On the dielectric theory of a crystalline slab of point molecules

We discuss the dielectric response of a crystalline slab of point molecules to an incident plane electromagnetic wave. The slab is assumed to be made up of non-polar, polarizable molecules (a) lying at points of a simple cubic lattice and (b) interacting only via the electromagnetic field. Expressions for the dispersion relations, polarisation and electric fields and the transmission coefficient are derived. Conditions under which a point dielectric equation of state holds are obtained. This simple system exhibits three resonances near the transverse optic frequency.     

On the theory of reflectivity and transmissivity of a lossless nonlinear dielectric slab

For the transverse electric polarization case (TE) we present a treatment of the optical reflectivity and transmissivity of a slab whose dielectric coefficient is a real valued function of the light intensity. If this function is numerically integrable with respect to the light intensity, our treatment can serve as an algorithm for a numerical solution of the nonlinear wave equation. If the dielectric function is proportional to the intensity, an analytical solution of the cubic wave equation is given for the electric field strength and for the phase of the field in terms of Weierstrass' elliptic functions and first elliptic theta functions, respectively. Evaluating this solution by means of a computer algebra system yields the reflectivity, transmissivity and phase dependency on the incident field intensity and on parameters characteristic for the problem. Certain combinations of the parameters lead to bistable and multivalued behavior. The solution found is used to determine the relative extrema of the reflectivity and the critical values of the thickness and of the incident intensity. The results are a generalization of linear optics results. Application of the analysis to the cubic-quintic wave equation yields the general analytic solution which is used to detemine the reflectivity of a semi-infinite nonlinear medium.     

On the theory of dielectric relaxation

The Kirkwood expression for the static dielectric constant of a polar substance is extended to non-zero frequencies by a means which avoids the introduction of spherical specimens and the connection between the dipoledipole correlation functions of distinct spatial regions. The procedure is based on a previously derived relation between the dynamic dielectric constant and the current-current susceptibility and on the use of the Callen-Welton theorem to relate the susceptibility to fluctuations. Surface effects are eliminated at the outset by consideration of media which are infinite in extent. A general relation between the long-range dipole-dipole correlations (which fall off as the inverse cube of the distance) and short-range correlations in a specimen composed of non-polarizable molecules is found from a consistency relation. It is shown that the two microscopic relaxation times which result from the existence of but one relaxation time in the dielectric constant correspond to the transverse and longitudinal relaxation times with the longitudinal time being screened relative to the transverse time by the static dielectric constant.     

A molecular theory of the dielectric permittivity of a nematic liquid crystal

We present a theory of the dielectric permittivity in which the intermolecular dipole-dipole correlations are treated explicitly. The results for the static permittivity agree with those which have previously been obtained by continuum calculations. The frequency dependence of the permittivity is related to two relaxation times which contain the effects of only short range intermolecular correlations. Approximate relationships are derived between these times and independently measurable properties.     

Polaron self-energy in a dielectric slab

The lowering of the ground state energy of an electron below the bottom of the conduction band by virtue of its interaction with the longitudinal optical phonons is calculated as a function of the dielectric's thickness. The bulk result, —α$\text{h}\text{?}$;ω, is found as the thickness approaches infinity.     

Resonant properties of a dielectric slab with equidistant strip electrodes

It is shown that a slab with a high dielectric constant and electrodes arranged in the form of narrow parallel equidistant strips may serve as a simple and effective generator of electromagnetic radiation for the very high frequency region. Its resonant properties may serve for accurate measurements of the dielectric constant in that frequency region.     

The electrostatic potential in a crystalline slab

The electrostatic potential in a crystalline slab of point charges is expressed as a sum of three types of terms, an intrinsic term, microscopic fringing terms and a macroscopic term.     

On the theory of the universal dielectric relaxation

Dielectric relaxation has been investigated within the framework of a modified mean field theory, in which the dielectric response of an arbitrary condensed matter system to the applied electric field is assumed to consist of two parts, a collective response and a slowly fluctuating response; the former corresponds to the cooperative response of the crystalline or noncrystalline structures composed of the atoms or molecules held together by normal chemical bonds and the latter represents the slow response of the strongly correlated high-temperature structure precursors or a partially ordered nematic phase. These two dielectric responses are not independent of each other but rather constitute a dynamic hierarchy, in which the slowly fluctuating response is constrained by the collective response. It then becomes clear that the dielectric relaxation of the system is actually a specific characteristic relaxation process modulated by the slow relaxation of the nematic phase and the relationship governing such a process can be defined as the universal dielectric relaxation law. Furthermore, we have shown that seemingly different relaxation relationships, such as the Debye relaxation law, the Cole-Cole equation, the Cole-Davidson equation, the Havriliak-Negami relaxation, the Kohlrausch-Williams-Watts function, Jonscher’s universal dielectric relaxation law, etc. are only the variants of this universal law under different circumstances.     

