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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 ]
Dispersion of gravity–capillary waves on the surface of deep water. Phase and group velocity divided by 4 √ gσ / ρ as a function of inverse relative wavelength 1 / λ √ σ / ρg. Blue lines (A): phase velocity c p, Red lines (B): group velocity c g. Drawn lines: gravity–capillary waves. Dashed lines: gravity waves.
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.
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 ...
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 ...
1 Nm 3 of any gas (measured at 0 °C and 1 atmosphere of absolute pressure) equals 37.326 scf of that gas (measured at 60 °F and 1 atmosphere of absolute pressure). 1 kmol of any ideal gas equals 22.414 Nm 3 of that gas at 0 °C and 1 atmosphere of absolute pressure ... and 1 lbmol of any ideal gas equals 379.482 scf of that gas at 60 °F and ...
In shallow water, the group velocity is equal to the shallow-water phase velocity. This is because shallow water waves are not dispersive. In deep water, the group velocity is equal to half the phase velocity: {{math|c g = 1 / 2 c p. [7] The group velocity also turns out to be the energy transport velocity.
In the other family it is antisymmetric. The phenomenon of velocity dispersion leads to a rich variety of experimentally observable waveforms when acoustic waves propagate in plates. It is the group velocity c g, not the above-mentioned phase velocity c or c p, that determines the modulations seen in the observed waveform. The appearance of the ...