In analogy with the refractive index, the group index (or group refractive index) ng of a material can be defined as the ratio of the vacuum velocity of light to the group velocity in the medium:
For calculating this, one obviously needs to know not only the refractive index at the wavelength of interest, but also its frequency dependence.
The group index is used, e.g., to calculate time delays for ultrashort pulses propagating in a medium, or the free spectral range of a resonator containing a dispersive medium.
For crystals or glasses, the group index in the visible or near-infrared spectral range is typically larger than the ordinary refractive index, which determines the phase velocity. This implies that the group velocity is often (but not always) lower than the phase velocity.
Note that for optical fibers and other waveguides, one uses the so-called effective refractive index instead of the ordinary refractive index in order to calculate the group velocity, since waveguide dispersion has to be taken into account. Based on that, an effective group index of a fiber could be calculated.
See also: group velocity, refractive index
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