  Recent progress in nanoscale optical physics is associated with the
development of a new branch of nanophotonics exploring strong Mie resonances in
dielectric nanoparticles with high refractive index. The high-index resonant
dielectric nanostructures form building blocks for novel photonic metadevices
with low losses and advanced functionalities. However, unlike extensively
studied cavities in photonic crystals, such dielectric resonators demonstrate
low quality factors (Q-factors). Here, we uncover a novel mechanism for
achieving giant Q-factors of subwavelength nanoscale resonators by realizing
the regime of bound states in the continuum. We reveal strong mode coupling and
Fano resonances in high-index dielectric finite-length nanorods resulting in
high-Q factors at the nanoscale. Thus, high-index dielectric resonators
represent the simplest example of nanophotonic supercavities, expanding
substantially the range of applications of all-dielectric resonant
nanophotonics and meta-optics.
