Multipole couplings in dielectric nanodisk arrays and their polarization effects

Abstract

In this paper, we study the optical properties of a planar array consisting of nanodisks using the coupled multipole model (CMM). As we demonstrate, this model shows its advantages in uncovering the complex inter-particle mutual interaction mechanisms, which are usually obscured by direct numerical simulations. We first propose a method to compute the polarizabilities of the individual non-spherical particles up to the magnetic quadrupole. Then, the multipole moments of the arrayed nanodisks can be readily calculated. Using the results, we were able to trace the dominant contributions from the various couplings between these multipole sources. From such analysis, we reveal the mechanisms of multipole resonance shifts and possible manipulation strategies. These insights rendered by the CMM make it possible to design the array as a polarizer by tuning the lattice periods. We further evaluated the polarizer performance under different working wavelengths and incident angles. As the disk shape is relatively less challenging for fabrication, our model shows great promise in optimizing and designing functional structures for nano-optics applications.