A Comprehensive Multipolar Theory for Periodic Metasurfaces

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.

43 pages (Main: 23, SM: 20), 9 Figures, 2 Tables

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• A Perfect Metamaterial Absorber
• High-efficiency light-wave control with all-dielectric optical Huygens' metasurfaces
• Metasurface holography: from fundamentals to applications
• Cooperative resonances in light scattering from two-dimensional atomic arrays
• Theory of metasurface based perfect absorbers
• Theory, design, and experimental verification of a reflectionless bianisotropic Huygens' metasurface for wide-angle refraction
• Full transmission through perfect-conductor subwavelength hole arrays
• Interference between the modes of an all-dielectric meta-atom
• Isotropic Huygens dipoles and multipoles with colloidal particles
• Optical Force and Torque on Dipolar Dual Chiral Particles

Cited by in corpus (15)

• Minireview on Disordered Optical Metasurfaces
• Multipolar theory of bianisotropic response
• A T-matrix Based Approach to Homogenize Artificial Materials
• Inverse Design of All-dielectric Metasurfaces with Bound States in the Continuum
• Design of reconfigurable Huygens metasurfaces based on Drude-like scatterers operating in the epsilon-negative regime
• Exploring Functional Photonic Devices made from a Chiral Metal-Organic Framework Material by a Multiscale Computational Method
• Lattice Sums Accommodating Multiple Sublattices for Solutions of the Helmholtz Equation in Two and Three Dimensions
• Inverse-designed dispersive time-varying nanostructures
• Quadrupolar susceptibility modeling of substrated metasurfaces with application to the generalized Brewster effect
• Optical Supertorque Induced by Mie-Resonant Modes
• Lattice-induced sound trapping in biperiodic metasurfaces of acoustic resonators
• Generalizing the exact multipole expansion: Density of multipole modes in complex photonic nanostructures
• Analyzing the acceleration time and reflectance of light sails made from homogeneous and core-shell spheres
• Cartesian and spherical multipole expansions in anisotropic media
• Singular value decomposition to describe bound states in the continuum in periodic metasurfaces