Parallel-Plate Waveguide Formed by Time-Varying Impenetrable Metasurfaces

In this paper, we investigate the eigenmode of a parallel-plate waveguide formed by two impenetrable metasurfaces with arbitrary homogeneous surface capacitances. We begin by deriving the dispersion relations under stationary conditions, where the capacitance remains fixed over time. Subsequently, we analytically explore the band structure under time-varying conditions, assuming the surface capacitance is uniform in space but periodically modulated in time. Notably, we demonstrate that the momentum bandgap of this system can be manipulated by adjusting the phase differences of the modulation function applied to two parallel sheets.