Inhomogeneous Dielectric Medium Research Articles

Transfer Relations for Electromagnetic Wave Scattering From Periodic Dielectric One-Dimensional Interface: Te Polarization

Some general statements for theory of wave multiple scattering in a three-dimensional inhomogeneous layered dielectric medium are established using the composition rule of the scattering (T-matrix) operators to show that the problem of wave scattering from dielectric interface may be studied similar to the problem of volume wave scattering. The medium is thought as being a stack of n layers, each of them is confined by perpendicular to the z axis planes and consists of a three-dimensional discrete or continuous inhomogeneous medium. The layers do not intersect between them and are embedded into a homogeneous background. A result of the paper is a mixed system of exact operator equations (transfer relations) for the operator wave reflection and transmission coefficients of the medium and the operator wave amplitudes of waves in splits between layers. It is shown that the transfer relations lead to a separate recurrent system of operator equations, which describe the incremental change of the operator wave reflection and transmission coefficients of stack of n - 1 layers upon attachment of a n's layer to the stack. We derive from this recurrent equations a generalized Riccati equation for the operator wave reflection coefficient of the medium and an corresponding equation for the operator wave transmission coefficient of the medium, the coefficients of the Riccati equation and the corresponding equation being expressed in terms of the operator wave reflection and transmission coefficients of a thin slice of the medium and embedding parameter being taken along the z axis. The derived Riccati equation is applied to the problem of electromagnetic wave reflection from a periodic one-dimensional interface of two dielectric half-spaces, the interface being varied in the x axis direction and the wave electric field vector being parallel to the y axis. A solution to the Riccati equation for this problem is found numerically, taking into account with the aid of the Bloch (Floquet) theorem both the propagating and evanescent waves and not invoking the Rayleigh hypothesis. A resonant effect related to the Wood anomalies is discussed.

Variational estimates of matrices of capacitative and potential coefficients of a system of conductors located in an inhomogeneous dielectric medium

Variational principles are used to obtain simple upper and lower estimates for the matrices of the capacitative coefficients of a system of conductors located in an inhomogeneous dielectric medium. The test function used in the energy functional is the potential distribution of the same system of conductors but located in a homogeneous medium.

Interleaving two-dimensional lattices to create three-dimensional photonic bandgap structures

A two-dimensional lattice consists of an inhomogeneous dielectric medium which has periodic variations of permittivity along two linear directions, and is uniform in the third dimension. The paper considers a class of three-dimensional photonic band gap materials formed by the interleaving of a pair of two-dimensional lattices whose uniform directions are mutually orthogonal, the so-called 'woodpile' geometry. It is shown by numerical calculations that the strong polarisation discrimination exhibited by the constituent two-dimensional sublattices in their respective stopbands leads to a completely three-dimensional photonic bandgap crystal in all polarisations when the two sublattices are interleaved. For a general class of such synthetic crystals having arbitrary two-dimensional distributions in the sublattices, many properties of the three-dimensional interleaved crystal can be predicted directly from a knowledge of the properties of the sublattices, thereby radically reducing the computational cost of their determination.

Path-integral quantization of electrodynamics in dielectric media

In the present paper we study the Faddeev-Popov path-integral quantization of electrodynamics in an inhomogeneous dielectric medium. We quantize all polarizations of the photons and introduce the corresponding ghost fields. Using the heat kernel technique, we express the heat kernel coefficients in terms of the dielectricity and calculate the ultraviolet divergent terms in the effective action. No cancellation between ghosts and `non-physical' degrees of freedom of the photon is observed.

An improved multigrid technique for quasi-TEM analysis of a microstrip embedded in an inhomogeneous anisotropic medium

An improved multigrid technique for the quasi-TEM analysis of a microstrip line embedded in an inhomogeneous anisotropic dielectric medium is presented. A general finite-difference form for the inhomogeneous anisotropic medium is derived by the finite-volume discretization of Gauss's theorem. By the analogy between the quasi-TEM and the steady current problems, this general form can be interpreted by Kirchhoff's current law. Then, the electric potential distribution in this complicated dielectric structure can be regarded as that on a resistive network, which makes the formulation easier. The resulting matrix equation for the potential distribution on the finest grid is solved by the improved multigrid iteration, where the coarse-grid operator is derived directly from the finest grid operator by the help of an equivalent resistive network. Three numerical examples show that the convergence rate is hardly dependent of the number of unknowns and the complexity of the dielectric media. Moreover, the numerical results are in good agreement with those by the other method when special cases are considered.

On the treatment of the propagation of electromagnetic waves in an isotropic inhomogeneous dielectric medium as waves in a medium with effective anisotropy described by the permeability tensor

We show that plane E and H waves in a smoothly inhomogeneous isotropic plane-stratified medium (plasma) can be considered as normal waves in a uniaxial medium with isotropic permittivity and effective-permeability tensor.

