We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Hel...We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Helmholtz equations. We prove the classical reciprocity principle, a general scattering theorem and an optical theorem in R<sup>2</sup>. Using Herglotz wave functions we define the corresponding far field operator. Applying the general scattering theorem useful relations are proved for the reconstruction of the scatterer. We also prove that for real chirality measure of the penetrable scatterer the far field operator has a countable number of eigenvalues which lie on a circle.展开更多
A study has been made on the reflected and transmitted powers generated when an arbitrarily polarized plane wave impinges at a planar interface separating an isotropic achiral medium(IAM) and an isotropic chiral mediu...A study has been made on the reflected and transmitted powers generated when an arbitrarily polarized plane wave impinges at a planar interface separating an isotropic achiral medium(IAM) and an isotropic chiral medium(ICM). It follows that the theoretical formulas are derived for the normalized reflection and transmission powers from an IAM–ICM interface for an arbitrary polarized incident wave, and those at an ICM–IAM interface for right-hand circularly polarized(RCP) or left-hand circularly polarized(LCP) incident wave are also obtained. The behavior of the reflected and transmitted waves in different cases is studied, and the dependence of the reflection/transmission of the incident wave on the incident angle and the parameters of the media is investigated in detail. Our numerical results show that high transmission is exhibited under the impedance matching condition and the incident wave can be split into two waves of the same circular polarization state in the case of the ICM–IAM interface, which indicates that circular polarizing beam splitter is achieved.展开更多
In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2...In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2 × 2 Zorn's vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca–Maxwell's equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.展开更多
In this paper, an implicit finite difference scheme of Box method is presented for analyzing the electromagnetic (EM) wave propagation in the case of axial symmetry. Typical numerical examples, which are about EM wa...In this paper, an implicit finite difference scheme of Box method is presented for analyzing the electromagnetic (EM) wave propagation in the case of axial symmetry. Typical numerical examples, which are about EM wave propagation in free space and chiral media, are presented. Such method has the advantage of high accuracy and easy boundary handling.展开更多
We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering pr...We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.展开更多
The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence ...The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering 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.展开更多
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...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.展开更多
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...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.展开更多
The scattering of time-harmonic electromagnetic waves propagating in a homo- geneous chiral environment by a chiral grating is studied. The problem is simplified to a two-dimensional scattering problem, and the existe...The scattering of time-harmonic electromagnetic waves propagating in a homo- geneous chiral environment by a chiral grating 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 di?raction problem is solved by a finite element method with perfectly matched absorbing layers. Our computational experiments indicate that the method is e?cient.展开更多
文摘We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Helmholtz equations. We prove the classical reciprocity principle, a general scattering theorem and an optical theorem in R<sup>2</sup>. Using Herglotz wave functions we define the corresponding far field operator. Applying the general scattering theorem useful relations are proved for the reconstruction of the scatterer. We also prove that for real chirality measure of the penetrable scatterer the far field operator has a countable number of eigenvalues which lie on a circle.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61431010 and 61501350)the National Key Basic Research Program of China(Grant No.2014CB340203)
文摘A study has been made on the reflected and transmitted powers generated when an arbitrarily polarized plane wave impinges at a planar interface separating an isotropic achiral medium(IAM) and an isotropic chiral medium(ICM). It follows that the theoretical formulas are derived for the normalized reflection and transmission powers from an IAM–ICM interface for an arbitrary polarized incident wave, and those at an ICM–IAM interface for right-hand circularly polarized(RCP) or left-hand circularly polarized(LCP) incident wave are also obtained. The behavior of the reflected and transmitted waves in different cases is studied, and the dependence of the reflection/transmission of the incident wave on the incident angle and the parameters of the media is investigated in detail. Our numerical results show that high transmission is exhibited under the impedance matching condition and the incident wave can be split into two waves of the same circular polarization state in the case of the ICM–IAM interface, which indicates that circular polarizing beam splitter is achieved.
文摘In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2 × 2 Zorn's vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca–Maxwell's equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.
文摘In this paper, an implicit finite difference scheme of Box method is presented for analyzing the electromagnetic (EM) wave propagation in the case of axial symmetry. Typical numerical examples, which are about EM wave propagation in free space and chiral media, are presented. Such method has the advantage of high accuracy and easy boundary handling.
文摘We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.
基金Supported by the Key Project of Chinese Ministry of Education(102088)the NNSF of China(10431030).
文摘The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering 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.
基金The Special Funds for Major State Basic Research Projects (G1999032802) in China the NNSF (10076006) of China.
文摘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.
基金The Special Funds for Major State Basic Research Projects (G1999032802) in China and the NNSF (10076006) of China.
文摘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.
文摘The scattering of time-harmonic electromagnetic waves propagating in a homo- geneous chiral environment by a chiral grating 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 di?raction problem is solved by a finite element method with perfectly matched absorbing layers. Our computational experiments indicate that the method is e?cient.
