Spacetime Metamaterials

ABSTRACT

This paper presents the authors’ vision ofthe emerging field of spacetime metamaterials in a cohesive and pedagogical perspective. For this purpose, it systematically builds up the physics, modeling and applications of these media upon the foundation of their pure-space and pure-time counterparts. First, it introduces spacetime metamaterials as ageneralization of (bianisotropic) metamaterials, presented in the holistic perspective of direct and inverse spacetime scattering,where spacetime variance and dispersion offer unprecedented medium diversity despite some limitations related to the un-certainty principle. Then, it describes the fundamental physical phenomena occurring in spacetime systems, such as frequency transitions, nonreciprocity, Fizeau dragging, bianisotropy trans-formation, and superluminality, allowed when the medium moves perpendicularly to the direction of the wave. Next, it ex-tends some principles and tools of relativity physics, particularlya medium-extended version of the spacetime (or Minkowski)diagrams, elaborates a general strategy to compute the fields scattered by spacetime media, and presents a gallery of possible spacetime media, including the spacetime step discontinuity,which constitutes the building brick of any spacetime meta-material. From this point, it describes the phenomenology of such a spacetime interface, deduces from it the related electro-magnetic boundary conditions, and derives the corresponding scattering (Fresnel-like) coefficients and frequency transitions, culminating with a section that generalizes time reversal to spacetime compansion (compression and expansion). Then, a section illustrates the new physics of spacetime metamaterials with the examples of spacetime mirrors and cavities, the inverse prism and chromatic birefringence, and spacetime crystals.Finally, the paper discusses various applications – categorized as frequency multiplication and mixing, matching and filtering, nonreciprocity and absorption, cloaking, electromagnetic processing, and radiation. Ultimately, the conclusion section provides a 23-item list that concisely summarizes the key results and teachings of the overall document.