### Brechungsindex

To measure the spatial variation of refractive index in a sample phase-contrast imaging methods are used. Durch Vergleich mit dem komplexen Brechungsindex in den beiden o. Jede linear polarisierte Welle kann als Überlagerung zweier zirkularer Wellen mit entgegengesetztem Umlaufsinn interpretiert werden.

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Light propagation in absorbing materials can be described using a complex -valued refractive index. The concept of refractive index applies within the full electromagnetic spectrum , from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity , the speed at which the pulse of light or the envelope of the wave moves.

The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in The ratio had the disadvantage of different appearances.

Newton , who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like " to " or "nearly 4 to 3"; for water.

Young did not use a symbol for the index of refraction, in In the next years, others started using different symbols: For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodium , with a wavelength of nanometers , as is conventionally done. Almost all solids and liquids have refractive indices above 1. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.

Most plastics have refractive indices in the range from 1. For infrared light refractive indices can be considerably higher. Moreover, topological insulator material are transparent when they have nanoscale thickness. These excellent properties make them a type of significant materials for infrared optics.

According to the theory of relativity , no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be lower than 1. The refractive index measures the phase velocity of light, which does not carry information. This can occur close to resonance frequencies , for absorbing media, in plasmas , and for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 exceptions close to some resonance frequencies. An example of a plasma with an index of refraction less than unity is Earth's ionosphere.

Since the refractive index of the ionosphere a plasma , is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" see Geometric optics allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.

See also Radio Propagation and Skywave. Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values.

The resulting negative refraction i. At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom primarily the electrons proportional to the electric susceptibility of the medium.

Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility. As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.

The light wave traveling in the medium is the macroscopic superposition sum of all such contributions in the material: This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies see scattering.

Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:. The refractive index of materials varies with the wavelength and frequency of light. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberration , which often needs to be corrected for in imaging systems.

In regions of the spectrum where the material does not absorb light, the refractive index tends to decrease with increasing wavelength, and thus increase with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength. For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number: For a more accurate description of the wavelength dependence of the refractive index, the Sellmeier equation can be used.

Sellmeier coefficients are often quoted instead of the refractive index in tables. Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectral emission lines ; for example, n D usually denotes the refractive index at the Fraunhofer "D" line, the centre of the yellow sodium double emission at When light passes through a medium, some part of it will always be attenuated.

This can be conveniently taken into account by defining a complex refractive index,. Therefore, these two conventions are inconsistent and should not be confused. See Mathematical descriptions of opacity. Dielectric loss and non-zero DC conductivity in materials cause absorption. Good dielectric materials such as glass have extremely low DC conductivity, and at low frequencies the dielectric loss is also negligible, resulting in almost no absorption.

However, at higher frequencies such as visible light , dielectric loss may increase absorption significantly, reducing the material's transparency to these frequencies.

Forouhi and Bloomer then applied the Kramers—Kronig relation to derive the corresponding equation for n as a function of E. The same formalism was applied to crystalline materials by Forouhi and Bloomer in For X-ray and extreme ultraviolet radiation the complex refractive index deviates only slightly from unity and usually has a real part smaller than 1.

Optical path length OPL is the product of the geometric length d of the path light follows through a system, and the index of refraction of the medium through which it propagates, [30]. This is an important concept in optics because it determines the phase of the light and governs interference and diffraction of light as it propagates. According to Fermat's principle , light rays can be characterized as those curves that optimize the optical path length.

When light moves from one medium to another, it changes direction, i. When light enters a material with higher refractive index, the angle of refraction will be smaller than the angle of incidence and the light will be refracted towards the normal of the surface.

The higher the refractive index, the closer to the normal direction the light will travel. When passing into a medium with lower refractive index, the light will instead be refracted away from the normal, towards the surface. Apart from the transmitted light there is also a reflected part. The reflection angle is equal to the incidence angle, and the amount of light that is reflected is determined by the reflectivity of the surface.

The reflectivity can be calculated from the refractive index and the incidence angle with the Fresnel equations , which for normal incidence reduces to [32]: At a certain angle called Brewster's angle , p-polarized light light with the electric field in the plane of incidence will be totally transmitted.

Brewster's angle can be calculated from the two refractive indices of the interface as [1]: The focal length of a lens is determined by its refractive index n and the radii of curvature R 1 and R 2 of its surfaces. The power of a thin lens in air is given by the Lensmaker's formula: The resolution of a good optical microscope is mainly determined by the numerical aperture NA of its objective lens.

