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<!--:''This page is about the Kerr nonlinear optical effect. For the magneto-optic phenomenon of the same name, see [[Kerr magneto-optic effect]].''-->
'''Керов ефекат''' или '''квадратни електро-оптички ефекат''' ('''КЕО ефекат''') је проемена [[индекс преламања|индекса преламања]] материјала под утицајем [[електричног поља]]. Ефекат се разликује од [[Покелов ефекат|Покеловог]] по томе што је промена индекса преламања пропорционална ''квадтату'' поља (E<sup>2</sup>) уместо његовој величини (Е). Сви материјали показују Керов ефекат само што је он код већине толико мали да се може опазити тек врло прецизним мерењима. Ефекат је открио шкотски физичар Џон Кер (John Kerr) 1875.
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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'''.-->
==Керов електро-оптички ефекат==
:<math>\Delta n = \lambda K E^2\ ,</math>
где је ''λ'' таласна дужина светлости, ''К'', ''Керова константа'' и ''Е'' јачина елетричног поља. Због ове разлике у индексима преламања материјал почиње да делује као [[таласна плочица]] када се осветли у правцу нормалном на правац поља. Када се материјал стави изнеђу два улрштена линеарна поларизатора, када је поље искључено светлост не пролази кроз поларизаторе. Међутим, када се поље укључи, због изазваног двојног преламања, светлост пролази кроз поларизаторе. Интензитет пропуштене светлости расте са Керовом константом, тј, са вешом Керовом константом потпуна трансмисија светлости може да се псотигне са мањим елетричним пољима.
<!--Some [[Polar molecule|polar]] liquids, such as [[nitrotoluene]] (C<sub>5</sub>H<sub>7</sub>NO<sub>2</sub>) and [[nitrobenzene]] (C<sub>6</sub>H<sub>5</sub>NO<sub>2</sub>) exhibit very large Kerr constants. A glass cell filled with one of these liquids is called a ''Kerr cell''. These are frequently used to [[modulation|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 [[gigahertz|GHz]]. Because the Kerr effect is relatively weak, a typical Kerr cell may require voltages as high as 30 [[kilovolt|kV]] to achieve complete transparency. This is in contrast to [[Pockels cell]]s, which can operate at much lower voltages. Another disadvantage of Kerr cells is that the best available material, nitrobenzene, is both poisonous and explosive. Some transparent crystals have also been used for Kerr modulation, although they have smaller Kerr constants.-->
==Оптички Керов ефекат==
<!--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 optics|nonlinear optical]] effects of [[self focusing (optics)|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 [[laser]]s.
-->
==Теорија==
===Једносмерни Керов ефекат===
:<math> \mathbf{E} = \mathbf{E}_0 + \mathbf{E}_\omega \cos(\omega t), </math>
<!--where '''E'''<sub>ω</sub> 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 <math>\chi^{(3)}|\mathbf{E}_0|^2 \mathbf{E}_\omega</math>:-->
:<math>\mathbf{P} \simeq \varepsilon_0 \left( \chi^{(1)} + 3 \chi^{(3)} |\mathbf{E}_0|^2 \right) \mathbf{E}_\omega \cos(\omega
t),</math>
<!--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 changed of susceptibility produces a change in refractive index in the direction of the electric field:-->
:<math> \Delta n = \lambda_0 K |\mathbf{E}_0|^2, </math>
<!--where λ<sub>0</sub> 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.-->
<!--The values of ''K'' depend on the medium and are about 9.4×10<sup>-14</sup> [[metre|m]] [[volt|V]]<sup>-2</sup> for [[water]], and 4.4×10<sup>-12</sup> m V<sup>-2</sup> for [[nitrobenzene]].
For [[crystal]]s, the susceptibility of the medium will in general be a [[tensor]], and the Kerr effect produces a modification of this tensor.-->
===Наизменични Керов ефекат===
<!--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:
:<math> \mathbf{E} = \mathbf{E}_\omega \cos(\omega t), </math>
where '''E'''<sub>ω</sub> 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<sup>(3)</sup>|'''E'''<sub>ω</sub>|<sup>3</sup>:
:<math> \mathbf{P} \simeq \varepsilon_0 \left( \chi^{(1)} + \frac{3}{4} \chi^{(3)} |\mathbf{E}_\omega|^2 \right) \mathbf{E}_\omega \cos(\omega t).</math>
As before, this looks like a linear susceptibility with an additional non-linear term:
:<math> \chi = \chi_{\mathrm{LIN}} + \chi_{\mathrm{NL}} = \chi^{(1)} + \frac{3\chi^{(3)}}{4} |\mathbf{E}_\omega|^2,</math>
and since:
:<math> 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)</math>
where ''n''<sub>0</sub>=(1+χ<sub>LIN</sub>)<sup>1/2</sup> is the linear refractive index. Using a [[Taylor expansion]] since χ<sub>NL</sub> << ''n''<sub>0</sub><sup>2</sup>, this give an ''intensity dependent refractive index'' (IDRI) of:
:<math> n = n_0 + \frac{3\chi^{(3)}}{8 n_0} |\mathbf{E}_{\omega}|^2 = n_0 + n_2 I</math>
where ''n''<sub>2</sub> 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 ''n''<sub>2</sub> are relatively small for most materials, on the order of 10<sup>-20</sup> m<sup>2</sup> W<sup>-1</sup> for typical glasses. Therefore beam intensities ([[irradiance]]s) on the order of 1 GW cm<sup>-2</sup> (such as those produced by lasers) are necessary to produce significant variations in refractive index via the AC Kerr effect.
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 (optics)|dispersion]], can produce optical [[soliton]]s.
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.
{{FS1037C}}-->
==Види још==
* [[Jeffree cell]] -- An early acousto-optic modulator
==Спољашње везе==
* [http://www.tvhistory.tv/1935%20TV%20Today%20Part%202.htm Kerr cells in early television ] (Scroll down the page for several early articles on Kerr cells.)
[[Категорија:Физичка хемија]]
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