Diffraction Phenomena in Time-Varying Metal-Based Metasurfaces

Abstract

This paper presents an analytical framework for the analysis of time-varying metal-based metamaterials. Specifically, we particularize the study to time-modulated metal-air interfaces embedded between two different semi-infinite media that are illuminated by monochromatic plane waves of frequency ${\ensuremath{\omega}}_{0}$. The formulation is based on a Floquet-Bloch modal expansion, which takes into account the time periodicity of the structure (${T}_{s}=2\ensuremath{\pi}/{\ensuremath{\omega}}_{s})$ and integral-equation techniques. It allows us to extract the reflection and transmission coefficients as well as to derive nontrivial features about the dynamic response and dispersion curves of time-modulated metal-based screens. In addition, the proposed formulation has an associated analytical equivalent circuit that gives a physical insight into the diffraction phenomenon. Similarities and differences between space- and time-modulated metamaterials are discussed via the proposed circuit model. Finally, some analytical results are presented to validate the present framework. Good agreement is observed with numerical computations provided by a self-implemented finite-difference time-domain (FDTD) method. Interestingly, the present results suggest that time-modulated metal-based screens can be used as pulsed sources (when ${\ensuremath{\omega}}_{s}\ensuremath{\ll}{\ensuremath{\omega}}_{0}$), beam formers (${\ensuremath{\omega}}_{s}\ensuremath{\sim}{\ensuremath{\omega}}_{0}$) to redirect energy in specific regions of space, and analog samplers (${\ensuremath{\omega}}_{s}\ensuremath{\gg}{\ensuremath{\omega}}_{0}$).