Complete multipolar description of reflection and transmission across a metasurface for perfect absorption of light

Relating the electromagnetic scattering and absorption properties of an individual particle to the reflection and transmission coefficients of a two-dimensional material composed of these particles is a crucial concept that has driven both fundamental and applied physics. It is at the heart of both the characterization of material properties as well as the phase and amplitude engineering of a wave. Here we propose a multipolar description of the reflection and transmission coefficients across a monolayer of particles using a vector spherical harmonic decomposition. This enables us to provide a generalized condition for perfect absorption which occurs when both the so-called \textit{generalized Kerker condition} is reached and when the superposition of odd and even multipoles reaches a critical value. Using these conditions, we are able to propose two very different designs of two-dimensional materials that perfectly absorb a plane electromagnetic wave under normal incidence. One is an infinite array of silica microspheres that operates at mid-infrared frequencies, while the other is an infinite array of germanium nano-clusters that operates at visible frequencies. Both systems operate in a deeply multipolar regime. Our findings are important to the metamaterials and metasurfaces communities who design materials mainly restricted to the dipolar behavior of individual resonators, as well as the self-assembly and nanochemistry communities who separate the individual particle synthesis from the materials assembly.