Abstract

Photonic waveguides are prime candidates for integrated and parallel photonic interconnects. Such interconnects correspond to large-scale vector matrix products, which are at the heart of neural network computation. However, parallel interconnect circuits realized in two dimensions, for example, by lithography, are strongly limited in size due to disadvantageous scaling. We use three-dimensional (3D) printed photonic waveguides to overcome this limitation. 3D optical couplers with fractal topology efficiently connect large numbers of input and output channels, and we show that the substrate’s area and height scale linearly. Going beyond simple couplers, we introduce functional circuits for discrete spatial filters identical to those used in deep convolutional neural networks.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (7)

L. Yang, A. Münchinger, M. Kadic, V. Hahn, F. Mayer, E. Blasco, C. Barner-Kowollik, and M. Wegener, “On the Schwarzschild effect in 3D two-photon laser lithography,” Adv. Opt. Mater. 7, 1901040 (2019).
[Crossref]

A. Neckar, S. Fok, B. V. Benjamin, T. C. Stewart, N. N. Oza, A. R. Voelker, C. Eliasmith, R. Manohar, and K. Boahen, “Braindrop: a mixed-signal neuromorphic architecture with a dynamical systems-based programming model,” Proc. IEEE 107, 144–164 (2019).
[Crossref]

D. Pierangeli, G. Marcucci, and C. Conti, “Large-Scale photonic Ising machine by spatial light modulation,” Phys. Rev. Lett. 122, 213902 (2019).
[Crossref]

E. Khoram, A. Chen, D. Liu, L. Ying, Q. Wang, M. Yuan, and Z. Yu, “Nanophotonic media for artificial neural inference,” Photon. Res. 7, 823 (2019).
[Crossref]

A. Nesic, M. Blaicher, T. Hoose, A. Hofmann, M. Lauermann, Y. Kutuvantavida, M. Nöllenburg, S. Randel, W. Freude, and C. Koos, “Photonic-integrated circuits with non-planar topologies realized by 3D-printed waveguide overpasses,” Opt. Express 27, 17402 (2019).
[Crossref]

Y. Zhang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, C. Roberts, P. Robinson, B. Bohlin, C. Ríos, H. Lin, M. Kang, T. Gu, J. Warner, V. Liberman, K. Richardson, and J. Hu, “Broadband transparent optical phase change materials for high-performance nonvolatile photonics,” Nat. Commun. 10, 1–9 (2019).
[Crossref]

Y.-G. Park, H. Min, H. Kim, A. Zhexembekova, C. Y. Lee, and J.-U. Park, “Three-dimensional, high-resolution printing of carbon nanotube/liquid metal composites with mechanical and electrical reinforcement,” Nano Lett. 19, 4866–4872 (2019).
[Crossref]

2018 (3)

T. Heuser, J. Große, A. Kaganskiy, D. Brunner, and S. Reitzenstein, “Fabrication of dense diameter-tuned quantum dot micropillar arrays for applications in photonic information processing,” J. Appl. Phys. 3, 1–6 (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 (2018).
[Crossref]

H. Peng, M. A. Nahmias, T. F. de Lima, A. N. Tait, and B. J. Shastri, “Neuromorphic photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24, 1–15 (2018).
[Crossref]

2017 (3)

D. A. Miller, “Attojoule optoelectronics for low-energy information processing and communications,” J. Light. Technol. 35, 346–396 (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]

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6, 561–576 (2017).
[Crossref]

2016 (2)

J. Pyo, J. T. Kim, J. Lee, J. Yoo, and J. H. Je, “3D printed nanophotonic waveguides,” Adv. Opt. Mater. 4, 1190–1195 (2016).
[Crossref]

J. Moughames, S. Jradi, T. M. Chan, S. Akil, Y. Battie, A. E. Naciri, Z. Herro, S. Guenneau, S. Enoch, L. Joly, J. Cousin, and A. Bruyant, “Wavelength-scale light concentrator made by direct 3D laser writing of polymer metamaterials,” Sci. Rep. 6, 33627 (2016).
[Crossref]

2015 (3)

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2, 747 (2015).
[Crossref]

C. Rios, M. Stegmaier, P. Hosseini, D. C. Wang, T. C. Scherer, C. Wright, H. Bhaskaran, and W. E. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9, 725–732 (2015).
[Crossref]

