Refractive Index Dispersion And Absorption Anisotropy

The speed of all electromagnetic radiation in vacuum is the same, approximately 3×10⁸ meters per second, and is denoted by . So if is the phase velocity of radiation of a specific frequency in a specific material, the refractive index is given by

This number is typically bigger than one: the denser the material, the more the light is slowed down. However, at certain frequencies (e.g. near absorption resonances, and for x-rays), will actually be smaller than one. This does not contradict the theory of relativity, which holds that no information-carrying signal can ever propagate faster than , because the phase velocity is not the same as the group velocity or the signal velocity .

The phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. It is the group velocity that (almost always) represents the rate that information (and energy) may be transmitted by the wave, for example the velocity at which a pulse of light travels down an optical fibre.

Sometimes, a "group velocity refractive index", usually called the group index is defined:

where is the group velocity. This value should not be confused with , which is always defined with respect to the phase velocity.

At the microscale an electromagnetic wave is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the permittivity. This oscillation of charges itself causes the radiation of an electromagnetic wave that is slightly out-of- phase with the original. The sum of the two waves creates a wave with the same frequency but shorter wavelength than the original, leading to a slowing in the wave's travel.

If the refractive indices of two materials are known for a given frequency, then one can compute the angle by which radiation of that frequency will be refracted as it moves from the first into the second material from Snell's lawSnell's law is the simple formula used to calculate the refraction of light when travelling between two media of differing refractive index. It is named for its discoverer, Dutch mathematician Willebrord van Roijen Snell ( 1580- 1626). Overview Refraction.

Recent research has also demonstrated the existence of negative refractive index which can occur if and are simultaneously negative. Not thought to occur naturally this can be achieved with so called metamaterialIn electromagnetism (covering areas like optics and photonics), a meta material (or metamaterial is an object that gains its (electromagnetic) material properties from its structure rather than inheriting them directly from the materials it is composed ofs and offers the possibility of perfect lenses and other exotic phenomena such as a reversal of Snell's lawSnell's law is the simple formula used to calculate the refraction of light when travelling between two media of differing refractive index. It is named for its discoverer, Dutch mathematician Willebrord van Roijen Snell ( 1580- 1626). Overview Refraction.

1 Dispersion and Absorption

The refractive index of a material varies with frequencyFrequency is the measurement of the number of times that a repeated event occurs per unit time. To calculate the frequency, one fixes a time interval, counts the number of occurrences of the event within that interval, and then divides this count by the l (except in vacuum, where all frequencies travel at the same speed, ). This effect, known as dispersionIn optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the wave's speed on its frequency. It is most often described in light waves, though it may happen to an, is what causes a prismIn optics, a prism is a device used to refract light, reflect it or break it up (to disperse it) into its constituent spectral colors (colors of the rainbow), traditionally built in the shape of a right prism with triangular base. As light moves from one to divide white light into its constituent spectral colorFor alternative meanings, see color (disambiguation). visual arts. Color (or colour is a sensation which (in humans) derives from the ability of the fine structure of the eye to distinguish three differently filtered analyses of a view. The perception ofs, explains rainbows, and is the cause of chromatic aberration in lenses. In regions of the spectrum where the material does not absorb, the refractive index increases with frequency. Near absorption peaks, the refractive index decreases with frequency.

The Sellmeier equation is an empirical formula that works well in describing dispersion, and Sellmeier coefficients are often quoted instead of the refractive index in tables. For some representative refractive indices at different wavelengths, see list of indices of refraction.

Sometimes the refractive index is defined as a complex number, with the imaginary part of the number representing the absorption of the material. This is particularly useful when analysing the propagation of electromagnetic waves in metals. The real and imaginary parts of the complex refractive index are related by the Kramers-Kronig relations.

2 Anisotropy

The refractive index of certain media may be different depending on the polarization and direction of propagation of the light through the medium. This is known as birefringence or anisotropy and is described by the field of crystal optics. In the most general case, the dielectric constant is a rank-2 tensor (a 3 by 3 matrix), which cannot simply be described by refractive indices except for polarizations along principal axes.

In magneto-optic (gyro-magnetic) and optically active materials, the principal axes are complex (corresponding to elliptical polarizations), and the dielectric tensor is complex- Hermitian (for lossless media); such materials break time-reversal symmetry and are used e.g. to construct Faraday isolators.

3 Nonlinearity

The strong electric field of high intensity light (such as output of a laser) may cause a medium's refractive index to vary as the light passes through it, giving rise to nonlinear optics. If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as self-focusing and self phase modulation . If the index varies linearly with the field (which is only possible in materials that do not possess inversion symmetry ), it is known as the Pockels effect.

4 Inhomogeneity

If the refractive index of a medium is not constant, but varies gradually with position, the material is known as a gradient-index medium and is described by gradient index optics. Light travelling through such a medium can be bent or focussed, and this effect can be exploited to produce lenses, some optical fibers and other devices. Some common mirages are caused by a spatially-varying refactive index of air.

5 See also

List of indices of refraction

Chemical properties Optics

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