Optical Nonlinearity in Silicon Nanowires Enabled by Bound States in the Continuum.

Intense electromagnetic fields localized within resonant photonic nanostructures provide versatile opportunities for engineering nonlinear optical effects on a subwavelength scale. For dielectric structures, optical bound states in the continuum (BICs, resonant nonradiative modes that exist within the radiation continuum) are an emerging strategy to localize and intensify fields. Here, we report efficient second and third harmonic generation from Si nanowires (NWs) encoded with BIC and quasi-BIC resonances. In situ dopant modulation during vapor-liquid-solid NW growth was followed by wet-chemical etching to periodically modulate the diameter of the Si NWs and create cylindrically symmetric geometric superlattices (GSLs) with precisely defined axial and radial dimensions. By variation of the GSL structure, BIC and quasi-BIC resonant conditions were created to span visible and near-infrared optical frequencies. To probe the optical nonlinearity of these structures, we collected linear extinction spectra and nonlinear spectra from single-NW GSLs, demonstrating that quasi-BIC spectral positions at the fundamental frequency are directly correlated with enhanced harmonic generation at second and third harmonic frequencies. Interestingly, we find that deliberate geometric detuning from the BIC condition leads to a quasi-BIC resonance with maximal harmonic generation efficiency by providing a balance between the capacity to trap light and the capacity to couple to the external radiation continuum. Moreover, under focused illumination, as few as 30 geometric unit cells are required to achieve more than 90% of the approximate maximum theoretical efficiency of an infinite structure, indicating that nanostructures with projected areas smaller than ∼10 µm2 can support quasi-BICs for efficient harmonic generation. The results represent an important step toward the design of efficient harmonic generation at the nanoscale and further highlight the photonic utility of BICs at optical frequencies in ultracompact one-dimensional nanostructures.