Automated optimization of photonic crystal slab cavities

Abstract

Thanks to their high quality factor, combined to the smallest modal volume, defect-cavities in photonic crystal slabs represent a promising, versatile tool for fundamental studies and applications in photonics. In paricular, the L3, H0, and H1 defects are the most popular and widespread cavity designs, due to their compactness, simplicity, and small mode volume. For these cavities, the current best optimal designs still result in Q-values of a few times 105 only, namely one order of magnitude below the bound set by fabrication imperfections and material absorption in silicon. Here, we use a genetic algorithm to find a global maximum of the quality factor of these designs, by varying the positions of few neighbouring holes. We consistently find Q-values above one million – one order of magnitude higher than previous designs. Furthermore, we study the effect of disorder on the optimal designs and conclude that a similar improvement is also expected experimentally in state-of-the-art systems.

Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon

“…An optimization algorithm based on the guided-mode expansion method 10,11 was utilized to sweep the parameter space within specified constraints for the highest attainable Q-factors. The optimization runs yielded cavities with a theoretical Q-factor of 1.1 × 10 5 for both L3 and H0 cavities resonant near λ = 1300 nm, while Q-factors of 2.2 × 10 5 and 1.2 × 10 5 were obtained for L3 and H0 cavities, respectively, resonant near λ = 1550 nm.…”

High-Q silicon photonic crystal cavity for enhanced optical nonlinearities

“…The original H0 design 16,20,21 has a mode volume V ¼ 0.23(k/n) 3 -i.e., the smallest mode volume among PhC slab nanocavities. 22,23 Its quality factor had previously been optimized to a moderate theoretical Q ¼ 280 000, while in our recent work 13 we reached a theoretical value close to 2 Â 10 6 using similar variational parameters. The optimal cavity design that we consider is illustrated in Fig.…”

“…32,33 The present nanocavity thus ranks among those with the highest Q/V ratio ever reported. 1,6,11,15,17,[34][35][36] In the present work, we have additionally investigated an alternate optimal design 13 characterized by a smaller modal volume, that was obtained by introducing a stricter upper bound S 1x < 0.25a in the optimization procedure. The design has an ideal GMEcomputed Q-factor 1.05 Â 10 6 (FDTD: 1.0 Â 10 6 ) and a smaller modal volume V ¼ 0.25(k/n) 3 .…”

“…[5][6][7][8] Few specific designs, where the nanocavity originates as a local defect in a PhC waveguide, have reached measured Q-factors exceeding 1 Â 10 6 . 9-12 More recently, 13 by combining a fast simulation tool to a genetic optimization algorithm, we have systematically optimized the three most widespread cavity designs-the H0, H1, and L3 designs-to theoretical quality factors largely exceeding 1 Â 10 6 , using only shifts in the positions of a few neighboring holes. Compared to previous optimization attempts, 4,14-20 the Q-factors of these cavities were thus improved sometimes by more than one order of magnitude, while their modal volumes were not significantly increased when compared to the unoptimized designs.…”

“…13. The original H0 design 16,20,21 has a mode volume V ¼ 0.23(k/n) 3 -i.e., the smallest mode volume among PhC slab nanocavities.…”