Construction of Green's functions of parallel plates with periodic texture with application to gap waveguides – a plane-wave spectral-domain approach

Abstract

This study presents Green's functions of parallel-plate structures, where one plate has a smooth conducting surface and the other an artificial surface realised by a one-dimensional or two-dimensional periodic metamaterial-type texture. The purpose of the periodic texture is to provide cutoff of the lowest order parallel-plate modes, thereby forcing electromagnetic energy to follow conducting ridges or strips, that is, to form a gap waveguide as recently introduced. The Green's functions are constructed by using the appropriate homogenised ideal or asymptotic boundary conditions in the plane-wave spectral domain, thereby avoiding the complexity of the Floquet-mode expansions. In the special case of a single ridge or strip, an additional numerical search for propagation constants is needed and performed in order to satisfy the boundary condition on the considered ridge or strip in the spatial domain. The results reveal the dispersion characteristics of the quasi-transverse electromagnetic modes that propagate along the ridges or strips, including their lower and upper cutoff frequencies, as well as the theoretical decay of the modal field in the transverse cutoff direction. This lateral decay shows values of 50-100 dB per wavelength for realisable geometries, indicating that the gap waveguide modes are extremely confined. The analytical formulas for the location of the stopband of the lowest order parallel-plate modes obtained by small-argument approximation of the dispersion equation are also shown. To verify the proposed analysis approach, the results are compared with the results obtained with a general electromagnetic solver showing very good agreement.

A frequency-dependent equivalence between groove gap waveguide and rectangular waveguide

“…Homogenization of the structure based on metamaterial analogies has led to analytical models [17]- [19], however unlike metamaterials, the periodic structure in GGW can be comparable with the operating wavelength, thus calling into question their general applicability, [17]- [21].…”

Analytical Dispersion Characteristic of a Gap-Groove Waveguide

“…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].…”

Analysis and design of efficient passive components for the millimeter-wave and THz bands

“…In [883], the previous work is extended and posed in a detailed and organized way. In this case, not only the periodic structure is considered, but the fundamental mode propagating in a RGW is also calculated through the SD approach.…”