Dielectric Half-space Research Articles

Применение модифицированного метода дискретных источников в задаче дифракции импульсной волны на подповерхностном импедансном цилиндре

In contrast to the classical method of auxiliary sources (MAS) with the location of discrete sources (DS) on a closed additional contour, this article investigates the use of a complete system of functions for describing DS fields localized on an open curve in a modified MAS (MMAS). The MMAS was applied to solve a two-dimensional diffraction problem of a broadband electromagnetic impulse on an impedance cylinder located in free space and in the subsurface. The electric thread was a source of external current, excited by an impulse of 1.6 ns duration with a spectrum width from 122 MHz to 726 MHz (at the level of -6 dB). In various combinations, fresh water, thawed and frozen soil, air, and ice were used as the filling medium of the cylinder and the dielectric half-space. The complete system of functions for describing the fields of DS was constructed based on the Hankel functions of the first kind of zero order, the corresponding Green's function for the layered medium problem, and their derivatives in the direction of normal to the curve on which the DS was placed. When compared with the finite difference time domain method (FDTD), it is shown that the MMAS, using Leontovich impedance boundary conditions, can describe impulse fields, scattered by a dielectric cylinder with practically significant accuracy. It has been established that in the case of an elliptical cylinder, the MMAS requires approximately half as many auxiliary DSs compared to the classical MAS while achieving the same accuracy of the solution. In general, this article confirms the possibility of using a complete system of functions to describe the fields of DSs, localized on an open curve for the solving of impulse diffraction problems on subsurface impedance cylinders.

A Complete Nonuniform Asymptotic Expansion of the Dyadic Green’s Function for Dielectric Half-Space

A Complete Nonuniform Asymptotic Expansion of the Dyadic Green’s Function for Dielectric Half-Space

Casimir Interaction of Chern–Simons Layers on Substrates via Vacuum Stress Tensor

We develop a Green’s functions scattering method for systems with Chern–Simons plane boundary layers on dielectric half-spaces. The Casimir pressure is derived by evaluation of the stress tensor in a vacuum slit between two half-spaces. The sign of the Casimir pressure on a Chern–Simons plane layer separated by a vacuum slit from the Chern–Simons layer at the boundary of a dielectric half-space is analyzed for intrinsic Si and SiO2 glass substrates.

Complete Uniform Asymptotic Expansion of Finite-Range Integral Representation of Dyadic Green’s Function for Ordinary Dielectric Half-Space

Complete Uniform Asymptotic Expansion of Finite-Range Integral Representation of Dyadic Green’s Function for Ordinary Dielectric Half-Space

Localized source above a time-modulated dielectric half-space: Green's function theory

In this paper, we explore the two-dimensional Green's function problem above an instantaneous time-modulated dielectric half-space. In particular, we focus on studying the excitation dynamic with modulation that is carried out near the critical angle and the total internal reflection regime, where an impinging spectrum of waves expects the so-called lateral wave excitation on the interface. We start by analyzing the reflection of a plane wave, with detailed attention given to the difference between two cases: a slow quasistatic modulation versus a relatively fast modulation that leads to substantial excitation of intermodulation frequencies. Next, we provide a space-time representation to the space-domain Green's function, and later, we move to evaluate the spectral integral both in a brute-force numerically exact manner and using integration along the steepest descent path and the branch cuts, which unravel the distinction between different wave phenomena associated with the excitation problem. Thus, we identify different wave species that can be associated with reflected rays and waves that resemble the known head wave in the classical problem of stationary stratified media. We examine the unique time-dependent behavior of each wave species that arises as a consequence of the interface between the time-harmonics of the reflected space-time plane wave spectrum. Lastly, we demonstrate the broader validity of our analytical predictions, also in the case of a dispersive and finite time-modulated medium. To that end, we use a full-wave simulation of a source above a finite time-modulated thick layer that is implemented using a time-varying wire medium. These full-wave results are compared with our current analytical model with effective (homogenized) parameters of the time-modulated wire medium taken from . Published by the American Physical Society 2024

Pulsed Electromagnetic Excitation of a Narrow Slot Between Two Dielectric Halfspaces

The transient electromagnetic (EM) excitation of a narrow slot in a perfectly electrically conducting (PEC) screen that separates two homogeneous dielectric halfspaces, a simplified model of a typical feeding structure of leaky lens antennas, is analyzed numerically in the time domain (TD). The problem is formulated using the TD reciprocity theorem of the time-convolution type and subsequently solved with the aid of the Cagniard-DeHoop method of moments (CdH-MoM). Numerical results are validated using a general-purpose EM-field solver.

