Refractive index

The index of refraction, the refracting power, an optical material characteristic. This dimensionless physical parameter specifies the factor by which the wavelength and the phase velocity of light are smaller than in vacuum.

At the interface of two media of different refractive indices, the light is refracted and reflected. This is called the medium with the higher refractive index of the optically denser. This is not to be confused with the " optical density " as a measure of the extinction.

3.1 orders of magnitude
3.2 Air
3.3 wavelength dependence

4.1 Faraday effect
4.2 Polarization-dependent absorption

8.1 history
8.2 Non diffraction limited lenses

Physical Basics

The term " refractive index " comes from the term refraction and its occurrence in the Snell's law. The refractive index is a dimensionless physical quantity. It indicates the ratio of the vacuum speed of light propagation velocity of light in the medium:

Complex refractive index

To take account of the absorption of the wave in the medium, the refractive index can also be expressed as a complex number. Here, different equivalent representations are common:

As the sum of the real part and the imaginary unit i multiplied imaginary part of a complex number Example: or or
As a difference of the real part and the imaginary part i multiplied by a complex number. Example: or
The product of the real refractive index and a complex number. example:

The minus sign contained in some representations before the imaginary part is chosen so that the imaginary part ( or ) with absorbent material gets a positive sign. This imaginary part is called the extinction coefficient or absorption index. Deviating describe writers who use the representation as a product, by the absorption index, so divided the imaginary part.

Both the real part and the imaginary part of the refractive index is in general of the frequency and thus of the wavelength -dependent. This referred to as dispersion effect allows for example the separation of white light into its spectral colors by a prism. The frequency dependency of the refractive index in the material can be reasonably well described by the model of the Lorentz oscillator.

Permittivity

The complex refractive index is related to the dielectric constant ( permittivity ), and the permeability coefficient:

In this case, all sizes are generally complex and frequency dependent. It must be noted that the concepts of the permittivity and the permeability are approximations that are suitable depending on the system better or worse to describe the effects of the polarization or magnetization.

If one wants to determine the wavelength dependence (dispersion) of the refractive index of a material theoretically, it passes through the electrical susceptibility that captures the contributions of the various mechanisms in the material properties and opens in the complex permittivity. In the case of non-magnetic material and the complex refractive index can be specified directly from real ( ) and imaginary part ( ) of the permittivity:

From this one can calculate the sizes and:

Group refractive index

The ratio of the vacuum speed of light and the group velocity of light in the medium is the group refractive index. This is dependent on the wavelength of the light material property is also called the group index.

The group velocity has the same value as the phase velocity in a vacuum. In addition, this value is independent of the wavelength of light. In the medium which is not necessarily the case. Particularly at wavelengths for which the material shows large dispersion, there are differences.

Other definitions

The definition of the refractive index was above the speed at which light travels in the material. This approach is reasonable, but not applicable in all cases. For example, meta- materials have (see below) the geometrical ray path after a negative refractive index. However, a negative value of the speed of light does not make sense defined.

Alternative definitions of the refractive index in which this problem does not occur, are:

About the Fermat's principle, according to which the light travels between two points that way, for it requires an extreme amount of time.
About the Huygens' principle, which states that every point of a wave front can be regarded as the starting point of a spherical wave and the interference of all these waves results in the further propagating wavefront.
About the ray optics. After the mentioned Snell's law of refraction, n corresponds to the sine ratio of angle of incidence and angle broken.

Refractive index of air and other substances

Orders of magnitude

Vacuum has, by definition, has a refractive index of exactly 1 in the visible range of real materials, the refractive indices are almost always greater than 1, for each material, however, there are wavelengths ( for example, above the visible range ) in which the refractive index is less than 1 (but remains positive). For very small wavelength ( X-ray radiation, gamma radiation), the refractive index is always smaller than 1, and approaches with decreasing wavelength in the 1 from below. For example, in X-rays, the representation is common, with typical values of between 10-9 and 10-5 are ( strongly dependent on the wavelength, depending on the atomic number and density of the material ).

