Modeling four-dimensional metamaterials: a T-matrix approach to describe time-varying metasurfaces.

Exploring the interaction of light with materials periodically structured in space and time is intellectually rewarding and, simultaneously, a computational challenge. Appropriate computational tools are urgently needed to explore how such upcoming photonic materials can control light on demand. Here, we introduce a semi-analytical approach based on the transition matrix (also known as T-matrix) to analyze the optical response of a spatiotemporal metasurface. The metasurface consists of a periodic arrangement of time-varying scattering particles. In our approach, we depart from an individual scatterer's T-matrix to construct the effective T-matrix of the metasurface. From that effective T-matrix, all observable properties can reliably be predicted. We verify our semi-analytical approach with full-wave numerical simulations. We demonstrate a speed-up with our approach by a factor of more than 500 compared to a finite-element simulation. Finally, we exemplify our approach by studying the effect of time modulation on a Huygens' metasurface and discuss some emerging observable features.

Excitation of nonradiating magnetic anapole states with azimuthally polarized vector beams.

Nonradiating current configurations have been drawing the attention of the physics community for many years. It has been demonstrated recently that dielectric nanoparticles provide a unique platform to host such nonradiating modes, called "anapoles". Here we study theoretically the excitation of such exotic anapole modes in silicon nanoparticles using structured light. Alternative illumination configurations, properly designed, are able to unlock hidden behavior of scatterers. Particularly, azimuthally polarized focused beams enable us to excite ideal anapole modes of magnetic type in dielectric nanoparticles. Firstly, we perform the decomposition of this type of excitation into its multipolar content and then we employ the T-matrix method to calculate the far-field scattering properties of nanoparticles illuminated by such beams. We propose several configuration schemes where magnetic anapole modes of simple or hybrid nature can be detected in silicon nanospheres, nanodisks and nanopillars.