  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 high-index dielectric, 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, 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 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.
