# Parallel-Plate Waveguides Formed by Penetrable Metasurfaces

## TL;DR

This paper introduces a theoretical framework for parallel-plate waveguides made of penetrable metasurfaces, analyzing guided modes, dispersion relations, and practical realizations for microwave and optical applications.

## Contribution

It provides a comprehensive analysis of guided modes and dispersion relations for penetrable metasurface-based waveguides, including practical simulation validation.

## Key findings

- Guided modes depend on metasurface impedance and separation.
- Resonant and non-resonant metasurfaces support different mode behaviors.
- Theoretical results are validated with full-wave simulations.

## Abstract

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.