Closed-form Green's function representations in cylindrically stratified media for Method of Moments applications

Abstract

Closed-form Green's function (CFGF) representations for cylindrically stratified media, which can be used as the kernel of an electric field integral equation, are developed. The developed CFGF representations can safely be used in a method of moments solution procedure, as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder (such as the air-dielectric and dielectric-dielectric interfaces) including the axial line (= and =), which has not been available before. In the course of obtaining these expressions, the conventional spectral domain Green's function representations are rewritten in a different form so that i) we can attack the axial line problem and ii) the method can handle electrically large cylinders. Available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently. Lastly, the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method, where a modified two-level approach is used. Numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain CFGF representations. Index Terms-Closed-form Green's functions, discrete complex image method (DCIM), generalized pencil of function (GPOF) method, method of moments (MoM).

An Efficient Asymptotic Extraction Approach for the Green's Functions of Conformal Antennas in Multilayered Cylindrical Media

“…This is followed by the proposed asymptotic DGF formulation, which is fundamentally different from that presented in earlier studies [4]- [7].…”

“…In earlier studies, no analytical expression has been formulated for the asymptotic expansion coefficient C(k z ), hence it has been determined numerically [5], [7]. As a result, it wasn't possible to make a direct use of the Sommerfeld identity for integrals such as (18).…”

“…0 (k i j 0 0 j), with the singularity at = 0 handled using the small argument approximation [7]. Furthermore another level of asymptotic extraction has been used as k z !1for the efficient computation of the Sommerfeld integral in (18).…”

“…Efficient computation of dyadic Green's functions (DGF) for antennas in the vicinity of a layered dielectric cylinder has been the focus of several studies in recent years [1]- [7]. The infinite series involved converges slowly however, or even diverge, when the source and observation points are located at the same dielectric interface, that is when 0 = = a i .…”

“…The expressions developed in [5] can be used to model source and field points that are at the same dielectric interface with a small azimuth separation 1. However, they are singular when = 0 , hence further investigations have been reported to eliminate the singularity, involving either a hybrid approach [6], or a small argument Hankel function approximation [7]. In the aforementioned studies asymptotic extraction has been considered twice; once for the proper truncation of the infinite series as n !1where an n independent asymptotic expansion coefficient has been introduced, and secondly as k z !1…”