J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” in Advances in Neural Information Processing Systems (2012), pp. 2951–2959.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

J. Bergstra and Y. Bengio, “Random search for hyper-parameter optimization,” J. Mach. Learn. Res. 13, 281–305 (2012).

M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: training deep neural networks with weights and activations constrained to +1 or -1,” arXiv:1602.02830 (2016).

J. Bergstra and Y. Bengio, “Random search for hyper-parameter optimization,” J. Mach. Learn. Res. 13, 281–305 (2012).

M. Hermans, M. Burm, T. Van Vaerenbergh, J. Dambre, and P. Bienstman, “Trainable hardware for dynamical computing using error backpropagation through physical media,” Nat. Commun. 6, 6729 (2015).

[Crossref]

M. Hermans, M. Burm, T. Van Vaerenbergh, J. Dambre, and P. Bienstman, “Trainable hardware for dynamical computing using error backpropagation through physical media,” Nat. Commun. 6, 6729 (2015).

[Crossref]

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

H. J. Caulfield, J. Kinser, and S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).

[Crossref]

E. Khoram, A. Chen, D. Liu, Q. Wang, Z. Yu, and L. Ying, “Nanophotonic media for artificial neural inference,” arXiv:1810.07815 (2018).

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: training deep neural networks with weights and activations constrained to +1 or -1,” arXiv:1602.02830 (2016).

M. Hermans, M. Burm, T. Van Vaerenbergh, J. Dambre, and P. Bienstman, “Trainable hardware for dynamical computing using error backpropagation through physical media,” Nat. Commun. 6, 6729 (2015).

[Crossref]

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: training deep neural networks with weights and activations constrained to +1 or -1,” arXiv:1602.02830 (2016).

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

T. W. Hughes, M. Minkov, Y. Shi, and S. Fan, “Training of photonic neural networks through in situ backpropagation and gradient measurement,” Optica 5, 864–871 (2018).

[Crossref]

T. W. Hughes, M. Minkov, I. A. Williamson, and S. Fan, “Adjoint method and inverse design for nonlinear nanophotonic devices,” ACS Photon. 5, 4781–4787 (2018).

[Crossref]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level-set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19, 1371–1378 (2010).

[Crossref]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level-set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19, 1371–1378 (2010).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

M. Hermans, M. Burm, T. Van Vaerenbergh, J. Dambre, and P. Bienstman, “Trainable hardware for dynamical computing using error backpropagation through physical media,” Nat. Commun. 6, 6729 (2015).

[Crossref]

M. Hermans and T. Van Vaerenbergh, “Towards trainable media: Using waves for neural network-style training,” arXiv:1510.03776 (2015).

V. Nair and G. E. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proceedings of the 27th International Conference on Machine Learning (ICML-10) (2010), pp. 807–814.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: training deep neural networks with weights and activations constrained to +1 or -1,” arXiv:1602.02830 (2016).

T. W. Hughes, M. Minkov, I. A. Williamson, and S. Fan, “Adjoint method and inverse design for nonlinear nanophotonic devices,” ACS Photon. 5, 4781–4787 (2018).

[Crossref]

T. W. Hughes, M. Minkov, Y. Shi, and S. Fan, “Training of photonic neural networks through in situ backpropagation and gradient measurement,” Optica 5, 864–871 (2018).

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

E. Khoram, A. Chen, D. Liu, Q. Wang, Z. Yu, and L. Ying, “Nanophotonic media for artificial neural inference,” arXiv:1810.07815 (2018).

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

H. J. Caulfield, J. Kinser, and S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).

[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” in Advances in Neural Information Processing Systems (2012), pp. 2951–2959.

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level-set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19, 1371–1378 (2010).

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

E. Khoram, A. Chen, D. Liu, Q. Wang, Z. Yu, and L. Ying, “Nanophotonic media for artificial neural inference,” arXiv:1810.07815 (2018).

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).

[Crossref]

T. W. Hughes, M. Minkov, Y. Shi, and S. Fan, “Training of photonic neural networks through in situ backpropagation and gradient measurement,” Optica 5, 864–871 (2018).

[Crossref]

T. W. Hughes, M. Minkov, I. A. Williamson, and S. Fan, “Adjoint method and inverse design for nonlinear nanophotonic devices,” ACS Photon. 5, 4781–4787 (2018).

[Crossref]

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

V. Nair and G. E. Hinton, “Rectified linear units improve restricted Boltzmann machines,” in Proceedings of the 27th International Conference on Machine Learning (ICML-10) (2010), pp. 807–814.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photon. 5, 301–305 (2017).

