Kerr effect theory

B. M. Ladanyi and T. Keyes. Theory of the static Kerr effect in dense fluids. Molec. Phys., 34 1643, 1977. 

The usefulness of electrical response measurements of solutions is not limited to effects linear in applied field. Transient birefringence induced by polarizing electric fields (the transient or dynamic Kerr effect) has given valuable information about biopolymers in solution the effect must by symmetry be an even function of E(t), beginning with terms in E (t). In both cases, a response theory treatment of transient behavior meets with difficulties not encountered in linear problems, but recent progress in deriving correlation function expressions for such effects is described in III. 

This outline of the response theory has for simplicity been limited to molecules with axial symmetry of y and Aa and to the field on, field off cases, but can be extended in both respects without basic difficulties. Detailed comparisons with experiment have not yet been made, but it already is clear that Kerr effect relaxation data can now provide more valuable and better defined information about orientational dynamics of biopolymers and other molecules than was previously possible. With the increasing accuracy and time resolution of digital methods, it should be possible to study not only slow overall rotations of large molecules (microseconds or longer) but small conformational effects and small molecule reorientations on nano and picosecond time scales. Moreover, one can anticipate the possibilities, for simple problems at least, of extending response theory to other quadratic and higher order effects of strong electric fields on observable responses. 

The following section contains a more detailed treatment of the theory behind the nonresonant spectroscopy of liquids. This will be followed by a description of the experimental implementation and data analysis techniques for a common OKE scheme, optical-heterodyne-detected Raman-induced Kerr-effect spectroscopy (22). We will then discuss the application of this technique to the study of the temperature-dependent dynamics of simple liquids composed of symmetric-top molecules. 

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. 

Electro-optical properties molar r raction and molecular correlation the Kerr effect its component terms and molecular theory molecular angular correlation non-linear polarizability generalized Kerr effect translational and molecular field fluctuations electric saturation. 

Molecular Theory for a Molecular Dilute State. In presenting the theory of the Kerr effect, we shall begin with the simple case of a molar volume Im free of molecular fields. This is equivalent to assuming the relation (145) for the dipole moment induced in molecule i by the electric field of the light wave Eo(r, t). Equations (142)—(145) now yield the molar refraction in the presence of an electric field E(0) in the form ... 

To Buckingham et al. is due the theory of the Kerr effect in dilute solutions, whereas Kielich developed a statistical theory of the effect for multi-component systems of an arbitrary degree of concentration and showed the Kerr constant of real solutions to be a non-additive quantity. 

This complexity of the saturation phenomenon, though a drawbadr, is at the same time an asset from the theoretical point of view. The reader vrill have noted from the theory discussed above that electric saturation makes directly apparent the participation of reorientation of the electric poles of molecides and macromolecules. In this respect, saturation is unique, owing to the part played in it, in addition to the various molecular processes specific to other effects e.g. the Kerr effect), by entirely new processes provi ng valuable information on the interactions between molecules in condensed phases and their internal structure. We believe it... 

The clasdcal fundamentals of the theory of the Kerr effect are due to Voigt in terms of dectron theory of the atom as an anharmonic oscillator and to Langevin in terms of statistical optical reorioitation of anisotropic molecules in a static dectric fidd. Buckingham proposed a theory and method of measurement of the optical birefringence induced by the gradient of a static electric field permitting the determination of electric quadrupole moments. 

The expansions (205)—(207) in coiyunction with formulae (191) and (192) define the complete molecular-statisticed theory of the Kerr effect in very dense media. They can be particularized to various cases. ... 

Only a smaU number of researchers have attempted to interpret the experiments data on the Kerr effect from the standpoint of theories based on a rotational isomer medianism of chain flexibility and tensor additivity of the polarizability of chain bonds > These attempts did not yield good agreement between theory and experimental data. This may result from both the unreliability of the data and the inadequacy of some suggestions used in the theory (additivity of optical properties of vSence bonds, character of the internal field etc.). 

For this purpose, the Kerr effect in the alternatii (sinusoidal) field can be used. The theory of this effect for solutions of kinetically rigid molecules has been formulated by Peterlin and Stuart According to this theory, the character of the dependence of the observed birefringence An on frequency v = co/2 n of the applied field clearly differs for the two cases ... 

The values of A, S, d and X obtained from experimental data on the kinetics of the Kerr effect agree qualitatively with those determined for the same polymers by translational diffusion and sedimentation (Table 3). The agreement between geometrical molecular characteristics obtained from the phenomena of rotattonal and translational friction indicates that the hydrodynamic and the oinformational models on which this theory is based are valid. This is an evidence of the kinetic r idity of the investigated chains. 

It has been shown that the main medianism responsible for EB in solutions of rigid-chain polymers is the rotation of their polar molecules as a whole whereas the anisotropy of the dielectric polarizability of the macromolecules only provides a small contribution to the Kerr effect. Hence, the general theory of the Kerr effect for rigid dipole particles with axial symmetry of the optical polarizability can be... 

D. A. Dunmur and N. E. Jessup. The influence of intermolecular interactions on the Kerr effect in gases I. Statistical theory for spherical top molecules. Molec. Phys., 57 697-711 (1979). 

Other Work on Water-Related Systems. Sonoda et al.61 have simulated a time-resolved optical Kerr effect experiment. In this model, which uses molecular dynamics to represent the behaviour of the extended medium, the principle intermolecular effects are generated by the dipole-induced-dipole (DID) mechanism, but the effect of the second order molecular response is also include through terms involving the static molecular / tensor, calculated by an MP2 method. Weber et al.6S have applied ab initio linear scaling response theory to water clusters. Skaf and Vechi69 have used MP2/6-311 ++ G(d,p) calculation of the a and y tensors of water and dimethylsulfoxide (DMSO) to carry out a molecular dynamics simulation of DMSO/Water mixtures. Frediani et al.70 have used a new development of the polarizable continuum model to study the polarizability of halides at the water/air interface. 

Piekara, A. A theory of electric polarization, electro-optical kerr effect and electric saturation in liquids and solutions, Proc. Royal Soc. London. Series A, Math. Phys. Sci. 172(950), 360-383 (1939)... 

Photonics is playing an ever-increasing role in our modern information society. Photon is gradually replacing the electron, the elementary particle in electronics. Several hooks and reviews have appeared dealing with the theory of nonlinear optics and the structural characteristics and applications of nonlinear optical molecules and materials [1—18]. Tlie earliest nonlinear optical (NLO) effect discovered was the electro-optic (EO) effect. The linear EO coefficient defines the Pockel effect, discovered in 1906, while the quadratic (nonlinear) EO coefficient s,i relates to the Kerr effect, discovered 31 years later (1875). Truly, all-optical NLO effects were not discovered until the discovery of lasers. Second harmonic generation (SHG) was first observed in a single crystal of quartz by Franken et al. [1] in 1961. They frequency doubled the output of a ruby laser (694.3 nm) into the 383... 

---