Abstract

Neural network–based inverse design of nanophotonic device network is computationally and time efficient, but in general suffers the problems of robustness and stability against variation of the input target electromagnetic response. The inverse design network is required to be robust against the input electromagnetic response and to be capable of approximating the given electromagnetic response, even under the circumstances that the exact target response may not exist. We introduce a modified denoising autoencoder network to ensure the robustness of neural network–based inverse design, which consists of (1) a pre-trained network as a substitute of numerical simulation and (2) an inverse design network. We further purposely train the network with certain random disturbances added to the training dataset generated by the pre-trained network. Consequently, our modified denoising autoencoder network is more robust and more accurate than the conventional fully connected neural network. The strength and flexibility of our proposed network is illustrated via three concrete examples of achieving the desired scattering spectra of layered spherical scatterers.

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

Full Article  |  PDF Article
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References

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2019 (6)

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and structures via deep learning: Demonstration of dipole resonance engineering using core-shell nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

E. W. Wang, D. Sell, T. Phan, and J. A. Fan, “Robust design of topology-optimized metasurfaces,” Opt. Mater. Express 9(2), 469–482 (2019).
[Crossref]

S. D. Campbell, D. Sell, R. P. Jenkins, E. B. Whiting, J. A. Fan, and D. H. Werner, “Review of numerical optimization techniques for meta-device design,” Opt. Mater. Express 9(4), 1842–1863 (2019).
[Crossref]

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

R. E. Christiansen, F. Wang, and O. Sigmund, “Topological insulators by topology optimization,” Phys. Rev. Lett. 122(23), 234502 (2019).
[Crossref]

W. Li, D. Tan, J. Xu, S. Wang, and Y. Chen, “Finite element based green’s function integral equation for modelling light scattering,” Opt. Express 27(11), 16047–16057 (2019).
[Crossref]

2018 (10)

Y. Sun, Z. Xia, and U. S. Kamilov, “Efficient and accurate inversion of multiple scattering with deep learning,” Opt. Express 26(11), 14678–14688 (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]

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]

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]

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 db power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

T. Asano and S. Noda, “Optimization of photonic crystal nanocavities based on deep learning,” Opt. Express 26(25), 32704–32717 (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. 4(6), eaar4206 (2018).
[Crossref]

R. Pestourie, C. Pérez-Arancibia, Z. Lin, W. Shin, F. Capasso, and S. G. Johnson, “Inverse design of large-area metasurfaces,” Opt. Express 26(26), 33732–33747 (2018).
[Crossref]

S. Inampudi and H. Mosallaei, “Neural network based design of metagratings,” Appl. Phys. Lett. 112(24), 241102 (2018).
[Crossref]

2017 (2)

2016 (1)

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (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(6), 374–377 (2015).
[Crossref]

2014 (1)

2011 (1)

2008 (1)

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[Crossref]

2007 (1)

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antennas Propag. 55(3), 556–567 (2007).
[Crossref]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Ao, Y.

Arieli, U.

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

Asano, T.

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(6), 374–377 (2015).
[Crossref]

Bengio, Y.

P. Vincent, H. Larochelle, Y. Bengio, and P.-A. Manzagol, “Extracting and composing robust features with denoising autoencoders,” in Proceedings of the 25th international conference on Machine learning, (ACM, 2008), pp. 1096–1103.

Bruna, J.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

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]

Campbell, S. D.

S. D. Campbell, D. Sell, R. P. Jenkins, E. B. Whiting, J. A. Fan, and D. H. Werner, “Review of numerical optimization techniques for meta-device design,” Opt. Mater. Express 9(4), 1842–1863 (2019).
[Crossref]

D. Z. Zhu, E. B. Whiting, S. D. Campbell, P. L. Werner, and D. H. Werner, “Inverse design of three-dimensional nanoantennas for metasurface applications,” in 2019 International Applied Computational Electromagnetics Society Symposium (ACES), (IEEE, 2019), pp. 1–2.

S. D. Campbell, J. Nagar, P. L. Werner, and D. H. Werner, “Multi-objective analysis of multi-layered core-shell nanoparticles,” in 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), (2017), pp. 1–3.

