Definition: the ratio of the vacuum velocity of light to the group velocity in a medium
Alternative term: group refractive index
Formula symbol: ng
Units: (dimensionless)
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, for example, for calculating time delays for ultrashort pulses propagating in a medium, or the free spectral range of a resonator containing a dispersive medium.
For optical crystals or glasses, the group index in the visible or near-infrared spectral range is typically larger than the ordinary refractive index: the group velocity is somewhat smaller than the phase velocity. In certain special (artificial) situations, one obtains dramatically reduced group velocities (→ slow light), i.e., a very large group index.
Figure 1: Refractive index (solid lines) and group index (dotted lines) of silica versus wavelength at temperatures of 0 °C (blue), 100 °C (black) and 200 °C (red).
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.
