Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization

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...

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Vydáno v:	Nanophotonics (Berlin, Germany) Ročník 12; číslo 10; s. 1913 - 1921
Hlavní autoři:	Kim, Jae-Hyun, Kim, Dong In, Lee, Sun Sook, An, Ki-Seok, Yim, Soonmin, Lee, Eungkyu, Kim, Sun-Kyung
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Germany De Gruyter 01.05.2023 Walter de Gruyter GmbH
Témata:	Algorithms antireflective multilayer Binary digits calcium fluoride lens Datasets deep ultraviolet spectrum discrete binary optimization factorization machine Figure of merit Lanthanum fluorides Magnesium fluorides Multilayers Optimization Photonics Reflectance Training deep ultraviolet spectrum factorization machine calcium fluoride lens discrete binary optimization antireflective multilayer
ISSN:	2192-8614, 2192-8606, 2192-8614
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Shrnutí:	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 /LaF multilayers. For discrete optimization, a multilayer was encoded into a binary vector with multiple bits; a 10 nm thick MgF or LaF 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 /LaF multilayers with a variety of bit levels were created to attain a minimum average angular (0°–45°) reflectance at 193 nm. A MgF /LaF 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 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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Jae-Hyun Kim and Dong In Kim contributed equally to this work.
ISSN:	2192-8614 2192-8606 2192-8614
DOI:	10.1515/nanoph-2023-0102