Multipolar modeling of spatially dispersive metasurfaces

Abstract

An optical metasurface may be modeled using boundary conditions that relate the fields interacting with it to the response of its scattering particles usually expressed in terms of electric and magnetic dipolar responses. Additionally, these boundary conditions also typically account for weak spatial dispersion, such as bianisotropy, to properly model effects like chirality. While such modeling approaches are sufficient for operations in the paraxial limit, they usually fail when larger angles of propagation or electrically large scattering particles are considered. To overcome these limitations, we derive boundary conditions that include dipolar and quadrupolar responses and higher-order spatially dispersive effects and show in which situations they can be useful. Since, this approach requires the introduction of many new effective material parameters in the form of hypersusceptibilities, we also provide an extension to the Lorentz reciprocity and Poynting theorems.