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# Group Index

Definition: the ratio of the vacuum velocity of light to the group velocity in a medium

Alternative term: group refractive index

German: Gruppenindex

Formula symbol: ng

Units: (dimensionless)

Author:

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. 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.

## Questions and Comments from Users

2020-04-01

I wonder what is determining the wavelengths of cavity resonances, e.g. in a silicon ring resonator – is it group index or the effective refractive index?

In short: a combination of both!

The mode spacing (the frequency spacing of the resonator modes) is determined by the group delay for one resonator round-trip. For a silicon ring resonator, containing a waveguide, the group delay is proportional to the geometrical round-trip length and to the effective group index. Here, “effective” means that we do not simply take a material property, but an effective value calculated for the waveguide structure. Further, “group index” means that we do not simply calculate the effective refractive index, which is relevant only for the phase delay, but the group index, which is relevant for the group delay. That calculation involves the use of frequency derivatives of propagation constants.

2020-07-21

Which kind of index should be used to calculate refraction angles in the crystal?

The refractive index, not the group index.

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