A Comprehensive Multipolar Theory for Periodic Metasurfaces

TL;DR

This paper introduces a comprehensive analytical theory for periodic metasurfaces, enabling precise prediction of their optical response and facilitating the design of advanced flat optical devices.

Contribution

The authors develop a closed-form, analytical framework linking scatterer properties to metasurface optical response, applicable to various incidence angles and multipolar orders.

Findings

Analytical expressions for metasurface response up to octupolar order.

Design of novel fully-diffracting metagratings and polarization filters.

New insights into Huygens' metasurfaces under oblique incidence.

Abstract

Optical metasurfaces consist of a 2D arrangement 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 rapidly growing advances in nanofabrication have made the versatile design and analysis of these ultra-thin surfaces an ever-growing necessity. However, despite their importance, a comprehensive theory to describe the optical response of periodic metasurfaces in closed-form and analytical expressions has not been formulated, and prior attempts were frequently approximate. Here, we develop a theory that analytically links the properties of the scatterer, from which a periodic metasurface is made, to its optical response via the lattice coupling matrix. The scatterers are represented by their polarizability or T matrix, and our theory works for normal and oblique incidence. We provide explicit expressions for the optical response up to octupolar order in both spherical and Cartesian coordinates. Several examples demonstrate that our analytical tool constitutes a paradigm shift in designing and understanding optical metasurfaces. Novel fully-diffracting metagratings and particle-independent polarization filters are proposed, and novel insights into the response of Huygens' metasurfaces under oblique incidence are provided. Our analytical expressions are a powerful tool for exploring the physics of metasurfaces and designing novel flat optics devices.