Abstract

The field of chiral plasmonics has registered considerable progress with machine-learning (ML)-mediated metamaterial prototyping, drawing from the success of ML frameworks in other applications such as pattern and image recognition. Here, we present an end-to-end functional bidirectional deep-learning (DL) model for three-dimensional chiral metamaterial design and optimization. This ML model utilizes multitask joint learning features to recognize, generalize, and explore in detail the nontrivial relationship between the metamaterials’ geometry and their chiroptical response, eliminating the need for auxiliary networks or equivalent approaches to stabilize the physically relevant output. Our model efficiently realizes both forward and inverse retrieval tasks with great precision, offering a promising tool for iterative computational design tasks in complex physical systems. Finally, we explore the behavior of a sample ML-optimized structure in a practical application, assisting the sensing of biomolecular enantiomers. Other potential applications of our metastructure include photodetectors, polarization-resolved imaging, and circular dichroism (CD) spectroscopy, with our ML framework being applicable to a wider range of physical problems.

© 2020 Chinese Laser Press

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2020 (3)

Z. Liu, D. Zhu, K. T. Lee, A. S. Kim, L. Raju, and W. Cai, “Compounding meta-atoms into metamolecules with hybrid artificial intelligence techniques,” Adv. Mater. 32, 1–7 (2020).
[Crossref]

J. X. Bao, N. Liu, H. W. Tian, Q. Wang, T. J. Cui, W. X. Jiang, S. Zhang, and T. Cao, “Chirality enhancement using Fabry–Pérot-like cavity,” Research 2020, 7873581 (2020).
[Crossref]

L. Mao, K. Liu, S. Zhang, and T. Cao, “Extrinsically 2D-chiral metamirror in near-infrared region,” ACS Photon. 7, 375–383 (2020).
[Crossref]

2019 (7)

C. Gilroy, S. Hashiyada, K. Endo, A. S. Karimullah, L. D. Barron, H. Okamoto, Y. Togawa, and M. Kadodwala, “Roles of superchirality and interference in chiral plasmonic biodetection,” J. Phys. Chem. C 123, 15195–15203 (2019).
[Crossref]

I. Sajedian, J. Kim, and J. Rho, “Finding the optical properties of plasmonic structures by image processing using a combination of convolutional neural networks and recurrent neural networks,” Microsyst. Nanoeng. 5, 27 (2019).
[Crossref]

W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy,” Adv. Mater. 31, 1901111 (2019).
[Crossref]

P. R. Wiecha and O. L. Muskens, “Deep learning meets nanophotonics: a generalized accurate predictor for near fields and far fields of arbitrary 3D nanostructures,” Nano Lett. 20, 329–338 (2019).
[Crossref]

T. F. De Lima, H. T. Peng, A. N. Tait, M. A. Nahmias, H. B. Miller, B. J. Shastri, and P. R. Prucnal, “Machine learning with neuromorphic photonics,” J. Lightwave Technol. 37, 1515–1534 (2019).
[Crossref]

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” Nanophotonics 8, 339–366 (2019).
[Crossref]

J. Zou, M. Huss, A. Abid, P. Mohammadi, A. Torkamani, and A. Telenti, “A primer on deep learning in genomics,” Nat. Genet. 51, 12–18 (2019).
[Crossref]

2018 (11)

X. T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal circular dichroism induced by plasmon resonances in chiral metamaterial absorbers and bolometers,” Nano Lett. 18, 2001–2008 (2018).
[Crossref]

D. Silver, T. Hubert, J. Schrittwieser, I. Antonoglou, M. Lai, A. Guez, M. Lanctot, L. Sifre, D. Kumaran, T. Graepel, T. Lillicrap, K. Simonyan, and D. Hassabis, “A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play,” Science 362, 1140–1144 (2018).
[Crossref]

J. R. Mejía-Salazar and O. N. Oliveira, “Plasmonic biosensing,” Chem. Rev. 118, 10617–10625 (2018).
[Crossref]

X. T. Kong, L. V. Besteiro, Z. Wang, and A. O. Govorov, “Plasmonic chirality and circular dichroism in bioassembled and nonbiological systems: theoretical background and recent progress,” Adv. Mater., 1801790 (2018).
[Crossref]

