Field of an axially circular cylinder clad with an inhomogeneous dielectric

This paper is concerned with the problem of an axial slot on a circular cylinder clad with a radially inhomogeneous dielectric of the form
\epsilon(\rho)=(\rho/b)^{2p}, a \leq \rho \leq b
, where
a
is the radius of the conducting cylinder,
b
is the outer radius of the dielectric coating, and
p
is an arbitrary parameter. The assumed profile is capable of representing an inhomogeneous cold plasma when
p > 0
and a real dielectric when
p < 0
. The apparent advantage of the present formulation is that the wave equation can be solved in terms of known functions and the solution can be extended to large cylinders. Field expressions appropriate to small and large cylinders are found using standard methods of harmonic series representation, Watson transformation, and saddle point integration. In the case of large cylinders coated with cold plasma, the radiation patterns are plotted for various combinations of the cylinder radius, thickness of the coating, and the inhomogeneity gradient. The radiation patterns are in good agreement with qualitative arguments of geometric optics.