Surface waves on periodic horizontal structures over a flat earth

An analytic theory is presented for the surface waves supported by three types of transmission lines: a Goubau line (C-line), a coaxial line with periodic 360 deg circumferential slots (C-line) and a coaxial line with periodic partial circumferential slots (R-line), in free space as well as in the presence of a lossy flat earth. The theory for the surface waves on an R-line centered in a cylindrical tunnel with earth walls is also derived. A transcendental equation is derived for each of the three lines in free space to determine complex propagation constants gamma = alpha + j beta of the surface waves. For the C- and R-lines, suitable trial functions are chosen for the aperture field distribution in the slots. Numerical results for the C-line agree closely with published results. No comparable check data were found in the literature for the C-line or R-line although certain internal consistency tests were verified.