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18, 6570–6576 (2018).
[Crossref]

N. Dordević, J. S. Beckwith, M. Yarema, O. Yarema, A. Rosspeintner, N. Yazdani, J. Leuthold, E. Vauthey, and V. Wood, “Machine learning for analysis of time-resolved luminescence data,” ACS Photon. 5, 4888–4895 (2018).
[Crossref]

L. Pilozzi, F. A. Farrelly, G. Marcucci, and C. Conti, “Machine learning inverse problem for topological photonics,” Commun. Phys. 1, 57 (2018).
[Crossref]

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12, 6326–6334 (2018).
[Crossref]

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light Sci. Appl. 7, 60 (2018).
[Crossref]

P. Yu, L. V. Besteiro, Y. Huang, J. Wu, L. Fu, H. H. Tan, C. Jagadish, G. P. Wiederrecht, A. O. Govorov, and Z. Wang, “Broadband metamaterial absorbers,” Adv. Opt. Mater. 7, 1800995 (2018).
[Crossref]

P. Yu, L. V. Besteiro, J. Wu, Y. Huang, Y. Wang, A. O. Govorov, and Z. Wang, “Metamaterial perfect absorber with unabated size-independent absorption,” Opt. Express 26, 20471–20480 (2018).
[Crossref]

2017 (8)

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

Y. Z. Cheng, M. L. Huang, H. R. Chen, Y. J. Zhou, X. S. Mao, and R. Z. Gong, “Influence of the geometry of a gammadion stereo-structure chiral metamaterial on optical properties,” J. Mod. Opt. 64, 1487–1494 (2017).
[Crossref]

Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 6 (2017).
[Crossref]

X. Gibert, V. M. Patel, and R. Chellappa, “Deep multitask learning for railway track inspection,” IEEE Trans. Intell. Transp. Syst. 18, 153–164 (2017).
[Crossref]

Z. S. Ballard, D. Shir, A. Bhardwaj, S. Bazargan, S. Sathianathan, and A. Ozcan, “Computational sensing using low-cost and mobile plasmonic readers designed by machine learning,” ACS Nano 11, 2266–2274 (2017).
[Crossref]

R. Tullius, G. W. Platt, L. Khosravi Khorashad, N. Gadegaard, A. J. Lapthorn, V. M. Rotello, G. Cooke, L. D. Barron, A. O. Govorov, A. S. Karimullah, and M. Kadodwala, “Superchiral plasmonic phase sensitivity for fingerprinting of protein interface structure,” ACS Nano 11, 12049–12056 (2017).
[Crossref]

S. Singh, A. Okun, and A. Jackson, “Artificial intelligence: learning to play Go from scratch,” Nature 550, 336–337 (2017).
[Crossref]

D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T. Lillicrap, F. Hui, L. Sifre, G. Van Den Driessche, T. Graepel, and D. Hassabis, “Mastering the game of Go without human knowledge,” Nature 550, 354–359 (2017).
[Crossref]

2016 (7)

S. Zu, Y. Bao, and Z. Fang, “Planar plasmonic chiral nanostructures,” Nanoscale 8, 3900–3905 (2016).
[Crossref]

A. Maurer, M. Pontil, and B. Romera-Paredes, “The benefit of multitask representation learning,” J. Mach. Learn. Res. 17, 2853–2884 (2016).

P. Yu, J. Wu, E. Ashalley, A. Govorov, and Z. Wang, “Dual-band absorber for multispectral plasmon-enhanced infrared photodetection,” J. Phys. D 49, 365101 (2016).
[Crossref]

C. Zhang, Z. Q. Li, X. Yang, Z. Chen, and Z. Wang, “Controlling third harmonic generation with gammadion-shaped chiral metamaterials,” AIP Adv. 6, 125014 (2016).
[Crossref]

S. Wu, P. P. Qu, J. Q. Liu, D. D. Lei, K. Y. Zhang, S. T. Zhao, and Y. Y. Zhu, “Giant circular dichroism and its reversal in solid and inverse plasmonic gammadion-shaped structures,” Opt. Express 24, 27763–27770 (2016).
[Crossref]

