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

Abstract

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 millimetre and sub-millimetre 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. The evanescent fields in the two side regions decay very rapidly away from the ridge, being in the order of 100dB per lower cutoff wavelengths over most of the single-mode bandwidth.

Analytical Dispersion Characteristic of a Gap-Groove Waveguide

“…The eigenvalue k T M y1 (ω) can be real or purely imaginary depending on wether the frequency is in or out of the stop band of the bed of nails, respectively. This behavior has been widely discussed in [8,9], then we address the reader to those former publications for a better understanding. As clear from Fig.…”

“…Actually, we will see in Section 2.2 that the groove dominant mode is much less dispersive than the T E 10 mode in a waveguide. In [8] we have studied a configuration where the bed of nails is covered by a perfectly conducting (PEC) metal plate, placed at a certain distance h λ from the surface of the nails. In this configuration, the PEC-HIS faces form a parallel plate waveguide, and the dispersion equation for the wavenumber k y of the dominant T E-y and T M -y modes bouncing between the two faces can be described by imposing the vanishing of the tangential electric field at the PEC wall (we stress here that we will use the T M and T E terminology with reference to the y axis).…”

“…For the T E-y mode, the solution is found by the transverse resonance between two PEC walls separated by h + d, since the T E-y mode does not significantly interact with the nails. For the T M -y mode, the wave bounces between a PEC wall and a surface which can be equivalently described through its reflection coefficient Γ s (k y ) [10] or its surface impedance Z s (k y ) [8]. To this purpose, the equivalent impedance of the homogenized surface can be written through a wavenumber-dependent linear combination of the equivalent impedances associated to the TEM and T M modes penetrating in the equivalent homogeneous wire medium.…”

“…Therefore, the demand of low losses and cheap to manufacture waveguides is still a challenge, especially above 30 GHz. In [1][2][3][4][5][6][7][8][9], a basic geometry has been investigated, namely a ridge waveguide comprising two parallel conducting surfaces separated by a small gap. One of the surfaces is provided with metallic pins, and it is known as "bed of nails".…”

“…In this frequency range, called stop-band, the field is prevented from a lateral leakage, thus guaranteeing an excellent confinement in the ridge region. Analytical expressions of the fields in the waveguide have been provided in [5,8,9]. Also, the bed of nails can be substituted by other textures or thin multilayer structures, providing similar HIS conditions [6].…”