Abstract

Inverse design techniques in the context of nanophotonics have helped in discovery of compact and counter-intuitive structures/shapes. We introduce the concept of spectral domain inverse design to search through the optical trade-space (dispersive permittivity) of nanocomposite metamaterials. We develop a hybrid optimization technique that combines genetic algorithms and gradient descent methods. We utilize this technique to inverse design an ultra-thin thermophotovoltaic emitter coating material. Our work can lead to an efficient approach to search for new multi-functional optical/thermal metamaterials with desired complex permittivity.

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

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References

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2019 (3)

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

S. So, J. Mun, and J. Rho, “Simultaneous Inverse-Design of Material and Structure via Deep-Learning: Demonstration of Dipole Resonance Engineering using Core-Shell Nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

F. Stefanello, V. Aggarwal, L. S. Buriol, and M. G. C. Resende, “Hybrid algorithms for placement of virtual machines across geo-separated data centers,” J. Comb. Optim. 38(3), 748–793 (2019).
[Crossref]

2018 (7)

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

J. Wang, Y. Shi, T. Hughes, Z. Zhao, and S. Fan, “Adjoint-based optimization of active nanophotonic devices,” Opt. Express 26, 3236 (2018).
[Crossref] [PubMed]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

Y. Shi, W. Li, A. Raman, and S. Fan, “Optimization of multi-layer optical films with a memetic algorithm and mixed integer programming,” ACS Photon. 5, 684–691 (2018).
[Crossref]

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures,” ACS Photonics 5, 1365–1369 (2018).
[Crossref]

2017 (1)

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

2016 (1)

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

2015 (1)

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

2014 (2)

A. Malasi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

2013 (3)

2011 (2)

2006 (2)

W. W. Hager and H. Zhang, “A new active set algorithm for box constrained optimization,” SIAM J. Optim. 17(2), 526–557 (2006).
[Crossref]

C.-A. Guérin, P. Mallet, and A. Sentenac, “Effective-medium theory for finite-size aggregates,” J. Opt. Soc. Am. A 23(2), 349–358 (2006).
[Crossref]

2002 (1)

1996 (2)

1994 (1)

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4(2), 65–85 (1994).
[Crossref]

1990 (1)

1989 (1)

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39(14), 9852–9858 (1989).
[Crossref]

1981 (1)

Aggarwal, V.

F. Stefanello, V. Aggarwal, L. S. Buriol, and M. G. C. Resende, “Hybrid algorithms for placement of virtual machines across geo-separated data centers,” J. Comb. Optim. 38(3), 748–793 (2019).
[Crossref]

Arieli, U.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Babinec, T. M.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Bezdek, J. C.

J. C. Bezdek and R. J. Hathaway, “Some notes on alternating optimization,” AFSS International Conference on Fuzzy Systems. (Springer, 2002.)

Bhargava, S.

Bloom, A. L.

Buriol, L. S.

F. Stefanello, V. Aggarwal, L. S. Buriol, and M. G. C. Resende, “Hybrid algorithms for placement of virtual machines across geo-separated data centers,” J. Comb. Optim. 38(3), 748–793 (2019).
[Crossref]

Cai, W.

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Cano-Renteria, F.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Chang, C. P.

Csiszár, I.

I. Csiszár, “Information geometry and alternating minimization procedures,” Statistics and Decisions 1 (1984): 205–237.

DeBell, G. W.

DeLacy, B. G.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Dewalt, C. J.

Dobrowolski, J. A.

Doshay, S.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Doyle, W. T.

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39(14), 9852–9858 (1989).
[Crossref]

Dyachenko, P. N.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Edee, K.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Eich, M.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Fan, J. A.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Fan, S.

Y. Shi, W. Li, A. Raman, and S. Fan, “Optimization of multi-layer optical films with a memetic algorithm and mixed integer programming,” ACS Photon. 5, 684–691 (2018).
[Crossref]

J. Wang, Y. Shi, T. Hughes, Z. Zhao, and S. Fan, “Adjoint-based optimization of active nanophotonic devices,” Opt. Express 26, 3236 (2018).
[Crossref] [PubMed]

Fedosejevs, R.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Garcia, H.

A. Malasi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

Guérin, C.-A.

Hager, W. W.

W. W. Hager and H. Zhang, “A new active set algorithm for box constrained optimization,” SIAM J. Optim. 17(2), 526–557 (2006).
[Crossref]

Hathaway, R. J.

J. C. Bezdek and R. J. Hathaway, “Some notes on alternating optimization,” AFSS International Conference on Fuzzy Systems. (Springer, 2002.)

Hu, H.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Hughes, T.

Jacob, Z.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

S. Molesky, C. J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21(S1), A96–A110 (2013).
[Crossref]

Jensen, J. S.

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

Jin, W.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

Jing, L.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Joannopoulos, J. D.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Johnson, S. G.

