Dielectric Bodies Research Articles

Simple, Method of Moments Solution for the Integral Equations for Multiple Dielectric Bodies of Arbitrary Shape in Time Domain

In this work, we present a straightforward and simple method of moments (MOM) solution procedure, with minimum mathematical manipulations, to solve the coupled integral equations for multiple, homogeneous and inhomogeneous, dielectric bodies of arbitrary shape directly in the time domain. The standard surface and volume integral equation formulations are used for homogeneous and inhomogeneous bodies, respectively. The numerical solution procedure does not involve a time-marching process as is usually adopted for time domain problems and seems to be one of the primary reasons for the late-time instabilities as a result of error accumulation. The present solution method is stable for a very long time as evidenced by several representative numerical examples presented for validation.

Method of characteristic modes

In recent years, the number of works on the method of characteristic modes and problems solved with its help has increased significantly, which indicates an awareness of its potential and, in connection with this, a growing interest in this approach. The attractiveness of this method lies in the fact that it provides a clear physical picture of the occurring phenomena and the ensuing opportunity to build on this basis methods for creating structures with the required parameters and combating undesirable phenomena. Unfortunately, in the Russian-speaking segment of applied electrodynamics, very few researchers are engaged in the development and application of the approach under consideration. The purpose of this work is to increase the interest of Russian-speaking researchers in the method of characteristic modes. A review of publications devoted to the method of characteristic modes, both early, fundamental and already classic, associated with the names of R.J. Garbacz and R.F. Harrington, and those which have appeared in recent years and offer generalizations of the method for various electrodynamic structures, has been carried out. This includes composite structures consisting of a set of metal and dielectric bodies of various configurations. In addition, variants of the method for antenna arrays of both infinite periodic and finite sizes have been considered. Issues related to modal tracking problems, orthogonal properties of characteristic modes and improving the convergence of solutions have been considered. Much attention is paid to works containing solutions to specific practical electrodynamic problems using the method of characteristic modes. The works have been shown, in which simple and effective approaches based on the method of characteristic modes are given for the design of a ship's HF antenna system, on-board aircraft antennas in the short-wave region, antennas placed on the platform of a battle tank, and the concept of designing an antenna for an electrically small-unmanned aerial vehicle has been presented. Options for solving the problem of reducing the mutual coupling of elements in antenna arrays have been shown. Attention is paid to MIMO antennas, antennas for smartphones, systems with specified radiation zeros, antennas using metasurfaces. According to the authors, the characteristic mode method, taking into account the increasing possibilities of its application, will make it possible to take the next step in the development, analysis or synthesis of new antenna structures that meet ever-increasing modern requirements.

Scattering of an Electromagnetic Wave by a Thin Perfectly Conducting Cylinder Located Inside a Dielectric Body

Scattering of an Electromagnetic Wave by a Thin Perfectly Conducting Cylinder Located Inside a Dielectric Body

Decreasing the memory of the discontinuous Galerkin volume integral equation method for scattering from inhomogeneous dielectric objects.

A memory-efficient implementation scheme for the discontinuous Galerkin volume integral equation method (DGVIE) using Schaubert-Wilton-Glisson (SWG) basis functions is proposed to analyze electromagnetic scattering from inhomogeneous dielectric objects. For this proposed scheme, almost no half-SWG basis functions are needed for the elements separating nonconformal meshes, while these half-SWG basis functions are indispensable for the conventional DGVIE-SWG method. This is realized by applying the divergence-free condition of the electric displacement vector explicitly for nonconformal meshes separating neighboring subdomains of an inhomogeneous dielectric body. Therefore, the number of unknowns of the conventional DGVIE method can be further reduced. As a result, the memory of the proposed DGVIE method is only about half of the conventional one for inhomogeneous dielectric problems. Meanwhile, the total solution time has been reduced by the use of the proposed scheme. Particularly, the proposed DGVIE-SWG method is efficient in memory usage not only for inhomogeneous dielectric cases with high contrast ratio but also for cases with relatively low contrast ratio.

A Semi-Explicit Solution of Scattering From Dielectric Bodies Using the Method of Moments

This work presents a novel closed-form expression based on the Method of Moments (MoM) for solving the scattering problem in piecewise homogeneous media. Using point-matching with pulse basis functions in MoM, we derive an expression represents the scattered field as an explicit function of the permittivity value of each homogeneous part. The coefficient matrix depends on the permittivity values in the MoM solution to the scattering problem. Therefore, it requires matrix inversion whenever these values change slightly. Here, we propose a new expression where the matrix coefficients are independent of the permittivity values of each homogeneous part. Accordingly, when the geometry does not change, we propose a semi-explicit procedure for updating the solution with less computational complexity. Although the proposed method can be used for all 2D and 3D problems, the formulation details are implemented for 2D problems, TM incidence. Based on this explicit form, we derive some simple approximate expressions for three specific cases of permittivity perturbations. Our proposed solution is appropriate for microwave imaging, particularly when a priori information is utilized.

