  High refractive index dielectric nanostructures provide original optical
properties thanks to the occurrence of size- and shape-dependent optical
resonance modes. These modes commonly present a spectral overlap of broad,
low-order modes (\textit{e.g}. dipolar modes) and much narrower, higher-order
modes. The latter are usually characterized by a rapidly varying
frequency-dependent phase, which - in superposition with the lower order mode
of approximately constant phase - leads to typical spectral features known as
Fano resonances. Interestingly, such Fano resonances occur in dielectric
nanostructures of the simplest shapes. In spheroidal nanoparticles,
interference between broad magnetic dipole and narrower electric dipole modes
can be observed. In high aspect-ratio structures like nanowires, either the
electric or the magnetic dipolar mode (depending on the illumination
conditions) interferes with higher order multipole contributions of the same
nature (electric or magnetic). Using the analytical Mie theory, we analyze the
occurrence of Fano resonances in high-index dielectric nanowires and discuss
their consequences like unidirectional scattering. By means of numerical
simulations, we furthermore study the impact on those Fano resonances of the
shape of the nanowire cross-sections as well as the coupling of two parallel
nanowires. The presented results show that all-dielectric nanostructures, even
of simple shapes, provide a reliable low-loss alternative to plasmonic
nanoantennas.
