Group Delay Dispersion
The group delay dispersion (also sometimes called second-order dispersion) of an optical element is a quantitative measure for chromatic dispersion. It is defined as the derivative of the group delay, or the second derivative of the change in spectral phase, with respect to the angular optical frequency:
That derivative is always evaluated at a certain angular optical frequency – for example, at the center frequency of a laser pulse when considering the impact of chromatic dispersion on that pulse. If the group delay dispersion is independent of optical frequency, we have pure second-order dispersion and no higher-dispersion. Otherwise, third-order and other higher-order dispersion may be calculated via frequency derivatives of group delay dispersion.
The fundamental unit of group delay dispersion is s2 (seconds squared), but in practice it is usually specified in units of 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.
Spectral Phase and Group Delay
If an optical element has only second order dispersion, i.e., a frequency-independent D2 value and no higher-order dispersion, 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.
Relation to Group Velocity Dispersion
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).
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