Scattering from a dielectric cylinder axially loaded with periodic metallic rings

Interest has been moving to the numerical study of the scattering from cylindrical corrugated structures which have longitudinal periodicity. As a matter of fact new antenna struts, that minimize the reduction of the directivity and the increase of side lobes levels, have been designed by making the strut non-uniform in the axial direction. In this context, to give a reference solution to validate present and future numerical models, an analytical solution for the electromagnetic scattering by an infinitely long cylinder of circular cross section coated by metallic annular rings placed at the same distance from each other is presented. The solution is given in terms of a superposition of the field scattered from the cylinder in the absence of and in the presence of the annular rings. This choice permits one to take advantage of the well-known solution of the scattering from a uniform permeable cylinder as well as to write easier boundary conditions for the field that takes into account the periodic rings which are explicitly independent from the polarization of the incident plane wave. The periodicity of the structure has been taken into account expressing the solution of the axially periodic problem in terms of cylindrical Floquet harmonics. Then the expressions of the electric and magnetic transverse coefficients of the cylindrical periodic expansion are provided in closed form.