Group Velocity Dispersion

Ask RP Photonics for advice on any aspect of group velocity dispersion.

Group velocity dispersion is the phenomenon that the group velocity of light in a transparent medium depends on the optical frequency or wavelength.
The term can also be used as a precisely defined quantity, namely the derivative of the inverse group velocity with respect to the angular frequency (or sometimes the wavelength), called β2:

where k is the frequency-dependent wavenumber.
(For waveguides, it is replaced with the phase constant β.)

The group velocity dispersion is the group delay dispersion per unit length.
The basic SI units are s2/m.
For example, the group velocity dispersion of fused silica is +35 fs2/mm at 800 nm and −26 fs2/mm at 1500 nm.
Somewhere between these wavelengths (at about 1.3 μm), there is the zero-dispersion wavelength.

For optical fibers (e.g. in the context of optical fiber communications), the group velocity dispersion is usually defined as a derivative with respect to wavelength (rather than angular frequency).
This can be calculated from the above-mentioned GVD parameter:

where c is the vacuum velocity of light.
One can also relate Dλ to the second wavelength derivative of the refractive index:

This quantity is usually specified with units of ps/(nm km) (picoseconds per nanometer wavelength change and kilometer propagation distance).
For example, 20 ps/(nm km) at 1550 nm (a typical value for telecom fibers) corresponds to −25 509 fs2/m.

Conversion of Chromatic Dispersion Values

Center wavelength:

Group velocity dispersion:

calc

(1 fs2 = 1e-30 s2)

Dispersion parameter:

calc

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It is important to realize the different signs of GVD and Dλ, resulting from the fact that longer wavelengths correspond to smaller optical frequencies.
In order to avoid confusion, the terms normal and anomalous dispersion can be used instead of positive and negative dispersion.
Normal dispersion implies that the group velocity decreases for increasing optical frequency; this is the most common situation.

Depending on the situation, group velocity dispersion can have different important effects:

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See also: chromatic dispersion, group delay dispersion, group velocity mismatch
and other articles in the categories general optics, fiber optics and waveguides, light pulses

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