Electro-optical Kerr effect

The T(3) rtjk gives the linear electro-optic (Pockels) effect, while the 7(4) ptjkl is responsible for the quadratic electro-optic (Kerr) effect qtjkl is the photoelastic tensor. 

A combination of molecular mechanics calculations and electric birefringence (electro-optical Kerr effect) measurements of group IVB aryl compounds has been used to study conformational effects in these molecules12731. 

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). 

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)... 

The first contribution to the polarization induces a modification of the wave propagation in the material, for both its amplitude and phase, but without any frequency change. This phenomenon is known as the optical Kerr effect, by analogy with the magneto-optic and electro-optic Kerr effects where the medium refractive index varies proportionally with the square of the applied magnetic or electric static field. The second contribution corresponds to the third harmonics generation (THG). 

In this paper we review the linear and nonlinear optical properties studies performed on solutions or thin film of rotaxanes and catenanes. Tlte linear optical properties were studied by U V-Vis spectrometry and m-line techniques. Tlte nonlinear optical properties were studied by second (SHG) and third (THG) harmonic generation in thin films and by electro-optic Kerr effect measurements in solutions. 

The nonlinear optical properties of rotaxanes and catenanes were studied mainly by three techniques the optical second and third harmonic generation and the electro-optic Kerr effect. As already mentioned, the harmonic generation techniques give the fast, electronic in origin, molecular and bulk hyperpolarizabili-ties, whereas the electro-optic methods are sensitive to all effects which induce optical birefringence, such as e.g. the rotation of molecules. Therefore the last technique is very useful to study the rotational mobility of molecules and/or their parts. 

Figure 28. Schematic representation of the experimentai set up for electro-optic Kerr effect measurements. The normal to the sample is tilted by 45 degrees with respect to the beam propagation direction and the incident polarization makes an angle of 45° with incidence plane...

Large electro-optic Kerr effect was also observed in BAG solutions in dioxan (cf. Fig. 32). At the concentration of 10 mol dm and at the field strength of... 

We have shown that the electro—optic Kerr effect in solution is a useful tool to study the relative motion of these molecules. We observed a strong birefringence at frequencies that correspond to the rate at which the molecular cycle pirouettes ... 

Niziol et al. review the linear and NLO properties of some catenanes and rotaxanes studied in solutions or tliln films. Techniques like UV-Vis spectrometry, second and tlilrd harmonic generation in thin films and electro-optic Kerr effects in solution have been employed. They review the synthesis and material processing of tlrese derivatives. Niziol et al. describe how the rotation rate of the macrocycle in catenane solutions is more than an order of magnitude larger than in rotaxanes. They comment on the factors on which the rate of rotation depends. This new class of molecules, with mobile subparts, is very likely to have useful applications including tire construction of synthetic molecular machines and all-optical switching elements. 

Y(- , 0,0) dc-Kerr effect dc-K Electro-optical Kerr Effect (EOKE)... 

Isotropic media can be made birefringent by application of an electric field. This phenomenon is an electro-optic effect.5 There are in fact several electro-optic effects the Pockels effect, the electro-optic Kerr effect, the Stark effect in atoms and molecules, the Franz-Keldysh effect in semiconductors, etc. (see Table 4.6). We will limit our discussion in this section to the Pockels effect and the electro-optic Kerr effect. 

Furthermore, they examined the performance of different density functionals, including a local-density approximation and a generalized-gradient approximation as well as the functional of van Leeuwen and Baerends that has been constructed to have the correct asymptotic behaviour. Moreover, they considered different frequency-dependent processes, including third-harmonic generation [THG, corresponding to y( 3electric-field-induced second harmonic generation (EFISH, y( 2 optical rectification [OR, /S(0 [Pg.161]

FuIIerenes. - Perpete, Champagne and Kirtman have computed the vibrational contributions to the main non-linear optical response functions for the fiillerene Ceo- They use normal co-ordinates obtained in a DFT approximation combined with Hartree-Fock ab initio calculations of the electrical properties. Vibrational contributions to the electro-optic Kerr effect and degenerate four wave mixing are found to be comparable with the electronic effects. 

Y. Haseba, H. Kikuchi, T. Nagamura, and T. Kajiyama, Large electro-optic Kerr effect in nano-stractured chiral liquid-crystal composites over a wide temperature range, Adv. Mater. 17, 2311 (2005). 

Figure 11 shows the change in the refractive indices AWj and Ang as a function of an applied dc electric field for a PLZT (9.5/65/35) ceramic. The dc field was cycled from 0 to +1.1 MV.m+ down to -1.1 MV.m i, and back up to 0. Awj remained near zero while Afig decreased quadratically with the dc field, due to the electro-optic Kerr effect, until a minimum of -... 

It may be mentioned here that two stage (or double) percolation has been reported by Ray and Moulik [92] and Maiti et al. [93] for (water/AOT/decanol) and water/DTAB (octadecyltrimethylammonium bromide)-butanol/heptane microemulsion systems, respectively. The double percolation process for AOT/ decane/NaCl (0.5%) was also reported by Eicke et al. by conductivity, viscosity, and electro-optical Kerr effect [94]. The two processes demarcated three structural regimes viz, o/w, w/o, and oil or water continuous. 

Our recent independent studies of the hydrodynamical and electro-optical (Kerr effect) properties of DNA-DDCA complexes in chloroform demonstrated that the compact conformation of DNA molecules in the complex maintain in organic media [14]. 

Particle tracking can also be used to monitor particle orientation. Cheng and Mason studied rotational motion of micron-size a-eicosane microdiscs in 900 kDa polyethylene oxide(92). Hill and Soane examined the rotation of collagen molecules in aqueous 4 MDa polyethylene oxide using the electro-optic Kerr effect(93). 

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