A. Poyedinchuk

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.

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.

Resonances in Reverse Vavilov-Cherenkov Radiation Produced by Electron Beam Passage over Periodic Interface

Resonances in reverse Vavilov-Cherenkov radiation produced by the charged particles beam passage over periodic boundary of dispersive left-handed medium are found out and studied. Analysis and modeling are performed on the base of rigorous mathematical approaches. For the first time, several physical peculiarities owing to these effects are considered in the conditions of possible resonant scattering of electromagnetic waves.

Reconstruction of periodic boundary between dielectric media

We propose a robust and clear modification of the known C method for solving the problem of wave scattering by an arbitrarily shaped surface. This approach makes a reliable basis for the solution of the recognition problem, the reconstruction of surface profile and material parameters of media from known data on the scattered field. For the direct problem solution, the C-method in combination with /spl alpha/ regularisation has been chosen. This enables us to reduce the original 2D problem of linearly polarized plane wave diffraction by an arbitrary boundary of dielectric media to an operator equation.

The plane H-polarized wave diffraction by a metal grating with a magnetoactive plasma

A periodic grating of infinitely thin, perfectly conducting metal strips is considered The subspace is occupied by a magnetoactive plasma with magnetic field. The plasma is characterized by a tensor. A plane H-polarized electromagnetic wave is normally incident on the grating plate.

1D inverse problems of electromagnetic theory of layered inhomogeneous anisotropic media

The inverse problems of the reconstruction of the dielectric permittivity tensor of multilayered inhomogeneous anisotropic slab by the reflection (transmission) coefficients known at the discrete sets of frequencies and angles of incidence are considered. The inverse problems have been reduced to optimal control problems for the Riccati equation. An analytical- numerical method for solving these problems has been developed. Numerical experiments demonstrating the computational efficiency of the proposed method have been carried out.

Inverse problems of electromagnetic sounding: Gradient medium and periodic boundary

The problems of the periodic interface profile reconstruction and the recognition of dielectric constant of the layered medium according to the values of the reflection coefficients for a finite set of probing frequencies are rather urgent in connection with the development of modern non-destructive testing methods. To solve them the original problems are reduced to the search for the optimal control (the profile of the dielectric constant) of the Cauchy problem for the Riccati equation. Construction of optimal control in the class of polynomial functions is based on the minimization of the corresponding functional. The criterion of selection of polynomial approximations for profile permittivity uses the separation of input data into Training and Testing sequences of probing frequency. An analysis of errors of the reconstruction of the imaginary part of permittivity of the layered medium was carried out.

Analytical-numerical method for solving problems of electromagnetic wave diffraction by the local cylindrical inhomogeneity

An analytical-numerical method for studying the diffraction characteristics of the inhomogeneous magnetodielectric circular isotropic cylinder excited by linearly polarized plane electromagnetic wave is suggested. The method is based on the construction of special solutions to the Cauchy problem for the Riccati equation and gives the opportunity to investigate the diffraction process for this type of structures.

Resonant Cherenkov type radiation in dispersive metamaterials

The radiation of moving charged particles makes a fundamental problem in modern physics and has long been the subject of a thorough study [1-26]. As early as 1889, O. Heaviside considered the electromagnetic field of a point charge uniformly moving in a dispersion-less medium and was seemingly the first (as follows from the literature) to ask himself: What happens when the charged particle velocity, u exceeds the velocity of light v in the medium? He found that the spherical wave front of particle radiation takes a conical shape with the semi-angle θ = ν/u reported in his Theory of Electromagnetism, volume 3, 1905 [1]. Later, Lord Kelvin got also curious about the matter and proposed in his lecture on thermal radiation [2], in 1900 that an atom moving at a speed exceeding the speed of light produces a conical wave, as it holds upon Mach principle in acoustics. In 1904, A. Sommerfeld considered a purely theoretic and even hypothetic problem on electron movement in a vacuum at a velocity exceeding the velocity of light there and concluded about the directional property of electron radiation [3]. However the advent of the relativity theory did Sommerfelds conclusions out of question, for the relativity theory keeps physical bodies away from the movement at a velocity equal or, the more so, exceeding the velocity of light. This conflict with the relativity theory might give a reason why the problem of supraluminal speed movement of charged particles was left out of consideration.

Resonant radiation of electron beam, moving near periodic boundary of metamaterial

The study of the electromagnetic filed produced by charged particles moving with constant velocity in the vicinity of various objects is one of principal problems of modern electromagnetic theory. Among various structures for which the solution of corresponding boundary value problems can be obtained by means of reliable mathematical methods, the periodic ones are of the biggest practical and physical interest [1].