Determination of the electric field strength of high-voltage substations

The electric field strength is one of the main factors influencing sensitive microprocessor equipment and personnel on power stations and substations, power lines. Determining its level is an important applied task for ensuring the safe operation of electrical installations. The aim is to develop calculation relationships for determining the electric field strength created by the busbar of high-voltage substations in the working areas of personnel. The solution of the problem was based on the use of the method of equivalent charges to determine the strength of the electric field created by the complex busbar of high-voltage substations. Methodology. The development was based on solving the problem of the potential of the electric field of a point charge located in a dielectric half-space for a cylindrical coordinate system. By representing the electrode in the form of a set of point charges and subsequent integration, an expression for calculating the potential is obtained, created by a busbar of arbitrary orientation of finite length in an analytical form. Using the principle of superposition of fields and the definition of the derivative, expressions were obtained for calculating the vertical component of the electric field strength at given heights. Results. Based on the obtained expressions, using Visual Basic, the simulation of the distribution of the electric field strength under a three-phase power line with a voltage of 150 kV was performed. Comparison with the known calculation results obtained on the basis of analytical expressions for infinitely long conductors showed that the obtained expressions have an error of no more than 7%. The scientific novelty lies in the fact that for the first time expressions were obtained for determining the electric field strength created by a system of electrodes of finite length, based on the analytical method for solving differential equations. Practical significance. The proposed technique is implemented as a test module of the LiGro specialized software package, which allows modeling complex busbar systems typical for power stations and substations and power lines. A test calculation was carried out for an operating substation of regional electric networks with a voltage class of 110 kV. By comparing the duration of the calculation of switchgears with a diagonal of about 500 m, it was found that the calculation time in the LiGro complex based on the analytical method is several tens of times less than the calculation based on the finite element method. In addition, a more powerful computer was used for the end element simulation.

Modified Babinet Principle for Complementary Antennas in a Dielectric Half-Space

In this letter, the modified Babinet principle is applied to complementary antennas on the substrate interface. First, it is verified that the existing Babinet principle only holds for complementary metallic elements in the homogenized substrate. Then, the effective relative permittivity is introduced into the substrate interface through the zero-thickness effective substrate, which can keep the electromagnetic behavior (such as total electrical field and surface current density) of metallic element unchanged. Thereby, the modified Babinet principle can be established for arbitrary complementary metallic elements on the substrate interface. Finally, the proposed theory is applied to input impedances of complementary antennas on the substrate interface. The simulation strongly supports the proposed theory, regardless of the substrates and antenna sizes. The study not only establishes the modified Babinet principle for complementary metallic elements on the substrate interface, but also clarifies the electromagnetic influence of effective relative permittivity for the metallic element at the substrate interface.

Casimir-Polder interaction with Chern-Simons boundary layers

Green functions scattering method is generalized to consider mixing of electromagnetic polarizations after reflection from the plane boundary between different media and applied to derivation of the Casimir-Polder potential in systems with Chern-Simons plane boundary layers. The method is first applied to derive the Casimir-Polder potential of an anisotropic atom in the presence of a Chern-Simons plane boundary layer on a dielectric half-space. Then a general result for the Casimir-Polder potential of an anisotropic atom between two dielectric half-spaces with Chern-Simons plane parallel boundary layers is derived. The Casimir-Polder potential of an anisotropic atom between two Chern-Simons plane parallel layers in vacuum is expressed through special functions. Novel P-odd three-body vacuum effects are discovered and analyzed in the system of two Chern-Simons plane parallel layers and a neutral atom in its ground state between the layers. Remarkably, P-odd three-body vacuum effects arising due to 180 degree rotation of one of the Chern-Simons layers can be verified in experiments with neutral atoms having QED dipole interaction with an electromagnetic field.

Time-Domain Electromagnetic Leaky Waves

A causality preserving interpretation of the electromagnetic (EM) leaky-wave (LW) propagation in space and time is proposed for the first time. The Cagniard–deHoop (CdH) joint transform technique is applied for elucidating the relation between time-domain (TD) head waves (HWs), body waves (BWs), Cherenkov wave effects, and LWs. It is conjectured that the LW phenomenon in the TD is associated with a local maximum in the observed signal that occurs between the arrivals of the HW and BW constituents. A quantitative analysis that enables the space-time localization of the LW effect is performed theoretically and, then, illustrated via representative examples including the pulsed EM radiation from both a line source above a dielectric half-space, and narrow-slot antennas.

