Characteristics of electromagnetic wave absorption in cylindrical black holes with positive and negative refractive indexes

The problem of plane electromagnetic wave scattering by cylindrical “black holes” with radial profile of dielectric permittivity and magnetic permability in the shell chosen in the form $\varepsilon(\rho)=\mu(\rho)\sim1/\rho^{2}$ and with constant permittivity and permeability in the central region is considered. The problem in rigorous formulation is solved both analytically for a basic model of the absorber and numerically using the one-dimensional method of finite elements for a modified model. The results obtained for absorption efficiency, radar cross-section, and field distribution in the cylinder are presented and discussed. It is shown that the absorption efficiency of the cylinder with negative refractive index at realistic values of parameters of the cylinder remains higher than the absorption efficiency of a similar cylinder with positive refractive index. However the indicated advantage is not so great as the advantage compared to the absorption efficiency of the black body predicted in the previous publications for the case of extremely low losses at the surface of the cylinder and extremely high magnitudes of negative permittivity and permeability and losses in the central region of radius approaching zero.