Application of the Generalized Method of Eigenoscillations to the Solution of the Problems of Scattering on Nanostructures

We study the problem of scattering of electromagnetic waves on small-sized dielectric bodies by using the generalized method of eigenoscillations. The inhomogeneous problem is formulated on the basis of a version of the generalized method of eigenoscillations in which the dielectric permittivity plays the role of an eigenvalue. The corresponding homogeneous problem is solved with the use of Debye potentials. We obtain a system of linear algebraic equations for the unknown expansion coefficients. For the solution of this system, we use the method of successive approximations. The results of the performed numerical analyses confirm the efficiency of the proposed method.

Volume integral operators in electromagnetic scattering by homogeneous anisotropic dielectric bodies

Volume integral operators in electromagnetic scattering by homogeneous anisotropic dielectric bodies

A Study on Characteristic Mode Equations of Radiation Problems Contrasted with Scattering Problems for Dielectric Bodies

This paper is concerned with the extractions of electromagnetic characteristic modes (CMs) for lossless dielectric bodies, for which spurious modes are prone to generate using the traditional definition of CMs based on the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) equations. It is found that the impedance matrix of PMCHWT equations cannot distinguish (i) which domain is the dielectric body and which domain is the background and (ii) from which domain the excitation source was applied. If the system is taken as a scattering problem, the spurious modes are solutions to a reverse media problem, i.e., exchanging the media of the dielectric body and the background space. However, if the system is taken as a radiation problem, no appropriate CMs that meet the specified boundary conditions are obtained. These phenomena indicate that CMs developed from scattering systems are not suitable for radiation systems. To clarify the issue, four cases with reverse media and with excitation sources in either domain are examined. The four cases are distinct in essence, but the PMCHWT equations cannot distinguish them. As a result, definitions of CMs for the four cases should be given along with their specific boundary conditions. Especially, the CMs for the radiation problems we consider here show that the excitation source inside the material object should be properly defined in order to be distinguished from scattering problems.

Uncertainty EM Scattering Prediction for Inhomogeneous Dielectric Bodies of Revolution

A perturbed volumetric integral equation is fabricated to predict the uncertain scattering characteristics for the in-homogeneous dielectric bodies of revolution (BoRs) targets. The transverse surface of the body of revolution is discretized in terms of the rectangular and triangular basis functions. In this way, all the unknowns are assigned to the electric flux density and the governing equation can be solved mode by mode. Both the geometrical and dielectric uncertainties are taken into consideration for EM scattering characteristics. On one hand, the geometrical shape uncertainty is described with the nonuniform rational B-spline surface by using several independent random variables. On the other hand, the dielectric uncertainty is represented by the perturbed permittivity. Thus, the volume integral equation is reconstructed by the perturbed electric flux density. Both the mean value and variance of the radar cross Section can be derived to account for the geometrical and dielectric uncertainties. Numerical results are given to show that the calculation efficiency of the proposed method is higher than that of the traditional Monte Carlo method.

Electromagnetic scattering analysis of large-area vegetation based on multilevel periodic fast multipole algorithm

The electromagnetic scattering of ground objects always has important application value in remote sensing, detection, anti-stealth and other fields. Among them, vegetation has received extensive attention due to its wide variety and uneven distribution. With the expansion of the scene, the theoretical model of vegetation electromagnetic scattering becomes more and more complex, the calculation amount increases sharply, and the solution accuracy decreases. It is urgent to establish a full-wave simulation method that can accurately and fast analyze the electromagnetic scattering of vegetation. To solve this problem, this paper establishes a hybrid integral equation for solving the objects with thin dielectric sheets (TDS) and dielectric bodies, and calculates the electromagnetic scattering of large-area vegetation by simulating an infinite periodic scene. In addition, the periodic Green's function (PGF) is expanded by the multilevel periodic fast multipole algorithm (MLP-FMA), which further improves the computational efficiency. The method proposed in this paper provides model and theoretical support for the electromagnetic scattering simulation of actual large-scale vegetation scenes.

Geometrically driven aggregation of unsymmetrical dielectric particles.

Understanding electrostatic interactions among dielectric bodies in the atmosphere and aerosols is central to controlling their aggregation. Polarization effects, which are frequently ignored, are crucial to determine interactions when geometrical anisotropies are present due to surface-induced charge segregation. Here, we adopt a direct integral formulation that accounts for the problem of charged dielectric bodies immersed in a continuum media to explore particle aggregation via geometrical tuning. We show that by breaking the structural symmetry and modifying the close-contact surface between particles of equal charge, it is possible to obtain attractive regimes at short and long distances. We evaluate the electrostatic forces and energy of a set of dimers and trimers composed of spheres, oblates, and prolates in a vacuum, where no counter-ions are present, to construct a phase diagram with the conditions required to form stable aggregates as a function of the geometrical anisotropy. We found that it is possible to direct the aggregation (or dispersion) of two and three positive dielectric particles by adjusting their geometry and controlling the contact surface among them. Our results give insight into a way to control the aggregation of dielectric systems and offer a prospect for directing the assembly of complex particle structures.

