Optimum Forward Light Scattering by Spherical and Spheroidal Dielectric Nanoparticles with High Refractive Index

High-refractive index dielectric nanoparticles may exhibit strong directional forward light scattering at visible and near-infrared wavelengths due to interference of simultaneously excited electric and magnetic dipole resonances. For a spherical particle shape, the so-called first Kerker's condition can be realized, at which the backward scattering practically vanishes for some combination of refractive index and particle size. However, realization of Kerker's condition for spherical particles is only possible at the tail of the scattering resonances, when the particle scatters light weakly. Here we demonstrate that significantly higher forward scattering can be realized if spheroidal particles are considered instead. For each value of refractive index n exists an optimum shape of the particle, which produces minimum backscattering efficiency together with maximum forward scattering. This effect is achieved due to the overlapping of magnetic and electric dipole resonances of the spheroidal particle at the resonance frequency. It permits the design of very efficient, low-loss optical nanoantennas. We show that the results obtained for spheroidal particles can accurately describe the response of a wide range of practical particle shapes with the same aspect ratio, which can be obtained in experiment.