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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

Category: general optics

Formula symbol: ng

Units: (dimensionless)

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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:

group index

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.

refractive index of silica
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


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?

Answer from the author:

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.


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

Answer from the author:

The refractive index, not the group index.


In an ideal Fabry–Perot resonator with R = 1, infinitely narrow linewidth and filled with a dispersive medium, is the free spectral range still determined by the group index?

Answer from the author:

Sure, it is!

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See also: group velocity, refractive index
and other articles in the category general optics


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