Y. Wang, J. Deng, G. Wang, T. Fu, Y. Qu, and Z. Zhang, “Plasmonic chirality of L-shaped nanostructure composed of two slices with different thickness,” Opt. Express 24, 2307–2317 (2016).
[Crossref]

H. Zhu, F. Yi, and E. Cubukcu, “Plasmonic metamaterial absorber for broadband manipulation of mechanical resonances,” Nat. Photonics 10, 709–714 (2016).
[Crossref]

2015 (5)

X. Yin, M. Schäferling, A. K. U. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15, 4255–4260 (2015).
[Crossref]

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6, 8379 (2015).
[Crossref]

A. Micsonai, F. Wien, L. Kernya, Y. H. Lee, Y. Goto, M. Réfrégiers, and J. Kardos, “Accurate secondary structure prediction and fold recognition for circular dichroism spectroscopy,” Proc. Natl. Acad. Sci. USA 112, E3095–E3103 (2015).
[Crossref]

J. Hirschberg and C. D. Manning, “Advances in natural language processing,” Science 349, 261–266 (2015).
[Crossref]

M. W. Libbrecht and W. S. Noble, “Machine learning in genetics and genomics,” Nat. Rev. Genet. 16, 321–332 (2015).
[Crossref]

2014 (3)

W. Huang, G. Song, H. Hong, and K. Xie, “Deep architecture for traffic flow prediction: deep belief networks with multitask learning,” IEEE Trans. Intell. Transp. Syst. 15, 2191–2201 (2014).
[Crossref]

W. Li and J. Valentine, “Metamaterial perfect absorber based hot electron photodetection,” Nano Lett. 14, 3510–3514 (2014).
[Crossref]

J. Yao, M. Xu, Z. Yan, W. Wu, and C. Yang, “Supramolecular photochirogenesis with cyclodextrins,” Chin. J. Org. Chem. 34, 26–35 (2014).
[Crossref]

2013 (4)

T. Cao, L. Zhang, R. E. Simpson, C. Wei, and M. J. Cryan, “Strongly tunable circular dichroism in gammadion chiral phase-change metamaterials,” Opt. Express 21, 27841–27851 (2013).
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B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3D chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
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T. J. Davis and E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).
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B. M. Maoz, Y. Chaikin, A. B. Tesler, O. Bar Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
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2012 (1)

2011 (2)

A. O. Govorov, “Plasmon-induced circular dichroism of a chiral molecule in the vicinity of metal nanocrystals. Application to various geometries,” J. Phys. Chem. C 115, 7914–7923 (2011).
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2010 (3)

A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10, 1374–1382 (2010).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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2008 (1)

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2004 (1)

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C. Gilroy, S. Hashiyada, K. Endo, A. S. Karimullah, L. D. Barron, H. Okamoto, Y. Togawa, and M. Kadodwala, “Roles of superchirality and interference in chiral plasmonic biodetection,” J. Phys. Chem. C 123, 15195–15203 (2019).
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D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T. Lillicrap, F. Hui, L. Sifre, G. Van Den Driessche, T. Graepel, and D. Hassabis, “Mastering the game of Go without human knowledge,” Nature 550, 354–359 (2017).
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B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3D chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
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J. X. Bao, N. Liu, H. W. Tian, Q. Wang, T. J. Cui, W. X. Jiang, S. Zhang, and T. Cao, “Chirality enhancement using Fabry–Pérot-like cavity,” Research 2020, 7873581 (2020).
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L. Mao, K. Liu, S. Zhang, and T. Cao, “Extrinsically 2D-chiral metamirror in near-infrared region,” ACS Photon. 7, 375–383 (2020).
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Carpy, T.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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Chaikin, Y.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. Bar Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
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Chen, H. R.

