Dielectric Bodies Research Articles

A well-posed surface currents and charges system for electromagnetism in dielectric media

The free space Maxwell dielectric problem can be reduced to a system of surface integral equations (SIE). A numerical formulation for the Maxwell dielectric problem using an SIE system presents two key advantages: first, the radiation condition at infinity is exactly satisfied, and second, there is no need to artificially define a truncated domain. Consequently, these SIE systems have generated much interest in physics, electrical engineering, and mathematics, and many SIE formulations have been proposed over time. In this article we introduce a new SIE formulation which is in the desirable operator form identity plus compact, is well-posed, and remains well-conditioned as the frequency tends to zero. The unknowns in the formulation are three dimensional vector fields on the boundary of the dielectric body. The SIE studied in this paper is derived from a formulation developed in earlier work by some of the authors~\cite{ganesh2014all}. Our initial formulation utilized linear constraints to obtain a uniquely solvable system for all frequencies. The new SIE introduced and analyzed in this article combines the integral equations from \cite{ganesh2014all} with new constraints. We show that the new system is in the operator form identity plus compact in a particular functional space, and we prove well-posedness at all frequencies and low-frequency stability of the new SIE.

Solution of the Problem of Diffraction by a Body of Revolution Located in a Dielectric Layer

Two methods for solving the problem of diffraction of a plane wave by a dielectric body of revolution located in a homogeneous dielectric layer are proposed. The methods are compared with each other using as an example the solution of the problem of scattering of a plane wave by a homogeneous spheroid and a circular cylinder of finite dimensions located in the layer. The results of calculations of the scattering diagram for the case of diffraction by a finite circular cylinder that is immersed into the layer and has variable material characteristics are presented. The dependences of the scattering diagram on the wavelength for plasmon particles located in a layered medium are obtained.

Self-stress on a dielectric ball and Casimir–Polder forces

It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir–Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt (2018), who find that the energy or self-stress of a homogeneous dielectric ball with permittivity ε begins with a term of order ε−1. Here we demonstrate that this cannot be correct. The only possible origin of a term linear in ε−1 lies in the bulk energy, that energy which would be present if either the material of the body, or of its surroundings, filled all space. Since Avni and Leonhardt correctly subtract the bulk terms, the linear term they find likely arises from their omission of an integral over the transverse stress tensor.

Two Solution Techniques for the Problem of Diffraction of a Plane Wave by a Revolution Body Located in a Dielectric Half-Space

Two techniques for calculation of the problem of diffraction of a plane wave by a dielectric revolution body located in a homogeneous dielectric half-space are suggested. The case, in which the permittivity of the medium inside the body is the coordinate function independent of the angular coordinate in the cylindrical coordinate system, is considered. When the first technique is used (in the case of a homogeneous medium of the body), the discrepancy of the boundary condition on the contour of the axial section of the body is constructed. Two methods are compared using the example of the problem of the plane wave scattering by a homogeneous sphere and circular cylinder of finite dimensions that are located in a half-space. The results of calculation of the field scattering pattern are presented for the case of diffraction by a finite circular cylinder having variable material characteristics.

Thermoelectric effect and temperature-gradient-driven electrokinetic flow of electrolyte solutions in charged nanocapillaries

A systematic theoretical study of thermoelectric effect and temperature-gradient-driven electrokinetic flow of electrolyte solutions in charged nanocapillaries is presented. The study is based on a semianalytical model developed by simultaneously solving the nonisothermal Poisson-Nernst-Planck-Navier-Stokes equations with the lubrication theory. Particularly, this paper clarifies the interplay and relative importance of the thermoelectric mechanisms due to (a) the convective transport of ions caused by the fluid flow, (b) the dependence of ion electrophoretic mobility on temperature, (c) the difference in the intrinsic Soret coefficients of cation and anion. Additionally, synergy conditions for the three thermoelectric mechanisms to fully cooperate are proposed for thermo-phobic/philic electrolytes. The temperature-gradient-driven electrokinetic flow is shown to be a nearly unidirectional flow whose axial velocity profiles vary with the axial location. Also, the flow can be regarded as a consequence of the counteraction or cooperation between a thermoelectric-field-driven electroosmotic flow and a thermo-osmotic flow driven by the osmotic pressure gradient and dielectric body force. Moreover, the Seebeck coefficient and the fluid average velocity are demonstrated to be affected by electrolyte-related parameters. The results are beneficial for understanding the temperature-gradient-driven electrokinetic transport in nanocapillaries and also serve as theoretical foundation for the design of low-grade waste heat recovery devices and thermoosmotic pumps.

