ИСПОЛЬЗОВАНИЕ МЕТОДА ДИАГРАММНЫХ УРАВНЕНИЙ ДЛЯ АНАЛИЗА ДИФРАКЦИИ НА МАЛЫХ РАССЕИВАТЕЛЯХ

Abstract

Scattering of electromagnetic waves by small particles is an important key task of diffraction theory. This is due to a wide range of practical applications of the effects associated with the scattering of electromagnetic waves by particles, small in com-parison with the wavelength. From the moment of the appearance of the first papers devoted to this subject and up to the present, the most used mathematical model used in solving the problem of scattering by small bodies is the dipole approximation (Rayleigh approximation). This approach is described in sufficient detail for particular cases of scattering by balls and ellipsoids, when the solution of the auxiliary electrostatic problem can be obtained in explicit form. Note that the solution of the problem in the electrostatic approximation in the general case, in itself, is quite complicated and time-consuming compared with the solution of the original wave problem. Existing methods for solving it have a number of fundamental limitations. In this paper, we developed a technique based on the use of the method of Pattern Equations Method (PEM), first proposed in 1992. In a significant number of publications, it has been clearly demonstrated that PEM have important advantages over many alternative methods and are very effective in solving a wide class of problems. In constructing a new approach to the analysis of scattering by small bodies, we used the high convergence rate of the PEM established in our previous papers. Indeed, as shown in previous works of the authors of this article, to solve the problem of scattering by impedance bodies, whose characteristic size is comparable with the wavelength of the incident field, it suffices to take into account, depending on the polarization of the incident field, one to three terms in the Fourier decomposition of the scattering pattern. This circumstance made it possible to obtain explicit formulas for the integral scattering characteristics applicable to complex-shaped impedance scatterers. In this work, explicit formulas are obtained for the integrated scattering characteristics that are applicable to small, compared with the incident radiation wavelength, scatterers. A review is given of the application of an approximate methodology for calculating the integral scattering characteristics of small diffusers of arbitrary shape, in particular, thin dielectric cylinders, based on the use of PEM. As the above results show, the approximate relations obtained have sufficient accuracy in a wide range of problem parameters.