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.
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