Perfect Electric Conductor Boundary Research Articles

Thin Dielectric Sheet Approximation-Based Characteristic Mode Formulations for Lossless Dielectric Coated Conducting Bodies

The thin dielectric sheet (TDS) approximation-based theory of characteristic modes (TCM) is formulated for lossless thin dielectric-coated conducting bodies. The proposed formulations are derived from the TDS-electric, magnetic, and combined field integral operators (TDS-EFIO, TDS-MFIO, and TDS-CFIO). Similar to the cases of perfect electric conductor (PEC) and impedance surface, the TDS-CFIO-based formulation can avoid modes corruption by spurious solutions at the internal resonant frequencies of the PEC cavity filled with the material of the background. Due to the utilization of TDS approximation and PEC boundary conditions, the eigencurrents are expressed only by electric currents on the surface of PEC. Therefore, the proposed formulations are more efficient than the conventional formulations based on the surface integral operator (SIO) or volume-surface integral operator (VSIO). The coating thickness of TDS approximation is recommended to be less than one tenth of a wavelength in the dielectric for accurate analysis of characteristic mode (CM). Several numerical examples are given to validate the proposed formulations.

Highly efficient wavefront control based on extremely anisotropic materials

In this paper, a new strategy to design phase gradient metasurfaces (PGMs) are proposed. Using this way, we can achieve highly efficient control of the electromagnetic wavefronts. Specifically, we design reflection-type PGMs formed by an extremely anisotropic medium and a perfect electric conductor boundary. Instead of using refractive index distributions of materials to control the phases, we use a uniform anisotropic medium to control the reflection phases by changing the shape of the boundary. Using this strategy, three devices of the reflection focusing lens, the generator of the quasi airy beam and the PGMs have been realized, which show excellent performance in wavefront control. Our method is also suitable for the design of transmission-type metasurfaces and other wavefront transformations, which provides a novel approach for wave manipulation.

Higher-order accurate finite-difference simulation for tunnel propagation modeling

PurposeThis paper aims to improve the computational efficiency of higher-order accurate Noye–Hayman [NH (9,9)] implicit finite difference scheme for the solution of electromagnetic scattering problems in tunnel environments.Design/methodology/approachThe proposed method consists of two major steps: First, the higher-order NH (9,9) scheme is numerically discretized using the finite-difference method. The second step is to use an algorithm based on hierarchical interpolative factorization (HIF) to accelerate the solution of this scheme.FindingsIt is observed that the simulation results obtained from the numerical tests illustrate very high accuracy of the NH (9,9) method in typical tunnel environments. HIF algorithm makes the NH (9,9) method computationally efficient for two-dimensional (2D) or three-dimensional (3D) problems. The proposed method could help in reducing the computational cost of the NH (9,9) method very close to O(n) usual O(n3) for a full matrix.Research limitations/implicationsFor simplicity, in this study, perfect electric conductor boundary conditions are considered. Future research may also include the utilization of meteorological techniques, including the effects of backward traveling waves, and make comparisons with the experimental data.Originality/valueThis study is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

FDTD Schemes for Maxwell’s Equations with Embedded Perfect Electric Conductors Based on the Correction Function Method

In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell’s equations with embedded perfect electric conductor boundary conditions. The CFM uses a minimization procedure to compute a correction to a given FD scheme in the vicinity of the embedded boundary to retain its order. The minimization problem associated with CFM approaches is analyzed in the context of Maxwell’s equations with embedded boundaries. In order to obtain a well-posed minimization problem, we propose fictitious interfaces to fulfill the lack of information, namely the surface current and charge density, on the embedded boundary. We introduce CFM-FDTD schemes based on the well-known Yee scheme and a fourth-order staggered FDTD scheme. We investigate the stability of these CFM-FDTD schemes using long time simulations. Convergence studies are performed in 2-D for various geometries of the embedded boundary. CFM-FDTD schemes have shown high-order convergence.

Investigation of corner states in second-order photonic topological insulator.

