TMz/TEz Vector Potentials Due to an Arbitrarily Oriented Dipole in 3‐D Space in the Presence of an Infinite Dielectric Cylinder

Abstract

AbstractThis manuscript provides a new formulation for the classic electromagnetic scattering problem of a point dipole source in the presence of an infinite lossy dielectric cylinder embedded within a lossy space. The formulation is in terms of the TMz and TEz vector potential components (scalar potentials) Az and Fz for an arbitrary dipole orientation. A new Bessel function identity, apparently derived here for the first time, shows that the new solution is equivalent to the previous dyadic vector wave function solutions that solve for the electric and magnetic fields directly. Expressions for the scattered potential coefficients, for a dipole inside or outside the cylinder, can be reduced to a linear set of two equations that has a simple closed‐form solution. The new potential formulation should find application in the numerical solution of various problems in electromagnetics and geophysics involving tunnels or other structures that can be modeled as cylinders.