Wide‐angle deep ultraviolet antireflective multilayers via discrete‐to‐continuous optimization
Jae‐Hyun Kim, Dong In Kim, Sun Sook Lee, Ki‐Seok An, Soonmin Yim, Eungkyu Lee, Sun‐Kyung Kim
Abstract
Abstract To date, various optimization algorithms have been used to design non‐intuitive photonic structures with unconventional optical performance. Good training datasets facilitate the optimization process, particularly when an objective function has a non‐convex shape containing multiple local optima in a continuous parametric space. Herein, we developed a discrete‐to‐continuous optimization algorithm and confirmed its validity by designing and fabricating deep‐ultraviolet antireflective MgF 2 /LaF 3 multilayers. For discrete optimization, a multilayer was encoded into a binary vector with multiple bits; a 10 nm thick MgF 2 or LaF 3 layer was assigned a binary digit of 0 or 1, respectively. Using the binary‐based training datasets, a factorization machine formulated a surrogate function, which discovered the ground binary vector representing a near‐optimal figure of merit. Then, the figure of merit was refined through continuous optimization (e.g., using an interior‐point method) of the ground binary vector. MgF 2 /LaF 3 multilayers with a variety of bit levels were created to attain a minimum average angular (0°–45°) reflectance at 193 nm. A MgF 2 /LaF 3 multilayer optimized at ten bits (i.e., a total thickness of approximately 100 nm) yielded an average reflectance of 0.2%, which agreed well with the experimental results. Moreover, an integrated ray‐wave optics simulation predicted that a single CaF 2 plano‐convex lens coated with the optimized multilayer could exhibit a transmittance of 99.7%. The developed optimization approach will be widely applicable to any photonic structures that can represent a binary vector with multiple bits, such as microwave metasurfaces, in addition to being useful for producing ideal optical multilayers.