Diffraction Phenomena in Time-Varying Metal-Based Metasurfaces

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 w0. The formulation is based on a Floquet-Bloch modal expansion, which takes into account the time periodicity of the structure (T-s = 2 pi/w(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 w(s) << w(0)), beam formers (ws similar to w(0)) to redirect energy in specific regions of space, and analog samplers (w(s) >> w(0)).