Dielectric Half-space Research Articles

Vertical dipole above a dielectric or metallic half space: Energy-flow considerations.

The emission pattern from a classical dipole located above and oriented perpendicular to a metallic or dielectric half space is calculated for a dipole driven at constant amplitude. Emphasis is placed on the fields in the metal or dielectric. It is shown that the radial Poynting vector in the metal points inwards when the frequency of the dipole is below the surface plasmon resonance frequency. In this case, energy actually flows out of the interface at small radii and the power entering the metal can actually oscillate as a function of radius. The Joule heating in the metal is also calculated for a cylindrical volume in the metal. When the metal is replaced by a dielectric having permittivity less than that of the medium in which the dipole is immersed, it is found that energy flows out of the interface for sufficiently large radii, a result reminiscent of the Goos-Hänchen effect.

Analytical method for monostatic radar cross section calculation of a perfectly conducting wind turbine model located over dielectric lossy half space

Radar cross section (RCS) of a wind turbine has a key role for determining possible effects of wind farms on radar and navigation systems. Closed form expressions of the physical optics technique are applied to calculate monostatic radar cross section of an electrically large wind turbine model over a dielectric, lossy half space. The model is constructed with perfectly conducting canonical structures. First-order effects of the half space to the electromagnetic scattering mechanism are approximated with four-path model. Doppler spectrogram of the turbine model over lossy ground is obtained using short-time Fourier transform. The closed form expressions provide very-fast RCS calculations for different broadside directions and blade rotation speeds. Performance of this proposed method shows that it is suitable for real-time simulations that analyse the effects of the wind farms to the radar and navigation systems performance.

Impulsive electromagnetic response of thin plasmonic metal sheets

The impulsive electromagnetic response of a thin metallic coating on a dielectric half-space is analytically investigated. Both TM- and TE-polarized electromagnetic fields in the configuration are excited by an impulsive line source. The problem is analytically solved with the help of the high-contrast thin-sheet boundary conditions and the extended Cagniard-DeHoop technique. Closed-form space-time expressions for electromagnetic fields are found, numerically evaluated, and discussed with regard to the pulsed excitation of surface plasmon phenomena.

Electromagnetic Scattering From a Buried Cylinder Using a Multiple Reflection Approach: TM Case

A simple, fast, and accurate analytical method is introduced to obtain the EM scattered fields due to an infinite circular cylinder buried in a homogeneous dielectric half-space, illuminated by a normally incident transverse magnetic (TM) plane wave. The method is applied to perfect electric conducting (PEC) and dielectric cylinders of complex permittivity with the host dielectric medium being lossy or lossless. The accuracy of this method is verified using a finite-difference time-domain code (FDTD) on a wide frequency range and the results are presented discussing the range of validity of this approach.

Patch contribution to near-field radiative energy transfer and van der Waals pressure between two half-spaces

Near-field effects in fluctuational electrodynamics leads to enhancement of radiative energy transfer as well as the emergence of van der Waals and/or Casimir pressure. While much has been learned from the analysis of near-field interactions between two half-spaces separated by a vacuum gap, we shed new light on the problem by finding how much of a surface patch on one of the half-spaces contributes to the energy transfer or van der Waals pressure at any location within the vacuum gap. We show that energy transfer and fluctuation-induced van der Waals pressure at any point on the surface of one half-space are qualitatively and quantitatively different due to the dissimilar zones of influence of interactions. We also show that the contributions from different surface patches are qualitatively similar for half-spaces with dielectric materials (silica, silicon carbide) and half-spaces with metals (gold).

