Kerr effect

The electro-optical Kerr effect , also Kerr effect (after John Kerr , who discovered it in 1875) or quadratic electro-optical effect , is a non-linear special case of the general electro-optical effect . This describes the change in the optical properties of a material by applying an external electric field ; the linear special case of the electro-optical effect is the Pockels effect .

The electro-optical Kerr effect is z. B. applied in the Kerr cell and in the Kerr lens .

Explanation

The application of an electric field of the field strength to a medium changes u. a. its optical properties, as it causes a nonlinear realignment or reorientation of the charge carriers in the material. This process may attract a. a change in the refractive index of the material, which can be mathematically developed by a Taylor series : ${\ displaystyle E}$ ${\ displaystyle n (E)}$

{\ displaystyle n (E) = n_ {0} + S_ {1} \ cdot E + S_ {2} \ cdot E ^ {2} + \ dots}

The higher orders of the nonlinear refractive index can be determined from the frequency- dependent absorption of the medium with the help of the Kramers-Kronig relation . The term causes the electrical Kerr effect , whereas the optical Kerr effect describes the case in which all parameters are negligible compared to the parameter : The material shows a change in the refractive index from the ordinary (o) and extraordinary (e) axis proportional to the Square of the applied electric field strength: ${\ displaystyle S_ {2}}$ ${\ displaystyle S_ {1}, S_ {3}, \ dots}$ ${\ displaystyle S_ {2}}$

{\ displaystyle | n _ {\ rm {o}} - n _ {\ rm {e}} | \ propto E ^ {2}.}

The result is that the material can produce birefringence .

The "strength" of the Kerr effect depends on the material properties, in some transparent media, e.g. B. some crystals and liquids , it is particularly strong and therefore easy to observe, also from the direction of propagation and polarization of the light in the material and from the direction and strength of the electric field in relation to the crystal axes .

In most cases, the change in the refractive index caused by the Kerr effect is only very small: in crystals of the order of 10 ⁻⁴ and in liquids of 10 ⁻⁹ . However, if light travels a longer distance (i.e. a few thousand wavelengths ) in the material , the effect accumulates and a phase shift of 0 to can be achieved by applying the electric field . ${\ displaystyle 2 \ pi}$

Different approach

The Kerr effect describes how the polarization state of light can be influenced by external electric fields. The starting point is an optically isotropic medium (e.g. liquids) in which there are anisotropically polarizable, i.e. elongated molecules. The application of an external electric field induces a dipole moment , which leads to alignment of most of these elongated molecules. Although not all molecules are aligned due to the thermal activity of the liquids (e.g. water), the number of aligned molecules is sufficient to cause birefringence . ${\ displaystyle E_ {K}}$

The light that is polarized parallel to it receives a different or extraordinary refractive index than the ordinary refractive index . ${\ displaystyle E_ {K}}$ ${\ displaystyle n_ {e}}$ ${\ displaystyle n_ {o}}$

The difference between the two is:

{\ displaystyle \ Delta n = n_ {e} -n_ {o} = \ lambda \ cdot K \ cdot E_ {K} ^ {2}}

With

the wavelength ${\ displaystyle \ lambda}$
a constant K .

literature

PP Ho, RR Alfano: Optical Kerr effect in liquids . In: Physical Review A . tape 20 , no. 5 , October 1979, p. 2170 , doi : 10.1103 / PhysRevA.20.2170 .

Otto Ernst Mittelstaedt: The determination of the speed of light using the electro-optical Kerr effect, Bibliographisches Institut, Leipzig 1928, DNB 570598672 (Philosophical dissertation University of Leipzig 1928, 34 pages).

Individual evidence

^ John Kerr: A new relation between electricity and light: Dielectrified media birefringent . In: Philosophical Magazine . tape 50 , no. 332 , November 1875, p. 337-348 ( tandfonline.com ).

[1] John Kerr: A new relation between electricity and light: Dielectrified media birefringent . In: Philosophical Magazine . tape 50 , no. 332 , November 1875, p. 337-348 ( tandfonline.com ).