Schelkunoff Formulation of the Sommerfeld Integral for the Hertzian Dipole Located in the Vicinity of Cylindrical Structures

Abstract

AbstractA numerical integration of the Sommerfeld integral is performed using the Schelkunoff formulation for cylindrical media. The Schelkunoff kernel for cylindrical media involves higher order modified Bessel functions with azimuthal summation over higher order modes. As such, the convergence characteristics of the cylindrical integral kernel are strongly dependent on complex linear combinations of higher order Bessel/Hankel/modified Bessel functions, compared to the case of the planar media where only a single Bessel/modified Bessel function of zeroth order is present. Two cylindrical configurations are analyzed using the new formulation, viz. a conducting cylinder and a dielectric‐coated conducting cylinder. The branch‐point singularity in the first configuration is removed using the angular transformation for the Sommerfeld/Schelkunoff formulations. A path deformation technique is used for the second configuration to address the problem of poles and branch‐point singularities on the real axis of integration. The in‐depth analysis of the cylindrical kernels and the integrals with variation in the location of the observation point clearly bring out the relative merits of both formulations for the cylindrical configurations, with the TE/TM coupling for the coated cylinder considered.