Abstract

Recently, a novel machine learning model has emerged in the field of reinforcement learning known as deep Q-learning. This model is capable of finding the best possible solution in systems consisting of millions of choices, without ever experiencing it before, and has been used to beat the best human minds at complex games such as, Go and chess, which both have a huge number of possible decisions and outcomes for each move. With a human-level intelligence, it has solved the problems that no other machine learning model has done before. Here, we show the steps needed for implementing this model to an optical problem. We investigate the colour generation by dielectric nanostructures and show that this model can find geometrical properties that can generate much purer red, green and blue colours compared to previously reported results. The model found these results in 9000 steps from a possible 34.5 million solutions. This technique can easily be extended to predict and optimise the design parameters for other optical structures.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref] [PubMed]

2017 (4)

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

2016 (4)

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

T. D. James, P. Mulvaney, and A. Roberts, “The plasmonic pixel: large area, wide gamut color reproduction using aluminum nanostructures,” Nano Lett. 16(6), 3817–3823 (2016).
[Crossref] [PubMed]

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

2015 (3)

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
[Crossref] [PubMed]

2014 (3)

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

A. S. Roberts, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Subwavelength plasmonic color printing protected for ambient use,” Nano Lett. 14(2), 783–787 (2014).
[Crossref] [PubMed]

2012 (2)

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

2009 (1)

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

2007 (1)

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

1996 (1)

L. P. Kaelbling, M. L. Littman, and A. W. Moore, “Reinforcement learning: A survey,” JAIR 4, 237–285 (1996).
[Crossref]

1995 (1)

G. Tesauro, “Temporal difference learning and TD-Gammon,” Commun. ACM 38(3), 58–68 (1995).
[Crossref]

Albrektsen, O.

A. S. Roberts, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Subwavelength plasmonic color printing protected for ambient use,” Nano Lett. 14(2), 783–787 (2014).
[Crossref] [PubMed]

Antonoglou, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Arbouet, A.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

Atwater, H. A.

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Badia, A. P.

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Beattie, C.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Bellemare, M. G.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

A. S. Roberts, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Subwavelength plasmonic color printing protected for ambient use,” Nano Lett. 14(2), 783–787 (2014).
[Crossref] [PubMed]

Burgos, S. P.

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Busch, K.

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

Cheng, F.

W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref] [PubMed]

Choi, S.-e.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Dieleman, S.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Dong, Z.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Duan, H.

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Fidjeland, A. K.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Fu, Y. H.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Ge, J.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Girard, C.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

Goh, X. M.

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

Graepel, T.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Graves, A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Grewe, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Gu, Y.

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
[Crossref] [PubMed]

Guez, A.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Halas, N. J.

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

Harley, T.

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Hassabis, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Hegde, R. S.

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Ho, J.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Højlund-Nielsen, E.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Huang, A.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Jalali, M.

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

James, T. D.

T. D. James, P. Mulvaney, and A. Roberts, “The plasmonic pixel: large area, wide gamut color reproduction using aluminum nanostructures,” Nano Lett. 16(6), 3817–3823 (2016).
[Crossref] [PubMed]

Joannopoulos, J. D.

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Kaelbling, L. P.

L. P. Kaelbling, M. L. Littman, and A. W. Moore, “Reinforcement learning: A survey,” JAIR 4, 237–285 (1996).
[Crossref]

Kalchbrenner, N.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Kavukcuoglu, K.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Khoram, E.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Kim, H.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Kim, J.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

King, H.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Koh, S. C.

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Kristensen, A.

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Kumar, K.

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Kumaran, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Kuznetsov, A. I.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Kwon, S.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Lanctot, M.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Larrieu, G.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

Leach, M.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Lecestre, A.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

Lee, H.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Legg, S.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Levy, U.

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

Lillicrap, T.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Linden, S.

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

Link, S.

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

Littman, M. L.

L. P. Kaelbling, M. L. Littman, and A. W. Moore, “Reinforcement learning: A survey,” JAIR 4, 237–285 (1996).
[Crossref]

Liu, D.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Liu, Y.

W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref] [PubMed]

Ma, W.

W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
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Maddison, C. J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Mingaleev, S.

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

Mirza, M.

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Mnih, V.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Moore, A. W.

L. P. Kaelbling, M. L. Littman, and A. W. Moore, “Reinforcement learning: A survey,” JAIR 4, 237–285 (1996).
[Crossref]

Mortensen, N. A.

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Mulvaney, P.

T. D. James, P. Mulvaney, and A. Roberts, “The plasmonic pixel: large area, wide gamut color reproduction using aluminum nanostructures,” Nano Lett. 16(6), 3817–3823 (2016).
[Crossref] [PubMed]

Ng, R. J. H.

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

Nham, J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Nordlander, P.

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

Ostrovski, G.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Paillard, V.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

Paniagua-Dominguez, R.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Panneershelvam, V.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Park, W.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Petersen, S.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Pors, A.

A. S. Roberts, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Subwavelength plasmonic color printing protected for ambient use,” Nano Lett. 14(2), 783–787 (2014).
[Crossref] [PubMed]

Qiu, C.-W.

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
[Crossref] [PubMed]

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

Riedmiller, M.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Rinnerbauer, V.

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Roberts, A.

T. D. James, P. Mulvaney, and A. Roberts, “The plasmonic pixel: large area, wide gamut color reproduction using aluminum nanostructures,” Nano Lett. 16(6), 3817–3823 (2016).
[Crossref] [PubMed]

Roberts, A. S.