Y. Z. Cheng, M. L. Huang, H. R. Chen, Y. J. Zhou, X. S. Mao, and R. Z. Gong, “Influence of the geometry of a gammadion stereo-structure chiral metamaterial on optical properties,” J. Mod. Opt. 64, 1487–1494 (2017).
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D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T. Lillicrap, F. Hui, L. Sifre, G. Van Den Driessche, T. Graepel, and D. Hassabis, “Mastering the game of Go without human knowledge,” Nature 550, 354–359 (2017).
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C. Zhang, Z. Q. Li, X. Yang, Z. Chen, and Z. Wang, “Controlling third harmonic generation with gammadion-shaped chiral metamaterials,” AIP Adv. 6, 125014 (2016).
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Y. Z. Cheng, M. L. Huang, H. R. Chen, Y. J. Zhou, X. S. Mao, and R. Z. Gong, “Influence of the geometry of a gammadion stereo-structure chiral metamaterial on optical properties,” J. Mod. Opt. 64, 1487–1494 (2017).
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Choi, S. H.

T. Li, H. G. Park, H. S. Lee, and S. H. Choi, “Circular dichroism study of chiral biomolecules conjugated with silver nanoparticles,” Nanotechnology 15, S660–S663 (2004).
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P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
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R. Cipolla, Y. Gal, and A. Kendall, “Multi-task learning using uncertainty to weigh losses for scene geometry and semantics,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2018), pp. 7482–7491.

Cohen, A. E.

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
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L. Pilozzi, F. A. Farrelly, G. Marcucci, and C. Conti, “Machine learning inverse problem for topological photonics,” Commun. Phys. 1, 57 (2018).
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R. Tullius, G. W. Platt, L. Khosravi Khorashad, N. Gadegaard, A. J. Lapthorn, V. M. Rotello, G. Cooke, L. D. Barron, A. O. Govorov, A. S. Karimullah, and M. Kadodwala, “Superchiral plasmonic phase sensitivity for fingerprinting of protein interface structure,” ACS Nano 11, 12049–12056 (2017).
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Coppens, Z. J.

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6, 8379 (2015).
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Cryan, M. J.

Cubukcu, E.

H. Zhu, F. Yi, and E. Cubukcu, “Plasmonic metamaterial absorber for broadband manipulation of mechanical resonances,” Nat. Photonics 10, 709–714 (2016).
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J. X. Bao, N. Liu, H. W. Tian, Q. Wang, T. J. Cui, W. X. Jiang, S. Zhang, and T. Cao, “Chirality enhancement using Fabry–Pérot-like cavity,” Research 2020, 7873581 (2020).
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T. J. Davis and E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).
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Deng, J.

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N. Dordević, J. S. Beckwith, M. Yarema, O. Yarema, A. Rosspeintner, N. Yazdani, J. Leuthold, E. Vauthey, and V. Wood, “Machine learning for analysis of time-resolved luminescence data,” ACS Photon. 5, 4888–4895 (2018).
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Endo, K.

C. Gilroy, S. Hashiyada, K. Endo, A. S. Karimullah, L. D. Barron, H. Okamoto, Y. Togawa, and M. Kadodwala, “Roles of superchirality and interference in chiral plasmonic biodetection,” J. Phys. Chem. C 123, 15195–15203 (2019).
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B. M. Maoz, Y. Chaikin, A. B. Tesler, O. Bar Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
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A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10, 1374–1382 (2010).
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S. Zu, Y. Bao, and Z. Fang, “Planar plasmonic chiral nanostructures,” Nanoscale 8, 3900–3905 (2016).
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L. Pilozzi, F. A. Farrelly, G. Marcucci, and C. Conti, “Machine learning inverse problem for topological photonics,” Commun. Phys. 1, 57 (2018).
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Frank, B.

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3D chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Fu, L.

P. Yu, L. V. Besteiro, Y. Huang, J. Wu, L. Fu, H. H. Tan, C. Jagadish, G. P. Wiederrecht, A. O. Govorov, and Z. Wang, “Broadband metamaterial absorbers,” Adv. Opt. Mater. 7, 1800995 (2018).
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Furtak, T. E.

Gadegaard, N.

