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
In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave func...In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.展开更多
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 fin...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展开更多
This paper is concerned with the reconstruction of the radiation wave field in the exterior of a bounded two- or three-dimensional domain from the knowledge of Cauchy data on a part of the boundary of the aforemention...This paper is concerned with the reconstruction of the radiation wave field in the exterior of a bounded two- or three-dimensional domain from the knowledge of Cauchy data on a part of the boundary of the aforementioned domain. It is described by the Cauchy problem for the Helmholtz equation. By using the Dirichlet-to-Neumann map, this problem is transformed into an operator equation with compact operator. We rigorously justify the asymptotic behaviors of singular values of the compact operator. Then a projection method with regularization is applied to solve the operator equation, and the convergence of the regularization method is discussed. Finally, several numerical examples are presented to illustrate the approach. The results demonstrate that the algorithm is effective.Mathematics subject classification： 35R25, 35R30, 78A40.展开更多
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.
基金The authors would like to thank the reviewers and Dr.Zheng Enxi for many valuable suggcstions. This work is supported by the National Natural Science Foundation of China （Grant No. 11371172, 51178001）, Science and technology research project of the education department of Jilin Province （Grant No. 2014213）.
文摘In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.
基金The research was supported by the Special Funds for Major State Basic Research Projects(G1999032802) in Chinathe NNSF(10076006)of China
文摘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
文摘This paper is concerned with the reconstruction of the radiation wave field in the exterior of a bounded two- or three-dimensional domain from the knowledge of Cauchy data on a part of the boundary of the aforementioned domain. It is described by the Cauchy problem for the Helmholtz equation. By using the Dirichlet-to-Neumann map, this problem is transformed into an operator equation with compact operator. We rigorously justify the asymptotic behaviors of singular values of the compact operator. Then a projection method with regularization is applied to solve the operator equation, and the convergence of the regularization method is discussed. Finally, several numerical examples are presented to illustrate the approach. The results demonstrate that the algorithm is effective.Mathematics subject classification： 35R25, 35R30, 78A40.