Quasi-static analysis of lightning-radiated electric field in the vicinity of sea-land structure

A quasi-static approach is presented to compute electric field radiated by a lightning return stroke above the sea-land structure modeled as a dielectric half space with a perfectly conducting half plane situated in its interface. It appears that the quasi-static approach provides a closed-form time-domain solution for the radiated electric field. The proposed approach is mainly based on the electrostatic solution of the structure. The governing Poisson's equation in the presence of the sea-land structure is solved in three dimensions, using the contributions of dielectric half space and perfectly conducting half plane. The solution, expressed in terms of image contributions, consists of two point images in physical space. The validity domain of the time-domain quasi-static approach is investigated by comparison of the obtained electric fields with full-wave results obtained using the finite-difference time-domain method. The proposed approach has a reasonable accuracy at near (200m) distance range from the lightning channel.

On the computation of Casimir stresses in open media and Lifshitz theory

A classification of the electromagnetic modes on open and closed spatial domains containing media with piecewise homogeneous permittivities is used to facilitate the derivation of quantum induced Casimir stresses in dielectrics. By directly exploiting the complex analytic properties of solutions of the macroscopic Maxwell equations for open systems it is shown how regular expressions for such stresses can be expressed in terms of double integrals involving either real or pure imaginary frequencies associated with harmonic modes in conformity with the Lifshitz theory for separated planar dielectric half-spaces. The derivation is self-contained without recourse to the Krein formula for a density of states or mode regularization and offers a more direct approach to other open systems.

Scattering from a buried perfect electromagnetic conductor of circular cylindrical shape and coated by a chiral material

The scattering effects of different types of chiral materials used as coating on a perfect electromagnetic conductor (PEMC) circular cylinder buried in a dielectric half space have been investigated in this paper. The coating layers of double positive (DPS) chiral, double negative (DNG) chiral, and chiral nihility have been considered in the analysis. The spectral plane wave solution is used to handle the multiple interactions between the buried cylinder and the dielectric interface separating the two half spaces. Numerical results obtained for scattering of a perpendicularly polarized electromagnetic plane wave from this configuration have been presented.

Electromagnetic boundary conditions in multipole theory

Multipole expansions for the macroscopic charge and current densities in a dielectric half-space involve a hierarchy of singular functions comprising the Dirac delta function and its derivatives. For these, Maxwell's differential equations yield corresponding singular expansions of the macroscopic electromagnetic fields E and B, and the response fields D and H, together with their boundary conditions (in terms of macroscopic multipole moment densities) at a dielectric–vacuum (or dielectric–dielectric) interface. Explicit results are obtained up to electric octopole–magnetic quadrupole order. These show that published expressions for boundary conditions are incomplete beyond electric dipole order, due to an invalid assumption concerning two-dimensional behaviour at the interface. The effect of this on studies of certain reflection effects for anisotropic media is detailed. Comparison of the differential theory with the standard integral formulation shows that, beyond electric dipole order, the latter is incomplete and redundant.

Multiple Scattering Between Cylinders in Two Dielectric Half-Spaces

The two-dimensional scattering of a plane wave from an arbitrary arrangement of infinite cylinders in two dielectric half-spaces is considered. The electromagnetic fields are decomposed into cylindrical waves so that the boundary conditions for the cylinders can be satisfied directly. The boundary conditions for the planar interface separating the two dielectric half-spaces are addressed by decomposing the cylindrical waves into plane waves and applying the planar reflection/transmission coefficients. This decomposition produces integrals that can be evaluated numerically. When the cylinders are significantly separated from the planar interface, the method of stationary phase can be used to approximate the integrals.

A Connected Array of Slots Supporting Broadband Leaky Waves

In this paper, we investigate the properties of a finite array of slots that support broadband leaky waves. The slots are etched on a ground plane located in the close proximity of a dense dielectric half space and each slot is fed at a finite number of locations. A quasi-analytical spectral procedure is presented, which can be used to evaluate the near and far fields that emerge from each separate feed of the array. In fact, the structure can be used to realize hundreds of independent beams in the overlaying dense dielectric over a band in the order of 4:1. The spectral procedure can also be used to evaluate the mutual coupling between the elements. This latter limits the lower frequency at which the different beams are independent and directive. These arrays are mainly proposed to be used as feeders for dielectric lens antennas. The formulation presented here is very general and can be applied to any finite array of long slots, independently from their capability to support leaky waves.