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. 4(6), eaar4206 (2018).
[Crossref]

Capasso, F.

Chang, W.

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 db power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref]

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

Chen, Y.

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]

Cheng, M.

Christiansen, R. E.

R. E. Christiansen, F. Wang, and O. Sigmund, “Topological insulators by topology optimization,” Phys. Rev. Lett. 122(23), 234502 (2019).
[Crossref]

Dal Negro, L.

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

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. 4(6), eaar4206 (2018).
[Crossref]

Deng, L.

Erhan, D.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

Fan, J. A.

E. W. Wang, D. Sell, T. Phan, and J. A. Fan, “Robust design of topology-optimized metasurfaces,” Opt. Mater. Express 9(2), 469–482 (2019).
[Crossref]

S. D. Campbell, D. Sell, R. P. Jenkins, E. B. Whiting, J. A. Fan, and D. H. Werner, “Review of numerical optimization techniques for meta-device design,” Opt. Mater. Express 9(4), 1842–1863 (2019).
[Crossref]

J. A. Fan, “Generating high performance, topologically-complex metasurfaces with neural networks,” in CLEO: Applications and Technology, (Optical Society of America, 2019), pp. AM4K-4.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Data-driven metasurface discovery,” arXiv preprint arXiv:1811.12436v1 (2018).

Fergus, R.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

Forestiere, C.

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

Frandsen, L. H.

L. H. Frandsen and O. Sigmund, “Inverse design engineering of all-silicon polarization beam splitters,” in Photonic and Phononic Properties of Engineered Nanostructures VI, vol. 9756 (International Society for Optics and Photonics, 2016), p. 97560Y.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Goodfellow, I.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

He, Y.

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

Hickey, J.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Data-driven metasurface discovery,” arXiv preprint arXiv:1811.12436v1 (2018).

Hougaard, K.

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[Crossref]

Hoyer, S.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Data-driven metasurface discovery,” arXiv preprint arXiv:1811.12436v1 (2018).

Hu, H.

Inampudi, S.

S. Inampudi and H. Mosallaei, “Neural network based design of metagratings,” Appl. Phys. Lett. 112(24), 241102 (2018).
[Crossref]

Jenkins, R. P.

Jensen, J. S.

Jha, D.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

Jiang, J.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Data-driven metasurface discovery,” arXiv preprint arXiv:1811.12436v1 (2018).

Jin, N.

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antennas Propag. 55(3), 556–567 (2007).
[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(11), 659–670 (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. 4(6), eaar4206 (2018).
[Crossref]

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. 4(6), eaar4206 (2018).
[Crossref]

Johnson, S. G.

Kamilov, U. S.

Khoo, Y.

Y. Khoo and L. Ying, “Switchnet: a neural network model for forward and inverse scattering problems,” arXiv preprint arXiv:1810.09675 (2018).

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]

Kirby, R. M.

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Koenderink, A. F.

Koike-Akino, T.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

Kojima, K.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[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(6), 374–377 (2015).
[Crossref]

Larochelle, H.

P. Vincent, H. Larochelle, Y. Bengio, and P.-A. Manzagol, “Extracting and composing robust features with denoising autoencoders,” in Proceedings of the 25th international conference on Machine learning, (ACM, 2008), pp. 1096–1103.

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]

Lei, B.

Li, D.

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

Li, W.

Lin, C.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[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(11), 659–670 (2018).
[Crossref]

R. Pestourie, C. Pérez-Arancibia, Z. Lin, W. Shin, F. Capasso, and S. G. Johnson, “Inverse design of large-area metasurfaces,” Opt. Express 26(26), 33732–33747 (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(4), 1365–1369 (2018).
[Crossref]

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 db power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref]

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

Liu, W.

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]

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(6), 374–377 (2015).
[Crossref]

Lu, L.

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 db power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref]

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

Ma, H.

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).
[Crossref]

Malkiel, I.

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

Manzagol, P.-A.

P. Vincent, H. Larochelle, Y. Bengio, and P.-A. Manzagol, “Extracting and composing robust features with denoising autoencoders,” in Proceedings of the 25th international conference on Machine learning, (ACM, 2008), pp. 1096–1103.