Application of the method of continued boundary conditions to the solution of the problems of wave diffraction on various types of scatterers with complex structure

The article considers the application of the method of continued boundary conditions to the two-dimensional problem of diffraction of electromagnetic waves by a dielectric body with a cross section of complex geometry and to the problem of diffraction by a Janus sphere in the form of a permeable sphere partially covered by an absolutely soft or an absolutely rigid spherical screen. The results of calculating the scattering pattern for a large set of bodies of different geometry, including fractal-like scatterers, are obtained. It is illustrated that in the case of a smooth body boundary, the algorithm based on the Fredholm equations of the 1st kind makes it possible to obtain results with greater accuracy than for equations of the 2nd kind. The correctness of the method was confirmed by verifying the implementation of the optical theorem for various bodies and by comparing with the results of calculations obtained by other methods.

Super-Operator Linear Equations and Their Applications to Quantum Antennas and Quantum Light Scattering

In this paper, we develop a resolvent method for super-operator equations with applications in quantum optics. Our approach is based on the novel concept of a linear super-operator acting on the Hilbert subspace of vector or scalar linear operators satisfying physically reasonable commutation relations. The super-operator equations for the electromagnetic (EM) field operators are formulated for the problems of quantum antenna emission and quantum light scattering by a dielectric body. The general solution of super-operator equation is presented in terms of the classical resolvent. In contrast to the classical case, it includes the ancillary components associated with the quantum noise even in the absence of absorption. The reason for this lies in the energy exchange between different spatial regions with various bases for the field presentation (which looks like losses or gain from the point of view of the correspondent region). A number of examples (a two-element dipole antenna, a plane dielectric layer, and a dielectric cylinder with a circular cross section) which demonstrate the physical mechanism of the appearance of noise are considered. It is shown that antenna emission or scattering transforms the coherent properties of quantum light. This leads to a new way of controlling coherence in a direction-dependent manner, a feature that can be useful in various applications of quantum technologies, including quantum radars and lidars, and quantum antennas.

Fast Computation of Electromagnetic Scattering From Dielectric Objects Using Quadrilateral Piecewise Sinusoidal Basis and Characteristic Basis Function Method

A method of moments (MoM)-based procedure is developed to calculate the scattering from homogeneous dielectric bodies. The technique uses quadrilaterals for the approximation of geometry and piecewise sinusoidal (PS) basis functions for the approximation of surface currents. The notable advantage of the PS basis is its radiated fields can be expressed in closed-form. The proposed approach therefore circumvents the need to use Green’s function in formulating the integral equations. Combined with a simple testing procedure, the matrix filling time is reduced and the concern of singularity is removed. To further reduce the computational complexity and enhance the performance, a characteristic basis function method (CBFM) is implemented and embellished with a new characteristic basis function (CBF) generation strategy. Specifically, a cubical surface bounding the entire target is first specified and discretized. A set of auxiliary sources are then defined in a manner similar to that done for a scattering body. These auxiliary sources are defined once and shared by different blocks. In comparison to the traditional plane wave spectrum (PWS) method, the CBFs generated by the new approach are valid not only for plane wave excitations but also for localized excitations. Numerical results are provided to validate the efficacy of the proposed algorithm.

Modified Poisson–Boltzmann equations and macroscopic forces in inhomogeneous ionic fluids

We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary reference fluid system. We obtain a modified Poisson–Boltzmann (PB) equation as the Euler–Lagrange equation for the obtained functional. Applying Noether’s theorem to this functional, we derive a general mean-field expression for the stress tensor consistent with the respective modified PB equation. We derive a general expression for the macroscopic force acting on the dielectric or conductive body immersed in an ionic fluid. In particular, we derive a general mean-field expression for the disjoining pressure of an ionic fluid in a slit pore. We apply the developed formalism to describe three ionic fluid models of practical importance: nonpolarizable models (including the well-known PB and Poisson–Fermi equations), polarizable models (ions carry nonzero permanent dipole or static polarizability), and models of ion-dipole mixtures (including the well-known PB–Langevin equation). For these models, we obtain modified PB equations and respective stress tensors, which could be valuable for different applications, where it is necessary to estimate the macroscopic forces acting on the dielectric or conductive bodies (electrodes, colloids, membranes, etc) together with the local electrostatic potential (field) and ionic concentrations.

