$Q$ Factors Exceeding $10^{4}$ in Wavelength-to-Subwavelength-Scale Free-Space Resonators

Abstract

Free-space-addressable optical resonators that combine long photon lifetimes (high $Q$ factors) with strong spatial localization of optical fields (small mode volumes, $V_m$) enhance light-matter interactions with facile far-field excitation. The Purcell factor governing spontaneous emission enhancement scales as $Q\,V_m^{-1}$. Periodically asymmetric resonators, in which perturbations convert bound modes into radiating modes, offer a route to free-space resonances, with the radiative $Q$ factor tuned by the geometric and optical strength of the asymmetry-inducing perturbations. However, free-space resonators that simultaneously achieve high $Q$ and small $V_m$ have remained rare. This limitation arises in part because existing designs do not tailor geometric and optical asymmetries concurrently, thus limiting access to high-$Q$ regimes. Here, we show that jointly tuning geometric and optical asymmetries unlocks a biaxial radiative landscape with iso-$Q$ contours that connect disparate perturbations with equivalent $Q$ factors. We demonstrate this framework with very-large-scale-integrated single-crystalline Si nanoantenna pixels (VINPix) with out-of-plane perturbations of 35-150 nm amorphous Si, SiN$_x$, and SiO$_2$. We experimentally establish biaxial $Q$ factor control in air and achieve $Q$ factors up to $76,000$ at wavelength-scale mode volumes ($V_m \sim 1.7\,\lambda_0^3\,n_{\mathrm{eff}}^{-3}$) in simultaneously imaged arrays of $>80$ resonators in water. Furthermore, we computationally demonstrate 50-nm-wide slotted VINPix that reach $Q$ factors of $10^6$ at subwavelength mode volumes ($V_m \sim 0.2\,\lambda_0^3\,n_{\mathrm{eff}}^{-3}$) with 20 nm SiO$_2$ perturbations, yielding Purcell factors as high as $5 \times 10^5$ in an all-dielectric free-space resonator.