Molesky, S.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

Mosallaei, H.

S. Inampudi and H. Mosallaei, “Neural network based design of metagratings,” Appl. Phys. Lett. 112(24), 241102 (2018).
[Crossref]

Mrejen, M.

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

Mun, J.

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and structures via deep learning: Demonstration of dipole resonance engineering using core-shell nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and parameters of core-shell nanoparticle via deep-learning: Demonstration of dipole resonance engineering,” arXiv preprint arXiv:1904.02848 (2019).

Nagar, J.

S. D. Campbell, J. Nagar, P. L. Werner, and D. H. Werner, “Multi-objective analysis of multi-layered core-shell nanoparticles,” in 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), (2017), pp. 1–3.

Nagler, A.

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

Noda, S.

Pan, Z.

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

Parsons, K.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

Pérez-Arancibia, C.

Pestourie, R.

Petykiewicz, J.

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[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(6), 374–377 (2015).
[Crossref]

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. 4(6), eaar4206 (2018).
[Crossref]

Phan, T.

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(11), 659–670 (2018).
[Crossref]

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[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(6), 374–377 (2015).
[Crossref]

Rahmat-Samii, Y.

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antennas Propag. 55(3), 556–567 (2007).
[Crossref]

Ren, X.

Rho, J.

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and structures via deep learning: Demonstration of dipole resonance engineering using core-shell nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and parameters of core-shell nanoparticle via deep-learning: Demonstration of dipole resonance engineering,” arXiv preprint arXiv:1904.02848 (2019).

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(11), 659–670 (2018).
[Crossref]

Sell, D.

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. 4(6), eaar4206 (2018).
[Crossref]

Shin, W.

Sigmund, O.

R. E. Christiansen, F. Wang, and O. Sigmund, “Topological insulators by topology optimization,” Phys. Rev. Lett. 122(23), 234502 (2019).
[Crossref]

F. Wang, J. S. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28(3), 387–397 (2011).
[Crossref]

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[Crossref]

L. H. Frandsen and O. Sigmund, “Inverse design engineering of all-silicon polarization beam splitters,” in Photonic and Phononic Properties of Engineered Nanostructures VI, vol. 9756 (International Society for Optics and Photonics, 2016), p. 97560Y.

So, S.

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and structures via deep learning: Demonstration of dipole resonance engineering using core-shell nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and parameters of core-shell nanoparticle via deep-learning: Demonstration of dipole resonance engineering,” arXiv preprint arXiv:1904.02848 (2019).

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. 4(6), eaar4206 (2018).
[Crossref]

Su, L.

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref]

Suchowski, H.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

Sun, Y.

Sutskever, I.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

Szegedy, C.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

Tahersima, M. H.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

Tan, D.

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]

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. 4(6), eaar4206 (2018).
[Crossref]

Unni, R.

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” arXiv preprint arXiv:1810.11709 (2018).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Vincent, P.

P. Vincent, H. Larochelle, Y. Bengio, and P.-A. Manzagol, “Extracting and composing robust features with denoising autoencoders,” in Proceedings of the 25th international conference on Machine learning, (ACM, 2008), pp. 1096–1103.

Vuckovic, J.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[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(6), 374–377 (2015).
[Crossref]

Wang, B.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

Wang, E. W.

Wang, F.

R. E. Christiansen, F. Wang, and O. Sigmund, “Topological insulators by topology optimization,” Phys. Rev. Lett. 122(23), 234502 (2019).
[Crossref]

F. Wang, J. S. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28(3), 387–397 (2011).
[Crossref]

Wang, R.

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

Wang, S.

Werner, D. H.

S. D. Campbell, D. Sell, R. P. Jenkins, E. B. Whiting, J. A. Fan, and D. H. Werner, “Review of numerical optimization techniques for meta-device design,” Opt. Mater. Express 9(4), 1842–1863 (2019).
[Crossref]

D. Z. Zhu, E. B. Whiting, S. D. Campbell, P. L. Werner, and D. H. Werner, “Inverse design of three-dimensional nanoantennas for metasurface applications,” in 2019 International Applied Computational Electromagnetics Society Symposium (ACES), (IEEE, 2019), pp. 1–2.