Recently, higher-order topological insulators have been investigated as a novel topological phase of matter that obey an extended topological bulk-boundary correspondence principle. In this paper, we study the influence of BNN interaction on photonic higher-order corner states. We find both next-nearest-neighbor (NNN) hopping and perfect electric conductor (PEC) boundaries can solely result in two kinds of corner states which are quite different from the traditional "zero-energy" state. To demonstrate this intuitively, we design a novel all-dielectric structure that can effectively shield the influence of NNN couplings while remain the effect of PEC boundaries, so that we can distinguish the contributions from NNN hopping and PEC boundaries. In addition, we also investigate the total contribution on corner states when NNN couplings and PEC boundaries coexist, and some interesting features are revealed. These findings may expand our understanding of the high-order corner modes in a more general framework.

A 2D Slotted Rod Type PhC Cavity Inertial Sensor Design for Impact Sensing

A tunable 2D rod type Si Photonic Crystal cavity based impact sensing configuration is proposed and numerically analyzed. The cavity is sandwiched by perfect electric conductor (PEC) boundaries in order to provide out-of-plane light confinement. An on-purpose air slot is introduced between the Si rods and top PEC plate moving the light confinement into the slotted region and making the cavity highly responsive to the displacement of top PEC boundary. Optomechanical coupling strength is calculated to be on the order of 300 GHz/nm. Proposed light confinement inside the slot shows similar characteristics to slot waveguiding phenomenon and offers valuable opportunities for mechanical sensing applications. For a practical approach, PEC boundaries are replaced by Gold plates and the potential of the structure as an inertial sensor is investigated with a specific focus on impact sensing applications to be used in automotive security systems. Numerical analyses indicate that the device, whose sensing area is only $106.6~\mu $ m2, has a response time of $16.6~\mu \text{s}$ asserting that the proposed sensor can sense the presence of an impact faster than several commercially available ones, in a much more compact form.

A Unidirectional TM-Wave Cloak With Full Parameters

Unidirectional cloaks or carpet cloaks have become an essential branch of invisibility cloaks due to non-extreme parameters that are relatively easy for realization and potential applications. So far, a unidirectional cloak for transverse electric (TE) polarized wave has been successfully realized to hide an object in the air along a single direction with almost ideal performance. However, a practical method to achieve a unidirectional cloak for transverse magnetic (TM) polarization is still missing. In this paper, we successfully have designed, fabricated, and measured a full-parameter unidirectional TM-wave cloak in free space. In comparison to the previously-realized TE-wave counterpart, our cloak uses a perfect electric conductor boundary to obey the free-space symmetry condition of the TM incident wave and is therefore much more convenient to fabricate. The cloaking performance of the fabricated sample has been demonstrated via both full-wave numerical simulation and near-field measurement.

Efficient schemes for Maxwell's equations with PEC boundary condition

High-order compact discretization has been successfully applied to Maxwell's equations with periodic boundary conditions. However, the discretization cannot be applied to Maxwell's equations with perfect electric conductor boundary condition directly since the stencil involves the exterior nodal values of the electric and magnetic fields at/near the boundary. Combining the perfect electric conductor boundary condition with Maxwell's equations, we establish a relationship between the interior and exterior nodal values. The given relationship ensures the stability and accuracy of the high-order compact discretization. Two efficient splitting schemes are developed for Maxwell's equations. Numerical results show the good performance of the proposed schemes.

A Fundamental LOD-FDTD Method in Cylindrical Coordinates

An efficient implicit finite-difference time-domain (FDTD) algorithm in cylindrical coordinates is developed on the basis of a fundamental locally 1-D scheme. The Sherman–Morrison formula is introduced to treat a cyclic matrix and the image theory is utilized to impose the perfect electric conductor boundary condition. The effectiveness of the present method is investigated through the analysis of a metal disc-type terahertz surface wave splitter. The computation time is found to be reduced to less than half that of the explicit FDTD method, while maintaining a comparable accuracy.

