Nataliya P. Yashina

Surface Resonances of Metal Stripe Grating on the Plane Boundary of Metamaterial

The paper is devoted to the study of the interaction of the electromagnetic waves with the structure composed of perfectly conducting strip grating, situated on the plane boundary of metamaterial with effective permittivity, depending on the frequency of the wave of excitation. The rigorous solution to the relevant diffraction boundary value problem is developed. The extensive numerical experiments, performed with a help of corresponding algorithm constructed, allowed to establish several regularities in the complicated process of interaction of electromagnetic waves with grating on dispersive metamaterial. The efficient association of analytical and numerical study has provided the understanding of the nature of resonant phenomena appearing in this process.

C-Method: Several Aspects of Spectral Theory of Gratings

The goal of the present paper is two folded. The first, the methodological one, is the complementation of well established in diffraction theory of gratings C method with certain elements of spectral theory and the development of interactive numerical algorithm that made feed back conjunction between diffraction and spectral problems. As a natural result the second goal appeared: the appearing of such tool for numerical experiments resulted in profound qualitative and quantitative study of rather peculiar phenomena in resonant scattering from periodic surface. Special attention has been paid to the investigation of electromagnetic waves diffraction from periodic boundaries of material with single and double negative parameters.

RADIATION FROM SURFACE WITH PERIODIC BOUNDARY OF METAMATERIALS EXCITED BY A CURRENT

The rigorous modeling and analysis of electromagnetic wave transformation and radiation from the periodic boundary of metamaterial are presented. The nature of the phenomenon of resonant radiation and the influence of various parameters on it are investigated. The study is carried out with the objective of potential applications to antenna design. Simulated results show that very high directivity can be obtained and that beam steering can be achieved by adjusting proper parameters.

Explicit Conditions for Virtual Boundaries in Initial Boundary Value Problems in the Theory of Wave Scattering

This paper deals with the problem of finding a correct way of restricting the computational domain in the FDTD-method in its application to the analysis of transient wave processes in infinite homogeneous regions containing compact inhomogeneities. The formulation of the explicit ABCs (Absorbing Boundary Conditions) in such a way that they do not distort the physical model simulated by the mathematics, and the incorporation of these ABCs in the computational scheme form the basis of the approach presented here. A number of numerical results are given, illustrating in particular the performance of the exact ABCs in comparison with lower order approximations.

Periodic boundaries of metamaterials: eigen regimes and resonant radiation

The paper is focused on the study of eigen surface waves of the periodic interfaces of metamaterials. A wide range of numerical experiments is performed on the basis of an accurate solution to the eigen boundary value problem. The peculiarities of eigen waves in dispersive media are revealed. The results obtained in the study help in the understanding of the nature of the diverse types of electromagnetic wave resonant transformation by the periodic surfaces of metamaterials.

Modeling and analysis of transients in periodic gratings. II. Resonant wave scattering

In this paper we represent a number of new physical results obtained using time domain methods and based on equivalent replacement of initially open electrodynamic problems with closed ones. These results prove the high efficiency and reliability of the approach, being grounded in our companion paper in this issue.

Nonstationary Model Problems for Waveguide Open Resonator Theory

ABSTRACT The paper takes a fresh look at rigorous approaches and algorithms for model problems of electromagnetic theory of waveguide discontinuities. Numerical experiment is still the main tool for investigation the resonant wave scattering phenomena, which are characteristic for such structures. The mathematical approaches employed for such purposes have to fit certain requirements for accuracy, efficiency and versatility, for ability to be focused on particular details of various practically interesting regimes. The approaches for analysis of transient processes in waveguide open resonators considered herein satisfy all these requirements. They rely on the description of scattering properties of discontinuities in regular waveguides in terms of transform operators related to “evolutionary basis” of nonstationary signals, which are qualitatively the same for all guiding structures. The prototypes of such approaches in frequency domain (FD) have been verified by large body of boundary value problems (BVP...

Electrodynamic Properties of Open Wavegide Resonators

ABSTRACT Spectral and diffraction characteristics of cylindrical resonators loaded on various cylindrical or coaxial waveguides are investigated. The partial inversion method is used to solve this class of problems and to develop the corresponding numerical algorithms. It is demonstrated that the observed effects of total resonant reflection and transmission are caused by the excitation of induced oscillations close to the eigenmodes of the problem. The spectral domain solution enables us to predict the effects of complete mode transformation by open waveguide resonators (OWR). Detailed investigation of coupled eigenmodes in OWRs has determined that the phenomenon is due to the Morse critical points (MCP) of the characteristic determinant of the boundary value problem.

MATHEMATICAL MODELING OF ELECTROMAGNETIC WAVE SCATTERING BY WAVY PERIODIC BOUNDARY BETWEEN TWO MEDIA

The extension of C method, combined with idea of Tikhonov’s regularization is proposed. The regularizing algorithm for numerical solution of electromagnetic wave diffraction by the boundary of dielectric media is developed. This algorithm is based on the solution of the system linear algebraic equations of C method as subject of regularizing method of A. N. Tikhonov. The numerical calculations of scattered field in the case of E-polarization are presented. The efficiency and reliability of the method for the solution of the problems of boundary shape reconstruction have been proved and demonstrated numerically for several situations.

Profile reconstruction of periodic interface.

The reconstruction problem for periodic (arbitrary profiled within a period) boundary between two homogeneous media is considered. Our approach to the solution of the inverse problem is based on the Tikhonov regularization technique, which requires successive selection of the boundaries on the basis of multiple solutions of the direct problem of wave diffraction by the candidate boundaries. The analytical numerical C method has been chosen as a simple but rather efficient tool for the direct problem solving. The scheme for numerical tests of algorithms and criteria for reconstruction accuracy have been suggested and verified. Results of numerical experiments that prove the validity of the approach are presented.