Dispersion Characteristics of a Metamaterial-Based Parallel-Plate Ridge Gap Waveguide Realized by Bed of Nails

The newly introduced parallel-plate ridge gap waveguide consists of a metal ridge in a metamaterial surface, covered by a metallic plate at a small height above it. The gap waveguide is simple to manufacture, especially at millimeter and sub-millimeter wave frequencies. The metamaterial surface is designed to provide a frequency band where normal global parallel-plate modes are in cutoff, thereby allowing a confined gap wave to propagate along the ridge. This paper presents an approximate analytical solution for this confined quasi-TEM dominant mode of the ridge gap waveguide, when the metamaterial surface is an artificial magnetic conductor in the form of a bed of nails. The modal solution is found by dividing the field problem in three regions, the central region above the ridge and the two surrounding side regions above the nails. The fields within the side regions are expressed in terms of two evanescent TE and TM modes obtained by treating the bed of nails as an isotropic impedance surface, and the field in the central ridge region is expanded as a fundamental TEM parallel-plate mode with unknown longitudinal propagation constant. The field solutions are linked together by equalizing longitudinal propagation constants and imposing point-continuity of fields across the region interfaces, resulting in a transcendental dispersion equation. This is solved and presented in a dispersion diagram, showing good agreement with a numerical solution using a general electromagnetic solver. Both the lower and upper cutoff frequencies of the normal global parallel-plate modes are predicted, as well as the quasi-TEM nature of the gap mode between these frequencies, and the evanescent fields in the two side regions decay very rapidly away from the ridge.