Designing dielectric resonators on substrates: combining magnetic and electric resonances.

High-performance integrated optics, solar cells, and sensors require nanoscale optical components at the surface of the device, in order to manipulate, redirect and concentrate light. High-index dielectric resonators provide the possibility to do this efficiently with low absorption losses. The resonances supported by dielectric resonators are both magnetic and electric in nature. Combined scattering from these two can be used for directional scattering. Most applications require strong coupling between the particles and the substrate in order to enhance the absorption in the substrate. However, the coupling with the substrate strongly influences the resonant behavior of the particles. Here, we systematically study the influence of particle geometry and dielectric environment on the resonant behavior of dielectric resonators in the visible to near-IR spectral range. We show the key role of retardation in the excitation of the magnetic dipole (MD) mode, as well as the limit where no MD mode is supported. Furthermore, we study the influence of particle diameter, shape and substrate index on the spectral position, width and overlap of the electric dipole (ED) and MD modes. Also, we show that the ED and MD mode can selectively be enhanced or suppressed using multi-layer substrates. And, by comparing dipole excitation and plane wave excitation, we study the influence of driving field on the scattering properties. Finally, we show that the directional radiation profiles of the ED and MD modes in resonators on a substrate are similar to those of point-dipoles close to a substrate. Altogether, this work is a guideline how to tune magnetic and electric resonances for specific applications.