Theory of characteristic modes for lossy structures: Formulation and interpretation of eigenvalues

AbstractVolume integral equation (VIE) and surface integral equation (SIE) based characteristic mode (CM) formulations are investigated in the case of lossy objects. Imperfectly conducting metallic structures modelled with an impedance boundary condition and lossy dielectric bodies are considered. Two types of CM formulations are studied. In the first one, the generalized eigenvalue equation is expressed in terms of the Hermitian parts of the integral operators. In the second one, the weighting operator of the eigenvalue equation is defined so that the eigenvectors form a weighted orthogonal set, weighted with respect to radiated power. The first approach gives real eigensolutions and is found to lead to clustering of the eigenvalues as losses are increased. From these solutions it is difficult to separate contributions of radiated, reactive, and dissipated power. This separation appears naturally in the second approach that gives complex eigensolutions. As applications including lossy materials, CM analyses of a graphene sheet and a plasmonic nanoparticle are presented.

An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects

Fast, high-accuracy algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of Müller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges and points. Several numerical examples are provided to demonstrate the efficiency and accuracy of the aforementioned algorithm in various geometries.

Absorbing Two-Dimensionally Periodic Structures on New Plasmonic Materials

We study theoretically two-dimensionally periodic gratings of plasmonic strips on substrates which contain dielectric and plasmonic layers. The developed electrodynamic model is based on solving the vector integro-differential equation of diffraction by three-dimensional dielectric bodies by the Galerkin method. It is shown that at the resonant frequencies of the surface plasmon polariton, these structures absorb almost 100% of the energy of the incident radiation in a wide wavelength range. The use of nonmetal plasmonic materials makes it possible to create a wideband absorber of infrared waves.

On the performance of an ENZ-based sensor using transmission line theory and effective medium approach

In this paper we perform an in-depth theoretical study of a sensing platform based on epsilon-near-zero (ENZ) metamaterials. The structure proposed for sensing is a narrow metallic waveguide channel. An equivalent circuit model is rigorously deduced using transmission line theory, considering several configurations for a dielectric body (analyte sample) inserted within the narrow channel, showing good agreement with results obtained from numerical simulations. The transmission line model is able to reproduce even the most peculiar details of the sensing platform response. Its performance is then evaluated by varying systematically the size, position and permittivity of the analyte, and height of the ENZ channel. It is shown that the sensor is capable of detecting changes in the permittivity/refractive index or position even with deeply subwavelength analyte sizes (∼0.05λ0), giving a sensitivity up to 0.03 m/RIU and a figure of Merit ∼25. The effective medium approach is evaluated by treating the inhomogeneous cross-section of the analyte as a transmission line filled with a homogeneous material.

Coupling of Characteristic Modes on PEC and Lossy Dielectric Structures

The surface integral equation-based theory of characteristic modes (TCM) is presented for structures including perfect electric conductors (PECs) and lossy dielectric bodies. The formulation is a combination of the classical TCM formulation for PEC structures and a recently developed one for penetrable bodies. The potential of the methodology for practical antenna design problems is demonstrated by studying the coupling of the modes on a PEC plate (antenna ground plane) and an adjacent highly lossy dielectric block (user’s hand). This analysis reveals the existence of different types of modes having weak or strong interactions between PEC and dielectric parts.

Metal–Organic Framework Breathing in the Electric Field: A Theoretical Study

In this manuscript, we study the electrically induced breathing of a metal–organic framework (MOF) within a 2D lattice model. The Helmholtz free energy of the MOF in the electric field consists of two parts: the electrostatic energy of the dielectric body in the external electric field and the elastic energy of the framework. The first contribution is calculated from the first principles of statistical mechanics with an account of MOF symmetry. By minimizing the obtained free energy and solving the resulting system of equations, we obtain the local electric field and the parameter of the unit cell (angle α). The paper also studies the cross-sectional area of the unit cell and the polarization as functions of the external electric field. We obtain the hysteresis in the region of the structural transition of the framework. Our results are in qualitative agreement with the literature data of the molecular dynamics simulation of MIL-53(Cr).

A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω→0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.

Ambipolar SB-FinFETs: A New Path to Ultra-Compact Sub-10 nm Logic Circuits

Ultracompact sub-10-nm logic gates based on ambipolar characteristics of Schottky-barrier (SB) FinFETs and gate workfunction engineering (WFE) approach are introduced. Novel logic gate designs are proposed using WFE, whereby adjustment of workfunction in the contacts as well as two independently biased FinFET gates leads to an unprecedented degree of freedom for logic functionality that has not been explored before. The use of SB contacts, along with the high-k gate dielectric and ultrathin body, bestows a high-degree of short-channel immunity to the SB-FinFETs with ambipolar current–voltage characteristics down to 5 nm. The unique trait of the proposed novel logic gates is to lower CMOS transistor count by 50% and hence reduce overall area and power dissipation significantly. To illustrate this potential, an entirely novel conjugate (n/p channel) CMOS pass-gate transistor that can function as a two-transistor (2T) XOR and minimalist 2T NAND/NOR gates is designed and verified with TCAD simulations. Depending on the gate designed, TCAD simulations indicate that judicious choice of gate workfunctions between 3.7 and 5.2 eV can lead to CMOS logic gates with a power–delay product (PDP) at ${5}\times {10}^{-{18}}$ J level with immunity to ±0.1-eV workfunction variations. It is shown that WFE in independent-gate SB-FinFETs can lead to ultracompact logic circuits with 50% reduction in area and up to 10 times reduction in power, without significant degradation to overall PDP performance due to slower switching response compared with the conventional designs with p-n junction FinFET counterparts.