Complete Nonuniform Asymptotic Expansion of Sommerfeld Integral for Dielectric Half-Space

Generally, the Sommerfeld integral (SI) for a dielectric half-space is approximated based on the steepest descent method. A higher order approximation of the integral requires higher order derivatives of the integrand in the steepest descent path in the complex domain, whose explicit formulation may be cumbersome. Recently, a new finite-range integral representation of the SI has been proposed, whose integrand is written in terms of the SI for an impedance half-plane. Based on the known complete nonuniform asymptotic expansion of the SI for an impedance half-plane, the complete nonuniform asymptotic expansion can be analytically formulated for the dielectric half-space. Moreover, the completeness is mathematically proven such that the expansion satisfies the recurrence relation for the Wilcox expansion. The accuracy of the proposed expansion is numerically examined for several propagation scenarios. Furthermore, a numerical procedure is proposed to calculate the higher order terms of the expansion by partially using the impedance approximation for a large relative permittivity of the half-space.

Развитие и обобщение метода отражений в задачах электростатики и теплопроводности плоскослоистых сред

The method of mirror reflections of electrostatics for a point charge located next to a plane-layered medium consisting of a single film on a dielectric half-space is formulated. The method is generalized to the case of an arbitrary system of charges. The proposed approach is applied to mathematically similar problems of electrostatics and stationary heat conduction of plane-layered media. In particular, the problems of finding distributions of the electrostatic potential around a conducting sphere, an ellipsoid of revolution and a drop-shaped body located near the dielectric film on the dielectric half-space. It is shown how to apply the results obtained for electrostatic problems to similar problems of finding the temperature distribution of uniformly heated bodies of the same geometry located near a heat-conducting film in a heat-conducting half-space.

Development and generalization of the method of reflections in problems of electrostatics and thermal conductivity of plane-layered media

The method of mirror reflections of electrostatics for a point charge located next to a plane-layered medium consisting of a single film on a dielectric half-space is formulated. The method is generalized to the case of an arbitrary system of charges. The proposed approach is applied to mathematically similar problems of electrostatics and stationary heat conduction of plane-layered media. In particular, the problems of finding distributions of the electrostatic potential around a conducting sphere, an ellipsoid of revolution and a drop-shaped body located near the dielectric film on the dielectric half-space. It is shown how to apply the results obtained for electrostatic problems to similar problems of finding the temperature distribution of uniformly heated bodies of the same geometry located near a heat-conducting film in a heat-conducting half-space. Keywords: plane-layered medium, mirror reflection method, electrostatics, thermal conductivity.

Magnetic and fractional parametric control of Goos-Hänchen shifts in the anisotropic yttrium-iron-garnet film surrounded by isotropic fractal dielectric half-spaces

This article focuses on the controllability of reflected and transmitted Goos-Hänchen shifts for a planar anisotropic yttrium-iron-garnet film. The yttrium-iron-garnet film, being magneto-optical material, is magnetized along the z-direction. For richer control of the Goos-Hänchen shifts and the characteristics of reflectivity/transmitivity, the externally magnetized film is surrounded by isotropic fractal dielectric half-spaces. The tuning of Goos-Hänchen shifts from positive to negative and vice versa, has been obtained by varying the values of incidence frequency in the microwave regime, incidence angle, fractional dimensional parameter, external magnetic field, and slab thickness.

Analysis of Love waves propagation in a functionally graded porous piezoelectric composite structure

Propagation of Love waves in a composite structure, containing a functionally graded porous piezoelectric material layer over a dielectric elastic half space, is studied. The material properties gradually vary with the layer thickness. Constitutive equations for a functionally graded porous piezoelectric material layer are laid down and then their analytical solutions are derived by using the Wentzel-Kramers-Brillouin method. Variations in the mechanical properties and electrical properties are considered and dispersion equations are derived for both electrically short and open boundaries. The effects of porosity and grade coefficients on the phase velocity of the Love waves and on electro-mechanical coupling are discussed. Numerical computation of the phase velocity and electromechanical coupling factor is done for different levels of thickness of the layer and results, obtained, are validated by deriving earlier results as a special case of this study. This study finds application in making high-performance surface acoustic wave devices.

