Extended Kerr effect

In the voltage-off state, the BPLC is optically isotropic. Its refractive index can be described through Maxwell relation (e = n ) as 

To validate this approximation, let us assume that the BPLC composite has rie= 1.70 and Wo = 1.50. The difference between Equation (14.14) and Equation (14.15) is only -0.2%. When an electric field is applied, the refractive index is changed from n,- to rio E)  

The optic axis of the induced refractive-index ellipsoid is along the electric field direction. From Equation (14.15) and (14.16), we can rewrite the induced birefringence as [37] 

It is interesting to note that if we expand Equation (14.19) into a power series, we can obtain the E term (Kerr effect) under the weak field approximation, and the Kerr constant can be written as 

---

Figure 14.6 Measured refractive index change (open drcles) and fittings with truncation model (Equation (14.13) dotted lines). Equation (14.18) (gray line), the model including second-, fourth-, and sixth-order terms (dashed lines), and the extended Kerr effect Equation (14.19) (black line). X = 633 nm. Reproduced with permission from the American Physical Society.

J. Yan, H. C. Cheng, S. Gauza, et al.. Extended Kerr effect of polymer-stabilized blue-phase liquid crystals, Appl Phys. Lett. 96, 071105 (2010). 

As was proven later by Bishop [19], the coefficient A in the expansion (73) is the same for all optical processes. If the expansion (73) is extended to fourth-order [4,19] by adding the term the coefficient B is the same for the dc-Kerr effect and for electric field induced second-harmonic generation, but other fourth powers of the frequencies than are in general needed to represent the frequency-dependence of 7 with process-independent dispersion coefficients [19]. Bishop and De Kee [20] proposed recently for the all-diagonal components yaaaa the expansion... 

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). 

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. 

Bending moduli can in principle be obtained for two types of systems (i) extended, flat surfaces or interfaces, the subject matter of this section, and (ii) surfaces that are already strongly curved, and for which y is zero or extremely low, such as in vesicles or micro-emulsions. For instance such moduli can be inferred from shape fluctuations, from the Kerr effect (sec. 1.7.14] or from polydispersity using some scattering technique. We repeat that this type of measurement is often ambiguous because the bending contributions to the Helmholtz energy can only be estimated when all other contributions are accurately known. 

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. 

The approach developed may also be extended to treat all the other averages (P (cos i)))(t) characterizing orientational relaxation in fluids [43]. In particular, the evaluation of the average of the second-order Legendre polynomial (/Tfcos 0))(t) (e.g., this quantity describes the dynamic Kerr effect [8]) is given in Appendix III. 

The collection presented here is far from being complete. Extended bibliographies including more than 10.000 references on relativistic theory in chemistry and physics have been published by Pekka Pyykko [32-34]. We took much advantage of his careful and patient work when preparing this chapter. Specialized on solid state effects are recent reviews on magnetooptical Kerr spectra [35] and on density functional theory applied to 4f and 5f elements and metallic compounds [24]. 

---