Cartesian multipole expansion for millimeter-wave metasurfaces design

Abstract

Metasurfaces in the microwave and millimeter-wave frequency ranges are conventionally designed through trial-and-error approaches using full-wave electromagnetic simulation packages that rely on discretization techniques to numerically solve differential equations. Although some studies in the literature propose semi-analytical approaches to improve design efficiency, a purely analytical framework remains elusive. Here, we apply the multipole expansion method, a classic approach from electromagnetism courses typically used for isolated scatterers, which has recently gained attention in the field of nanophotonics. In contrast to nanophotonics, where precise modeling requires detailed permittivity information, metals at microwave and millimeter-wave frequencies exhibit negligible penetration depths and limited electromagnetic–matter interaction. This simplification allows us to focus on conduction currents alone (given σ≫ωε) to describe the material’s response. Notably, we show that only four non-zero multipole terms are needed to achieve high accuracy in reproducing full-wave electromagnetic simulations, with results that also exhibit excellent qualitative agreement with experimental data.