1202 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 48, NO. 8, AUGUST 2000 A Method of Moments Solution for Electromagnetic Scattering by Inhomogeneous Dielectric Bodies of Revolution Andrzej A. Kucharski Abstract—A method of calculating the electromagnetic scat- tering from and internal field distribution of inhomogeneous dielectric bodies of revolution (BOR) is presented. The method uses typical mode-by-mode solution scheme. The electric flux density is chosen as the unknown quantity, which, together with the special construction of basis and testing functions, enables considerable reduction of the number of unknowns. A key element in this technique is expressing of the azimuthal field components of basis functions in terms of transverse components. A Galerkin testing procedure is used, with special attention put on the effi- ciency of calculating scalar potential term. Results of calculation for a few classes of dielectric bodies are given and compared with calculations done by other authors. Index Terms—Dielectric bodies, integral equations, method of moments (MoM). I. INTRODUCTION T HE problem of scattering of electromagnetic waves by di- electric bodies has been extensively studied by many au- thors because of its importance in areas such as propagation through rain or snow, medical diagnostics, power absorption in biological bodies, performance of antennas in the presence of dielectric inhomogenity. Especially important is the problem of the rigorous solution of Maxwell equations in the situation when the size of dielectric body is comparable to the wavelength. In this intermediate size region (resonance region) asymptotic methods developed for large or very small bodies cannot be used. The era of using computer techniques to solve dielectric in- teraction problems began with the early works of Richmond [1]. Then a great number of methods have been developed for scat- tering problems [2]–[22]. A special attention is usually paid into those of these methods which use a method of moments (MoM) as the solution scheme [4]–[16]. More recently, a number of hybrid methods [17]–[22] have been proposed, which use the method of moments to properly model radiation condition at the boundary of dielectric region and another technique like fi- nite-element method to model fields inside the region. In MoM methods, some have been developed for ho- mogeneous [4]–[9], partially homogeneous [10]–[12] or Manuscript received October 16, 1997; revised May 4, 2000. This work was supported in part by the State Committee for Scientific Research of Poland under Grant 8T11D02311. The author is with the Radio Department, Institute of Telecommunications and Acoustics, Wroclaw University of Technology, 50-370 Wroclaw, Poland. Publisher Item Identifier S 0018-926X(00)07707-3. heterogeneous [13]–[16] bodies. In three-dimensional (3-D) models the number of unknowns in matrix equation is usually very large. Therefore, researchers often make use of certain symmetries present in some classes of objects in order to reduce the total number of unknowns. Among those techniques the case of bodies of revolution (BOR) plays an important role [4]–[8], [10]–[12]. Among methods developed for BORs, some concern homo- geneous bodies [4]–[8], other inhomogeneous ones [10]–[12], however, most of methods use surface currents in order to satisfy boundary conditions. This leads to serious computational prob- lems, when the great number of very small homogeneous parts has to be treated in the model. This is particularly true, when one wants to model objects with continuously varying dielec- tric constant. Up until now, mainly hybrid methods mentioned before are well suited for solving such problems, which usually seriously complicates the solution scheme. Recently, the works of Viola [23], [24] have given a theoret- ical background for efficient modeling of highly heterogeneous BORs using the MoM techniques. Electric field integral equa- tions (EFIEs) presented have the feature that differential oper- ators do not act on field components, which enables applying simple expansion scheme (pulse-basis functions). However, it is done with the assumption that the dielectric constant is a well-behaved (continuously differentiable) function of position. In fact, it means that incorporating for example step discontinu- ities in permittivity profiles requires taking into account addi- tional surface integrals [25]. In this paper, another attitude is presented having similar to Viola’s solution efficiency factors (reducing the number of un- knowns). The main features of this solution can be summarized as follows: 1) differentiation operators acting on fields are left in equa- tions; 2) piecewise constant permittivity profile is assumed; 3) basis functions with linear capabilities are used in expan- sion scheme; this allows to avoid convergence problems mentioned in [26]; 4) basis functions for nonzeroth modes are divergenceless, which is achieved by applying Gauss’ law and calculating azimuthal field components from transverse ones [23]; 5) zeroth mode equations for azimuthal and transverse com- ponents are decoupled and solved separately; 6) solution procedure remains within convenient mixed po- tential integral equation (MPIE) scheme; 0018–926X/00$10.00 © 2000 IEEE