The relation between creeping waves, leaky waves, and surface waves

In this paper, we examine the creeping wave propagation wavenumbers, modal impedance, and field behavior on a dielectric coated circular cylinder. The physical interpretation is assisted by comparing the cylinder's pole waves with the leaky waves and surface waves that occur on a flat, grounded dielectric slab. The propagation wavenumbers and modal impedance are computed in the complex wavenumber plane. The cylinder propagation wavenumbers come from a transcendental equation involving Hankel functions, which are entire functions of complex order, whereas for the slab, branch-point singularities are present. This difference is examined, so that one can better understand how a coated cylinder behaves like a flat slab, when the cylinder radius is large. It is found that for the cylinder, the Stokes line for the asymptotic expansion of the Hankel function plays a role that is similar to the planar slab branch cut.