[Crossref]

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

[Crossref]

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

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

[Crossref]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photon. 5, 301–305 (2017).

[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

P. R. Prucnal and B. J. Shastri, Neuromorphic Photonics (CRC Press, 2017).

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

H. J. Caulfield, J. Kinser, and S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).

[Crossref]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photon. 5, 301–305 (2017).

[Crossref]

S. Saxena and J. Verbeek, “Convolutional neural fabrics,” in Advances in Neural Information Processing Systems (The MIT Press, 2016), pp. 4053–4061.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

P. R. Prucnal and B. J. Shastri, Neuromorphic Photonics (CRC Press, 2017).

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” in Advances in Neural Information Processing Systems (2012), pp. 2951–2959.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: training deep neural networks with weights and activations constrained to +1 or -1,” arXiv:1602.02830 (2016).

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

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

[Crossref]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photon. 5, 301–305 (2017).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

L. Jing, Y. Shen, T. Dubcek, J. Peurifoy, S. Skirlo, Y. LeCun, M. Tegmark, and M. Soljačić, “Tunable efficient unitary neural networks (EUNN) and their application to RNNs,” in Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1733–1741.

M. Hermans, M. Burm, T. Van Vaerenbergh, J. Dambre, and P. Bienstman, “Trainable hardware for dynamical computing using error backpropagation through physical media,” Nat. Commun. 6, 6729 (2015).

[Crossref]

M. Hermans and T. Van Vaerenbergh, “Towards trainable media: Using waves for neural network-style training,” arXiv:1510.03776 (2015).

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

S. Saxena and J. Verbeek, “Convolutional neural fabrics,” in Advances in Neural Information Processing Systems (The MIT Press, 2016), pp. 4053–4061.

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photon. 5, 301–305 (2017).

[Crossref]

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

[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).

[Crossref]

E. Khoram, A. Chen, D. Liu, Q. Wang, Z. Yu, and L. Ying, “Nanophotonic media for artificial neural inference,” arXiv:1810.07815 (2018).

T. W. Hughes, M. Minkov, I. A. Williamson, and S. Fan, “Adjoint method and inverse design for nonlinear nanophotonic devices,” ACS Photon. 5, 4781–4787 (2018).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level-set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19, 1371–1378 (2010).

[Crossref]

H. G. Chen, S. Jayasuriya, J. Yang, J. Stephen, S. Sivaramakrishnan, A. Veeraraghavan, and A. Molnar, “ASP vision: optically computing the first layer of convolutional neural networks using angle sensitive pixels,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 903–912.

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

E. Khoram, A. Chen, D. Liu, Q. Wang, Z. Yu, and L. Ying, “Nanophotonic media for artificial neural inference,” arXiv:1810.07815 (2018).

E. Khoram, A. Chen, D. Liu, Q. Wang, Z. Yu, and L. Ying, “Nanophotonic media for artificial neural inference,” arXiv:1810.07815 (2018).

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photon. 5, 301–305 (2017).

[Crossref]

T. W. Hughes, M. Minkov, I. A. Williamson, and S. Fan, “Adjoint method and inverse design for nonlinear nanophotonic devices,” ACS Photon. 5, 4781–4787 (2018).

[Crossref]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level-set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19, 1371–1378 (2010).

[Crossref]

J. Bergstra and Y. Bengio, “Random search for hyper-parameter optimization,” J. Mach. Learn. Res. 13, 281–305 (2012).

M. Hermans, M. Burm, T. Van Vaerenbergh, J. Dambre, and P. Bienstman, “Trainable hardware for dynamical computing using error backpropagation through physical media,” Nat. Commun. 6, 6729 (2015).

[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).

[Crossref]

D. A. Miller, “All linear optical devices are mode converters,” Opt. Express 20, 23985–23993 (2012).

[Crossref]

T. W. Hughes, M. Minkov, Y. Shi, and S. Fan, “Training of photonic neural networks through in situ backpropagation and gradient measurement,” Optica 5, 864–871 (2018).

[Crossref]

J. Bueno, S. Maktoobi, L. Froehly, I. Fischer, M. Jacquot, L. Larger, and D. Brunner, “Reinforcement learning in a large-scale photonic recurrent neural network,” Optica 5, 756–760 (2018).

[Crossref]

H. J. Caulfield, J. Kinser, and S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).

[Crossref]

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

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

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