In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency,[1][2]
![{\displaystyle {\text{GVD}}(\omega _{0})\equiv {\frac {\partial }{\partial \omega }}\left({\frac {1}{v_{g}(\omega )}}\right)_{\omega =\omega _{0}},}](//wikimedia.org/api/rest_v1/media/math/render/svg/62e81d3d50482de4ad79c0381fd9c73e9eab89f2)
where
and
are angular frequencies, and the group velocity
is defined as
. The units of group-velocity dispersion are [time]2/[distance], often expressed in fs2/mm.
Equivalently, group-velocity dispersion can be defined in terms of the medium-dependent wave vector
according to
![{\displaystyle {\text{GVD}}(\omega _{0})\equiv \left({\frac {\partial ^{2}k}{\partial \omega ^{2}}}\right)_{\omega =\omega _{0}},}](//wikimedia.org/api/rest_v1/media/math/render/svg/bd794d6a57c2da746e7e35772c22f7e53d65e5d7)
or in terms of the refractive index
according to
![{\displaystyle {\text{GVD}}(\omega _{0})\equiv {\frac {2}{c}}\left({\frac {\partial n}{\partial \omega }}\right)_{\omega =\omega _{0}}+{\frac {\omega _{0}}{c}}\left({\frac {\partial ^{2}n}{\partial \omega ^{2}}}\right)_{\omega =\omega _{0}}.}](//wikimedia.org/api/rest_v1/media/math/render/svg/012a1386f6188a776ede6f0bb0c1a7f24395c48f)