On the Complete Radiation Pattern of a Vertical Hertzian Dipole Above a Low-Loss Ground

The complete radiation field pattern of a vertical Hertzian dipole antenna on or above a lossless or low-loss dielectric half-space is studied using a rigorous Sommerfeld formalism. The reflected fields in the air above the interface and the subsurface fields transmitted into the dielectric are computed by numerical integration of the Sommerfeld integrals. Furthermore, to facilitate the physical interpretation of these results, a detailed asymptotic saddle-point integration method analysis is presented, which includes terms that vary in magnitude with the second power of the inverse distance from the dipole. It is shown that the second-order field constituents are dominant at the interface, where the first-order geometrical fields vanish. These second-order terms comprise an evanescent wave propagating along the interface in the upper half-space and a lateral wave, also known as the head wave, which propagates in the subsurface along the direction of the critical angle. The two waves only exist between two cones whose half-angles are equal to the critical angle, and their interference with the geometrical-optics fields determines the radiation pattern for elevation angles near the horizon. The far zone surface fields on either side of the interface comprise two second order waves that propagate along the interface, one with the phase velocity in the air, and the other with the phase velocity in the dielectric. Away from the interface, the leading field components vary with the first power of the inverse distance, which explains the sharp dip in the field pattern at the interface-a phenomenon known as the interface pattern extinction. Another distinctive phenomenon, observed in the subsurface field pattern, is the rippling that occurs in the angular range between the critical angle cone and the interface. The asymptotic analysis has shown that this pattern scalloping results from the interference of the lateral wave with the geometrical-optics spherical wave.

Green Functions Scattering in the Casimir Effect

We propose Green functions scattering method to obtain the Casimir–Polder potential between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure between two dielectric half-spaces separated by a vacuum slit is derived within the same method. The method is also applied to known conducting systems including graphene which are overviewed.

Superlens coupling to object and image: A secondary resonance mechanism to improve single-negative imaging of electromagnetic waves

Superlens slabs rely on the coherent superposition of multiply reflected evanescent waves to amplify and restore the fine details of an object at the image plane. If a superlens slab is placed in close proximity to a source object and image detector, similar interactions with these external components can introduce resonances outside of the superlens. In this work, we explore the role of external resonances on single-negative slab superlens performance by considering a complete electromagnetic imaging system containing a physical source object and image detector, each modeled as a planar dielectric half-space. In studying the transmission of spectral components that carry real power through this system, we find that resonances outside the lens can have a dramatic impact on single-negative superlens performance. In particular, we find that the resonances external to a μ-negative lens can be used to extend the imaging range beyond the extreme near field and maintain super-resolution even in the presence of loss.

Scattering by a Chiral Cylinder of Arbitrary Cross Section Above a Dielectric Half-Space

A simple numerical solution for electromagnetic scattering from a 2-D homogeneous chiral cylinder of arbitrary cross section placed above a dielectric half-space (DHS) is presented. A modified surface equivalence principle is used to obtain coupled electric field integral equations. For feasible application of method of moments, a perturbation method is used where a strip of finite width approximates the surface of the infinite half-space. The perturbed currents on the interface are expressed as a difference of the currents with the cylinder present and the exact solution (cylinder removed). The excitation vector now contains the reflected field from the DHS in addition to the incident field. Transverse magnetic (TM) and transverse electric (TE) excitations are treated. Computed results include perturbed currents on the dielectric interface and the scattered fields. Excellent agreement is observed for special cases available in the literature.

Scattering from an inhomogeneous dielectric cylinder partially buried in a dielectric half-space

A hybrid method is presented for computing the TM polarized plane wave scattered by an inhomogeneous penetrable cylinder embedded in the planar interface between two dielectric half-spaces. In this method, the infinite interface is represented by an unknown equivalent magnetic current, which is expressed in terms of the difference between the current with the cylinder present and the current of the known physical optics (PO) solution of the unperturbed (without cylinder) problem. Coupled integral equations for the equivalent surface electric and magnetic currents on the cylinder surface and the perturbed equivalent magnetic current on the finite section of the interface are obtained and solved by the Method of Moments (MoM). The half-space and the inhomogeneous cylinder configuration in this paper can be used in a wide range of settings.