  Bound states in the continuum (BICs) represent localized modes with energies
embedded in the continuous spectrum of radiating waves. BICs were discovered
initially as a mathematical curiosity in quantum mechanics, and more recently
were employed in photonics. Pure mathematical bound states have
infinitely-large quality factors (Q factors) and zero resonant linewidth. In
optics, BICs are physically limited by a finite size, material absorption,
structural disorder, and surface scattering, and they manifest themselves as
the resonant states with large Q factors, also known as supercavity modes or
quasi-BICs. Optical BIC resonances have been demonstrated only in extended 2D
and 1D systems and have been employed for distinct applications including
lasing and sensing. Optical quasi-BIC modes in individual nanoresonators have
been discovered recently but they were never observed in experiment. Here, we
demonstrate experimentally an isolated subwavelength nanoresonator hosting a
quasi-BIC resonance. We fabricate the resonator from AlGaAs material on an
engineered substrate, and couple to the quasi-BIC mode using structured light.
We employ the resonator as a nonlinear nanoantenna and demonstrate record-high
efficiency of second-harmonic generation. Our study brings a novel platform to
resonant subwavelength photonics.
