## Group Delay Dispersion | <<< | >>> | Feedback |

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Acronym: GDD

Definition: the frequency dependency of the group delay, or (quantitatively) the corresponding derivative with respect to angular frequency

German: Gruppenverzögerungsdispersion

Categories: general optics, light pulses

Formula symbol: *D*_{2}

Units: s^{2}

The group delay dispersion (also sometimes called *second-order dispersion*) of an optical element is the derivative of the group delay with respect to the angular frequency, or the second derivative of the change in spectral phase:

It is usually specified in fs^{2} or ps^{2}.
Positive (negative) values correspond to normal (anomalous) chromatic dispersion.
For example, the group delay dispersion of a 1-mm thick silica plate is +35 fs^{2} at 800 nm (normal dispersion) or −26 fs^{2} at 1500 nm (anomalous dispersion).
Another example is given in Figure 1.

If an optical element has only second order dispersion, i.e., a frequency-independent *D*_{2} value, its effect on an optical pulse or signal can be described as a change of the spectral phase:

where ω_{0} is the angular frequency at the center of the spectrum.

Note that the group delay dispersion (GDD) always refers to some optical element or to some given length of a medium (e.g. an optical fiber).
The GDD per unit length (in units of s^{2}/m) is the *group velocity dispersion* (GVD).

See also: chromatic dispersion, group velocity dispersion, group delay

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