Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core

Abstract

An analytical, closed-form solution to the scattering problem from an infinite lossless or lossy elliptical cylinder coating a circular metal core is treated in this work. The problem is solved by expressing the electromagnetic field in both elliptical and circular wave functions, connected with one another by well-known expansion formulas. The procedure for solving the problem is cumbersome because of the nonexistence of orthogonality relations for Mathieu functions across the dielectric elliptical boundary. The solution obtained, which is free of Mathieu functions, is given in closed form, and it is valid for small values of the eccentricity h of the elliptical cylinder. Analytical expressions of the form S(h)=S(0)[1+g(2)h2+g(4)h4+O(h6] are obtained, permitting an immediate calculation for the scattering cross sections. The proposed method is an alternative one, for small h, to the standard exact numerical solution obtained after the truncation of the system matrices, composed after the satisfaction of the boundary conditions. Both polarizations are considered for normal incidence. The results are validated against the exact solution, and numerical results are given for various values of the parameters.

Efficient and Accurate Calculation of the Cutoff Wavenumbers of Coaxial Elliptical-Circular and Circular-Elliptical Metallic Waveguides

“…an elliptical dielectric cylinder [12] or the scattering by an elliptical dielectric cylinder having a circular metallic core [13]. Nonetheless, the scattering problems require a straightforward solution of nonhomogeneous matrix equations, unlike the waveguide problems where the roots of homogeneous matrix equations must be determined.…”

“…Nonetheless, the scattering problems require a straightforward solution of nonhomogeneous matrix equations, unlike the waveguide problems where the roots of homogeneous matrix equations must be determined. Thus, the circular-elliptical geometry of the present work can be considered as an extension of [13], where the roots of the corresponding matrix equations are determined. In [14], an attempt was made for the calculation of the cutoff wavenumbers in coaxial elliptical-circular and circular-elliptical metallic waveguides, but the results in that paper turn out to be ambiguous, as it can be concluded from the numerical results of this paper.…”

Διάδοση Και Σκέδαση ΗΜ Κυμάτων Σε Ελλειπτικές Κυλινδρικές Και Σφαιροειδείς Διατάξεις

“…Another attempt for obtaining analytical formulas for the cutoff wavenumbers of coaxial elliptical-circular and circular-elliptical metallic waveguides was made in [30], although some of the results in that paper turn out to be ambiguous. Apart from the problem of the calculation of the cutoff wavenumbers, closedform methods were also applied in the solution of scattering problems, like the scattering from an elliptical dielectric cylinder [28], or the scattering from an elliptical dielectric cylinder having a circular metallic core [29]. Nonetheless, scattering problems require the straightforward solution of a non homogeneous linear system of equations, contrary to waveguiding problems where a homogeneous system is obtained and the roots of its determinant must be evaluated.…”

“…Με αυτό τον τρόπο, οι συγγραφείς της [26] εξήγαγαν εκφράσεις σε κλειστή μορφή για τα μήκη κύματος αποκοπής ενός απλού ελλειπτικού μεταλλικού κυματοδηγού, ενώ στην [27] αποκτήθηκαν εκφράσεις κλειστής μορφής για τους κυματαριθμούς αποκοπής ελλειπτικών διελεκτρικών κυματοδηγών. Η ίδια μέθοδος έχει εφαρμοστεί και για τη λύση, σε κλειστή μορφή, προβλημάτων σκέδασης από διατάξεις ελλειπτικών διηλεκτρικών κυλίνδρων απείρου μήκους [28,29]. Η διαφορά έγκειται στο ότι τα προβλήματα σκέδασης οδηγούν σε μη ομογενή γραμμικά συστήματα εξισώσεων, ενώ τα προβλήματα κυματοδήγησης οδηγούν σε ομογενή συστήματα, η ορίζουσα των οποίων τίθεται ίση με μηδέν προκειμένου να ανακτηθούν οι κυματαριθμοί αποκοπής.…”