of three free electrons traveling over a field 0.4 ångströms in width. The momentum per unit mass (proper velocity) of the middle electron is lightspeed, so that its group velocity is 0.707 c. The top electron ...
Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The dispersion relation for such waves is curious: For a freely-propagating internal wave packet, the direction of propagation of energy (group velocity) is perpendicular to the direction of propagation of wave crests and troughs (phase velocity).
Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency, which results in group-velocity dispersion = d 2 k/dω 2. If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the ...
Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity √ gh as a function of relative depth h / λ. Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √ gh valid in shallow water.
Sketches of Rossby waves’ fundamental principles. a and b The restoring force.c–e The waveform’s velocity. In a, an air parcel follows along latitude at an eastward velocity with a meridional acceleration = when the pressure gradient force balances the Coriolis force.