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Encyclopedia > Kerr effect

The Kerr effect or the quadratic electro-optic effect (QEO effect) is a change in the refractive index of a material in response to an electric field. It is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric field instead of to the magnitude of the field. All materials show a Kerr effect, but certain liquids display the effect more strongly than other materials do. The Kerr effect was found in 1875 by John Kerr, a Scottish physicist. The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... The Pockels effect, or Pockels electro-optic effect, produces birefringence in an optical medium induced by a constant or varying electric field. ... This article is about proportionality, the mathematical relation. ... 1875 (MDCCCLXXV) was a common year starting on Friday (see link for calendar). ... Rev. ...

Two special cases of the Kerr effect are normally considered: the Kerr electro-optic effect, or DC Kerr effect, and the optical Kerr effect, or AC Kerr effect.

## Kerr electro-optic effect

The Kerr electro-optic effect, or DC Kerr effect, is the special case in which the electric field is a slowly varying external field applied by, for instance, a voltage on electrodes across the material. Under the influence of the applied field, the material becomes birefringent, with different indexes of refraction for light polarized parallel to or perpendicular to the applied field. The difference in index of refraction, Δn, is given by International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... A calcite crystal laid upon a paper with some letters showing the double refraction Birefringence, or double refraction, is the division of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on... In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ...

$Delta n = lambda K E^2 ,$

where λ is the wavelength of the light, K is the Kerr constant, and E is the amplitude of the electric field. This difference in index of refraction causes the material to act like a waveplate when light is incident on it in a direction perpendicular to the electric field. If the material is placed between two "crossed" (perpendicular) linear polarizers, no light will be transmitted when the electric field is turned off, while nearly all of the light will be transmitted for some optimum value of the electric field. Higher values of the Kerr constant allow complete transmission to be achieved with a smaller applied electric field. A half-wave plate. ... A polarizer is a device that converts an unpolarized or mixed-polarization beam of electromagnetic waves (e. ...

Some polar liquids, such as nitrotoluene (C7H7NO2) and nitrobenzene (C6H5NO2) exhibit very large Kerr constants. A glass cell filled with one of these liquids is called a Kerr cell. These are frequently used to modulate light, since the Kerr effect responds very quickly to changes in electric field. Light can be modulated with these devices at frequencies as high as 10 GHz. Because the Kerr effect is relatively weak, a typical Kerr cell may require voltages as high as 30 kV to achieve complete transparency. This is in contrast to Pockels cells, which can operate at much lower voltages. Another disadvantage of Kerr cells is that the best available material, nitrobenzene, is poisonous. Some transparent crystals have also been used for Kerr modulation, although they have smaller Kerr constants. A commonly-used example of a polar compound is water (H2O). ... Nitrobenzene, also known as nitrobenzol or oil of mirbane, is a poisonous organic compound with an almond odor and chemical formula C6H5NO2. ... In telecommunications, modulation is the process of varying a periodic waveform, i. ... A gigahertz is a billion hertz or a thousand megahertz, a measure of frequency. ... The volt is the SI derived unit for electric potential and voltage (derived from the ampere and watt). ... The Pockels effect, or Pockels electro-optic effect, is the production of birefringence in an optical medium induced by a slowly-varying electric field. ...

## Optical Kerr effect

The optical Kerr effect, or AC Kerr effect is the case in which the electric field is due to the light itself. This causes a variation in index of refraction which is proportional to the local irradiance of the light. This refractive index variation is responsible for the nonlinear optical effects of self-focusing and self-phase modulation, and is the basis for Kerr-lens modelocking. This effect only becomes significant with very intense beams such as those from lasers. Irradiance, radiant emittance, and radiant exitance are radiometry terms for the power of electromagnetic radiation at a surface, per unit area. ... Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ... Rather than being dispersed, a beam of charged particles travelling in a gas environment sometimes becomes narrower. ... Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction. ... Kerr-lens modelocking is a method of modelocking lasers via a nonlinear optical process known as the optical Kerr effect. ... For other uses, see Laser (disambiguation). ...

