A spectral-iteration technique for analyzing scattering from arbitrary bodies, Part I: Cylindrical scatterers with E-wave incidence

In the past, methods for solving electromagnetic scattering problems in the frequency domain have been developed largely for the low-frequency (moment method) and high-frequency (asymptotic techniques) regimes. The intermediate frequency range has been analyzed by combinations of these two approaches or by separation of variables, when possible. This paper is devoted to the development of an independent approach, viz., the "stacked spectral-iteration technique," which is capable of handling arbitrary scatterers with dimensions ranging from small to moderately large. The method takes advantage of the simplicity with which the planar-source planar-field relationships are expressed in the spectral domain. The boundary conditions or constitutive relationships, on the other hand, are expressed most simply in the spatial domain. Alternating between the two domains is carried out with the aid of the fast Fourier transform (FFT) algorithm. The spectral-iteration technique (SIT) was applied in the past to thin planar structures which allow the analysis to be carried out on a plane. The generalization of the two-dimensional formulation to arbitrary three-dimensional bodies can be accomplished by sampling the current distribution on the scatterer over a number of parallel planes, and using the simple spectral-domain interaction relationships between the planes. This new approach involves no matrix inversion and is capable of analyzing scatterers whose sizes far exceed those treatable by the moment method. In addition to being arbitrarily shaped, the scatterer may be conducting, dielectric, or lossy dielectric. Thus, the SIT provides an efficient approach to filling the much-needed gap between low- and high-frequency conventional techniques, e.g., the moment method (MoM) and the geometrical theory of diffraction (GTD), and to extending the range of applicability to dielectric scatterers, with or without loss. Though the concepts presented herein are applicable to arbitrary three-dimensional scatterers, the problem of arbitrary cylinders with
E
-polarized excitation is addressed in this paper, while the
H
-case is treated in an accompanying work. The three-dimensional case is to be reported in a future communication which treats the problem of scattering by a lossy inhomogeneons dielectric cylinder of finite length.