S. D. Campbell, J. Nagar, P. L. Werner, and D. H. Werner, “Multi-objective analysis of multi-layered core-shell nanoparticles,” in 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), (2017), pp. 1–3.

Werner, P. L.

S. D. Campbell, J. Nagar, P. L. Werner, and D. H. Werner, “Multi-objective analysis of multi-layered core-shell nanoparticles,” in 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), (2017), pp. 1–3.

D. Z. Zhu, E. B. Whiting, S. D. Campbell, P. L. Werner, and D. H. Werner, “Inverse design of three-dimensional nanoantennas for metasurface applications,” in 2019 International Applied Computational Electromagnetics Society Symposium (ACES), (IEEE, 2019), pp. 1–2.

Whiting, E. B.

S. D. Campbell, D. Sell, R. P. Jenkins, E. B. Whiting, J. A. Fan, and D. H. Werner, “Review of numerical optimization techniques for meta-device design,” Opt. Mater. Express 9(4), 1842–1863 (2019).
[Crossref]

D. Z. Zhu, E. B. Whiting, S. D. Campbell, P. L. Werner, and D. H. Werner, “Inverse design of three-dimensional nanoantennas for metasurface applications,” in 2019 International Applied Computational Electromagnetics Society Symposium (ACES), (IEEE, 2019), pp. 1–2.

Wolf, L.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

Xia, Z.

Xie, W.

Xu, J.

Yang, J.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Data-driven metasurface discovery,” arXiv preprint arXiv:1811.12436v1 (2018).

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. 4(6), eaar4206 (2018).
[Crossref]

Yao, K.

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” arXiv preprint arXiv:1810.11709 (2018).

Ying, L.

Y. Khoo and L. Ying, “Switchnet: a neural network model for forward and inverse scattering problems,” arXiv preprint arXiv:1810.09675 (2018).

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]

Zaremba, W.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

Zhang, J.

Zhang, M.

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 db power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref]

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

Zhang, Y.

Zheng, Y.

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” arXiv preprint arXiv:1810.11709 (2018).

Zhou, F.

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

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]

Zhu, D. Z.

D. Z. Zhu, E. B. Whiting, S. D. Campbell, P. L. Werner, and D. H. Werner, “Inverse design of three-dimensional nanoantennas for metasurface applications,” in 2019 International Applied Computational Electromagnetics Society Symposium (ACES), (IEEE, 2019), pp. 1–2.

ACS Appl. Mater. Interfaces (1)

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and structures via deep learning: Demonstration of dipole resonance engineering using core-shell nanoparticles,” ACS Appl. Mater. Interfaces 11(27), 24264–24268 (2019).
[Crossref]

ACS Nano (1)

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref]

ACS Photonics (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]

C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse design of metal nanoparticles’ morphology,” ACS Photonics 3(1), 68–78 (2016).
[Crossref]

Appl. Phys. Lett. (1)

S. Inampudi and H. Mosallaei, “Neural network based design of metagratings,” Appl. Phys. Lett. 112(24), 241102 (2018).
[Crossref]

IEEE Trans. Antennas Propag. (1)

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antennas Propag. 55(3), 556–567 (2007).
[Crossref]

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

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. Photonics (2)

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (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(6), 374–377 (2015).
[Crossref]

Opt. Express (7)

Opt. Mater. Express (2)

Phys. Rev. Lett. (2)

R. E. Christiansen, F. Wang, and O. Sigmund, “Topological insulators by topology optimization,” Phys. Rev. Lett. 122(23), 234502 (2019).
[Crossref]

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[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. 4(6), eaar4206 (2018).
[Crossref]

Sci. Rep. (2)

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019).
[Crossref]

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Other (13)

S. So, J. Mun, and J. Rho, “Simultaneous inverse design of materials and parameters of core-shell nanoparticle via deep-learning: Demonstration of dipole resonance engineering,” arXiv preprint arXiv:1904.02848 (2019).

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199 (2013).

