ANALYSIS OF TWO-DIMENSIONAL ELECTROMAGNETIC SCATTERING BY A PERFECTLY CONDUCTING OBSTACLE IN A HOMOGENEOUS CHIRAL ENVIRONMENT

The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered.A two-dimensional direct scat- tering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach.The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated.Result on the uniqueness of the inverse problem is proved.     

Analysis of FDTD to UPML for Maxwell equations in polar coordinates

An FDTD system associated with uniaxial perfectly matched layer(UPML) for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic(TM) mode to Maxwell’s equations is obtained by Yee’s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.     

Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low‐frequency theory

The scattering of plane time‐harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far‐field patterns are derived. A low‐frequency theory for the approximation of the solution to the above problem, and the derivation of the far‐field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Aspects of electromagnetic scattering in chiral media

In this work, we study two operators that arise in electromagnetic scattering in chiral media. We first consider electromagnetic scattering by a chiral dielectric with a perfectly conducting core. We define a chiral Calderon‐type surface operator in order to solve the direct electromagnetic scattering problem. For this operator, we state coercivity and prove compactness properties. In order to prove existence and uniqueness of the problem, we define some other operators that are also related to the chiral Calderon‐type operator, and we state some of their properties that they and their linear combinations satisfy. Then we sketch how to use these operators in order to prove the existence of the solution of the direct scattering problem. Furthermore, we focus on the electromagnetic scattering problem by a perfect conductor in a chiral environment. For this problem, we study the chiral far‐field operator that is defined on a unit sphere and contains the far‐field data, and we state and prove some of its properties that are preliminaries properties for solving the inverse scattering problem. Copyright © 2016 John Wiley & Sons, Ltd.     

The Two-dimensional Electromagnetic Scattering from Periodic Chiral Structures and Its Finite Element Approximation

In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.     

Calculating the surface currents in electromagnetic scattering by screens of complex geometry

The vector problem of scattering an external electromagnetic field by a perfectly conducting thin bounded screen is considered. The approximation property of rooftop basis functions is proven. Numerical solutions of the problem for a screen of canonical shape are obtained using the Galerkin method. Numerical solutions of the problem for screens of complex geometry are obtained by a subhierarchic method.     

On the domain derivative for scattering by impenetrable obstacles in chiral media

For scattering of electromagnetic waves in a chiral medium bysome perfectly conducting inclusions, we study the dependenceof the scattered field on the boundary of the inclusions andshow its Fréchet differentiability in appropriate spaces.Further, we derive a characterization of the derivative as asolution to some corresponding chiral boundary value problem.Our proof contains a new approach to rigorously derive thischaracterization.     

手性障碍电磁散射的PML有限元计算

该文建立了手性障碍电磁散射问题的二维模型, 给出问题的有限元分析, 并利用结合PML(perfectly matched layers)技术的有限元法进行数值模拟.     

Excitation of electromagnetic oscillations in a domain with chiral filling

The problem of excitation of electromagnetic oscillations by a given distribution of charges and currents in a domain with inhomogeneous chiral filling is examined. The domain in which the problem is considered may either be finite with a perfectly conducting boundary surface or be the complement of a perfectly conducting bounded body. A special functional space is defined on which a generalized initial-boundary value problem is formulated. The Galerkin method is used to prove the existence and uniqueness of a weak solution of this problem.     

An overfilled cavity problem for Maxwell's equations

This paper is concerned with the mathematical analysis of the scattering of a time‐harmonic electromagnetic plane wave by an open and overfilled cavity that is embedded in a perfect electrically conducting infinite ground plane, where the electromagnetic wave propagation is governed by the Maxwell equations. Above the flat ground surface and the open aperture of the cavity, the space is assumed to be filled with a homogeneous medium with a constant permittivity and permeability, whereas the interior of the cavity is filled with some inhomogeneous medium with a variable permittivity and permeability. The scattering problem is modeled as a boundary value problem over a bounded domain, with transparent boundary condition proposed on the hemisphere enclosing the inhomogeneity represented by the cavity. The existence and uniqueness of the weak solution for the model problem are established by using a variational approach. The perfectly matched layer (PML) method is investigated to truncate the unbounded electromagnetic cavity scattering problem. It is shown that the truncated PML problem attains a unique solution. An explicit error estimate is given between the solution of the original scattering problem and that of the truncated PML problem. The error estimate implies that the PML solution converges exponentially to the original cavity scattering problem by increasing either the PML medium parameter or the PML layer thickness. The convergence result is expected to be useful for determining the PML medium parameter in the computational electromagnetic scattering problem. Copyright © 2012 John Wiley & Sons, Ltd.     

