Isotropic dielectric coefficient

In conclusion, the correct analytical expressions have been derived for transmission and reflection coefficients of a three-layer periodic structure surrounded by two different isotropic dielectric media. On the basis of the given formulas it was shown that for three-layer SPS it is possible to realize the enhancement of resonant interaction of light with the structure. By this way one can achieve an increased light energy localization inside the structure and decreased group velocity of light inside SPS. It is necessary to point out that the enhancement of these phenomena is put into practice by using quasi-periodic structures. The possibility to enhance the resonant phenomena by the use of finite periodic structure, optical properties of which are predictable, easily calculated and practically realizable, opens wide perspectives for their application. 

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

The isotropic coefficient and the anisotropic coefficients b(m> and c(m) can have both bulk and surface contributions and depend on crystal symmetry. The linear and nonlinear dielectric constants of the material, as well as the appropriate Fresnel factors at co and 2co, are incorporated into the constants a, b m) and c(m). Table 3.1 shows the susceptibilities contained in each of these constants. The models of Tom... 

Consider an IR beam incident on the surface at an angle (p with respect to the surface normal (Fig. 4). The incident radiation can be resolved into components parallel (S-polarised) and normal (P-polarised) to the incident plane. The S-polarised radiation only has a component (S) parallel to the surface (in the y direction). However the p-polarised radiation has components parallel or tangential (Pt) to the surface, and perpendicular (P ) to the surface. Each layer (vacuum (e =1), adsorbate (e) and substrate (es)) is characterised by an isotropic complex dielectric constant (e) which is defined as 8 = (n + ik), where n in the refractive index, and k is the absorption coefficient. The change in reflectivity (AR) resulting from the adsorbate layer of thickness d for S- and P-polarised radiation is usually expressed as a ratio to the reflectivity (AR/R) -... 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

Tables 4.4-3-4.4-21 are arranged according to piezoelectric classes in order of decreasing symmetry (see Table 4.4-2), and alphabetically within each class. They contain a number of columns placed on two pages, even and odd. The following properties are presented for each dielectric material density q, Mohs hardness, thermal conductivity k, static dielectric constant Sij, dissipation factor tanS at various temperatures and frequencies, elastic stiffness Cmn, elastic compliance s n (for isotropic and cubic materials only), piezoelectric strain tensor di , elastooptic tensor electrooptic coefficients r k (the lat-...

The literature on the molecular theory of liquid crystals is enormous and in this chapter we have been able to cover only a small part of it. We have mainly been interested in the models for the nematic-isotropic, nematic-smectic A and smectic A-smectic C phase transitions. The existing theory includes also extensive calculations of the various parameters of the liquid crystal phases Frank elastic constants, dielectric susceptibility, viscosity, flexoelectric coefficients and so... 

A well-known example of this is that cubic crystals are optically isotropic, which means that the dielectric permittivity has spherical symmetry in a cubic crystal. Another example is that the thermal expansion coefficient of a cubic crystal is independent of direction. In fact, if it were not, the crystal would lose its cubic symmetry if it were heated. Thus, as far as thermal expansion is concerned, a cubic crystal looks isotropic just as it does optically. Since, according to Neumann s principle, the physical properties of a crystal may be of higher symmetry than the crystal, we will generally find that they range from the symmetry of the crystal to the symmetry of an isotropic body. A more general example of higher symmetry in properties is that such physical properties characterized by polar second rank tensors must be centrosymmetric, whether the crystal has a center of symmetry or not, cf. Fig. 27. For, if a second rank tensor T connects the two vectors p and q according to... 

It is often said that group 432 is too symmetric to allow piezoelectricity, in spite of the fact that it lacks a center of inversion. It is instructive to see how this comes about. In 1934 Neumann s principle was complemented by a powerful theorem proven by Hermann (1898-1961), an outstanding theoretical physicist with a passionate interest for symmetry, whose name is today mostly connected with the Hermann-Mau-guin crystallographic notation, internationally adopted since 1930. In the special issue on liquid crystals by ZeitschriftfUr Kristal-lographie in 1931 he also derived the 18 symmetrically different possible states for liquid crystals, which could exist between three-dimensional crystals and isotropic liquids [100]. His theorem from 1934 states [101] that if there is a rotation axis C (of order n), then every tensor of rank rcubic crystals, this means that second rank tensors like the thermal expansion coefficient a, the electrical conductivity Gjj, or the dielectric constant e,y, will be isotropic perpendicular to all four space diagonals that have threefold symme-... 

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