Air

The refractive index of visible light of air at sea level is 1.00028 (dry air at standard atmosphere). It depends on the density and thus temperature of the air, as well as upon the particular composition of air - in particular, the atmospheric humidity. Since the air density to the top - in accordance with the laws of gases in a gravitational field - decreases exponentially, see barometric formula, he is about 8 km height only 1.00011. Due to the astronomical refraction stars appear to be higher than would be the case without an atmosphere. In the technical field, sometimes the index of refraction of the materials is based on the air for simplicity.

Wavelength dependence

Since, as described in the introduction, the refractive index of each material on the wavelength of the incident light depends (which also applies to electromagnetic radiation outside the visible range ), it would be necessary to specify this also depends on the wavelength ( in tabular form or as a function ). But since this is not necessary for many simple applications, the refractive index is usually given for the wavelength of the sodium D line (589 nm). The left figure is presented as an example curves of the wavelength-dependent refractive index of some types of glass. They show the typical course of a normal dispersion.

The strength of the dispersion is given in first approximation by the Abbe number.

Refractive index of the plasma

Any linearly polarized wave can be interpreted as a superposition of two circular waves with opposite sense of rotation. Extends parallel to the direction of propagation of the magnetic field lines are obtained for the refractive indices n have the following formulas:

Where f is the frequency of the wave, fP plasma frequency of the free electrons in the plasma and fB the gyration frequency of these electrons. The difference between both formulas disappears when the wave vector of the magnetic field with the direction of a right angle, as is then fB = 0.

Faraday effect

If n is positive, can be so that the phase velocity of the wave

And in turn, the wavelength

Calculate. Because distinguish the right - or left-handed circular shafts in their wavelengths, one of which is further rotated after a certain path length by a small angle than the other. The resulting vector (and therefore the plane of polarization ) as the sum of two components will therefore be rotated as it passes through the plasma, which is known as the Faraday rotation. After a long haul, the total rotation can be very large and is constantly changing due to the movement of the ionosphere. A program in vertical polarization may also reach the receiver at irregular intervals horizontally polarized. If the receiving antenna does not respond to the signal strength changes very dramatically what is referred to as fading.

When radio communications with satellites differ nlinks and nrechts due to the much higher frequencies only slightly, according to the Faraday rotation is low.

Polarization-dependent absorption

The unbound free electrons in the ionosphere can move helically around the magnetic field lines and escape while a parallel electromagnetic wave energy when the frequency and direction of rotation coincide. This cyclotron resonance can be observed only in the rechtszirkulär polarized extraordinary wave, because for f = fB, the denominator in the above formula is zero. The linkszirkulär polarized ordinary wave can in this way do not lose energy in the plasma.

The field lines of the geomagnetic field are oriented so that they point to the northern hemisphere of the ionosphere to the earth, you " look " at them, so to speak, so must be reversed right and left. So here's a radiated upward linkszirkuläre wave is absorbed in the ionosphere HAARP is so heated.

Beam to the other hand ( in the northern hemisphere ) a wave in the lower short-wave range with the right sense of rotation from vertically upward, it loses in the ionosphere no energy by cyclotron resonance and is reflected in several hundred kilometers height of the ionosphere, if the plasma frequency is not exceeded. Beam is from a linearly polarized wave upward, heated half of the transmission energy, the ionosphere and only the rest is left circularly polarized again down here, because changing the direction of rotation upon reflection.

When radio communications with the satellite frequencies well above the plasma frequency of the ionosphere in order to avoid serious comparable phenomena.

Measurement in the optical range

For the experimental determination of the refractive index of a medium with (for example, non-magnetic) can be, for example, NMED measure the Brewster angle in the transition from air in this medium. Apply to this case. For the measurement of a refractometer is used.

