Uniform Asymptotic Solution for the Surface Magnetic Field Valid Both Within and Outside the Paraxial Region of a Perfect Electrically Conducting Circular Cylinder

摘要

High-frequency methods employed for the perfect electrically conducting circular cylinder form two sets. The uniform theory of diffraction (UTD)-based ones are valid outside the paraxial region while there are others that are accurate, close to the axis of the cylinder. Here we present a uniform asymptotic solution for the surface magnetic field valid both within and outside the paraxial region of a perfect electrically conducting circular cylinder. This is achieved by approximating the Hankel functions by a uniform asymptotic expansion within the spectral integral representation of the relevant Green's function. All the resulted integrals are evaluated analytically in an exact fashion. Such a solution is of interest both for theoretical and for practical reasons. From a theoretical point of view, it is important to have a closed-form solution that copes with the canonical problem of a perfect electrically conducting circular cylinder. From a practical point of view, such a solution provides mutual coupling results and thus predicts compatibility and interference between conformal slot antennas mounted on constant radius cylindrically shaped perfectly conducting hosts. Validity of the proposed asymptotic solution is provided by comparison with published results.