Nonlinear waves guided by a dielectric slab

An exact solution of Maxwell's equations is found for TM-polarized nonlinear guided waves which are guided by a linear dielectric slab embedded between two nonlinear uniaxial media. Additional waves in comparison with the linear case arise. Some of these waves have no counterpart in linear systems. Similarities and differences with respect to TE-polarized nonlinear guided waves are pointed out.     

Nonlinear waves guided by a dielectric slab

We consider dispersion relations and field structure of TE-polarized guided waves travelling along an asymmetric dielectric slab surrounded by two different nonlinear media. For a given configuration there are four types of guided waves. Three of this four types possess at least one field maximum outside the slab region and have no counterpart in linear waveguide optics. The solutions of the dispersion relations depend now on an additional parameter making them more flexible with respect to the linear limit.     

On the one-electron theory of crystalline solids in a homogeneous electric field

Assuming that the one-electron states of a perfect crystalline solid are known, an approach for the calculation of the one-electron states in the presence of external fields and/or other deviations from the periodic potential of the perfect crystal is suggested. The treatment is based on the Wannier representation and the use of a method for solving some operator non-polynomial differential equations. In the approximation of the one-band Wannier equation an exact solution of the problem for electron states of the crystals in a homogeneous external electric field is given. The results obtained in the tight binding approximation for cubic crystals show that the electron motion along the field is finite and the degree of its finiteness for a given electric field strength is greater, the smaller the width of the initial energy band considered. In the one-band approximation Considered the electron energy spectrum has the character of the Wannier-Stark ladder. It is also shown that an influence of transverse motion on the character of the finite motion along the field appears when a non-additivity in the initial energy band function with respect to the energies of motions parallel and perpendicular to the field direction is present.     

Local fields near the surface of a crystalline dielectric

We calculate the variation of the local electric field with depth near the surface of a crystalline dielectric, for the cases of induced atomic dipoles oriented perpendicular and parallel to the surface. The crystalline dielectric is modelled by a cubic lattice of polarizable atoms, with the surface in the (001) plane. Our calculations show that the departure of the local field from its bulk value is confined almost entirely to the outermost plane, and even there is small (at the most a few percent).     

Light propagation in a planar dielectric slab waveguide with step discontinuities

The common matrix formalism for multi-layer systems is generalized to describe the optical field propagation along an arbitrary cascade of step discontinuities in a planar dielectric waveguide. The reflection and transmission properties of the step cascade are modelled by rigorous operator relations in a Hilbert-space calculus. In this way the complete propagation problem is reduced to two basic transformations. TE- and TM-polarized fields are treated simultaneously.     

Voltage-controlled transmission through a dielectric slab doped with quantum dot molecules

Transmission and reflection of an electromagnetic pulse through a dielectric slab doped with the quantum dot molecules are investigated. It is shown that the transmission and reflection coefficients depend on the inter-dot tunneling effect and can be simply controlled by applying a gate voltage without any changing in the refractive index or thickness of the slab. Such simple controlling prepares an active beam splitter which can be used in all optical switching, optical limiting, and other optical systems.     

Pulse propagation in a nonlinear dielectric slab waveguide

The evolution of an optical pulse in a single-mode, step index dielectric slab waveguide which is characterized by an intensity dependent dielectric function in the core and cladding regions is treated by means of differential equation techniques. A cubic order non-linearity is considered. The electromagnetic field distribution in the slab waveguide region satisfies a non-linear wave equation. This field can be represented in terms of even TE guided modes with a slowly varying envelope amplitude function.Then using the well known approximation, based on the slowly varying character of the amplitude function, a non linear partial differential equation is obtained for the amplitude function. As the coefficients of this equation depend on the distance across the transverse direction X, an averaging technique over x is applied to reduce the nonlinear partial differential equation into a form that is easily transformed to the so-called non-linear Scroedinger differential equation.This equation is then attacked by means of the well known Inverse Scattering method in the case of reflection less potentials. The single and double soliton solutions are obtained explicitly for a single-mode slab waveguide. Finally numerical results are presented in the time domain.     

On the Mott-Littleton dielectric theory for alkali halides

It has been demonstrated that the Mott-Littleton theory of dielectric constant is consistent with the recent experimental data on the pressure dependence of dielectric constant of alkali halides. On the other hand, the Clausius-Mossotti and Drude models yield large deviations from the observed data.