On Describing the Radiation and Diffraction of Electromagnetic Waves by the Eigenfunction Method

Abstract

We consider applicability of the eigenfunctions of the integral operator to solution of the inner problem of electrodynamics (finding the source function of the electromagnetic field) by the method of moments. It is shown that the eigenfunctions can be determined on the basis of solving the complete eigenvalue problem for the moment matrix. In this case, this procedure has a better computation stability compared with the procedure for calculating the characteristic modes of the integral operator, which is based on the same scheme and has gained a wider spread at present. As an example, we consider the problem of diffraction of a plane electromagnetic wave by a helical particle, which is solved by the eigenfunction method. The results of numerical modeling are presented.

Approximation of the solution of an internal problem of electrodynamics by the method of eigenfunctions

“…PFS may be regarded as optimal if it converts the SLAE matrix to the diagonal form. In paper [3] it was proposed to solve this problem by using the eigenfunction method (EFM). As an alternative to EFM, the characteristicmode method may be regarded [4].…”

“…As an alternative to EFM, the characteristicmode method may be regarded [4]. In addition, paper [3] considered advantages and disadvantages of the mentioned methods; for example, solution by EFM of the problem of diffraction on a helical particle was presented. There was made a conclusion that EFM may become a good basis for creating approximation models (AM) for solving the internal problem of electrodynamics.…”

“…A drawback of the proposed AM is some loss of physical sense of data stored in the underlying arrays. In [3], we emphasized especial importance of extrema of the EN frequency dependences, which define the general character of the internal problem solution. Ideally, such information should be included in the underlying arrays in the explicit form.…”