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See also list of indices of
refraction.
The refractive index of a material at a particular frequency
is the factor by which electromagnetic radiation
of that frequency is slowed down (relative to vacuum) when it travels inside the material. For a non-magnetic material, the
square of the refractive index is the dielectric constant ε (sometimes multiplied by ε0, the
permittivity of free space).
The speed of all electromagnetic radiation in vacuum is the same, approximately 3×108 meters per second, and is
denoted by c. So if v is the phase velocity of radiation of a specific frequency in a specific material, the
refractive index is given by
- n = c/v.
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), n 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 c, 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:
- ng = c / vg,
where vg is the group velocity. This value should not be confused with n, 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 law.
Dispersion and Absorption
The refractive index of a material varies with frequency (except in vacuum, where all frequencies travel at the same speed,
c). This effect, known as dispersion, is what
causes a prism to divide white light into its constituent spectral
colors, 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.
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 optical isolators.
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.
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