Kalyanaraman, R.

A. Malasi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

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, 1365–1369 (2018).
[Crossref]

Kimerling, L. C.

Krekeler, T.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Krishnamurthy, S.

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

Lagoudakis, K. G.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Lalau-Keraly, C. M.

Lang, S.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Lee, K. T.

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Lee, Y. H.

Li, W.

Y. Shi, W. Li, A. Raman, and S. Fan, “Optimization of multi-layer optical films with a memetic algorithm and mixed integer programming,” ACS Photon. 5, 684–691 (2018).
[Crossref]

Lin, Z.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[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, 1365–1369 (2018).
[Crossref]

Liu, Z.

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Lu, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21(11), 13351–13367 (2013).
[Crossref]

Malasi, A.

A. Malasi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

Malkiel, I.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Mallet, P.

Michel, J.

Miller, O. D.

Molesky, S.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

S. Molesky, C. J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21(S1), A96–A110 (2013).
[Crossref]

Mrejen, M.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Mun, J.

S. So, J. Mun, and J. Rho, “Simultaneous Inverse-Design of Material and Structure via Deep-Learning: Demonstration of Dipole Resonance Engineering using Core-Shell Nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

Nagler, A.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Nazemifard, N.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Neumann, F.

F. Neumann and C. Witt, “Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity (Springer-Verlag, 2010).

Pendharker, S.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Petrov, A. Y.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
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Petykiewicz, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
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Peurifoy, J.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
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Phan, T.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Piggott, A. Y.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Poursoti, Z.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Pramanik, S.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Raman, A.

Y. Shi, W. Li, A. Raman, and S. Fan, “Optimization of multi-layer optical films with a memetic algorithm and mixed integer programming,” ACS Photon. 5, 684–691 (2018).
[Crossref]

Resende, M. G. C.

F. Stefanello, V. Aggarwal, L. S. Buriol, and M. G. C. Resende, “Hybrid algorithms for placement of virtual machines across geo-separated data centers,” J. Comb. Optim. 38(3), 748–793 (2019).
[Crossref]

Rho, J.

S. So, J. Mun, and J. Rho, “Simultaneous Inverse-Design of Material and Structure via Deep-Learning: Demonstration of Dipole Resonance Engineering using Core-Shell Nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

Ritter, M.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Rodrigues, S. P.

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Rodriguez, A. W.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

Sell, D.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Sentenac, A.

Shen, Y.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Sheng, X.

Shi, Y.

J. Wang, Y. Shi, T. Hughes, Z. Zhao, and S. Fan, “Adjoint-based optimization of active nanophotonic devices,” Opt. Express 26, 3236 (2018).
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Y. Shi, W. Li, A. Raman, and S. Fan, “Optimization of multi-layer optical films with a memetic algorithm and mixed integer programming,” ACS Photon. 5, 684–691 (2018).
[Crossref]

Sigmund, O.

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

Slovick, B. A.

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

So, S.

S. So, J. Mun, and J. Rho, “Simultaneous Inverse-Design of Material and Structure via Deep-Learning: Demonstration of Dipole Resonance Engineering using Core-Shell Nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

Soljacic, M.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Starko-Bowes, R.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Stefanello, F.

F. Stefanello, V. Aggarwal, L. S. Buriol, and M. G. C. Resende, “Hybrid algorithms for placement of virtual machines across geo-separated data centers,” J. Comb. Optim. 38(3), 748–793 (2019).
[Crossref]

Störmer, M.

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Suchowski, H.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Sullivan, B. T.

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, 1365–1369 (2018).
[Crossref]

Tegmark, M.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

Tempea, G.

Thundat, T.

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

Tikhonravov, A. V.

Trubetskov, M. K.

Vuckovic, J.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21(11), 13351–13367 (2013).
[Crossref]

Wang, E. W.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Wang, J.

Whitley, D.

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4(2), 65–85 (1994).
[Crossref]

Witt, C.

F. Neumann and C. Witt, “Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity (Springer-Verlag, 2010).

Wolf, L.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Wu, S. Y.

Yablonovitch, E.

Yakovlev, V.

Yang, J.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Yang, Y.

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[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, 1365–1369 (2018).
[Crossref]

Yu, Z. G.

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

Zhang, H.

W. W. Hager and H. Zhang, “A new active set algorithm for box constrained optimization,” SIAM J. Optim. 17(2), 526–557 (2006).
[Crossref]

Zhao, Z.

Zhu, D.