## Magneto-optic Kerr effect

Main article: Magneto-optic Kerr effect

The magneto-optic Kerr effect (MOKE) is the phenomenon that the light reflected from a magnetized material has a slightly rotated plane of polarization. It is similar to the Faraday effect where the plane of polarization of the transmitted light is rotated. Magneto-optic Kerr effect (MOKE) is one of the magneto-optic effects. ... In physics, the Faraday effect or Faraday rotation is a magneto-optical phenomenon, or an interaction between light and a magnetic field. ...

## Theory

### DC Kerr effect

For a nonlinear material, the electric polarization field P will depend on the electric field E: In electrostatics, the polarization is the vector field that results from permanent or induced electric dipole moments in a dielectric material. ...

$mathbf{P} = varepsilon_0 chi^{(1)} : mathbf{E} + varepsilon_0 chi^{(2)} : mathbf{E E} + varepsilon_0 chi^{(3)} : mathbf{E E E} + dots$

where ε0 is the vacuum permittivity and χ(n) is the n-th order component of the electric susceptibility of the medium. The ":" symbol represents the scalar product between matrices. We can write that relationship explicitly; the i-th component for the vector P can be expressed as: Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... The electric susceptibility Ï‡e of a dielectric material is a measure of how easily it polarizes in response to an electric field. ...

$P_i = varepsilon_0 sum_{j=1}^{3} chi^{(1)}_{i j} E_j + varepsilon_0 sum_{j=1}^{3} sum_{k=1}^{3} chi^{(2)}_{i j k} E_j E_k + varepsilon_0 sum_{j=1}^{3} sum_{k=1}^{3} sum_{l=1}^{3} chi^{(3)}_{i j k l} E_j E_k E_l + dots$

where i = 1,2,3. It is often assumed that P1 = Px, i.e. the component parallel to x of the polarization field; E2 = Ey and so on.

For a linear medium, only the first term of this equation is significant and the polarization varies linearly with the electric field.

For materials exhibiting a non-negligible Kerr effect, the third, χ(3) term is significant, with the even-order terms typically dropping out due to inversion symmetry of the Kerr medium. Consider the net electric field E produced by a light wave of frequency ω together with an external electric field E0:

$mathbf{E} = mathbf{E}_0 + mathbf{E}_omega cos(omega t),$

where Eω is the vector amplitude of the wave.

Combining these two equations produces a complex expression for P. For the DC Kerr effect, we can neglect all except the linear terms and those in $chi^{(3)}|mathbf{E}_0|^2 mathbf{E}_omega$:

$mathbf{P} simeq varepsilon_0 left( chi^{(1)} + 3 chi^{(3)} |mathbf{E}_0|^2 right) mathbf{E}_omega cos(omega t),$

which is similar to the linear relationship between polarization and an electric field of a wave, with an additional non-linear susceptibility term proportional to the square of the amplitude of the external field.

For non-symmetric media (e.g. liquids), this induced change of susceptibility produces a change in refractive index in the direction of the electric field:

$Delta n = lambda_0 K |mathbf{E}_0|^2,$

where λ0 is the vacuum wavelength and K is the Kerr constant for the medium. The applied field induces birefringence in the medium in the direction of the field. A Kerr cell with a transverse field can thus act as a switchable wave plate, rotating the plane of polarization of a wave travelling through it. In combination with polarizers, it can be used as a shutter or modulator. For other uses, see Wavelength (disambiguation). ... A calcite crystal laid upon a paper with some letters showing the double refraction Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals or boron... A wave plate is an optical device that alters the polarization state of a light wave travelling through it. ...

The values of K depend on the medium and are about 9.4×10-14 m V-2 for water, and 4.4×10-12 m V-2 for nitrobenzene. This article is about the unit of length. ... Josephson junction array chip developed by NIST as a standard volt. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... Nitrobenzene, also known as nitrobenzol or oil of mirbane, is a poisonous organic compound with an almond odor and chemical formula C6H5NO2. ...

