How to Exploit Light-Matter Interactions in Space (x,y,z) and Time (t) to Enable Spatiotemporal Effective Materials?

Research and innovation for a full control of light-matter interactions has been facilitated by the fields of metamaterials, optics, and photonics over the past few years. With metamaterials and metasurfaces, for instance, it is possible to make use of subwavelength unit cells arranged in a periodic (or aperiodic) lattice and to achieve effective parameters of permittivity
$(\varepsilon_{reff})$
and permeability
$(\mu_{reff})$
. Such feature has opened new avenues in light-matter manipulation as it is possible to engineer effective parameters with extreme values including near-zero or negative [1–6]. Controlling electromagnetic waves with metamaterials and photonic structures has been an active research topic with many applications being explored such as sensing, waveguiding, machine learning based designs, computing and quantum technologies, among others [7–14]. All these applications have been developed in the time-harmonic scenario exploiting spatial inhomogeneities of material parameters without considering temporal variations of the relative values of
$\varepsilon_{r}$
and
$\mu_{r}$
of the materials where the wave is traveling.