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

Analysis of Metallic Space-Time Gratings Using Lorentz Transformations

“…( 25). This result can serve as a basis to analyze the moving grating via Floquet-Bloch expansions (taking advantage of the space-time periodicity) together with integral-equation methods [42,64].…”

“…Other numerical approaches include the method of moments [36], circuital interpretations [37], and others [38,39]. In several cases, validations of the models are done by comparison with the results provided by home-made finite difference in the time-domain codes [33,[40][41][42][43][44].…”