Designing Multipolar Resonances in Dielectric Metamaterials

Dielectric resonators form the building blocks of nano-scale optical antennas and metamaterials. Due to their multipolar resonant response and low intrinsic losses they offer design flexibility and high-efficiency performance. These resonators are typically described in terms of a spherical harmonic decomposition with Mie theory. In experimental realizations however, a departure from spherical symmetry and the use of high-index substrates leads to new features appearing in the multipolar response. To clarify this behavior, we present a systematic experimental and numerical characterization of Silicon disk resonators. We demonstrate that for disk resonators on low-index quartz substrates, the electric and magnetic dipole modes are easily identifiable across a wide range of aspect-ratios, but that higher order peaks cannot be unambiguously associated with any specific multipolar mode. On high-index Silicon substrates, even the fundamental dipole modes do not have a clear association. When arranged into arrays, resonances are shifted and pronounced preferential forward and backward scattering conditions appear, which are not as apparent in individual resonators and may be associated with interference between multipolar modes. These findings present new opportunities for engineering the multipolar scattering response of dielectric optical antennas and metamaterials, and provide a strategy for designing nano-optical components with unique functionalities.