R. Tullius, G. W. Platt, L. Khosravi Khorashad, N. Gadegaard, A. J. Lapthorn, V. M. Rotello, G. Cooke, L. D. Barron, A. O. Govorov, A. S. Karimullah, and M. Kadodwala, “Superchiral plasmonic phase sensitivity for fingerprinting of protein interface structure,” ACS Nano 11, 12049–12056 (2017).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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Gal, Y.

R. Cipolla, Y. Gal, and A. Kendall, “Multi-task learning using uncertainty to weigh losses for scene geometry and semantics,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2018), pp. 7482–7491.

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X. Gibert, V. M. Patel, and R. Chellappa, “Deep multitask learning for railway track inspection,” IEEE Trans. Intell. Transp. Syst. 18, 153–164 (2017).
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B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3D chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
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Gilroy, C.

C. Gilroy, S. Hashiyada, K. Endo, A. S. Karimullah, L. D. Barron, H. Okamoto, Y. Togawa, and M. Kadodwala, “Roles of superchirality and interference in chiral plasmonic biodetection,” J. Phys. Chem. C 123, 15195–15203 (2019).
[Crossref]

Gong, R. Z.

Y. Z. Cheng, M. L. Huang, H. R. Chen, Y. J. Zhou, X. S. Mao, and R. Z. Gong, “Influence of the geometry of a gammadion stereo-structure chiral metamaterial on optical properties,” J. Mod. Opt. 64, 1487–1494 (2017).
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P. Yu, J. Wu, E. Ashalley, A. Govorov, and Z. Wang, “Dual-band absorber for multispectral plasmon-enhanced infrared photodetection,” J. Phys. D 49, 365101 (2016).
[Crossref]

Govorov, A. O.

P. Yu, L. V. Besteiro, Y. Huang, J. Wu, L. Fu, H. H. Tan, C. Jagadish, G. P. Wiederrecht, A. O. Govorov, and Z. Wang, “Broadband metamaterial absorbers,” Adv. Opt. Mater. 7, 1800995 (2018).
[Crossref]

P. Yu, L. V. Besteiro, J. Wu, Y. Huang, Y. Wang, A. O. Govorov, and Z. Wang, “Metamaterial perfect absorber with unabated size-independent absorption,” Opt. Express 26, 20471–20480 (2018).
[Crossref]

X. T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal circular dichroism induced by plasmon resonances in chiral metamaterial absorbers and bolometers,” Nano Lett. 18, 2001–2008 (2018).
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X. T. Kong, L. V. Besteiro, Z. Wang, and A. O. Govorov, “Plasmonic chirality and circular dichroism in bioassembled and nonbiological systems: theoretical background and recent progress,” Adv. Mater., 1801790 (2018).
[Crossref]

R. Tullius, G. W. Platt, L. Khosravi Khorashad, N. Gadegaard, A. J. Lapthorn, V. M. Rotello, G. Cooke, L. D. Barron, A. O. Govorov, A. S. Karimullah, and M. Kadodwala, “Superchiral plasmonic phase sensitivity for fingerprinting of protein interface structure,” ACS Nano 11, 12049–12056 (2017).
[Crossref]

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6, 8379 (2015).
[Crossref]

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. Bar Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref]

A. O. Govorov, “Plasmon-induced circular dichroism of a chiral molecule in the vicinity of metal nanocrystals. Application to various geometries,” J. Phys. Chem. C 115, 7914–7923 (2011).
[Crossref]

J. M. Slocik, A. O. Govorov, and R. R. Naik, “Plasmonic circular dichroism of peptide-functionalized gold nanoparticles,” Nano Lett. 11, 701–705 (2011).
[Crossref]

A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10, 1374–1382 (2010).
[Crossref]

Graepel, T.