A. S. Roberts, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Subwavelength plasmonic color printing protected for ambient use,” Nano Lett. 14(2), 783–787 (2014).
[Crossref] [PubMed]

Rusu, A. A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Sadik, A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Safari Dinachali, S.

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

Schrittwieser, J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Shen, Y.

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Sifre, L.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Silver, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

Soljacic, M.

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Stelmakh, V.

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Sutskever, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Tan, S. J.

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

Tan, Y.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Tesauro, G.

G. Tesauro, “Temporal difference learning and TD-Gammon,” Commun. ACM 38(3), 58–68 (1995).
[Crossref]

Tkeshelashvili, L.

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

van den Driessche, G.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Vannahme, C.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Veness, J.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Von Freymann, G.

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

Wang, I.

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Wang, L.

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

Wang, S.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Wang, Y. M.

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

Wegener, M.

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[Crossref]

Wei, J. N.

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Wiecha, P. R.

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

Wierstra, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Yan, W.

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

Yang, J. K.

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
[Crossref] [PubMed]

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Yang, J. K. W.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Yeo, S. P.

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
[Crossref] [PubMed]

Yin, Y.

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Yokogawa, S.

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Yu, Y.

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

Yu, Y. F.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref] [PubMed]

Yu, Z.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Zhang, L.

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
[Crossref] [PubMed]

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

Zheng, Y.

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
[Crossref] [PubMed]

Zhu, D.

S. J. Tan, L. Zhang, D. Zhu, X. M. Goh, Y. M. Wang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett. 14(7), 4023–4029 (2014).
[Crossref] [PubMed]

Zhu, X.

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
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W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
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ACS Photonics (3)

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

L. Wang, R. J. H. Ng, S. Safari Dinachali, M. Jalali, Y. Yu, and J. K. Yang, “Large area plasmonic color palettes with expanded gamut using colloidal self-assembly,” ACS Photonics 3(4), 627–633 (2016).
[Crossref]

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Commun. ACM (1)

G. Tesauro, “Temporal difference learning and TD-Gammon,” Commun. ACM 38(3), 58–68 (1995).
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A. S. Roberts, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Subwavelength plasmonic color printing protected for ambient use,” Nano Lett. 14(2), 783–787 (2014).
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Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. W. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
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[Crossref] [PubMed]

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Nanoscale (1)

Y. Gu, L. Zhang, J. K. Yang, S. P. Yeo, and C.-W. Qiu, “Color generation via subwavelength plasmonic nanostructures,” Nanoscale 7(15), 6409–6419 (2015).
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Nat. Commun. (1)

X. M. Goh, Y. Zheng, S. J. Tan, L. Zhang, K. Kumar, C.-W. Qiu, and J. K. Yang, “Three-dimensional plasmonic stereoscopic prints in full colour,” Nat. Commun. 5(1), 5361 (2014).
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Nat. Nanotechnol. (3)

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017).
[Crossref] [PubMed]

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

H. Kim, J. Ge, J. Kim, S.-e. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009).
[Crossref]

Nat. Rev. Mater. (1)

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017).
[Crossref]

Nature (2)

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529(7587), 484–489 (2016).
[Crossref] [PubMed]

Phys. Rep. (1)

K. Busch, G. Von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
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Sci. Adv. (1)

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
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V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, “Asynchronous methods for deep reinforcement learning,” in International conference on machine learning, 2016), 1928–1937.

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Figures (5)

Fig. 1
Fig. 1 The all-dielectric structure and reinforcement model. (a) A diagram of the structure used. Silicon (Si) nanodisks on an antireflective layer of silicon nitride (Si3N4), on an Si substrate. The diameter and thickness of nanodisks are given by D and NT, and the distance between them is given by L. The thickness of Si3N4 layer is given by AT. (b) A schematic of the design of the reinforcement model.
Fig. 2
Fig. 2 The double deep Q-learning model structure. Two similar models are created. One for predicting targets named as target model and one as the main model. (a) The targets are found by the combination of the reward and the Q-values predicted by the target model. The targets found by the target model are then used to train the main model. This procedure is repeated at each iteration. (b) The weights from the main model and the target model are combined to update the target model weights at each iteration.
Fig. 3
Fig. 3 The reward system used for the reinforcement model. Each state is converted to a reflectance spectrum by simulation software. The reflected spectrum is converted to XYZ colour values. The XYZ colour values are then converted to L*a*b* colour values. The reward is calculated from the colour difference between the resulting colour from the spectrum and the target colour.
Fig. 4
Fig. 4 The geometrical properties of the closest colours found by reinforcement learning (RL), for red (a), green (b) and blue (c) colours compared to those found by human researchers (calculated from geometrical properties of best found colours given in [8]). As can be seen the RL model found much closer colours for red and blue and almost the same green.
Fig. 5
Fig. 5 The progress of the DDQN model to reach pure blue. Each black dot shows a single structure. The model starts from an arbitrary point and after some exploration goes towards the target colour. The white triangle is the sRGB coverage and the blue outline is the colour coverage found in the previous research.

Tables (2)

Tables Icon

Table 1 Steps for a simplified reinforcement learning algorithm

Tables Icon

Table 2 Definitions of actions used in the reinforcement model.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

s 0 , a 0 , r 1 , s 1 , a 1 , r 2 ,..., s n1 , a n1 , r n , s n
R t = r t +γ r t+1 + γ 2 r t+2 +...+ γ nt r n = r t +γ( r t+1 +γ( r t+2 +...))= r t +γ R t+1
π(s)=arg max a Q(s,a)
Q(s,a)=r+γ max a Q( s , a )
Tw=Mw×τ+Tw×(1τ)
reward= (200CIEDE(obtainedcolortargetcolor)) 3 /10000

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