Group delay dispersion

In optics, group velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium will affect 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, In optics, group velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium will affect 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, where ω {displaystyle omega } and ω 0 {displaystyle omega _{0}} are angular frequencies, and the group velocity v g ( ω ) {displaystyle v_{g}(omega )} is defined as v g ( ω ) ≡ ∂ ω / ∂ k {displaystyle v_{g}(omega )equiv partial omega /partial k} . The units of group velocity dispersion are 2/, often expressed in fs2/mm. Equivalently, group velocity dispersion can be defined in terms of the medium-dependent wave vector k ( ω ) {displaystyle k(omega )} according to or in terms of the refractive index n ( ω ) {displaystyle n(omega )} according to Group velocity dispersion is most commonly used to estimate the amount of chirp that will be imposed on a pulse of light after passing through a material of interest. The relevant expression is given by A simple illustration of how GVD can be used to determine pulse chirp can be seen by looking at the effect of a transform-limited pulse of duration σ {displaystyle sigma } passing through a planar medium of thickness d. Before passing through the medium, the phase offsets of all frequencies are aligned in time, and the pulse can be described as a function of time according to the expression