D. Silver, T. Hubert, J. Schrittwieser, I. Antonoglou, M. Lai, A. Guez, M. Lanctot, L. Sifre, D. Kumaran, T. Graepel, T. Lillicrap, K. Simonyan, and D. Hassabis, “A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play,” Science 362, 1140–1144 (2018).
[Crossref]

D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T. Lillicrap, F. Hui, L. Sifre, G. Van Den Driessche, T. Graepel, and D. Hassabis, “Mastering the game of Go without human knowledge,” Nature 550, 354–359 (2017).
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D. Silver, T. Hubert, J. Schrittwieser, I. Antonoglou, M. Lai, A. Guez, M. Lanctot, L. Sifre, D. Kumaran, T. Graepel, T. Lillicrap, K. Simonyan, and D. Hassabis, “A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play,” Science 362, 1140–1144 (2018).
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D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T. Lillicrap, F. Hui, L. Sifre, G. Van Den Driessche, T. Graepel, and D. Hassabis, “Mastering the game of Go without human knowledge,” Nature 550, 354–359 (2017).
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C. Gilroy, S. Hashiyada, K. Endo, A. S. Karimullah, L. D. Barron, H. Okamoto, Y. Togawa, and M. Kadodwala, “Roles of superchirality and interference in chiral plasmonic biodetection,” J. Phys. Chem. C 123, 15195–15203 (2019).
[Crossref]

Hassabis, D.

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Figures (10)

Fig. 1.
Fig. 1. Schematic of (a) a single YNP chiral meta-absorber array with definition of incident circularly polarized lights and a unit cell with dimensions. (b) Three single YNP metastructure configurations: Au YNP/Glass (YG), Au YNP/PMMA/Glass (YPG), and Au YNP/PMMA/Au/Glass (YPAG). (c) Absorption and CD spectra of the three metastructure configurations (YG, YPG, and YPAG), showing their plasmonic resonances λp (λp=620  nm, 625 nm, and 645 nm, respectively) and revealing a strong chiroptical response for the metamaterial absorber case (YPAG). Here, R0=100  nm, t1=40  nm, t2=50  nm, t3=100  nm, and t4=200  nm.
Fig. 2.
Fig. 2. Schematic of the bidirectional multitask deep-learning model for chiral metamaterial design consisting of forward design path (FDP) and inverse design path (IDP). Each path is composed by shared layers and task specific layers with joint optimization functionality. The model is set up in an end-to-end fashion where the geometric design parameters, CD, and LCP/RCP absorption spectra can be treated as input or output at specific ports. Here, the geometric design parameters are the YNPs thickness, PMMA thickness, YNPs radius, and YNPs (respectively represented as xi, i=1,2,,6). x4 has been taken as a constant in the data shown in this study, but is nonetheless included in the model to represent the general parametrization of the system. The inset shows the metamaterial absorber geometry used to exemplify the use of the MDL.
Fig. 3.
Fig. 3. MDL model performance. (a) Numerical simulation and (b) MDL prediction CD results of the dimer structure at varying gap distance d (50–160 nm), across the visible and near-IR regime. R0=100  nm, t1=40  nm, t2=50  nm, and t3=100  nm. (c) Numerical simulation and (d) MDL prediction results of the dimer at varying YNP thickness (t1). The color legend has been truncated at ±0.2 for clarity. Inset, definition of the gap d. (e) Learning curve within 3000 epochs. (f) Discretized model performance at selected t1 = {60 nm, 80 nm, 100 nm} corresponding to the horizontal dots in (c) and (d). (g) Model performance at λ0=755  nm across varying t1, corresponding to the vertical short dashes through (c) and (d). Here, R0=100  nm, d=100  nm, t2=50  nm, and t3=100  nm.
Fig. 4.
Fig. 4. MDL-predicted CD progressions. (a) CD evolution by varying YNP radius at t3 = {100 nm, 150 nm, 200 nm}. CD map plot by varying concurrently, (b) YNP radius and polymer thickness at t1 = {5 nm, 25 nm, 50 nm} for λ0=780  nm, (c) YNP thickness and polymer thickness at R0 = {100 nm, 150 nm, 200 nm} and λ0=700  nm, and (d) YNP radius and YNP thickness at t2 = {10 nm, 45 nm, 100 nm} and λ0=650  nm. The color legend has been truncated at ±0.2 for clarity, but high-CD areas have been highlighted by adding the contour regions corresponding to CD values of 0.5.
