Group Delay Dispersion | <<< | >>> |
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: D2
Units: s2
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 fs2 or ps2. Positive (negative) values correspond to normal (anomalous) chromatic dispersion. For example, the group delay dispersion of a 1-mm thick silica plate is +35 fs2 at 800 nm (normal dispersion) or −26 fs2 at 1500 nm (anomalous dispersion). Another example is given in Figure 1.
Figure 1: Wavelength-dependent group delay dispersion of a Gires–Tournois interferometer made of a 5-μm thick silica layer on a high reflector.
If an optical element has only second order dispersion, i.e., a frequency-independent D2 value, its effect on an optical pulse or signal can be described as a change of the spectral phase:
where ω0 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 s2/m) is the group velocity dispersion (GVD).
Bibliography
| [1] | K. Naganuma et al., “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light”, Opt. Lett. 15 (7), 393 (1990) |
| [2] | A. P. Kovacs et al., “Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry”, Opt. Lett. 20 (7), 788 (1995) |
| [3] | S. Diddams and J.-C. Diels, “Dispersion measurements with white-light interferometry”, J. Opt. Soc. Am. B 13 (6), 1120 (1996) |
| [4] | A. Gosteva et al., “Noise-related resolution limit of dispersion measurements with white-light interferometers”, J. Opt. Soc. Am. B 22 (9), 1868 (2005) |
| [5] | T. V. Amotchkina et al., “Measurement of group delay of dispersive mirrors with white-light interferometer”, Appl. Opt. 48 (5), 949 (2009) |
See also: chromatic dispersion, group velocity dispersion, group delay
and other articles in the categories general optics, light pulses
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