Scattering of a Plane Electromagnetic Wave by a Metal Cylinder with Dielectric or Metamaterial Coating

Abstract

The problem of diffraction of a plane electromagnetic wave by a perfectly conducting infinitely long cylinder with coating for the cases of the E and H waves is solved. Calculations are performed using the classical electrodynamic solution, which allowed us to develop the spatial field distribution in the covering dielectric layer and compare it with that of the scattered field. To reveal the relation between the characteristics of the scattered field in the far zone and its structure in the dielectric layer, calculations were performed for various relationships between the wavelength and coating thickness. It is shown that the appearance of the sharp azimuthal and frequency irregularities in the reflected field is related to the coating resonances since the azimuthal structure of the scattered field is a function of the spatial distribution of the secondary sources in this layer, whereas the fine structure of the fast variations with frequency is related to variations in the azimuthal distribution of the secondary-source currents. It is demonstrated that using dielectric coatings, one cannot render the metal cylinder invisible in the wide frequency range. Scattering of plane electromagnetic waves by cylindrical objects is described in sufficient detail. The problems of the plane-wave scattering by perfectly conducting cylinders with dielectric coating with and without losses are discussed in [1] and the literature therein. However, the above-mentioned works lack discussion of the relationship among the characteristics of the scattered field in the far zone and its spatial structure in the layer covering the cylinder. We have calculated the scattered field in the far zone for various relationships between the wavelength and dielectric-coating thickness and attempted to relate the obtained results to the mode structure of the field in the dielectric layer. The results obtained in [1] are in good agreement with the data from other works. 2. FORMULATION OF THE PROBLEM Let us consider the problem of diffraction of a plane electromagnetic wave by a perfectly conducting cylinder with an infinite length and radius a1. The cylinder is covered by a dielectric layer with thickness h, which is characterized by complex permittivity e = e � − ie � and permeability μ = μ � − iμ �� . It is assumed that all fields are proportional to exp(iωt) in the complex form. The cylinder is in vacuum, while the vertical axis z of the cylindrical coordinate system ρ, z, ϕ is matched with the cylinder axis, so that the x and y axes correspond to ϕ =0a ndϕ = π, respectively. A plane monochromatic wave with unit amplitude is incident in the negative direction of the x axis. Such a vector problem is reduced to two scalar problems for two possible field polarizations. For the case of electric (transverse-magnetic (TM) type) polarization, the electric field in the incident wave is parallel to the cylinder axis, i.e., E inc = E inc . Such a wave is called E