Kerr external fields

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... 

Coherent External Field Modulated External Field Pulsed External Field Final Remarks Chaos in Kerr Oscillators A. Introduction Basic Equations... 

The application of an external field onto many materials will induce optical anisotropy. If the applied field oscillates, a time-dependent modulation of the polarization of the light transmitted by the device will result. Modulators of this sort include photoelastic modulators (PEM) [30,31], Faraday cells [32], Kerr cells [32], and Pockel cells. 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Finally, we mention the results of article three in the series, which considers an alternating external field F= F swf. The theory, for example, of the Kerr effect in an alternating electric field is confined to the case where the field is weak and has been reviewed by Kielich. Two processes have been identified according to the value of u. 

Fluctuations of the Molecular Fields. The second right-hand term of Kerr s constant (191), in the case of dipolar molecules, leads directly to the result (178). We shall now show that this part of the Kerr constant is non-zero even in liquids composed of non-dipolar molecules. This is due to the circumstance that in dense media, even if no external field is applied, intense molecular fields fluctuating in time and space have to be considered locally. The molecular fields Fm induce electric dipoles in the molecules in such regions, giving rise in the medium to the non-zero total dipole moment A/q occurring in the second part of the constant (191). In fact, we have in a linear approximation ... 

One sees that on taking the first term of the expansion, an optical birefringence (236) dependent on the square of the external field is obtained in accordance with Kerr s law. 

Birefringence of Dipolar Anisotropically Polarizable Microsystems. In the general case of microsystems which are dipolar and at the same time anisotropically polarizable in an external field E, the reorientation function for the Kerr effect is given by equation (233). Graphs of this reorientation function are shown in Figure 13 against the parameter Xi at parametrical values of X = X ln for = 1,4,9,16,25, 36,. 

The birefringence in external electric and magnetic fields (the Kerr and Cotton-Mouton effects) can be explained by the anisotropy of the properties of the medium that is due to either the orientation of anisotropic molecules in the external field (the Langevin-Bom mechanism) or the deformation of the electric or magnetic susceptibilities by this field, i.e., to hyperpolarizabilities (Voight mechanism). The former mechanism is effective for molecules that are anisotropic in the absence of the field and... 

Electro-optic effects refer to the changes in the refractive index of a material induced by the application of an external electric field, which modulates their optical properties [61, 62], Application of an applied external field induces in an optically isotropic material, like liquids, isotropic thin films, an optical birefringence. The size of this effect is represented by a coefficient B, called Kerr constant. The electric field induced refractive index difference is given by... 

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... 

Polymer solutions are isotropic at equilibrium. If there is a velocity gradient, the statistical distribution of the polymer is deformed from the isotropic state, and the optical property of the solution becomes anisotropic. This phenomena is called flow birefringence (or the Maxwell effect). Other external fields such as electric or magnetic fields also cause birefringence, which is called electric bire ingence (or Kerr effect) and magnetic birefiingence (Cotton-Mouton effect), respectively. 

The isotropic phase of nematogens differs from conventional isotropic liquids in two aspects. First, the pretransitional phenomena in the vicinity of the clearing point dramatically change the bulk properties (in particular, the Kerr constant) of the isotropic phase due to the short-range nematiclike order. Second, quasi-nematic surface layers form at the interface with a solid substrate. Due to their dielectric (and optical) anisotropy they can contribute to the electrooptical properties of cells filled with the isotropic phase. For example, they can be reoriented by an external field (an analogy with the Frederiks transition). We will discuss briefly both phenomena. 

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... 

Rizzo reviews in a unitary framework computational methods for the study of linear birefringence in condensed phase. In particular, he focuses on the PCM formulation of the Kerr birefringence, due to an external electric field yields, on the Cotton-Mouton effect, due to a magnetic field, and on the Buckingham effect due to an electric-field-gradient. A parallel analysis is presented for natural optical activity by Pecul Ruud. They present a brief summary of the theory of optical activity and a review of theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. 

Similarly as the trace, the anisotropy of the polarizability tensor of diatomic colli-sional systems can also be related to some macroscopic properties, namely to the refractive properties of atomic gases. The so-called Kerr constant, the anisotropy of the refractive index in the parallel and perpendicular directions to the external static electric field is given by,... 

The quadratic effect of an externally applied field on the refractive index n is described by the third-order susceptibility (- ) w,0,0) (Kerr susceptibility). The two independent components Yilzz and x ixx can be interpreted in terms of molar polarizabilities. The results for 2 symmetric molecules with only one significant component of the second-order polarizability are expressed in (113) and (114),... 

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