Global optimization of an encapsulated Si/SiO$_2$ L3 cavity for ultra-high quality factor

We optimize a silica-encapsulated silicon L3 photonic crystal cavity for ultra-high quality factor by means of a global optimization strategy, where the closest holes surrounding the cavity are varied to minimize out-of-plane losses. We find an optimal value of $Q_c=4.33\times10^7$, thus setting a new record for encapsulated low-index-contrast photonic crystal cavities. We also address the effects of structural imperfections on our optimal cavity design and predict an averaged $Q_c$ in the 2 million regime for state-of-the-art silicon fabrication tolerances.