Giant nonlinear response at the nanoscale driven by bound states in the continuum

Being motivated by the recent prediction of high-$Q$ supercavity modes in subwavelength dielectric resonators, we study the second-harmonic generation from isolated subwavelength AlGaAs nanoantennas pumped by a structured light. We reveal that nonlinear effects at the nanoscale can be enhanced dramatically provided the resonator parameters are tuned to the regime of the bound state in the continuum. We predict a record-high conversion efficiency for nanoscale resonators that exceeds by two orders of magnitude the conversion efficiency observed at the conditions of magnetic dipole Mie resonance, thus opening the way for highly-efficient nonlinear metadevices.