# Surface - lattice resonances in 2d arrays of spheres: multipolar interactions and a mode analysis

## TL;DR

This paper develops a multipolar model for surface-lattice resonances in 2D sphere arrays, revealing the roles of various multipoles, mode excitations, and their sensitivity to illumination, with implications for understanding band gaps and mode coupling.

## Contribution

It introduces a comprehensive multipolar model including non-resonant multipoles and links SLRs to array modes, advancing the understanding of resonant phenomena in 2D sphere arrays.

## Key findings

- Identification of dipolar and multipolar SLRs
- Importance of non-resonant multipoles in SLR description
- Explanation of band gap formation and mode coupling

## Abstract

We present a multipolar model of surface - lattice resonances (SLRs) in 2d arrays of spheres including the electric dipole, magnetic dipole, and electric quadrupole moments of the spheres. We identify SLRs of dipolar and multipolar character, show the importance of non-resonant multipoles in their description, and discuss the sensitivity of SLRs to illumination conditions. We link SLRs to an excitation of modes supported by the array, and we propose a simplified model of the mode dispersion relations that explains the sensitivity of SLRs and the band gap in mode dispersion found at low frequencies. Finally we discuss the resonant features associated with a direct coupling to a mode which can occur in addition to the diffractive coupling signalled by SLRs.