Order-N spectral method for electromagnetic waves.

We show that the eigenmodes for electromagnetic waves in an inhomogeneous dielectric medium can be obtained with an algorithm that scales linearly with the size of the system. The method employs discretization of the Maxwell equations in both the spatial and the time domain and the integration of the Maxwell equations in the time domain. The spectral intensity can then be obtained by a Fourier transform. We applied the method to a few problems of current interest, including the photonic band structure of a periodic dielectric structure, the effective dielectric constants of some three-dimensional and two-dimensional systems, and the defect states of a periodic dielectric structure with structural defects.

Reconstruction of multilayered dielectric models using oblique transverse electric or transverse magnetic incidence

Subsurface probing of inhomogeneous dielectric media has received considerable attention from the research community. Extensive work in this area has been presented either in the time or frequency domain. However, most of the algorithms presented are mainly devoted to continuous dielectric profile inversion. The fast Fourier transform (FFT) inversion method is newly introduced for discrete multilayer inversion. This method has the advantages of simplicity, a short computation time, and robustness with respect to noise. The FFT inversion method is applied to a discrete homogeneous multilayer dielectric model using oblique incidence and a limited bandwidth, provided that all dielectric media are lossless and nondispersive. For a given model, a uniform plane wave is obliquely incident on the top of its surface, with its polarization being either a transverse electric or a transverse magnetic wave. In each case, the corresponding reflection coefficient is sampled over a finite frequency range. The time-domain spectrum of the reflection coefficient is obtained by applying the FFT algorithm to its samples. An algorithm is developed for the deduction of the height and permittivity of each layer. The algorithm is tested by using the simulated data of a three-layer half-space dielectric model. The resulting relative errors in the inversion process are almost less than 10 -4 for all of the model parameters. When a random noise signal is superimposed on the sampled input data, the relative errors are comparable to the noise-to-level ratio.

Resonantly induced dipole-dipole interactions in the diffusion of scalar waves.

The induced dipole-dipole interaction can be understood in terms of recurrent elastic scattering of waves. We implement this notion into transport theory of scalar waves in inhomogeneous dielectric media and calculate rigorously the pivotal cooperative effect of pairs of polarizable dipoles.

Multimode squeezed states in tenuous dielectric medium

The “generalized coherent state” representation was applied to the model hamiltonian, describing the light propagation in a tenuous inhomogeneous dielectric medium. For multimode squeezed states, the “equation of motion” for squeezing and other parameters were derived. Some approximate solutions obtained suggest that under certain conditions the squeezing parameter may be increased due to the interaction between different modes in a process of multiple scattering.

Volume/surface formulation for analyzing scattering from coated periodic strips

A surface/surface formulation was used by Perte et al. (see IEEE Trans. Antennas. Propagat.) to analyze the scattering from periodic planar coated strips. This paper is an extension of that work where a combined volume/surface formulation has been used to solve the same problem. This formulation can be applied to problems which involve an inhomogeneous dielectric medium or/and a thick dielectric which requires the inclusion of the edge currents which were neglected as a simplification. Results obtained using the volume/surface formulation have been compared with the results published in the paper written by Petre et al. which were obtained using a surface/surface formulation. >

Wave-front conversion between a Gaussian beam with a cylindrical phase function and a plane wave in a monomode on-axis transmission holographic coupler

We present a coupled-wave-analysis-based treatment for a wave-front conversion problem between a Gaussian beam with a cylindrical phase and a plane wave for a two-dimensional on-axis geometry. A coupled-wave approach to the multiple-scattering process in an inhomogeneous dielectric medium offers a clear physically interpretable description of the diffraction phenomena in volume media as well as the possibility of an intelligible mathematical treatment. An analytical integral solution for the amplitudes of the two modes of diffraction is submitted. High diffraction efficiency (≈1) and the deterioration of reconstruction fidelity are predicted. It is of interest to apply the model to the analysis and design of a monomode holographic fiber-to-fiber coupler, wave-front correctors, and holographic interconnection devices.

Transient analysis of coupled, tapered transmission lines with arbitrary nonlinear terminations

A fast and efficient method of simulating the time-domain transient response of coupled, tapered transmission lines is presented. A time-domain scattering parameter formulation is used to derive the simple closed-form expression for the voltage variables for uniform lossless lines; this expression is applied to tapered lines by dividing the lines into many uniform section. Computational efficiency and stability are achieved using recursive time-domain algorithms. When a quasi-TEM propagation mode is assumed, the method is applicable to nonlinear terminations and inhomogeneous dielectric media. Memory requirements are minimized and are independent of the number of time steps. Simulation results showed good agreement with experimental results. >

Hybrid numerical method for harmonic 3-D Maxwell equations: scattering by a mixed conducting and inhomogeneous anisotropic dielectric medium

