The Kerr effect

Analysis of the light scattered by a free molecule has recently led to the development of a very effective means of drawing far-reaching conclusions regarding the symmetry and arrangement of the atoms in the molecule. Again, valence inclination is the main problem treated in this way but the free motion of parts of the molecule can also be so treated. Two effects are available for obtaining experimental evidence, the Kerr effect and the depolarization of the scattered beam. 

If a gas, a solution or a pure liquid is introduced between the plates of a charged condenser, the molecules strive, as already pointed out, to orientate themselves with the axis of their maximum polarizability or, if a permanent moment exists, with the axis of this moment, parallel to the direction of the field. Should the thermal agitation be such, however, that this orientation is effected only to a very small extent, the previously isotropic medium exhibits anisotropy which can be detected as double refraction on the passage of polarized light. This electric double refraction imposed by the presence of the external field is called the Kerr effect. The phenomenon is measured by the path difference AX, between the beam polarized in the direction of the field and that polarized perpendicular to the field. It is given by the equation 

Recently W. T. Busse and R. M. Fuoss have contributed very important applications of the dipole method by the investigation of polyvinylchloride and similar substances at different temperatures, frequencies and with different amounts of plasticizers. Cincinnati meeting of the ACS, April 1940. 

The Kerr constant is evaluated theoretically by means of a formula derived by Bom and Langevin, which relates primarily to systems with vanishing intermolecular reciprocal action— ideal gases or dilute solutions the form is 

N is the Loschmidt number while 0i and 02 are complex functions of the dipole moments and polarizabilities belonging to the molecule. The Kerr constant itself can be split into two terms of which one (Ki) merely expresses the anisotropy of the optical and electrical polarizability and is named the anisotropy term K, while the other represents the effect of possibly existing electric moments. This is called the dipole term K2. The two terms differ from each other in their dependence upon temperature the Kerr effect of dipole-free molecules is proportional to 1/T, that of dipole molecules is proportional to 1/T.  

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Combined dipole moment and Kerr effect studies are regularly used by Russian workers for the conformational analysis of phosphorus heterocyc1es.135 230 In a study of the interaction of phenol with phosphoryl groups the Kerr effect was used to evaluate not only the extent of hydrogen bonding but also the influence of changes in polarity and polarisation upon stability constants.231 In a similar study the orientation of the aryl groups of 1,3,5-triazaphosphorines (82) were shown to be less coplanar than biphenyl in the gas phase. 2 3 2... 

Experimental and theoretical results are presented for four nonlinear electrooptic and dielectric effects, as they pertain to flexible polymers. They are the Kerr effect, electric field induced light scattering, dielectric saturation and electric field induced second harmonic generation. We show the relationship between the dipole moment, polarizability, hyperpolarizability, the conformation of the polymer and these electrooptic and dielectric effects. We find that these effects are very sensitive to the details of polymer structure such as the rotational isomeric states, tacticity, and in the case of a copolymer, the comonomer composition. 

The Kerr effect is the birefringence induced in a medium by an external electric field (12). From such an experiment we deduce the molar Kerr constant mK, thus... 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

Note 3 The divergence temperature for nematogens can be measured by using the Kerr effect or Cotton-Mouton effect or by light-scattering experiments. 

Second-harmonic generation of light is a nonlinear phenomenon in which chaotic behavior was discovered in 1983 [83] (for details, see Secction ). In the Kerr effect with an external time-dependent pump, a chaotic output may also occur, which was proved for the first time in 1990 by Milbum [84] (see also Section III). 

Today generator matrices F are known for many properties,10 among them the population of different conformers, the relative stability of macromolecular diastereoisomers, the mean-square end-to-end distance, the radius of gyration, the molecular dipole moment, the molecular optical anisotropy (and, with it, the stress-optical coefficient, the Kerr effect, depolarized light scattering, and the... 

In the case of xanthene (8), the moment (1.14 D) is in agreement with the value of 1.15 D for diphenyl ether. On the basis of the Kerr effect, it was postulated that in solution the preferred conformation of xanthene is a folded arrangement in which the dihedral angle between the two aromatic planes is 160 6° <69JCS(B)980). However, the zero moment observed for 2,7-dibromoxanthene is considered to be supportive evidence for a planar xanthene molecule, arising from the equal but opposite directional properties of the resultant moment (1.5 D) of the two C—Br bonds and the moment of xanthene (72MI22205). It should be noted that the latter work is based on a moment of 1.43 D for xanthene, which is substantially higher than other reported values. 