Implementation of PEC boundary condition for Laguerre-RPIM meshless method with novel uniform nodal distribution

The implementation of perfect electric conductor (PEC) boundary condition for meshless radial point interpolation method (RPIM) with the weighted decaying Laguerre polynomial (WLP) is investigated. A novel uniform nodal placement is proposed and the number of H-nodes reduces to about a half of that for the conventional scheme. There are only E-nodes scattered on the PEC boundary. The E-node and H-node have the same scale of support domain nodes. The image theory is adopted to update the implicit electric equations on the PEC boundary. This scheme is also suitable for nonuniform node distribution. Numerical results have verified the accuracy of the proposed method.

Mixed Finite-Element Method for Resonant Cavity Problem With Complex Geometric Topology and Anisotropic Lossless Media

Electromagnetic eigenvalue problems are contaminated by nonphysical zero modes in the conventional finite-element method (FEM) with edge elements. Here, we investigate the cavities with anisotropic lossless media, complex geometry structure, and perfect electric conductor (PEC) walls and eliminate all nonphysical zero and nonzero modes successfully. We introduce a Lagrangian multiplier to deal with the constraint of divergence-free condition. Our method is based on the mixed FEM employing the first-order edge basis functions to expand electric field and linear element basis functions to expand Lagrangian multiplier. The validity of our method is confirmed by several numerical experiments. Meanwhile, the numerical experiments show that when the cavity has a connected boundary, there is no physical zero mode; when the cavity has several disconnected boundaries, then the number of physical zero modes is equal to one less than the number of disconnected PEC boundaries.

Equivalent Transmission Conditions for the Time-Harmonic Maxwell Equations in 3D for a Medium with a Highly Conductive Thin Sheet

We propose equivalent transmission conditions of order 1 and 2 for thin and highly conducting sheets for the time-harmonic Maxwell's equation in three dimensions. The transmission conditions are derived asymptotically for vanishing sheet thickness $\varepsilon$ where the skin depth is kept proportional to $\varepsilon$. The condition of order 1 turns out to be the perfect electric conductor boundary condition. The conditions of order 2 appear as generalized Poincareź--Steklov maps between tangential components of the magnetic field and the electric field, and they are of Wentzell type involving second order surface differential operators. Numerical results with finite elements of higher order validate the asymptotic convergence for $\varepsilon\to0$ and the robustness of the equivalent transmission condition of order 2.

A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries

We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain. The forcing, or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter, which then allows for higher order numerical methods. We present an efficient numerical method for constructing the penalty term, and discretize the resulting equations using a Fourier spectral method. We demonstrate convergence orders of up to 3.5 for the one-dimensional Maxwell's equations, and show that the numerical method does not suffer from dispersion (or pollution) errors. We also illustrate the approach in two dimensions and demonstrate convergence orders of 2.5 for transverse magnetic modes and 1.5 for the transverse electric modes. We conclude the paper with numerous test cases in dimensions two and three including waves traveling in an irregular waveguide, and scattering off of a windmill-like geometry.

Boundary Impedance Operator to Study Tipped Parallel Plate Waveguides

An integral method is proposed to compute the field at the vicinity of the tip of a full planar waveguide with perfect electric conductor boundaries. It is based on an impedance operator which permits to relate parallel components of the electromagnetic field so that the usual coupled integral equations with hypersingular kernels may be avoided. Comparison with a well-established finite-element-based approach shows good agreement. Because the method is fast, it could be incorporated in optimization procedures such as waveguide driven photonic jets enhancement.

Guided Modes in Uniaxial Chiral Waveguide of Circular Cross-Section under PEC Boundary

Propagation of electromagnetic waves through a circular waveguide of uniaxial anisotropic chiral medium is studied with the emphasis on the energy flux patterns. The outer surface of the guide is assumed to be bounded by a perfect electric conductor (PEC) medium. The dispersion relation of guide is derived by applying suitable boundary conditions, and the allowed values of propagation constants are computed. Energy flux patterns corresponding to three different types of uniaxial anisotropic chiral metamaterials are taken into account. The propagation of negative energy flux is observed, and attributed to the presence of backward waves in the waveguide structure.

