A Comprehensive Multipolar Theory for Periodic Metasurfaces

Abstract

Optical metasurfaces consist of 2D arrangements of scatterers, and they control the amplitude, phase, and polarization of an incidence field on demand. Optical metasurfaces are the cornerstone for a future generation of flat optical devices in a wide range of applications. The rapid advances in nanofabrication have made the versatile design and analysis of these ultra‐thin surfaces an ever‐growing necessity. However, a comprehensive theory to describe the optical response of periodic metasurfaces in closed‐form and analytical expressions has not been formulated, and prior attempts are frequently approximate. Here, a theory is developed that analytically links the properties of the scatterer, from which a metasurface is made, to its response via the lattice coupling matrix. The scatterers are represented by their polarizability or T matrix. Explicit expressions for the optical response up to octupolar order in both spherical and Cartesian coordinates are provided, for normal or oblique incidence. Several examples demonstrate that the proposed theoretical approach is a powerful tool for exploring the physics of metasurfaces and designing novel flat optics devices. Novel fully‐diffracting metagratings and particle‐independent polarization filters are proposed, and novel insights into bound states in the continuum, collective lattice resonances, and the response of Huygens’ metasurfaces under oblique incidence are provided.

A Multi‐Scale Approach for Modeling the Optical Response of Molecular Materials Inside Cavities

“…[23] (see also ref. [38]), $${T_{{\rm{eff}}}}$$ collects the multi‐scattering response of a unit cell in the lattice. In effect, one can then conceptually equate two systems: On the one hand, the infinite array of interacting unit cells, each characterized by $$T$$, that we have been considering so far, and, on the other hand, an infinite array of non‐interacting unit cells, each characterized by $${T_{{\rm{eff}}}}$$.…”

Exploring Functional Photonic Devices made from a Chiral Metal-Organic Framework Material by a Multiscale Computational Method

“…In this case, lattice resonances can collectively couple the multipoles sustained by the cylinders. To explain the emergence of lattice resonances and the characterization of the collective coupling of multipoles inside a lattice, see [66,67], for instance. The asymmetric Fano resonance observed in this spectral range in the circular dichroism spectra indicates an interference of different competing pathways determining whether the lattice resonance is left-or right-handed and, therefore, also the sign of the circular dichroism, see [61].…”

A T‐Matrix Based Approach to Homogenize Artificial Materials

“…Above such limit, we observe a resonance of the electric permittivity and an additional resonance of the magnetic permeability due to the electric quadrupole coupling to the magnetic dipole. [ 76 ] The first N = 7 multipolar orders were included in the calculations of $${{{\bf T}}_{{\rm{eff}}}}$$. The $$\tau ({{{\bf T}}_{{\rm{eff}}}})$$ metric of Equation () is shown in Figure 5f, where we see that $$\tau ({{{\bf T}}_{{\rm{eff}}}})$$ is more than two orders of magnitude higher than in the previous example, including a peak value of 0.045 in the homogenizable frequency range, and an increasing trend toward a very large peak well beyond the 240 THz limit.…”