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
which is also the derivative of the group delay per unit length with respect to angular frequency.
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.
It is also possible to specify TOD with respect to the vacuum wavelength rather than the optical frequency, which leads to units of fs/nm2, for example. It can be calculated as follows:
In practice, one often has the dispersion parameter Dλ and its wavelength derivative, called the dispersion slope, and can calculate the TOD from those as:
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.
Questions and Comments from Users
Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.
Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him e.g. via e-mail.
By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.