An estimate of the refractive index is possible with the so-called immersion method of dipping an object in transparent liquids with different densities. When the refractive index of the object and liquid are the same, the contours of the object to disappear. This method can easily be used to identify, for example rubies or sapphires, having a refractive index of about 1.76, by being immersed in a suitable heavy liquid, such as diiodomethane (refractive index = 1.74 ).

Application

The refractive index is one of the key determinants for optical lenses. The art of optical design for the interpretation of optical instruments ( lenses, Measuring instruments) based on the combination of different refractive lens surfaces with matching glass types.

In the chemistry of the refractive index is often used at a specific temperature in order to characterize liquid substances. The temperature and the wavelength at which the refractive index was determined to be, while the symbol for the refractive index is added, at 20 ° C and the sodium D-line, for example.

The determination of the refractive index allows an easy determination of the content of a particular substance in a solvent:

Sugar in wine, see Brix and Oechsle
Resin in solvent
Antifreeze (usually ethylene glycol ) in the cooling water of combustion engines or solar thermal systems

Microprocessors are manufactured using photolithography. The etching mask is transferred by ultraviolet light having a wavelength of 193 nanometers. Usually the smallest possible dimensions are limited by the half wavelength. By the use of fluids having a refractive index of 1.6 to form a grid of parallel lines having a thickness of 29.9 nanometers only succeeded. Thus, a further increase in future is possible for the chip preparation, using the same light source.

Related to the atomic structure of the material

The refractive index of a material is directly related to its atomic structure. The degree of crystallinity and the crystal lattice of the solid will affect the band structure and hence the refractive index. In the visible spectrum, this indicates, for example, when the shift of the band gap. By an anisotropic crystalline structure effects can also arise as the birefringence, in which the material has different refractive indices for different polarized light.

In semi-crystalline or amorphous materials, the atomic structure also has significant influence on the refractive index. So usually increases the refractive index of silicate and borosilicate glasses with their density. For example, lead silicate glasses also have a high refractive index with a high density. It should however be noted that, despite the general trend of the relationship between refractive index and density is not always linear and that exceptions occur, as shown in the left diagram. A relatively large refractive index and a small density can be obtained using glasses that contain metal oxides such as Li2O or light MgO, while the opposite with PbO and BaO - containing glasses is obtained.

Negative refractive indices

History

1968 described the Soviet physicist Victor Veselago the strange behavior of materials with negative refractive index, "Would the production succeed, it could be so finished lenses whose resolution would be far better than the ordinary lenses of optical materials ".

1999 struck Sir John Pendry before a design for metamaterials with negative refractive index for microwaves, which was implemented shortly thereafter.

2003, a group by Yong Zhang discovered Colorado that crystals of yttrium vanadate ( YVO4 ), a compound of yttrium, vanadium and oxygen, with or without further processing having a negative refractive index for light waves of a wide frequency range. The crystal consists of two nested lattices with symmetric optical axes. The negative refraction but only occurs in a certain angular range of the incident angle. In future experiments, the researchers want to find another alleged properties of negative refraction - such as the reversal of the Doppler effect and Cherenkov radiation.

In 2007, Vladimir Shalaev and his colleagues at Purdue University before a metamaterial with a negative refractive index for radiation in the near infrared range.

2007, it is physicists led by Ulf Leonhardt of the University of St Andrews using metamaterial with a negative refractive index ( " left-handed material " ) succeeded, the so-called Casimir effect reverse ( reverse Casimir effect, also known as quantum levitation ). This opens up the perspective for the future on an (almost ) smooth nanotechnology.

Not by diffraction limited lenses

In 2000, John Pendry showed that using a material with a negative refractive index lens can be made, where the resolution is not limited by the diffraction limit. A limiting condition is that the lens must be located in the near field of the object, so that the evanescent wave is not too faded away. For visible light, this means a distance of approximately < 1 micron. A few years later, researchers succeeded by Prof. Xiang Zhang at the University of Berkeley, to build a microscope with a resolution of one -sixth of the wavelength of the light used.

144815