Spectral domain method for the electromagnetic scattering by a buried sphere

A rigorous method to analyze the electromagnetic scattering of an elliptically polarized plane wave by a sphere buried in a dielectric half-space, is presented. The electric field components of the incident and the scattered monochromatic plane waves are expanded in series of vectorial spherical harmonics, with unknown expansion coefficients. The scattered-reflected and scattered-transmitted fields are computed by exploiting the plane-wave spectrum of the scattered field, considering the reflection and transmission of each elementary plane wave by the interface. The boundary-condition imposition leads to a linear system that returns the unknown coefficients of the scattered field. To achieve a numerical solution, a code has been implemented, and a truncation criterion for the involved series has been proposed. Comparisons with the literature and simulations performed with a commercial software are presented. A generalization of the method to the case of a short pulse scattered by a buried sphere is presented, taking into account the dispersive properties of the involved media.

Buried object adaptive shape reconstruction and ground parameters estimation using differential evolution

In this study, the capability of the opposition-based differential evolution stochastic searching algorithm in shape reconstruction of a two-dimensional conducting target buried in a lossy dielectric half-space is investigated using simulated backscattered fields calculated above the ground by both method of moment with far-field approximation and geometrical optics approximation at different observation and frequency points. For an efficient reconstruction, the target boundary is approximated by a non-uniform cubic B-spline curve with variable number of curve control parameters (CP). Using the knot insertion Oslo algorithm and through the optimisation process, the DE algorithm finds the optimum number of CP, successfully reconstructs the ground parameters (i.e. permittivity and conductivity) together with target upper part shape and location for moderate values of the signal-to-noise power ratio.

DIPOLE RADIATION NEAR ANISOTROPIC LOW-PERMITTIVITY MEDIA

We investigate radiation of a dipole at or below the interface of (an)isotropic Epsilon Near Zero (ENZ) media, akin to the classic problem of a dipole above a dielectric half-space. To this end, the radiation patterns of dipoles at the interface of air and a general anisotropic medium (or immersed inside the medium) are derived using the Lorentz reciprocity method. By using an ENZ half-space, air takes on the role of the denser medium. Thus we obtain shaped radiation patterns in air which were only previously attainable inside the dielectric half-space. We then follow the early work of Collin on anisotropic artiflcial dielectrics which readily enables the implementation of practical anisotropic ENZs by simply stacking sub-wavelength periodic bi-layers of metal and dielectric at optical frequencies. We show that when such a realistic anisotropic ENZ has a low longitudinal permittivity, the desired shaped radiation patterns are achieved in air. In such cases the radiation is also much stronger in air than in the ENZ media, as air is the denser medium. Moreover, we investigate the subtle difierences of the dipolar patterns when the anisotropic ENZ dispersion is either elliptic or hyperbolic.

Exact dispersion-force potentials: Interaction of an atom with a conductor-patched dielectric surface

We study the interaction between a neutral atom or molecule and a conductor-patched dielectric surface. We model this system by a perfectly reflecting disc lying atop of a non-dispersive dielectric half-space, both interacting with the neutral atom or molecule. We assume the interaction to be non-retarded and at zero temperature. We find an exact solution to this problem. In addition we generate a number of other useful results. For the case of no substrate we obtain the exact formula for the van der Waals interaction energy of an atom near a perfectly conducting disc. We show that the Casimir-Polder force acting on an atom that is polarized in the direction normal to the surface of the disc displays intricate behaviour. This part of our results is directly relevant to recent matter-wave experiments in which cold molecules are scattered by a radially symmetric object in order to study diffraction patterns and the so-called Poisson spot. Furthermore, we give an exact expression for the non-retarded limit of the Casimir-Polder interaction between an atom and a perfectly-conducting bowl.

