In this paper, we introduce and study parallel-plate waveguides formed by two penetrable metasurfaces having arbitrary isotropic sheet impedances. We investigate guided modes of this structure and derive the corresponding dispersion relations. The conditions under which transverse magnetic and transverse electric modes can exist are discussed, and different scenarios including lossless (reactive) metasurfaces, gain-and-loss sheets and extreme cases are under general consideration. Resonant and non-resonant dispersive sheets and corresponding extreme cases are investigated. Our theoretical results are confirmed with full-wave simulated results considering practical realizations of the proposed parallel-plate waveguide which exploit two frequency-selective surfaces. Finally, the obtained theoretical formulas are applied to study the dispersion diagrams for waves along resonant sheets at different distances between the two identical or different metasurfaces. We hope that this study is useful for future applications at both microwave and optical regimes.
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