Numerical Method for Recovering Permittivity of an Inhomogeneous Dielectric Body Placed in a Semi-Infinite Rectangular Waveguide

Numerical Method for Recovering Permittivity of an Inhomogeneous Dielectric Body Placed in a Semi-Infinite Rectangular Waveguide

3-D-Printed Wideband High-Efficiency Dual-Frequency Antenna for Vehicular Communications

A three-dimensional (3-D)-printed dual-fed dual-frequency dielectric antenna is investigated for vehicular communications. It combines a dielectric resonator (DR) antenna (DRA) and a dielectric lens antenna (DLA) for the low and high frequency bands, respectively. Both of the antenna parts share the same dielectric body that has three different effective dielectric constants. The DRA is excited by a vertical conducting adhesive strip on its sidewall, whereas the DLA is fed by a separate embedded slot-coupled cylindrical DRA. To verify the idea, a dual-frequency dielectric antenna operating at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -bands is designed and fabricated with a 3-D printer. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters, radiation patterns, antenna gains, and antenna efficiencies of the two antenna parts are measured, and reasonable agreement between the measured and simulated results is found. The prototype has wide measured <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -band 10-dB impedance bandwidths of 40.2% and 19.5%, respectively. Also, its measured isolation between the two ports is desirably over 40 dB across the two bands. The measured peak antenna gains are given by 5.8 and 12.0 dBi in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -bands, which are suitable for short-distance vehicle-to-basestation and long-distance vehicle-to-satellite communications, respectively.

Experimental demonstration of deeply subwavelength dielectric sensing with epsilon-near-zero (ENZ) waveguides

In this Letter, an all metallic sensor based on ε-near-zero (ENZ) metamaterials is studied both numerically and experimentally when working at microwave frequencies. To emulate an ENZ medium, a sensor is made by using a narrow hollow rectangular waveguide, working near the cutoff frequency of its fundamental TE10 mode. The performance of the sensor is systematically evaluated by placing subwavelength dielectric analytes (with different sizes and relative permittivities) within the ENZ waveguide and moving them along the propagation and transversal axes. It is experimentally demonstrated how this ENZ sensor is able to detect deeply subwavelength dielectric bodies of sizes up to 0.04λ and height 5 × 10−3 λ with high sensitivities (and the figure of merit) up to 0.05 1/RIU (∼0.6 GHz−1) and 0.6 1/RIU when considering the sensor working as a frequency- or amplitude-shift-based device, respectively.

Bandpass Filter and Diplexer Based on Dual-Mode Dielectric Filled Waveguide Resonators

This paper presents the designs of a bandpass filter (BPF) and a diplexer based on the TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">210</sub> mode and the TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">120</sub> mode of the dielectric filled waveguide resonators (DFWRs). The DFWR is designed by integrating a dielectric main body and a printed circuit board (PCB) cover. The PCB cover is electrically connected with the top surface of the dielectric body. For each mode, metallized blind holes can be set at its maximum electric-field points to excite or extract it and the other mode will not be influenced. Microstrip lines on the PCB are utilized to connect different pairs of the metallized blind holes to form the internal and external coupling structures. For verification, a BPF and a diplexer are designed, fabricated and measured based on the DFWRs. In measurement, the BPF is with a frequency band of 2.515 GHz - 2.675 GHz, an insertion loss of 0.6 dB, and a return loss of 20 dB. The two frequency bands of the proposed diplexer are 3.3 GHz - 3.4 GHz and 3.7 GHz - 3.8 GHz. For the two frequency bands, the measured insertion losses are 0.9 dB/0.85 dB and the isolations are better than 40 dB/50 dB.

Rigorous treatment of pairwise and many-body electrostatic interactions among dielectric spheres at the Debye\u2013H\xfcckel level

Electrostatic interactions among colloidal particles are often described using the venerable (two-particle) Derjaguin–Landau–Verwey–Overbeek (DLVO) approximation and its various modifications. However, until the recent development of a many-body theory exact at the Debye–Hückel level (Yu in Phys Rev E 102:052404, 2020), it was difficult to assess the errors of such approximations and impossible to assess the role of many-body effects. By applying the exact Debye–Hückel level theory, we quantify the errors inherent to DLVO and the additional errors associated with replacing many-particle interactions by the sum of pairwise interactions (even when the latter are calculated exactly). In particular, we show that: (1) the DLVO approximation does not provide sufficient accuracy at shorter distances, especially when there is an asymmetry in charges and/or sizes of interacting dielectric spheres; (2) the pairwise approximation leads to significant errors at shorter distances and at large and moderate Debye lengths and also gets worse with increasing asymmetry in the size of the spheres or magnitude or placement of the charges. We also demonstrate that asymmetric dielectric screening, i.e., the enhanced repulsion between charged dielectric bodies immersed in media with high dielectric constant, is preserved in the presence of free ions in the medium.Graphic abstract