SLAB BAG FERMIONIC CASIMIR EFFECT, CHIRAL BOUNDARIES AND VECTOR BOSON — MAJORANA FERMION PISTONS

In this paper we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions, while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We make use of supersymmetry, broken on the boundaries, to explain the number of fields that appear in all the studied cases. The effect of chiral boundary conditions in a fermion–boson system is investigated. Concerning the supersymmetry issue and the vanishing of the Casimir energy, we study a massive Dirac fermion–scalar boson system with bag and specific Robin type boundary conditions for which the Casimir energy vanishes. Finally, a two-scalar-boson system between parallel plates is presented in which the singularities vanish in the total Casimir energy.

Implementations of PMC and PEC Boundary Conditions for Efficient Fundamental ADI- and LOD-FDTD

This paper presents the implementations of perfect magnetic conductor (PMC) and perfect electric conductor (PEC) boundary conditions for efficient fundamental alternating-direction-implicit (ADI) and locally one-dimensional (LOD) finite-difference time-domain (FDTD). The PMC (or PEC) boundary equations for implicit updating of electric (or magnetic) fields in efficient fundamental ADI- and LOD-FDTD schemes are derived using image theory. Image theory facilitates the implementation of PMC and/or PEC boundary conditions regardless of whether the update equations for electric or magnetic fields are implicit. Comparison between the PMC and PEC boundary equations in conventional and efficient fundamental schemes of ADI- and LOD-FDTD signifies a reduction in the floating-point operations count, thus justifying the higher efficiency and simplicity for the fundamental schemes.

Alternative FDTD Updating Schemes for Anisotropic Materials

A novel way of looking at the anisotropic finite difference time domain(FDTD) method is proposed based on the finite element point of view, which allows for a systematic approach of deriving anisotropic FDTD stencils without resorting to interpolation. A new stencil for anisotropic material media that properly accounts for material interfaces and perfect electric conductor boundaries is derived. This new stencil is tested and compared to analytical solutions and numerical solutions based on implicit finite element methods.

A highly efficient numerical solution for dielectric-coated PEC targets

In this paper, the multi-layer TDS (thin dielectric sheet) integral equation approach is first proposed. This method divides the geometric model into multiple thin layers and assumes the flux density to be constant with respect to the normal direction within each layer. Consequently, the number of unknowns is significantly reduced while the precision of the results could be maintained. Then, the multi-layer TDS integral approach is combined with the PEC (perfect electric conductor) boundary conditions together to handle scattering from dielectric coated PEC objects. This new procedure simplifies the coupled surface (for the conductor)–volume (for dielectric) integral to a surface–surface integral with much fewer unknowns. Furthermore, a remedy approach is also presented in this paper to improve the deteriorated precision for open composed structures due to the significant singular currents near the boundary edges. Compared with traditional PEC-TDS methods, the method presented in this paper can deal with scattering from thick or stratified coatings with arbitrarily lateral or normal inhomogeneity. Its improvement is also capable of handling dielectric coatings on open PEC surfaces. The numerical results at the end show good agreement with the references, showing the accuracy and the validity of these solutions.

WAVEGUIDE SIMULATION USING THE HIGH-ORDER SYMPLECTIC FINITE-DIFFERENCE TIME-DOMAIN SCHEME

Abstract—The high-order symplectic finite-difference time-domain scheme is applied to modeling and simulation of waveguide structures. First, the perfect electric conductor boundary is treated by the image theory. Second, to excite all possible modes, an efficient source excitation method is proposed. Third, the modified perfectly matched layer is extended to its high-order form for absorbing the evanescent waves. Finally, a high-order scattering parameter extraction technique is developed. The cases of waveguide resonator, waveguide discontinuities, and periodic waveguide structure demonstrate that the high-order symplectic finite-difference time-domain scheme can obtain better numerical results than the traditional finite-difference timedomain method and save computer resources.