0018-926X (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2018.2823728, IEEE Transactions on Antennas and Propagation AP1707-1182 1 Abstract— The paper proposes an efficient method to analyze scattering from an inhomogeneous body of revolution (BOR) with anisotropic electromagnetic properties. Both the permittivity and permeability are assumed to be generalized tensors while there are no restrictions on the geometry of the BOR. The proposed method involves three stages. First, the volume equivalence principle is used to replace the BOR with volume electric and magnetic current densities. Requisite volume integral equations (VIEs) are then derived with the electric and magnetic flux densities inside the BOR being the unknown quantities. Finally, the VIEs are solved by the Galerkin’s method of moments. This is done by expanding the unknown flux densities in terms of appropriate basis functions compatible with the problem symmetry, and hence, reducing the integral equations to a matrix equation. The formation of the resultant matrix equation is elucidated in detail whereby it is shown that the computation burden is remarkably reduced as no double volumetric-type integrals are to be computed. The efficiency of the proposed method is demonstrated by comparing the simulation results of several case studies with those available in the literature, or computed by commercial numerical codes. Index Terms— Anisotropic media, Bodies of revolution, Electromagnetic scattering, Moment methods I. INTRODUCTION aterials with anisotropic behavior such as composites, plasmas, ferrites and metamaterials are widely used in radar absorbers, microstrip antenna substrates, microwave integrated circuit devices, and industry sections such as modern aircrafts manufacturing [1]-[3]. Depending on the nature of anisotropy in these materials, their electromagnetic (EM) properties are represented by second-order tensors with diagonal, symmetric, or arbitrary structures [4]. The EM analysis of objects with anisotropic material has been done for a number of known geometries, including planar [5], [6], cylindrical [7]-[9], spherical [10]-[12], and wedge-shape [13] structures. Since many real-world objects are manufactured with axisymmetric anisotropic objects, the EM analysis of such objects, known as bodies of revolution (BORs), is of great interest. For example, it is common practice in aviation industry M. Maddah-Ali and S. H. H. Sadeghi are with the Department of Electrical Engineering, Amirkabir University of Technology, Tehran 15914, Iran (e-mail: maddahali66@aut.ac.ir; sadeghi@aut.ac.ir). M. Dehmollaian is with the Center of Excellence on Applied Electromagnetic Systems, School of Electrical and to evaluate the electromagnetic scattering from aircraft nose cones that are made of composite fiber materials [14]. The EM analysis of BORs is also useful in cases where a non-symmetric structure is approximated with an approximate symmetric model to achieve computational gains [15]. In addition, scattering from rotationally symmetric targets (e.g., spheres, cylinders and ellipsoids) are of special interest for being the reference solutions in validation of new numerical techniques. This general fact applies specially to the anisotropic axisymmetric targets for which very few studies are reported up to now, and hence, the need for reliable benchmark solutions is pronounced [16]. Moreover, axisymmetric targets could be used in the calibration of RCS measurement setups, emphasizing that their scattering behavior is of practical interest. The general approaches proposed for EM scattering from 3- D arbitrary-shape anisotropic bodies [17]-[19] are obviously applicable to the special cases of axisymmetric targets. However, the computation time increases excessively as the size of the object becomes larger. This is due to the fact that the number of unknowns increases proportional to the object size. Besides, for large objects, the application of the general approaches is not practical, if not impossible, due to the huge required computational resources. Extensive efforts have been made since 1965 to analyze the EM scattering from a BOR. Early works in this area are related to isotropic homogenous materials with various geometries, including single-layer [20]-[22] and multilayer structures [23]. EM scattering from an axially inhomogeneous BOR has been reported where the governing coupled Fredholm integral equations are solved by the method of moments (MoM) [24], [25]. Also, the case of an inhomogeneous dielectric BOR has been treated, using the volume integral equation (VIE) in conjunction with the MOM [26]. The same problem has been solved with the aid of a hybrid finite element method (FEM)/MOM formulation [27]. In addition, the case of a bi- isotropic BOR with arbitrary-shape geometry has been reported where the MOM is adopted to solve the governing surface integral equation [28]. Moreover, BORs with isotropic and anisotropic impedance boundary conditions have been treated, Computer Engineering, University of Tehran, Tehran, Iran (e-mail: m.dehmollaian@ece.ut.ac.ir). A Method of Moments for Analysis of Electromagnetic Scattering from Inhomogeneous Anisotropic Bodies of Revolution Mojtaba Maddah-Ali, Seyed Hossein Hesamedin Sadeghi, Senior Member, IEEE and Mojtaba Dehmollaian, Senior Member, IEEE M