Electromagnetic wave scattering by a small impedance particle: Theory and modeling

Abstract

Electromagnetic (EM) waves, scattered by a small impedance particle of arbitrary shape, embedded in a homogeneous medium, are calculated by a new analytic formula. The range of applicability and the accuracy of this formula are illustrated by numerical results. The formula was derived in (*) A.G.Ramm, Optics Communications, 284,(2011), 3872–3877. The accuracy of the new formula is estimated by a comparison with the Mie-type solution for an impedance sphere. The novelty of our paper is in the demonstration of the range of applicability of the new formula and its practical value, by the numerical results and their comparison with the exact solution for EM wave scattering by impedance spheres. The exact solution is obtained in the form of Mie-type series, and is new. Estimate of the error of this series, in which five terms are kept, shows that the relative error of this solution is less than 10−3 for the parameters' range considered. The numerical results obtained are of interest to a wide audience, and the novelty of the formula from (*) is in its applicability to wave scattering by small particles of arbitrary shapes, when Mie-type solution is not applicable.