Polarized light is obtained when a beam of natural (unpolarized) light passes through some types of anisotropic matter. In optical instruments this is usually a birefringent crystal which splits the incident unpolarized beam into two beams of perpendicular linear polarization, known as the ordinary and extraordinary beams. Anisotropy can also be created by the effect of an electric field, this being known as the Kerr effect. 

Historically, the earliest nonlinear optical (NLO) effect discovered was the electro-optic effect. The linear electro-optic (EO) coefficient rij defines the Pockels effect, discovered in 1906, while the quadratic EO coefficient sijki relates to the Kerr effect, discovered even earlier (1875). True, all-optical NLO effects were not discovered until the advent of the laser. 

The linear susceptibility yy1 1 is related to optical refraction and absorption. The most common effects due to second-order susceptibility x(2) are frequency doubling x (-2co co, co) and the EO (Pockels) effect x(2)(- 0, co). The third-order susceptibility y 3) is responsible for such phenomena as frequency tripling and the Kerr effect. 

The Kerr effect is the result of applying an electric field to produce birefringence. This phenomena is commonly observed for both colloidal and polymeric liquids and is used in the characterization of the structure of these materials. Alternatively, by using an AC electric field, a modulation of the polarization of light can be affected. Such devices have rarely been used as modulators but do have the potential of allowing higher frequencies than the more common photoelastic devices. 

This approach is based on the introduction of molecular effective polarizabilities, i.e. molecular properties which have been modified by the combination of the two different environment effects represented in terms of cavity and reaction fields. In terms of these properties the outcome of quantum mechanical calculations can be directly compared with the outcome of the experimental measurements of the various NLO processes. The explicit expressions reported here refer to the first-order refractometric measurements and to the third-order EFISH processes, but the PCM methodology maps all the other NLO processes such as the electro-optical Kerr effect (OKE), intensity-dependent refractive index (IDRI), and others. More recently, the approach has been extended to the case of linear birefringences such as the Cotton-Mouton [21] and the Kerr effects [22] (see also the contribution to this book specifically devoted to birefringences). 

In 1875 John Kerr carried out experiments on glass and detected electric-field-induced optical anisotropy. A quadratic dependence of n on E0 is now known as the Kerr effect. In 1883 both Wilhelm Rontgen and August Kundt independently reported a linear electro-optic effect in quartz which was analysed by Pockels in 1893. The linear electro-optical effect is termed the Pockels effect. 

Because the scattering is proportional to ( p— m)2/ m2 it is expected to fall off rapidly as the refractive indices of the two phases become closer or as the birefringence of a single phase becomes less. However, if birefringence is introduced into an isotropic ceramic by the Kerr effect this may cause scattering in an otherwise transparent material. 

An issue that has been explored is how the relative distribution of charge and mass affect the viscosity of an ionic liquid. Kobrak and Sandalow [183] pointed out that ionic dynamics are sensitive to the distance between the centers of charge and mass. Where these centers are separated, ionic rotation is coupled to Coulomb interactions with neighboring ions where the centers of charge and mass are the same, rotational motion is, in the lowest order description, decoupled from an applied electric field. This is significant, because the Kerr effect experiments and simulation studies noted in Section III. A imply a separation of time scales for ionic libration (fast) and translation (slow) in ILs. Ions in which charge and mass centers are displaced can respond rapidly to an applied electric field via libration. Time-dependent electric fields are generated by the motion of ions in the liquid... 

Figure 1. Intensity profile of optical Kerr effect of NB at 25°C vs. time. The zero time is arbitrary and the peak transmission of the Kerr effect is about 10%. The rise time is 5.3 ps and the decay time is 15.2 ps. This decay time corresponds to a molecular orientation time of 30.4 ps (6).

Fig. 14.2. Principle of filamentation. The beam first self-focuses and collapses due to the Kerr effect. Ionization at the non-linear focus then defocuses the beam. A dynamical balance establishes between both processes over distances much over the Rayleigh length...

Although the Kerr effect involves the intensity, the occurrence of self-focusing is determined by the beam power rather than the beam intensity. However, once the self-focusing occurs, the beam diameter, and hence its intensity, determines the non-linear focal length, i.e. the point where the beam will collapse. The location Z of the non-linear focus for a power P is given by the empirical Marburger formula [38] ... 

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