Analytical Modeling of a Parallel-Plate Waveguide Partially Filled by Thick Pins for Gap Waveguide Technology Applications

Periodic pin-based metasurfaces, often referred to as bed-of-nails (BoN) structures, constitute a key enabling element in gap waveguide technology. When such a metasurface is employed as one wall of a parallel-plate waveguide (PPW) with a perfect electric conductor (PEC) on the opposite side, the resulting configuration inherits the guiding principles of gap waveguides while allowing for analytical treatment. In this framework, the metasurface response exhibits polarization selectivity. Under TMy excitation, it can be modeled as a dispersive surface reactance governed by an effective plasma wavenumber, whereas under TEy excitation, the dominant contribution arises from the metallic ground plane at the base of the pins and can be captured through an effective sheet impedance. An analytical boundary model for the metasurface is presented, and characteristic equations are derived for dispersion analysis in the PEC–metasurface PPW configuration. The resulting formulation provides a compact and efficient tool for predicting cut-on transitions and for evaluating the influence of key geometric parameters, including pin period, width, height, and the air gap to the PEC plate, within the design framework of gap waveguide technology. A central contribution of the proposed formulation is the extension of existing analytical models to realistic finite-width pin geometries. In addition to predicting the propagating dispersion branches, the model provides an estimate of the complex propagation constants inside the bandgap, including the attenuation constant associated with evanescent Bloch modes.