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

ACS Appl. Mater. Interfaces (1)

S. So, J. Mun, and J. Rho, “Simultaneous Inverse-Design of Material and Structure via Deep-Learning: Demonstration of Dipole Resonance Engineering using Core-Shell Nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

ACS Photon. (1)

Y. Shi, W. Li, A. Raman, and S. Fan, “Optimization of multi-layer optical films with a memetic algorithm and mixed integer programming,” ACS Photon. 5, 684–691 (2018).
[Crossref]

ACS Photonics (1)

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures,” ACS Photonics 5, 1365–1369 (2018).
[Crossref]

Appl. Opt. (4)

J. Comb. Optim. (1)

F. Stefanello, V. Aggarwal, L. S. Buriol, and M. G. C. Resende, “Hybrid algorithms for placement of virtual machines across geo-separated data centers,” J. Comb. Optim. 38(3), 748–793 (2019).
[Crossref]

J. Opt. (2)

A. Malasi, R. Kalyanaraman, and H. Garcia, “From Mie to Fresnel through effective medium approximation with multipole contributions,” J. Opt. 16(6), 065001 (2014).
[Crossref]

S. Pendharker, H. Hu, S. Molesky, R. Starko-Bowes, Z. Poursoti, S. Pramanik, N. Nazemifard, R. Fedosejevs, T. Thundat, and Z. Jacob, “Thermal graphene metamaterials and epsilon-near-zero high temperature plasmonics,” J. Opt. 19, 55101 (2017).
[Crossref]

J. Opt. Soc. Am. A (1)

Laser Photonics Rev. (1)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

Light. Sci. Appl. (1)

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Plasmonic nanostructure design and characterization via Deep Learning,” Light. Sci. Appl. 760 (2018).
[Crossref]

Light: Sci. Appl. (1)

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, “High-efficiency, large-area topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019).
[Crossref]

Nano Lett. (1)

Z. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Nat. Commun. (1)

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7(1), 11809 (2016).
[Crossref]

Nat. Photonics (2)

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659 (2018).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (2)

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39(14), 9852–9858 (1989).
[Crossref]

Sci. Adv. (1)

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljačić, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 44206 (2018).
[Crossref] [PubMed]

SIAM J. Optim. (1)

W. W. Hager and H. Zhang, “A new active set algorithm for box constrained optimization,” SIAM J. Optim. 17(2), 526–557 (2006).
[Crossref]

Stat. Comput. (1)

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4(2), 65–85 (1994).
[Crossref]

Other (3)

F. Neumann and C. Witt, “Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity (Springer-Verlag, 2010).

I. Csiszár, “Information geometry and alternating minimization procedures,” Statistics and Decisions 1 (1984): 205–237.

J. C. Bezdek and R. J. Hathaway, “Some notes on alternating optimization,” AFSS International Conference on Fuzzy Systems. (Springer, 2002.)

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Figures (5)

Fig. 1.
Fig. 1. Basic Idea: The spectral features of a N layered multilayer thermal emitter (TPV emitter) stack are mimicked by a single disordered nanocomposite metamaterial. Using a hybrid optimization technique we find the effective permittivity of this nanocomposite material that as the same reflection and transmission spectral features as the one shown.
Fig. 2.
Fig. 2. Hybrid Optimization: The flowchart shows the algorithm used to obtain the optimal solution. Gradient descent technique was used for optimizing $d$, $\rho$, $r$, and a discrete search (Genetic algorithm) was used for searching over the material database.
Fig. 3.
Fig. 3. Optimal solution: The figure shows the target spectra and the obtained spectra of single layer disordered metamaterial found using the hybrid optimization technique. The host medium was found to be TiN with HfO2 particle inclusions having a radius of $\sim 34.73nm$ and a fill fraction $\rho \sim 0.84$. Subplots (a), (b) and (c), show the reflection, transmission and absorption spectra respectively.
Fig. 4.
Fig. 4. Effective single layer permitivitty and tunning ENZ: The subplot (a) shows the effective permitivitty, $\epsilon = \epsilon ' + \iota \epsilon "$ of the single disordered nanocoposite layer. The subplot (b) shows real part of permitivitty $\epsilon '$ calculated for various fill fractions, $\rho$. The inset figure shows the red shift in the ENZ position with increasing fill fraction, $\rho$ = 0 and $\rho$ = 1 show the bounds within which the ENZ can be varied.
Fig. 5.
Fig. 5. FDTD simulations The subplot (a) shows the transmission spectrum obtained using FDTD simulations. The subplot (b) shows the reflection spectrum obtained using FDTD simulations. This shows qualitative agreement with the EMT.

Equations (3)

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ϵ e f f = ϵ m a t 3 ρ ϵ h 2 x 3 [ l = 1 N i ( 2 l + 1 ) ( a l + b l ) ] 1 + ρ ϵ h 2 x 3 [ l = 1 N i ( 2 l + 1 ) ( a l + b l ) ] ,
M F = λ [ ( R ( λ ) R ( λ ) ) 2 + ( T ( λ ) T ( λ ) ) 2 + ( A ( λ ) A ( λ ) ) 2 ] ,
[ d , r , ρ , n 1 , n 2 ] = a r g m i n M F ( d , r , ρ , n 1 , n 2 ) ,