# Group delay dispersion

The group delay dispersion (GDD) of an optical element is the derivative of the group delay with respect to angular frequency, and also the second derivative of the optical phase. ${\displaystyle D_{2}(\omega )=-{\frac {\partial T_{g}}{d\omega }}={\frac {d^{2}\phi }{d\omega ^{2}}}}$. It is a measure of the chromatic dispersion of the element. A parameter independent of the length of the material is the group velocity dispersion (GVD).
GDD is related to the total dispersion parameter ${\displaystyle D_{tot}}$ as
${\displaystyle D_{2}(\omega )=-{\frac {2\pi c}{\lambda ^{2}}}D_{tot}}$