Scattering From Cylinders Near a Dielectric Half-Space Using a General Method of Images

The two-dimensional scattering of an arbitrary beam of radiation from multiple dielectric cylinders near a dielectric half-space is considered using a general method of images (GMI). The electromagnetic fields are broken down into cylindrical waves so that the boundary conditions for the cylinders can be applied directly. Two approaches for calculating the multiple scattering between the cylinders and the planar interface are compared: the plane-wave integral method and the Fourier series method. The plane-wave integral method involves numerically integrating a plane-wave spectrum for the reflection from the planar interface. The Fourier series method avoids numerical integration but poses problems for evanescent fields. By introducing evanescent field correction terms we are able to show the equivalence of the two methods.

Accurate wire-grid modelling of buried conducting cylindrical scatterers

This work is focused on the wire-grid modelling of 2D (infinitely long) buried conducting objects. A circular cylinder is considered, embedded in a dielectric half-space and illuminated by a transverse magnetic monochromatic plane wave. The scattered near field is calculated by using the cylindrical-wave approach. This rigorous technique is briefly resumed in the paper, and its convergence properties in wire-grid modelling are discussed. Numerical results obtained for different wire-grid models are compared with the exact solution. It is shown that the well-known same-area criterion, in the considered cases, yields affordable results. However, it is not the optimum, and better results are obtained with a wire radius shorter than what was suggested by the rule.

Quantum electrodynamics near a dispersive and absorbing dielectric

We build up a consistent theory of quantum electrodynamics in the presence of macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive and absorbing dielectric medium and formulate the theory in terms of interacting quantum fields. We integrate out the damped polaritons by using diagrammatic techniques and find an exact expression for the displacement field (photon) propagator in the presence of a dispersive and absorbing dielectric half-space. This opens a new route to traceable perturbative calculations of the same kind as in free-space quantum electrodynamics. As a worked-through example we consider the interaction of a neutral atom with a dispersive and absorbing dielectric half-space. For that we use the multipolar coupling $\boldsymbol{\mu}\cdot\mathbf{D}$ of the atomic dipole moment to the electromagnetic displacement field. We apply the newly developed formalism to calculate the one-loop correction to the atomic electron propagator and find the energy-level shift and changes in the spontaneous decay rates for a neutral atom close to an absorptive dielectric mirror.

Transient Response of Nonlinearly Loaded Antennas Above a Lossy Dielectric Half-Space: A Modified MoM-AOM Approach

This paper proposes an entirely frequency-domain technique for the transient analysis of electromagnetic systems involving nonlinearly loaded wire antennas over a lossy dielectric half-space. The analysis involves two stages. In the first stage, the problem is transformed into a nonlinear microwave equivalent circuit with the circuit parameters of antenna extracted by the method of moment (MoM). The effect of lossy dielectric half-space is considered by proper implementation of the Sommerfeld asymptotic method in the MoM. In the second stage, the nonlinear microwave equivalent circuit is treated using the arithmetic operator method. To efficiently perform basic arithmetic operations in the frequency domain, a linear matrix transformation of respective spectra is introduced. To construct the transformation matrix for a transient excitation involving a large number of excitation frequencies, a fast algorithm is developed. The algorithm is based on the frequency arrangement of transformation matrix obtained by matrix multiplication property. The proposed technique is well suited for direct inclusion in the kernel of computational tools for solving problems involving the electric field integral equation. The accuracy of the proposed method is confirmed by comparing the simulation results of several case studies with those obtained using the time-domain methods available in the literature.

Casimir friction force between polarizable media

This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in EPL 91, 60003 (2010), which was restricted to a pair of particles with longitudinal polarization only. For simplicity the particles are taken to interact via the electrostatic dipole-dipole interaction. Thereafter, we consider the Casimir friction between one particle and a dielectric half-space, and also the friction between two dielectric half-spaces. Finally, we consider general polarizabilities (beyond the simple one-oscillator form), and show how friction occurs at finite temperature when finite frequency regions of the imaginary parts of polarizabilities overlap.