Slab, dielectric medium

Consider an infinite array of elements oriented in the direction located in slab m of a stratified dielectric medium as shown in Fig. 3.9. As throughout [61], the elements are assumed to be excited by an external plane wave. The plane wave spectrum generated by this array can be decomposed into five wave modes as described in references 66-71. Four of these modes involve the reflection coefficient from the dielectric interfaces bounding the m, slab, while the fifth mode does not and is referred to as the direct mode. It is this mode that requires special treatment and is the reason it is revisited in detail here. The direct mode field at some point / on a test element also located entirely in slab m and oriented in the p direction may be written [66, 68]... 

Several forms of e(z) admit exact solutions for f(z) and the corresponding surface modes for van der Waals interaction. To examine these solutions, consider the interaction of two semi-infinite regions L and R of spatially unvarying dielectric response l and sr, coated with slabs of thickness DL and Dr within which there is spatially variable dielectric response ea(z) and et,(z), separated by a medium m of constant sm and variable thickness Z (see Fig. L3.13). 

P.2.b.l. High dielectric-permittivity layer P.2.b.2. Small differences in s s and /Vs, with retardation P.2.b.3. Small differences in s s and /Vs, without retardation P.2.c. Finite planar slab with semi-infinite medium 118... 

Here, s, Sgm, and s are the dielectric functions of the particles, the surrounding, and the effective medium, respectively, and gk (k = 1, 2, 3) is the geometric (shape) factor, which determines the self-polarizing effect of the ellipsoid and has a value between zero (needle) and unity (slab) so that gi -h g2 + gs = 1 ... 

Let us consider a sample of an optically anisotropic medium. The sample is in the shape of an infinite slab of thickness d, where the dielectric tensor continuously rotates within the sample thickness, forming the angles 0(z), q>( z) with respect to a fixed reference system (x,y,z). The slab is parallel to the (x,y) plane (see Figure 1). 

Below, we explore the dielectric heating effects caused by the dielectric relaxation of if) by expanding the theoretical model to include the finite thermal conductivity of the bounding plates. Evidently, the temperature changes should depend not only on the electric field, properties of the NLC and bounding plates, but also on the thermal properties of the medium in which the NLC cell is placed however, to the best of our knowledge, this issue has not been explored in the prior work. To directly measure the temperature of the nematic slab in the broad range of field frequencies, one can use the direct method with a tiny thermocouple smaller than the cell thickness, as described in Ref [28],... 

It is also noteworthy that urea interacts with the alkali halide surfaces in aqueous solution hence, the surrounding medium effect seems to be important. To examine the effect of the solvent, we performed calculations with the continuum solvation model (COSMO). The dielectrics ( = 78.4 for water) was used in these cases. The optimized gas-phase slabs for KCI 100, 110, and 111 with urea were computed with the COSMO model. The calculated interaction energies are shown in Table 8.2. Interaction energies were found to be lower in water compared to the gas-phase results. Importantly, the interaction energies for urea with all three surfaces were found to be comparable. Based on these calculated results, one could predict that the additional stabilization cannot be achieved for the unstable surfaces such as 111 ... 

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