Polarizability anisotropic materials

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

For an anisotropic material, the polarizability will be a tensor that will depend on the relative orientation of the principal axes of the material and the incident electric field. If the polarizability is biaxial and of the form,... 

Because the electric vector of the light has components normal to the beam, in anisotropic materials they feel different electronic polarizabilities, i.e., different refractive indices. For this reason, the speed of the light of different polarization directions will be different Vo = c/n describes the speed of the "ordinary" wave, and Ve = c/n relates to the "extraordinary" beam, which exists only in anisotropic materials. Due to the differences of the speeds, there will be a phase difference between the ordinary and extraordinary vvaves. Since the wavevector k of the light relates to the wavelength, X as k =k = n = n-, the difference between the phases (the so called retardation) of the ordinary and extraordinary waved can be expressed as ... 

We usually think of van der Waals forces in terms of attraction or repulsion based on differences in polarizability. What if materials are anisotropic, for example, bire-fringent with different polarizabilities in different directions Imagine that substance A has a principal optical axis pointing parallel to the interface between A and m, that is, there is a dielectric response coefficient e parallel to the interface but a permittivity in directions perpendicular to the principal axis (see Fig. LI.20). 

In most of the synthesized materials of different compounds in ionic liquids, we obtained one-dimensional structures. The ionic-conductive nature and polarizability of the ionic liquids helps in the movement and polarization of ions under the rapidly changing electric field of the microwaves. This results in high heating and in the transient, anisotropic microdomains for the reaction system, which assists the anisotropic growth of the nanostructures. 

A condition for second-order nonlinear organic materials to double the frequency of an incident laser light is a noncentrosymmetric configuration on the molecular and macroscopic level. The term macroscopic implies that the compounds must have a noncentrosymmetric crystal structure, because only materials without a center of symmetry have anisotropic polarizability. 

Equation (27) presents a simple anisotropic attraction potential that favors nematic ordering. This potential has been used in the original Maier-Saupe theory [11, 12]. We note that the interaction energy (Eq. 27) is proportional to the anisotropy of the molecular polarizability Aa. Thus, this anisotropic interaction is expected to be very weak for molecules with low dielectric anisotropy. Such molecules, therefore, are not supposed to form the nematic phase. This conclusion, however, is in conflict with experimental results. Indeed, there exist a number of materials (for example, cyclo-... 

The combination of molecular order and fluidity in a single phase results in several remarkable properties unique to liquid crystals. By now, it is quite evident that the constituent molecules of liquid crystal mesophases are structurally very anisotropic. Because of this shape anisotropy, all the molecular response functions, such as the electronic polarizability, are anisotropic. The long range order in the liquid-crystal phases prevents this molecular anisotropy from being completely averaged to zero, so that all the macroscopic response functions of the bulk material, such as the dielectric constant, are anisotropic as well. We have, therefore, a flexible fluid medium whose response to external perturbations is anisotropic. 

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