This article deals with a hybrid numerical method for solving harmonic Maxwell equations in the classical electrodynamic context. This formulation can be used with any body of arbitrary three-dimensional geometry, of perfectly conducting material or dielectric, with locally inhomogeneous and anisotropic behavior laws, and with or without dielectric losses. The mathematical formulation is presented along with applications validating it. The exterior problem is treated by the integral equation method while local equations are used for the dielectric parts of the body. A global variational formulation of the coupled problem is developed for use in discretization by the finite element method. Boundary finite elements are used for integral operators connected with the exterior problem. Localized finite elements are used for the interior problem. Difficulties of irregular frequencies, also called resonant frequencies in the perfectly conducting case, arising from the integral formulation are analyzed in detail and an efficient solution is developed. >

Wave propagation in a radially inhomogeneous cylindrical dielectric structure: A general analytical solution

AbstractAnalytical solutions for wave propagation in a general inhomogeneous dielectric medium in a cylindrical coordinate system are presented. The solutions are built using series expansions of the Frobenius and Taylor types. The former includes the Bessel functions in a homogeneous medium; the latter seems to be new and allows the construction of a general and fast convergent algorithm for computing the modal characteristics. A simple criterium for hybrid mode classification is also presented. © 1992 John Wiley & Sons, Inc.

Enhancements of local electric fields in inhomogeneous dielectric media by microstructural defects

The complex microstructure present in most dielectric films prevents exact calculations of the film dielectric properties. We have developed a finite element method to determine the local electric field and polarization in inhomogeneous media. The local field intensities in media exhibit a much broader range of magnitudes than predicted or accommodated by effective medium approximation methods. These large fluctuations may contribute to the large variation in optical materials failure rates, especially when the failure mechanism is field-intensity dependent.

NUCLEAR MATTER STABILITY IN A SOLITON MODEL FOR FINITE NUCLEI

A relativistic band structure method for the computation of the electronic structure of atomic clusters is adapter to the Friedberg–Lee nontopological soliton model. Thus, finite nuclei can be studied in the soliton model. As a verification of our method, we calculated the equation of state of nuclear matter. In order to achieve nuclear matter stability, we added the colour magnetic interaction for an inhomogeneous dielectric medium as well as a phenomenological residual interaction to the soliton model. Both modifications are examined in detail. Nuclear matter stability near the empirical ground state density and binding energy has been achieved.

Structural viscosity of electrorheological fluids

To describe the Couette shear in high-concentration electrorheological fluids (ERF) in the presence of an electric field, the continuous inhomogeneous dielectric medium approximation is employed. In this approximation the forces of interaction of polarized particles are considered to originate as a result of the competition between Maxwellian tensions and pressures at the surface of contact between dielectrics. These forces are governed by the electric intensity jump at the interface. They consist of two components: the polarization component originating from the polarization of dielectric particles and appearance of bound charges, and the absorption component resulting from the accumulation of free charges on the surface of particles during the passage of leakage current. The polarization component depends on the ratio between the dielectric constants of dielectrics and on the electric field gradient in a gap between particles. It also depends on the size and shape of the particles. The absorption component is specified by the particle-to-disperse medium resistance ratio and depends on the time of charge accumulation at the interface of the dielectrics. This approximation has allowed ERF to be modelled as a dynamic array of bridges consisting of elementary condensers (a particle-a disperse medium-a particle). The tensile force of the bridge and its yield strength have been calculated. Also, an exponential dependence of the effective viscosity on the electric intensity and shear rate has been obtained, which in the limiting case is transformed into the Shvedov-Bingham law.

Split-operator electric field reflection techniques

The authors have analyzed several approximations for the reflection coefficient of an electric field incident on the interface between two inhomogeneous dielectric media. While existing expressions agree with exact results in certain limits, realistic waveguides with discontinuous refractive index changes are often more accurately modeled by dividing the incoming electric field into segments coinciding with the intervals over which the interface is continuous, and subsequently superimposing the reflection from each segment. >

Electrostatic interactions in lecithin-bilayer systems A Monte Carlo study

Monte Carlo simulations have been performed to study the electrostatic interaction between two planar zwitterionic surfaces. The mobile and orientable zwitterions are imbedded in an inhomogeneous dielectric medium and image charges have been used to account for the dielectric discontinuities. This is a simple model system for lecithin bilayers, emphasizing the molecular nature of the headgroups, while treating the intermediate aqueous region and the apotar interior of the bilayer as continua. The calculated lateral distribution functions and the inter-bilayer force are shown to be sensitive to the location of the dielectric discontinuities. For a structured system, which is the case when the zwitterions are confined to the apolar region, the inter-bilayer pressure is strongly repulsive. With zwitterions in the aqueous phase, the pressure is found to be attractive. The results are discussed in terms of an extension to the traditional Lifshitz theory of van der Waals forces.