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 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Germany
De Gruyter
01.05.2023
Walter de Gruyter GmbH |
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| ISSN: | 2192-8614, 2192-8606, 2192-8614 |
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| 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
/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. |
|---|---|
| AbstractList | 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. 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. 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. 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. 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.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. |
| Author | Lee, Sun Sook Lee, Eungkyu An, Ki-Seok Kim, Jae-Hyun Yim, Soonmin Kim, Dong In Kim, Sun-Kyung |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/39635137$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1038_s41598_025_99570_z crossref_primary_10_1002_mgea_73 crossref_primary_10_1002_adom_202401040 crossref_primary_10_1515_nanoph_2024_0619 crossref_primary_10_1515_nanoph_2024_0628 crossref_primary_10_3390_chemistry7050147 crossref_primary_10_1088_2632_2153_adf68d crossref_primary_10_1186_s40580_024_00425_6 crossref_primary_10_1515_nanoph_2024_0360 |
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| Copyright | 2023 the author(s), published by De Gruyter, Berlin/Boston. 2023. This work is published under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2023 the author(s), published by De Gruyter, Berlin/Boston 2023 the author(s), published by De Gruyter, Berlin/Boston GmbH, Berlin/Boston |
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| DOI | 10.1515/nanoph-2023-0102 |
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| Keywords | deep ultraviolet spectrum factorization machine calcium fluoride lens discrete binary optimization antireflective multilayer |
| Language | English |
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| SubjectTerms | 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 |
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| Title | Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization |
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