Quasi-Bound States in the Continuum-Induced Second Harmonic Generation Enhancement in High-$Q$ Triple Dielectric Nanoresonators

High-$Q$ optical nanocavities are fundamental to modern optics and photonics, enabling enhanced light-matter interactions. Previous studies have demonstrated that high-$Q$ supercavity modes can be constructed within a single dielectric resonator by leveraging quasi-bound states in the continuum. However, their $Q$-factors are limited to few tens or hundreds when such a resonator is subwavelength scale. Here, we propose a general recipe for achieving high-$Q$ resonances with $Q>10,000$ in triple subwavelength dielectric resonators. This is realized through destructive interference between two resonant modes, optimized by structural tuning. Multipole analysis confirms that destructive interference across radiation channels suppresses loss, forming the ultrahigh-$Q$ states. These resonances can be efficiently excited by azimuthally polarized light due to improved mode overlap. As a key application, we demonstrate efficient second harmonic generation under this excitation, achieving a conversion efficiency of $6.6\%$ at an incident intensity of 0.78 GW/cm$^2$. Our results may find exciting applications in developing ultracompact photonic devices with superior performance.