Refractive Index | previous | next | feedback |
Definition: a measure for the reduction in the velocity of light in a medium
The refractive index of a transparent optical medium, also called the index of refraction, is the factor by which the phase velocity is decreased relative to the velocity of light in vacuum, assuming linear propagation (i.e., with moderate optical intensities). Via the phase velocity, the refractive index also determines phenomena like refraction, reflection and diffraction at optical interfaces.
The refractive index can be calculated from the relative permittivity εr and the relative permeability μr of a material:
Note that the values of εr and μr at the optical frequency have to be used, which can substantially deviate from those at low frequencies. For usual optical materials, μr is close to unity.
The refractive index of a material depends on the optical frequency or wavelength; this dependency is called chromatic dispersion. Typical refractive index values for glasses and crystals (e.g. laser crystals) in the visible spectral region are in the range from 1.4 to 2.8, and typically the refractive index increases for shorter wavelengths (→ normal dispersion). This is a consequence of the fact that the visible spectral region, with high transmission of such materials, lies between spectral regions of strong absorbance: the ultraviolet region with photon energies above the bandgap, and the near- or mid-infrared region with vibrational resonances and their overtones.
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). The plots are based on data from M. Medhat et al., J. Opt. A: Pure Appl. Opt. 4, 174 (2002).
Semiconductors exhibit higher refractive indices in their transparency region. For example, gallium arsenide (GaAs) has a refractive index of ∼3.5 in the 1-μm region. This is caused by the strong absorption at wavelengths below the bandgap wavelength of ∼870 nm. Consequences of the high index of refraction are strong Fresnel reflections and a large critical angle for total internal reflection at semiconductor-air interfaces.
The wavelength-dependent refractive index of a transparent optical material can often be analytically described with a Sellmeier formula, which contains several empirically obtained parameters. Extended versions of such equations describe the temperature dependence as well; such an equation has been used for the graph shown above. A precise knowledge of wavelength and temperature dependence of the refractive index is important for phase matching of nonlinear frequency conversion in nonlinear crystal materials.
In anisotropic media, the refractive index generally depends on the polarization direction (→ birefringence) and the propagation direction (→ anisotropy). If a medium has a so-called optical axis, the refractive index for light propagation along this axis does not depend on the polarization direction.
A complex refractive index is sometimes used to quantify not only the phase change per unit length, but also (via its imaginary part) optical gain or propagation losses (e.g. caused by absorption).
There is another type of refractive index, the group index, which quantifies the reduction in the group velocity. Extreme excursions of the refractive index and particularly the group index can occur near sharp resonances, as are observed in certain quantum optics experiments. This can be related to extremely large or small values of the group velocity (→ slow light). Even a negative refractive index is possible for certain metamaterials (consisting e.g. of metal-dielectric composites), which have been demonstrated first in the microwave region, but begin to become a reality also in the optical domain. Negative refractive index values give rise to a range of intriguing phenomena.
For waveguides, an effective refractive index can be used to quantify the phase change per unit length of a given mode.
See also: velocity of light, Sellmeier formula, Kramers-Kronig relations, group index, effective refractive index, nonlinear index, modal index
