Third-order dispersion results from the frequency dependence of the group delay dispersion. In the Taylor expansion of the spectral phase versus angular frequency offset (see the article on chromatic dispersion), it is related to the third-order term. It can be written as
where Tg is the group delay.
The corresponding change in the spectral phase within a propagation length L is
The third-order dispersion of an optical element is usually specified in units of fs3, whereas the units of k''' are fs3/m.
In mode-locked lasers for pulse durations below roughly 30 fs, it is necessary to provide dispersion compensation not only for the average group delay dispersion (second-order dispersion), but also for the third-order dispersion and possibly for even higher orders.
In many cases, the investigation of the effect of third-order dispersion requires numerical pulse propagation modeling.