Electric and magnetic dipole and quadrupole coupling in an effective medium description of amorphous arrays of optical nanoresonators

Abstract

The optical properties of spherical nanoparticles are described by Mie theory which yields their multipole electric and magnetic resonances. Their characteristics (and presence) depend on nanoparticle size and material. For sufficiently small metallic nanoparticles the response is determined by the electric dipolar polarizability in the small particle limit. However, as the size increases, higher order electric multipoles have to be accounted for. Although, not particularly strong, the magnetic response of metallic nanoparticles can also lead to significant optical effects when the nanoparticle is placed in an array. It is, however, significantly stronger in dielectric nanoparticles due to circular displacement current of the electric field. The orientation of the induced magnetic dipole is perpendicular to that of the corresponding electric dipole. As in the case of metallic nanoparticles higher order multipoles have to be considered. This work focuses on amorphous arrays of nanoparticles in which the nanoparticles are placed randomly using a random sequential adsorption algorithm (RSA) with the condition that a minimum center-to-center distance (lcc) between the nanoparticles is present, lcc=CCxD, where D is the nanoparticle diameter and CC is a dimensionless parameter. For simplicity it is assumed that all the nanoparticles have the same diameter. Building upon previous work, we develop a framework in which a localized optical mode of an amorphous array of discrete nanoparticles is self-consistently calculated by assuming that, on average, the nanoparticle is excited by the same field consisting of the incident field and the average scattered field from all the other particles in the system. In this work, this approach is extended to include higher order modes as well as those of the magnetic character. First, the extinction cross-section spectra for dielectric spherical nanoparticles are analyzed as a function of size in terms of contributions from various multipoles. Then, the effective medium description of amorphous arrays of nanoparticles is presented and supported by numerical calculations with T-Matrix method.