Fig. 5.
Fig. 5. Inverse design with the MDL model. (a), (b) Simulated (green solid lines) and predicted (red dots) CD spectra. (c), (d) Corresponding simulated (green bars) and retrieved (red bars) geometric parameters. Red dots in (a), (b) are predicted from the MDL model with geometric parameters retrieved [red bar in (c), (d)] for the target simulated CD spectra in (a), (b). [See Figs. 9(a) and 9(b) in Appendix C for absorption spectra comparison.]
Fig. 6.
Fig. 6. Enantiomer detection. (a) The CD spectra of (red) left-handed medium (LHm), and (blue) right-handed medium (RHm) with molecular CD resonance (λm=380  nm) in the UV. (b) CD spectra comparison of the right-handed chiral metamaterial absorber (RHcma) with (blue) and without (red) chiral medium (CM). Inset is the electric field at the plasmonic resonance, λp (λp=665  nm), of the bare chiral metamaterial absorber for LCP and RCP light. (c) CD summation to remove metamaterial background CD signal to reveal the LH (blue solid line) and RH (green solid line) enantiomer pair CD signals. λm, λp, and λmp represent the resonant wavelengths for the CD of the bare molecules, the plasmonic chiral metamaterial absorber, and the metamaterial covered with chiral media, respectively. Inset, schematic representation of an enantiomeric protein molecular pair (L and D isomers). (d) Electric field, surface charge density, and optical chirality density distributions of the chiral metamaterial absorber covered by chiral media (CM) at λmp=720  nm.
Fig. 7.
Fig. 7. Electric field and surface charge density distributions of the three single YNP metastructure configurations (YG, YPG, YPAG) at their plasmonic resonances, showing huge enhancement for the metamaterial absorber case. The cut plane is through point A, the unit cell center [Fig. 1(a)].
Fig. 8.
Fig. 8. Optical and chiroptical properties of the chiral metamaterial absorber with 10 nm tip rounding radius. (a) Absorption and (b) reflection spectra of single yin-yang metamaterial absorber at varying polymer thicknesses. Corresponding (c) CD and (d) gCD from (a) exhibiting a strong peak in the visible regime (around 635 nm wavelength). CD response from three gapped configurations of the chiral metamaterial absorber: (e) dimer, varying gap length d, (f) circular, varying PMMA thickness, and (g) circular with central disk, varying central disk radius r. (h) Charge density distribution at the CD maxima (peak A) for the 60 nm PMMA thickness in (c).
Fig. 9.
Fig. 9. Inverse design plots. Simulated and MDL-retrieved absorption spectra comparison for the systems providing the data in (a) Fig. 5(a) and (b) Fig. 5(b). (c) Comparison between the CD values obtained with different variations of the ML techniques: separately training LCP and RCP spectra (black dashes), training only CD without auxiliary tasks (red dashes), training by our MDL model (blue dashes), and the ground-truth (pink solid line). The inset is a zoomed-in image at the resonances.
Fig. 10.
Fig. 10. MDL-predicted CD progressions. CD evolution when varying PMMA thickness at t1 = {30 nm, 60 nm, 90 nm} for R0=100  nm. This plot agrees with the Fig. 3, where we observe only CD maxima for t1=30  nm but both CD maxima and minima for t1=60  nm and t1=90  nm, establishing the consistency of the MDL model.

Equations (16)

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Xnorm,(a,b)=X(a,b)X¯bσ(Xb),
j(i(yjifj(xi;w))2),
D=ε0εrE+iξB,
H=B/μ0μr+iξE.
ξ=βc(1ω+ω0+iΓ12+1ωω0+iΓ12),
C=ε02ωIm(E*·B).
CD=ALCPARCP,gCD=ALCPARCP(ALCP+ARCP)/2,
ijlog(12πσjexp((yjifj(xi;w))2σj22)).
ij(log(2π)12logσj2(yjifj(xi;w))2σj22).
σj2i(12logσj2(yjifj(xi;w))2σj22)=0.
i(12σj2+(yjifj(xi;w))2σj42)=0.
N2σj2+i((yjifj(xi;w))2σj42)=0.
N+i((yjifj(xi;w))σj22)=0,
σj2=1Ni(yjifj(xi;w))2.
jlog(i(yjifj(xi;w))2).
j(i(yjifj(xi;w))2).