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Scattering Relations for Two-Dimensional Electromagnetic Waves in chiral media

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Journal of Applied Mathematics and Physics 2022年第4期10卷 1200-1216页

作者： Christodoulos E. Athanasiadis Evagelia S. Athanasiadou Paraskevi Roupa Department of Mathematics University of Athens Panepistimiopolis Athens Greece Department of Informatics and Telecommunications University of Athens Panepistimiopolis Athens Greece

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 R2. 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.

关键词： Reciprocity Principle chiral media Two-Dimensional Scattering Scattering Relations

Numerical Analysis of EM Wave Propagation in Free Space and chiral media

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Journal of Modern Transportation 1998年第2期15卷 30-34页

作者：方剑盛克敏任朗

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.

关键词： electromagnetic wave propagation numerical method chiral media

Inverse Electromagnetic Scattering by a Penetrable chiral Object

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Journal of Applied Mathematics and Physics 2024年第9期12卷 3081-3098页

作者： Sotiria Dimitroula Paraskevi Roupa Spyridon C. Athanasiadis Georgios Halikias Department of Mathematics National and Kapodistrian University of Athens Athens Greece Department of Informatics and Telecommunications National and Kapodistrian University of Athens Athens Greece School of Electrical and Computer Engineering National and Technical University of Athens Athens Greece

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.

关键词： chiral media Inverse Scattering Problem chiral Mixed Reciprocity Relation

COUPLING OF FINITE ELEMENT AND BOUNDARY ELEMENT METHODS FOR THE SCATTERING BY PERIODIC chiral STRUCTURES

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Journal of Computational Mathematics 2008年第3期26卷 261-283页

作者： Habib Ammari Gang Bao Centre de Mathématiques Appliquées CNRS UMR 7641 Ecole Polytechnique 91128 Palaiseau France Department of Mathematics Michigan State University East Lansing MI 48824 USA

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R^3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.

关键词： chiral media Periodic structures Finite element method Boundary element method Convergence

A FINITE ELEMENT METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY A PERIODIC chiral STRUCTURE

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Journal of Computational Mathematics 2007年第4期25卷 458-472页

作者： Deyue Zhang Fuming Ma School of Mathematics Jilin University Changchun 130012 China School of Computer Science and Technology Jilin University Changchun 130012 China School of Mathematics Jilin University Changchun 130012 China

Consider the diffraction of a time-harmonic wave incident upon a periodic chiral structure. The diffraction problem may be simplified to a two-dimensional one. In this paper, the diffraction problem is solved by a finite element method with perfectly matched absorbing layers （PMLs）. We use the PML technique to truncate the unbounded domain to a bounded one which attenuates the outgoing waves in the PML region. Our computational experiments indicate that the proposed method with complicated chiral grating structures. is efficient, which is capable of dealing

关键词： chiral media Perfectly matched layer Grating optics.

Tuning circular Bragg phenomenon of TiO2 sculptured thin films with chiral structure

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Chinese Optics Letters 2013年第13期11卷 6-8页

作者：罗迪帆黄辰迪江绍基 State Key Laboratory of Optoelectronic Materials and Technologies Sun Yat-sen University Guangzhou 510275 China

TiO2 chiral sculptured thin films （CSTFs） prepared using glancing angle deposition （GLAD） method based on electron beam evaporation are studied. The relationship between structural parameters and circular Bragg phenomenon （CBP） is investigated. Results demonstrate that, the central wavelength of Bragg regime red-shifts with the increasing pitch of helix, and peak value of selective transmittance will increase after adding more turns to the helix. After annealing, the central wavelength blue-shifts and the peak value rises. Tuning CBP by modulating the deposition parameters and annealing can optimize the performance of circularly polarized devices fabricated from CSTFs.

关键词： 310.1860 Deposition and fabrication 310.5448 Polarization, other optical properties 160.1585 chiral media

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

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Applied Mathematics(A Journal of Chinese Universities) 2007年第3期22卷 259-266页

作者： Gao Tianling Ma Fuming Zhang Deyue College of Mathematics Jilin University Changchun 130012 China

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.

关键词： chiral media Maxwell's equation far-field pattern direct problem inverse problem.

Polarization properties in helical metamaterials

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Frontiers of Optoelectronics 2012年第3期5卷 248-255页

作者： Zhenyu YANG Peng ZHANG Peiyuan XIE Lin WU Zeqin LU Ming ZHAO Wuhan National Laboratory for Optoelectronics College of Optoelectronic Science and Engineering Huazhong University of Science and Technology Wuhan 430074 China Hunan Electric Power Company Dispatches & Communication Center Changsha 410007 China

In the last few years, there has been growing interest in the research of helical metamaterials due to the advantages of giant circular dichroism; broad operation bands, and compact structures. However, most of the researches were in the cases of single-, circular-helical metamaterials, and normal incidences. In this paper, we reviewed recent simulation works in the helical metama- terials with the finite-difference time-domain （FDTD） method, which mainly included the optical performances of double-, three-, four-helical metamaterials, perfor- mances of elliptical-helical metamaterials, and the polar- ization properties under the condition of oblique incidences. The results demonstrate that the double-helical metamaterials have operation bands more than 50%, which is broader than those of the single-helical structures. But both of them have low signal-to-noise ratios about 10 dB. The three- and four-helical metamaterials have significant improvement in overall performance. For elliptical- helixes, simulation results suggest that the transmitted light can have elliptical polarization states. On the condition of oblique incidences, the novel property of tunable polarization states occurred in the helical metama- terials, which could have much broader potential applica- tions such as tunable optical polarizers, tunable beam splitters, and tunable optical attenuators.

关键词： finite-difference time-domain (FDTD)method polarization chiral media helical metamaterials

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

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Northeastern Mathematical Journal 2004年第2期20卷 236-252页

作者：张德悦马富明 School of Mathematics Jilin University Changchun 130012 School of Mathematics Jilin University Changchun 130012n 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.

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.

关键词： chiral media Maxwell equation Drude-Born-Fedorov equation quasi-periodic solution periodic structure