Modeling and Design of a Partially Air-Filled Slow Wave Substrate Integrated Waveguide

In this article, a partially air-filled and slow wave substrate integrated waveguide (PAF-SW-SIW) build in the metallic nanowires membrane (MnM) technology is studied, fabricated, and measured. The impact of the nanowire conductivity on the slow wave factor (SWF) is quantified, and expressions of the effective permittivity and the effective loss tangent are found for the considered propagation medium. These parameters are expressed as a function of the air layer thickness and the equivalent conductivity of copper nanowires embedded in the nanoporous membrane. Electromagnetic (EM) simulations are used to validate these expressions, and a good agreement is obtained on both of these parameters for a conductivity between 1 and 1M S/m and for various air layer thicknesses, from 5 to 20
$\mu \text{m}$
. In addition, the attenuation constant of nanowires is studied, and the results show a rapid increase of losses in the side walls of the waveguide for a conductivity lower than 100k S/m. Two sets of PAF-SW-SIW with the cutoff frequencies at 50 and 75 GHz, respectively, were fabricated and measured, resulting in attenuation constants between 0.25 and 0.38 dB/mm and between 0.28 and 0.75 dB/mm in the respective single-mode frequency band of these integrated waveguides.