均匀手性介质中理想导体光栅的电磁散射

§1Introduction Phenomenaofopticalactivityinspecialmaterialshavebeenknownsincethe beginningoflastcentury.Thoughopticalactivityhasbeenconsideredinopticsandin quantummechanicsformanyyears,itsanalysiswithintheframeworkofclassical electromagneticfieldtheoryarosemuchlater.Recently,therehasbeenaconsiderable interestinthestudyofscatteringanddiffractionbychiralmedium.Ingeneral,the electromagneticfieldsinsidethechiralmediumaregovernedbyMaxwellequations togetherwithDrude-Born-Fedorovequationsinwhichth…     

Electromagnetic Scattering by a Chiral Grating in a Homogeneous Chiral Environment and its Finite Element Method with Perfectly Matched Absorbing Layers

1 Introduction The phenomenon of optical activity in special materials has been known since the beginning of the last century. Whereas optical activity has been considered in optics and in quantum mechanics for many years, its analysis within the framewor…     

Control of boundary impedance in two-dimensional material-body cloaking by the wave flow method

Control problems are considered for a two-dimensional electromagnetic field model describing electromagnetic wave scattering in a unbounded homogeneous medium containing an anisotropic permeable inclusion with a partially covered (cloaked) boundary. The control is a function involved in the impedance boundary condition on the covered part of the boundary. The solvability of the original mixed transmission problem for the two-dimensional Helmholtz equation and of the control problems is proved. Optimality systems describing necessary extremum conditions are derived. The uniqueness and stability of optimal solutions with respect to certain perturbations of the cost functional and the incident wave are established.     

Acoustic scattering by a thin cylindrical screen with Dirichlet and impedance boundary conditions on opposite sides of the screen

A problem on scattering acoustic waves by a thin cylindrical screen is studied. In doing so, the Dirichlet condition is specified on one side of the screen, while the impedance boundary condition is specified on the other side of the screen. The solution of the problem is subject to the radiating condition at infinity and to the propagative Helmholtz equation. By using the potential theory the scattering problem is reduced to a system of singular integral equations with additional conditions. By regularization and subsequent transformations, this system is reduced to a vector Fredholm equation of the second kind and index zero. It is proved that the obtained vector Fredholm equation is uniquely solvable. Therefore the integral representation for a solution of the original scattering problem is obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Maxwell's equations in an unbounded structure

This paper is concerned with the mathematical analysis of the electromagnetic wave scattering by an unbounded dielectric medium, which is mounted on a perfectly conducting infinite plane. By introducing a transparent boundary condition on a plane surface confining the medium, the scattering problem is modeled as a boundary value problem of Maxwell's equations. Based on a variational formulation, the problem is shown to have a unique weak solution for a wide class of dielectric permittivity and magnetic permeability by using the generalized Lax–Milgram theorem. Copyright © 2016 John Wiley & Sons, Ltd.     

Absorbing boundary conditions for electromagnetic wave propagation

In this paper, the theoretical perfectly absorbing boundary condition on the boundary of a half-space domain is developed for the Maxwell system by considering the system as a whole instead of considering each component of the electromagnetic fields individually. This boundary condition allows any wave motion generated within the domain to pass through the boundary of the domain without generating any reflections back into the interior. By approximating this theoretical boundary condition a class of local absorbing boundary conditions for the Maxwell system can be constructed. Well-posedness in the sense of Kreiss of the Maxwell system with each of these local absorbing boundary conditions is established, and the reflection coefficients are computed as a plane wave strikes the artificial boundary. Numerical experiments are also provided to show the performance of these local absorbing boundary conditions

     

The scattering of electromagnetic wave at oblique incidence in a homogeneous chiral medium

We consider the scattering of a time-harmonic electromagnetic wave by a perfectly and imperfectly conducting infinite cylinder at oblique incidence respectively. We assume that the cylinder is embedded in a homogeneous chiral medium and the cylinder is parallel to the z axis. Since the x components and y components of electric field and magnetic field can be expressed in terms of their z components, we can derive from Maxwell's equations and corresponding boundary conditions that the scattering problem is modeled as a boundary value problem for the z components of electric field and magnetic field. By using Rellich's lemma and variational approach, the uniqueness and the existence of solutions are justified.     

周期手性结构电磁散射问题的积分方程方法

In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic fields inside the chiral medium are governed by Maxwell equations together with the Drude-BornFedorov equations. We simplify the problem to a two-dimensional scattering problem and discuss the existence and the uniqueness of solutions by an integral equation approach. We show that for all but possibly a discrete set of wave numbers, the integral equation has a unique solution.     

Numerical analysis for the scattering by obstacles in a homogeneous chiral environment

The scattering of time-harmonic electromagnetic waves propagating in a homogeneous chiral environment by obstacles is studied. The problem is simplified to a two-dimensional scattering problem, and the existence and the uniqueness of solutions are discussed by a variational approach. The diffraction problem is solved by a finite element method with perfectly matched absorbing layers. Our computational experiments indicate that the method is efficient.     

On the solvability of a boundary value problem for the Laplace equation on a screen with a boundary condition for a directional derivative

We consider a three-dimensional boundary value problem for the Laplace equation on a thin plane screen with boundary conditions for the “directional derivative”: boundary conditions for the derivative of the unknown function in the directions of vector fields defined on the screen surface are posed on each side of the screen. We study the case in which the direction of these vector fields is close to the direction of the normal to the screen surface. This problem can be reduced to a system of two boundary integral equations with singular and hypersingular integrals treated in the sense of the Hadamard finite value. The resulting integral equations are characterized by the presence of integral-free terms that contain the surface gradient of one of the unknown functions. We prove the unique solvability of this system of integral equations and the existence of a solution of the considered boundary value problem and its uniqueness under certain assumptions.