定义：
介质中群速度与频率之间的关系，或者群速度倒数对角频率的微分。

群速度色散是透明介质中光的群速度与光频率或者波长相关的现象。它通常具有准确的值，即群速度倒数对角频率（有时是对波长）的微分：

其中k是波数，与频率有关。（如果是在波导中，那么k由相位常数 β代替。）
群速度色散是单位长度的群时延色散。基本单位为s2/m。例如，二氧化硅的群速度色散在800nm时为+35 fs2/mm，而在1500nm时则为−26 fs2/mm。在这中间的某一波长（约1300 nm），是零色散波长。
在光纤中（例如，在光纤通信中），群速度色散通常定义为对波长的微分（而不是角频率）。可以通过之前提到的GVD参数来计算：

这一参数的单位为ps/(nm km)（单位纳米波长变化单位千米传输距离的皮秒数）。例如，在1550nm（通信光纤的典型值）为20ps/(nm km)对应于−25 509 fs2/m。
由于长波长对应于光频率较小，因此有时需要实现不同正负号的GVD和Dλ。为了避免混淆，可以采用正常和反常色散来代替正色散和负色散。正常色散表示，随着光频率的增加，群速度减小；大多数都是这种情况。
根据实际情况不同，群速度色散会产生不同的效应：

1. 产生色散时间展宽或者超短脉冲压缩。
2. 光纤中，非线性效应与群速度色散密切相关。例如，光谱展宽（甚至超连续光产生）或压缩，与色散性质有关。
3. 色散也会引起参量非线性相互作用中的群速度失配。例如，它会限制倍频器、光参量振荡器或者放大器中的相互作用带宽。

Acronym: GVD

Definition: the frequency dependence of the group velocity in a medium, or (quantitatively) the derivative of the inverse group velocity with respect to angular frequency

More general term: chromatic dispersion

Formula symbol: β₂

Units: s²/m

Group velocity dispersion is the phenomenon that the group velocity of light in a transparent medium depends on the optical frequency or wavelength. The term can also be used as a precisely defined quantity, namely the derivative of the inverse group velocity with respect to the angular frequency (or sometimes the wavelength), called β₂:

where k is the frequency-dependent wavenumber. (For waveguides, it is replaced with the phase constant β.)

The group velocity dispersion is the group delay dispersion per unit length. The basic SI units are s²/m. For example, the group velocity dispersion of fused silica is +35 fs²/mm at 800 nm and −26 fs²/mm at 1500 nm. Somewhere between these wavelengths (at about 1.3 μm), there is the zero-dispersion wavelength.

For optical fibers (e.g. in the context of optical fiber communications), the group velocity dispersion is usually defined as a derivative with respect to wavelength (rather than angular frequency). This can be calculated from the above-mentioned GVD parameter:

where c is the vacuum velocity of light. One can also relate D_λ to the second wavelength derivative of the refractive index:

This quantity is usually specified with units of ps/(nm km) (picoseconds per nanometer wavelength change and kilometer propagation distance). For example, 20 ps/(nm km) at 1550 nm (a typical value for telecom fibers) corresponds to −25 509 fs²/m.

It is important to realize the different signs of GVD and D_λ, resulting from the fact that longer wavelengths correspond to smaller optical frequencies. In order to avoid confusion, the terms normal and anomalous dispersion can be used instead of positive and negative dispersion. Normal dispersion implies that the group velocity decreases for increasing optical frequency; this is the most common situation.

Depending on the situation, group velocity dispersion can have different important effects:

• It is responsible for dispersive temporal broadening or compression of ultrashort pulses.
• In optical fibers, the effect of nonlinearities strongly depends on the group velocity dispersion. For example, there may be spectral broadening (even supercontinuum generation) or compression, depending on the dispersion properties.
• Dispersion is also responsible for the group velocity mismatch of different waves in parametric nonlinear interactions. For example, it can limit the interaction bandwidth in frequency doublers, optical parametric oscillators and amplifiers.