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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| Format: | Article |
| Language: | English |
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De Gruyter
2023-03-01
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| Series: | Nanophotonics |
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| Online Access: | https://doi.org/10.1515/nanoph-2023-0102 |
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| author | Kim Jae-Hyun Kim Dong In Lee Sun Sook An Ki-Seok Yim Soonmin Lee Eungkyu Kim Sun-Kyung |
| author_facet | Kim Jae-Hyun Kim Dong In Lee Sun Sook An Ki-Seok Yim Soonmin Lee Eungkyu Kim Sun-Kyung |
| author_sort | Kim Jae-Hyun |
| collection | DOAJ |
| description | 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 MgF2/LaF3 multilayers. For discrete optimization, a multilayer was encoded into a binary vector with multiple bits; a 10 nm thick MgF2 or LaF3 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. MgF2/LaF3 multilayers with a variety of bit levels were created to attain a minimum average angular (0°–45°) reflectance at 193 nm. A MgF2/LaF3 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 CaF2 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. |
| format | Article |
| id | doaj-art-d18ce64c66c94c809256482e7a8ccec0 |
| institution | Kabale University |
| issn | 2192-8614 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nanophotonics |
| spelling | doaj-art-d18ce64c66c94c809256482e7a8ccec02024-11-25T11:19:10ZengDe GruyterNanophotonics2192-86142023-03-0112101913192110.1515/nanoph-2023-0102Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimizationKim Jae-Hyun0Kim Dong In1Lee Sun Sook2An Ki-Seok3Yim Soonmin4Lee Eungkyu5Kim Sun-Kyung6Department of Applied Physics, Kyung Hee University, Gyeonggi-do 17104, Yongin, Republic of KoreaKorea Research Institute of Chemical Technology (KRICT), Daejeon34114, Republic of KoreaKorea Research Institute of Chemical Technology (KRICT), Daejeon34114, Republic of KoreaKorea Research Institute of Chemical Technology (KRICT), Daejeon34114, Republic of KoreaKorea Research Institute of Chemical Technology (KRICT), Daejeon34114, Republic of KoreaDepartment of Electronic Engineering, Kyung Hee University, Gyeonggi-do 17104, Yongin, Republic of KoreaDepartment of Applied Physics, Kyung Hee University, Gyeonggi-do 17104, Yongin, Republic of KoreaTo 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 MgF2/LaF3 multilayers. For discrete optimization, a multilayer was encoded into a binary vector with multiple bits; a 10 nm thick MgF2 or LaF3 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. MgF2/LaF3 multilayers with a variety of bit levels were created to attain a minimum average angular (0°–45°) reflectance at 193 nm. A MgF2/LaF3 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 CaF2 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.https://doi.org/10.1515/nanoph-2023-0102antireflective multilayercalcium fluoride lensdeep ultraviolet spectrumdiscrete binary optimizationfactorization machine |
| spellingShingle | Kim Jae-Hyun Kim Dong In Lee Sun Sook An Ki-Seok Yim Soonmin Lee Eungkyu Kim Sun-Kyung Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization Nanophotonics antireflective multilayer calcium fluoride lens deep ultraviolet spectrum discrete binary optimization factorization machine |
| title | Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization |
| title_full | Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization |
| title_fullStr | Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization |
| title_full_unstemmed | Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization |
| title_short | Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization |
| title_sort | wide angle deep ultraviolet antireflective multilayers via discrete to continuous optimization |
| topic | antireflective multilayer calcium fluoride lens deep ultraviolet spectrum discrete binary optimization factorization machine |
| url | https://doi.org/10.1515/nanoph-2023-0102 |
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