Editing Dispersion (optics) (section)

== Higher-order dispersion over broad bandwidths ==
When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an [[ultrashort pulse]] or a [[chirp]]ed pulse or other forms of [[spread spectrum]] transmission, it may not be accurate to approximate the dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading.

In particular, the dispersion parameter ''D'' defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as ''higher-order dispersion''.<ref>[http://www.rp-photonics.com/chromatic_dispersion.html Chromatic Dispersion], ''Encyclopedia of Laser Physics and Technology'' (Wiley, 2008).</ref><ref>{{Cite journal|last1=Mai|first1=Wending|last2=Campbell|first2=Sawyer D.|last3=Whiting|first3=Eric B.|last4=Kang|first4=Lei|last5=Werner|first5=Pingjuan L.|last6=Chen|first6=Yifan|author7-link=Douglas Werner|last7=Werner|first7=Douglas H.|date=2020-10-01|title=Prismatic discontinuous Galerkin time domain method with an integrated generalized dispersion model for efficient optical metasurface analysis|journal=[[Optical Materials Express]]|language=EN|volume=10|issue=10|pages=2542–2559|doi=10.1364/OME.399414|bibcode=2020OMExp..10.2542M|issn=2159-3930|doi-access=free}}</ref> These terms are simply a [[Taylor series]] expansion of the [[dispersion relation]] ''β''(''ω'') of the medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of [[Fourier transform]]s of the waveform, via integration of higher-order [[slowly varying envelope approximation]]s, by a [[split-step method]] (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full [[Maxwell's equations]] rather than an approximate envelope equation.