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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 ]
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. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as ...
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 ...
The red square moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square traverses the figure in the time it takes the green dot to traverse half. The dispersion relation for deep water waves is often written as
In astronomy, the velocity dispersion (σ) is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster.
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.
For optical fiber dispersion measurement purposes, the quantity of interest is group delay per unit length, which is the reciprocal of the group velocity of a particular mode. The measured group delay of a signal through an optical fiber exhibits a wavelength dependence due to the various dispersion mechanisms present in the fiber.
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.