P. Vincent, H. Larochelle, Y. Bengio, and P.-A. Manzagol, “Extracting and composing robust features with denoising autoencoders,” in Proceedings of the 25th international conference on Machine learning, (ACM, 2008), pp. 1096–1103.

S. D. Campbell, J. Nagar, P. L. Werner, and D. H. Werner, “Multi-objective analysis of multi-layered core-shell nanoparticles,” in 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), (2017), pp. 1–3.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Data-driven metasurface discovery,” arXiv preprint arXiv:1811.12436v1 (2018).

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” arXiv preprint arXiv:1810.11709 (2018).

I. Malkiel, A. Nagler, M. Mrejen, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for design and retrieval of nano-photonic structures,” arXiv preprint arXiv:1702.07949 (2017).

J. A. Fan, “Generating high performance, topologically-complex metasurfaces with neural networks,” in CLEO: Applications and Technology, (Optical Society of America, 2019), pp. AM4K-4.

W. Chang, M. Zhang, L. Lu, F. Zhou, D. Li, Z. Pan, and D. Liu, “Inverse design of an ultra-compact mode (de) multiplexer based on subwavelength structure,” in CLEO: Science and Innovations, (Optical Society of America, 2017), pp. SF1J-8.

D. Z. Zhu, E. B. Whiting, S. D. Campbell, P. L. Werner, and D. H. Werner, “Inverse design of three-dimensional nanoantennas for metasurface applications,” in 2019 International Applied Computational Electromagnetics Society Symposium (ACES), (IEEE, 2019), pp. 1–2.

I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, “Deep learning for the design of nano-photonic structures,” in 2018 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2018), pp. 1–14.

L. H. Frandsen and O. Sigmund, “Inverse design engineering of all-silicon polarization beam splitters,” in Photonic and Phononic Properties of Engineered Nanostructures VI, vol. 9756 (International Society for Optics and Photonics, 2016), p. 97560Y.

Y. Khoo and L. Ying, “Switchnet: a neural network model for forward and inverse scattering problems,” arXiv preprint arXiv:1810.09675 (2018).

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Figures (6)

Fig. 1.
Fig. 1. Architecture diagram of (a) FCNN and (b) MDAN. In the MDAN, there are fixed forward net (dark blue) and the inverse net (blue), cascaded with each other.
Fig. 2.
Fig. 2. (a) The core-shell spherical nanoparticle consists of Au, Ag, TiO$_2$ layers, and the hosting medium is air. (b) Loss function of the FCNN and the MDAN is plotted as a function of epoch. The final loss of the MDAN is higher than the the training loss, but lower than validation loss of the FCNN.
Fig. 3.
Fig. 3. (a)–(c)/(d)–(f) shows the scattering spectra as functions of wavelength for the FCNN/MDAN. The target spectra $S^t$ for the FCNN/MDAN are plotted with solid orange/blue lines, the disturbed spectra $S^{dt}$ with added noise for the FCNN/MDAN are plotted with dotted orange/blue lines, the design spectra $S^{ds}$ for the FCNN/MDAN are plotted with dashed orange/blue lines. $Q_{sca}$ represents the scattering efficiency.
Fig. 4.
Fig. 4. (a)–(b) shows the average relative error $err^{ave}_{r}$ of the structure as function of $a$ for the FCNN/MDAN. The three lines marked with circle, triangle and square represent the $err^{ave}_{r}$ of the Au, Ag, TiO$_2$ layers. The six inset box marked as A-F are corresponding to the panels as shown in in Figs. 3(a)–3(f), respectively.
Fig. 5.
Fig. 5. (a)–(b)–(c) shows the single peak/ double peaks/ sharp peak target spectrum $S^t$ and the designed spectrum $S^{ds}$ obtained by the FCNN and the MDAN.
Fig. 6.
Fig. 6. (a) The asymmetric eccentrical core-shell structure is characterized by $\varepsilon _1$, $\varepsilon _2$, $r_1, r_2, b_1, b_2$ and the hosting medium is air; (b) shows a standard far-field radiation; (c) and (d) shows the inverse design of double peaks and single peak target far-field radiation.

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