group index (original) (raw)

Author: the photonics expert (RP)

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

Alternative term: group refractive index

Category: article belongs to category general optics general optics

Related: group velocityrefractive index

Units: (dimensionless)

Formula symbol: ($n_\textrm{g}$)

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DOI: 10.61835/2bh Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

What is a Group Index?

In analogy with the refractive index, the group index (or group refractive index) ($n_\textrm{g}$) of a material can be defined as the ratio of the vacuum velocity of light to the group velocity in the medium: n_{\textrm{g}} = \frac{c}{\upsilon_{\textrm{g}}}Usingthedefinitionofgroupvelocity,thisleadsto:Using the definition of group velocity, this leads to:Usingthedefinitionofgroupvelocity,thisleadsto:n_{\textrm{g}} = \frac{c}{\upsilon_{\textrm{g}}} = c\frac{\partial k}{\partial \omega} = \frac{\partial }{\partial \omega}\left( \omega \;n(\omega ) \right) = n(\omega ) + \omega \;\frac{\partial n}{\partial \omega}$$

For calculating this, one obviously needs to know not only the refractive index at the wavelength of interest, but also its optical frequency derivative. That derivative may be estimated from multiple refractive index values at different wavelengths, or calculated from a Sellmeier formula.

Group Index and Time Delays

The group index is used, for example, for calculating time delays for ultrashort pulses propagating in a medium, as pulse envelopes travel with the group velocity. Also, the free spectral range of a resonator containing a dispersive medium is determined by its group index.

Values of the Group Index

For optical crystals or glasses, the group index in the visible or near-infrared spectral range is typically somewhat 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., an extremely large group index, while the refractive index stays in the “normal” region.

refractive index of silica

Figure 1: Refractive index (solid lines) and group index (dashed lines) of silica versus wavelength at temperatures of 0 °C (blue), 100 °C (black) and 200 °C (red). Data taken from M. Medhat et al., J. Opt. A: Pure Appl. Opt. 4, 174 (2002); doi:10.1088/1464-4258/4/2/309.

Just as the normal refractive index, the group index depends somewhat on the material's temperature; see Figure 1 as an example.

Effective Group Index of Fibers

Note that for optical fibers and other waveguides, one uses the so-called effective refractive index instead of the ordinary refractive index 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.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is the group index?

The group index ($n_\textrm{g}$) of a material is defined as the ratio of the speed of light in vacuum to the group velocity of light in that material. It is relevant for describing the propagation speed of the envelope of a light pulse.

The group index ($n_\textrm{g}$) depends not only on the refractive index ($n$) but also on its frequency derivative, according to the equation ($n_\textrm{g} = n(\omega) + \omega (\partial n/\partial\omega)$). In the visible and near-infrared region, the group index of optical materials is typically slightly larger than their refractive index.

What are typical applications of the group index?

The group index is used to calculate propagation time delays for ultrashort pulses in a medium, as their pulse envelopes travel with the group velocity. It also determines the free spectral range of an optical resonator containing a dispersive medium.

What is the effective group index of an optical fiber?

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