Scattering by arbitrary cross-section cylinders based on the T-Matrix approach and cylindrical to plane waves transformation

Abstract

Multiple scattering of parallel cylinders with arbitrary cross section is computed using the T-matrix of each single scatterer and the general translational matrix for cylindrical waves. Usually, the recommended golden rule to compute the translational matrix is Graf’s addition theorem. However, this approach cannot be properly implemented for some geometries, such as in a two-cylinder case when the center of one of them falls within the minimum circular cylinder that circumscribes the other one. In order to overcome this limitation, a transformation between cylindrical waves and plane waves, followed by propagation of the latter, is proposed. The new approach succeeds due to an adequate truncation of the evanescent plane wave spectrum. This strategy is demonstrated by studying the scattering of three infinite elliptic metallic cylinders for different electrical sizes and observing the convergence of the results as a function of the truncated spectrum. Finally, to conclusively show the interest and applicability of the approach, two more complex problems are treated: a group of infinite elliptic metallic cylinders where two different sizes are combined and a practical real-life filter in substrate integrated waveguide (SIW) technology, including several groups of rectangular dielectric cylinders.