Решение задачи дифракции на теле вращения, расположенном в диэлектрическом слое

Two methods for solving the problem of diffraction of the plane wave by the dielectric body of revolution located in the homogeneous dielectric layer are proposed. Two methods are compared using the example of the scattering of the plane wave by the homogeneous spheroid and the circular cylinder of finite dimensions located in the layer. The results of calculating the pattern for the case of diffraction by the finite circular cylinder which is immersed in the layer and has variable material characteristics are presented. The wavelength dependences of the pattern for plasmon particles located in the layered medium are obtained.

A Wideband Strongly Coupled Magnetic Resonance Wireless Power Transfer System and Its Circuit Analysis

Conventional strongly coupled magnetic resonance (SCMR) wireless power transfer (WPT) systems have high quality factor ( $Q$ ), leading to limited system bandwidths. In practical applications, especially in human-involved environments, the resonant frequency of SCMR resonators will shift due to the effect of highly dielectric human body. In this letter, a wideband four-coil SCMR WPT system is proposed by improving the coupling between the tx/rx coil and their corresponding resonators. The bandwidth is increased by over 100% compared to a conventional system without sacrificing the efficiency much. The wideband feature is demonstrated by both simulation and measurement. It is analyzed physically and by using an equivalent circuit analysis.

Perturbation Theory in the Problem of Light Scattering by a Dielectric Body

A modified Born approximation suitable for the problem of electromagnetic wave scattering by a dielectric body is constructed. A system of integral equations including exact boundary conditions at the surface is derived. It is shown that a modified series converges to the known analytical solution for the problem of a wave incident normally on a cylinder. The reason for the inapplicability of the quantum-mechanical Born approximation in optics is discussed.

Casimir self-stress in a dielectric sphere

The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric properties embedded in arbitrary homogeneous backgrounds, assuming only that both materials are isotropic and dispersionless. Our results agree with known special cases; most notably we reproduce the prediction of Boyer and Schwinger et al. of a repulsive Casimir force of a perfectly reflecting shell. Our results disagree with the literature in the dilute limit. We argue that the Casimir self-stress cannot be regarded as due to pair-wise Casimir–Polder interactions, but rather due to reflections of virtual electromagnetic waves.

Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of its permittivity. This is accomplished by introducing an auxiliary eigenvalue problem, based on a volume integral operator. With this modal basis the expansion coefficients of the scattered field are simple rational functions of the permittivity of the scatterer. We show, by studying the electromagnetic scattering from a sphere and a cylinder of dimensions comparable to the incident wavelength, that only a moderate number of modes is needed to accurately describe the scattered far field. This method can be used to investigate resonant scattering phenomena, including plasmonic and photonic resonances, and to design the permittivity of the object to pursue a prescribed tailoring of the scattered field. Moreover, the presented modal expansion is computationally advantageous compared to direct solution of the volume integral equation when the scattered field has to be computed for many different values of the dielectric permittivity, given the size and shape of the dielectric body.

Internal Natural Resonances Prediction Through the Theory of Characteristic Modes

AbstractSome aspects in the interpretation of the resonances provided by the theory of characteristic modes for dielectric bodies are analyzed. The analysis has been performed analytically based on the Poggio‐Miller‐Chang‐Harrington‐Wu‐Tsai formulation on a canonical problem, the infinite dielectric circular cylinder. First, natural resonances and characteristic mode resonances are presented and compared. It has been observed that characteristic mode resonances are in general near to internal natural resonances but not to external ones. It is also demonstrated that characteristic resonances become closer to internal natural ones as the relative permittivity of the dielectric cylinder is increased.

The FIT-MoM Hybrid Method for Analysis of Electromagnetic Scattering by Dielectric Bodies of Revolution

In this paper, the finite-integration technique (FIT) is hybridized with the method-of-moments (MoM) for the case of electromagnetic scattering by dielectric bodies of revolution (BoRs). A frequency-domain FIT is used to account for the inhomogeneous dielectric region, while the MoM is used to model the outer environment by means of dyadic Green’s functions. The assumption about the rotational symmetry of the analyzed object allows for the application of usual decoupling of azimuthal modes, thus reducing the original 3-D problem to a number of 2-D cases. This in turn results in much smaller linear equation sets. Moreover, for nonzero modes, we use the possibility to further reduce the number of unknowns by eliminating azimuthal field components from the final equations.