Dipole‐Quadrupole Model and Multipole Analysis of Resonant Membrane Metasurfaces

Membrane metasurfaces, formed by periodic arrangements of holes in a dielectric layer, are gaining attention for their easier
manufacturing via subtractive techniques, unnecessity of substrates, and access to resonant near fields. Despite their practical
relevance, their theoretical description remains elusive. Here, we present a semi-analytical dipole-quadrupole model for the
multipole analysis of numerically obtained reflection and transmission spectra in metasurfaces excited at arbitrary angles. Dipole
models are generally sufficient to study traditional metasurfaces made of solid nanostructures. However, the inclusion of electric
and magnetic quadrupoles is necessary to study membrane metasurfaces, which offer an ideal platform to showcase our method.
We demonstrate the importance of choosing the optimal position of a symmetric membrane metasurface’s unit cell to ensure the
sufficiency of the dipole-quadrupole approximation. We show that our formalism can explain complex phenomena arising from
inter-multipole interference, including lattice anapole and generalized Kerker effects, Fano resonances, and quasi-bound states in
the continuum. We also present the applicability of the method to membrane metasurfaces with non-centrosymmetric unit cells
(e.g., conical holes and surface voids). By enabling a deeper insight into the coupling mechanisms leading to the formation of
local and collective resonances, our method expands the electromagnetics toolbox to study, understand, and design conventional
and membrane metasurfaces.