For this reason oil immersion is commonly used to obtain high resolution in microscopy. In this technique the objective is dipped into a drop of high refractive index immersion oil on the sample under study. Thus refractive index in a non-magnetic media is the ratio of the vacuum wave impedance to the wave impedance of the medium.

In general, the refractive index of a glass increases with its density. However, there does not exist an overall linear relation between the refractive index and the density for all silicate and borosilicate glasses.

A relatively high refractive index and low density can be obtained with glasses containing light metal oxides such as Li 2 O and MgO , while the opposite trend is observed with glasses containing PbO and BaO as seen in the diagram at the right. Many oils such as olive oil and ethyl alcohol are examples of liquids which are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index.

Sometimes, a "group velocity refractive index", usually called the group index is defined: This value should not be confused with n , which is always defined with respect to the phase velocity. When the dispersion is small, the group velocity can be linked to the phase velocity by the relation [32]: In this case the group index can thus be written in terms of the wavelength dependence of the refractive index as.

When the refractive index of a medium is known as a function of the vacuum wavelength instead of the wavelength in the medium , the corresponding expressions for the group velocity and index are for all values of dispersion [41]. In , Hermann Minkowski calculated the momentum p of a refracted ray as follows: In , Max Abraham proposed the following formula for this calculation: A study suggested that both equations are correct, with the Abraham version being the kinetic momentum and the Minkowski version being the canonical momentum , and claims to explain the contradicting experimental results using this interpretation.

As shown in the Fizeau experiment , when light is transmitted through a moving medium, its speed relative to an observer traveling with speed v in the same direction as the light is:. The refractive index of a substance can be related to its polarizability with the Lorentz—Lorenz equation or to the molar refractivities of its constituents by the Gladstone—Dale relation. Molar refractivity , on the other hand, is a measure of the total polarizability of a mole of a substance and can be calculated from the refractive index as.

So far, we have assumed that refraction is given by linear equations involving a spatially constant, scalar refractive index. These assumptions can break down in different ways, to be described in the following subsections. In some materials the refractive index depends on the polarization and propagation direction of the light. In the simplest form, uniaxial birefringence, there is only one special direction in the material.

This axis is known as the optical axis of the material. For other propagation directions the light will split into two linearly polarized beams. For light traveling perpendicularly to the optical axis the beams will have the same direction. Many crystals are naturally birefringent, but isotropic materials such as plastics and glass can also often be made birefringent by introducing a preferred direction through, e.

This effect is called photoelasticity , and can be used to reveal stresses in structures. The birefringent material is placed between crossed polarizers. A change in birefringence alters the polarization and thereby the fraction of light that is transmitted through the second polarizer. References in periodicals archive? Smar, "Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection," Nature Photonics, Vol. Approximate model for universal broadband antireflection nano-structure.

The presented quantum-coherent left-handed atomic vapor that can exhibit high gain for overcoming the losses has four advantages they can also be viewed as four fascinating characteristics: Gain-assisted negative refractive index in a quantum coherent medium.

By sculpturing these artificial subwavelength nanostructures, the researchers were able to control the light dispersion so that a negative refractive index appeared in the medium. Metamaterial with zero refraction could revolutionize telecommunications.

At standard atmosphere conditions near the Earth surface, the radio refractive index is equal to approximately 1. As ambient temperature changes, the phase front at each wavelength generated by the arrayed waveguide will tilt due to the change in the refractive index of the optical waveguide and the linear expansion of the silicon substrate, causing a shift of the focusing point on the output waveguide within the slab waveguide [10].

Low loss a thermal arrayed waveguide grating AWG module for passive and active optical network applications. The refractive index of a medium is a measure of how much the speed of light or other waves such as sound waves is reduced inside the medium. Limitations of refractive index: They synthesize what they feel to be the most important and influential papers in the field of metamaterials, presenting chapters covering metamaterials and homogenization of composites, designing metamaterials with negative material parameters, negative refraction and photonic bandgap materials, theory and properties of media with epsilon and mu less than zero, energy and momentum in negative refractive index materials, plasmonics of media with negative material parameters, design of super-lenses lenses capable of subwavelength imaging , and electromagnetic invisibility.