For crystals, the susceptibility of the medium will in general be a tensor, and the Kerr effect produces a modification of this tensor. For other uses, see Crystal (disambiguation). ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...

### AC Kerr effect

In the optical or AC Kerr effect, an intense beam of light in a medium can itself provide the modulating electric field, without the need for an external field to be applied. In this case, the electric field is given by:

$mathbf{E} = mathbf{E}_omega cos(omega t),$

where Eω is the amplitude of the wave as before.

Combining this with the equation for the polarization, and taking only linear terms and those in χ(3)|Eω|3:

$mathbf{P} simeq varepsilon_0 left( chi^{(1)} + frac{3}{4} chi^{(3)} |mathbf{E}_omega|^2 right) mathbf{E}_omega cos(omega t).$

As before, this looks like a linear susceptibility with an additional non-linear term:

$chi = chi_{mathrm{LIN}} + chi_{mathrm{NL}} = chi^{(1)} + frac{3chi^{(3)}}{4} |mathbf{E}_omega|^2,$

and since:

$n = (1 + chi)^{1/2} = left( 1+chi_{mathrm{LIN}} + chi_{mathrm{NL}} right)^{1/2} simeq n_0 left( 1 + frac{1}{2 {n_0}^2} chi_{mathrm{NL}} right)$

where n0=(1+χLIN)1/2 is the linear refractive index. Using a Taylor expansion since χNL << n02, this give an intensity dependent refractive index (IDRI) of: As the degree of the taylor series rises, it approaches the correct function. ...

$n = n_0 + frac{3chi^{(3)}}{8 n_0} |mathbf{E}_{omega}|^2 = n_0 + n_2 I$

where n2 is the second-order nonlinear refractive index, and I is the intensity of the wave. The refractive index change is thus proportional to the intensity of the light travelling through the medium.

The values of n2 are relatively small for most materials, on the order of 10-20 m2 W-1 for typical glasses. Therefore beam intensities (irradiances) on the order of 1 GW cm-2 (such as those produced by lasers) are necessary to produce significant variations in refractive index via the AC Kerr effect. Irradiance, radiant emittance, and radiant exitance are radiometry terms for the power of electromagnetic radiation at a surface, per unit area. ...

The optical Kerr effect manifests itself temporally as self-phase modulation, a self-induced phase- and frequency-shift of a pulse of light as it travels through a medium. This process, along with dispersion, can produce optical solitons. Dispersion of a light beam in a prism. ... In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed; solitons are caused by a delicate balance between nonlinear and dispersive effects in the medium. ...

Spatially, an intense beam of light in a medium will produce a change in the medium's refractive index that mimics the transverse intensity pattern of the beam. For example, a Gaussian beam results in a Gaussian refractive index profile, similar to that of a gradient-index lens. This causes the beam to focus itself, a phenomenon known as self-focusing. In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian functions. ...

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain. Federal Standard 1037C, entitled Telecommunications: Glossary of Telecommunication Terms is a United States Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ... A work of the United States government, as defined by United States copyright law, is a work prepared by an officer or employee of the U.S. government as part of that persons official duties. ... The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...

In physics, the Faraday effect or Faraday rotation is a magneto-optical phenomenon, or an interaction between light and a magnetic field. ... The Jeffree cell was an early acousto-optic modulator, best known for its use in the Scophony system of mechanical television. ... In nonlinear optics, filament propagation is propagation of a beam of light through a medium without diffraction. ...

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 2.0 Magneto Optic Kerr Effect (MOKE) - Growth And Study Of Magnetostrictive FeSiBC Thin Films For Device Applications (9982 words) The magneto optical effects are characterised by the Kerr effect being proportional to the magnetisation. In the longitudinal and polar Kerr effects (Fig. Kerr images obtained using the longitudinal effect (sensitive to the magnetisation in the horizontal axis), and the transverse Kerr effect (sensitive to the magnetisation in the vertical axis).
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