2014 (1)

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 1–6 (2014).
[Crossref]

2013 (3)

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

M. Nahmias and B. Shastri, “A leaky integrate-and-fire laser neuron for ultrafast cognitive computing,” IEEE J. Sel. Top. Quantum Electron. 19, 1–12 (2013).
[Crossref]

C. Koos, J. Leuthold, W. Freude, N. Lindenmann, S. Koeber, G. Balthasar, J. Hoffmann, T. Hoose, P. Huebner, D. Hillerkuss, and R. Schmogrow, “Photonic wire bonding: connecting nanophotonic circuits across chip boundaries,” Proc. SPIE 8613, 86130W (2013).
[Crossref]

2012 (5)

2011 (3)

V. Venkatadri, B. Sammakia, K. Srihari, and D. Santos, “A review of recent advances in thermal management in three dimensional chip stacks in electronic systems,” J. Electron. Packag. 133, 041011 (2011).
[Crossref]

A. Frölich and M. Wegener, “Spectroscopic characterization of highly doped ZnO films grown by atomic-layer deposition for three-dimensional infrared metamaterials [Invited],” Opt. Mater. Express 1, 883 (2011).
[Crossref]

L. Appeltant, M. C. Soriano, G. V. D. Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

2010 (1)

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[Crossref]

2004 (1)

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

1989 (2)

J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311 (1989).
[Crossref]

H. Lee, X. Gu, and D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[Crossref]

1985 (1)

Agrawal, G.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Akil, S.

J. Moughames, S. Jradi, T. M. Chan, S. Akil, Y. Battie, A. E. Naciri, Z. Herro, S. Guenneau, S. Enoch, L. Joly, J. Cousin, and A. Bruyant, “Wavelength-scale light concentrator made by direct 3D laser writing of polymer metamaterials,” Sci. Rep. 6, 33627 (2016).
[Crossref]

Amant, R. R. S.

H. Esmaeilzadeh, E. Blem, R. R. S. Amant, K. Sankaralingam, and D. Burger, “Dark silicon and the end of multicore scaling,” IEEE Micro 32, 122–134 (2012).
[Crossref]

Antonik, P.

D. Brunner, P. Antonik, and X. Porte, “Introduction to novel photonic computing,” in Photonic Reservoir Computing, Optical Recurrent Neural Networks, B. Daniel, M. C. Soriano, and G. Van der Sande, eds. (De Gruyter, 2019), pp. 1–32.

Appeltant, L.

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. V. D. Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

Aviyente, S.

K. Huang and S. Aviyente, “Sparse representation for signal classification,” in Advances in Neural Information Processing Systems 19, B. Schölkopf, J. C. Platt, and T. Hoffman, eds. (MIT, 2007), pp. 609–616.

Baehr-Jones, T.

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]

Bajwa, R.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Balthasar, G.

C. Koos, J. Leuthold, W. Freude, N. Lindenmann, S. Koeber, G. Balthasar, J. Hoffmann, T. Hoose, P. Huebner, D. Hillerkuss, and R. Schmogrow, “Photonic wire bonding: connecting nanophotonic circuits across chip boundaries,” Proc. SPIE 8613, 86130W (2013).
[Crossref]

N. Lindenmann, G. Balthasar, D. Hillerkuss, R. Schmogrow, M. Jordan, J. Leuthold, W. Freude, and C. Koos, “Photonic wire bonding: a novel concept for chip-scale interconnects,” Opt. Express 20, 17667 (2012).
[Crossref]

Barner-Kowollik, C.

L. Yang, A. Münchinger, M. Kadic, V. Hahn, F. Mayer, E. Blasco, C. Barner-Kowollik, and M. Wegener, “On the Schwarzschild effect in 3D two-photon laser lithography,” Adv. Opt. Mater. 7, 1901040 (2019).
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Sizikov, G.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Skirlo, S.

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).
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Smerieri, A.

Snelham, M.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Soljacic, M.

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).
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Soriano, M. C.

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6, 561–576 (2017).
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D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
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Soukoulis, C. M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
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Souter, J.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Srihari, K.

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Staude, I.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
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Stegmaier, M.

C. Rios, M. Stegmaier, P. Hosseini, D. C. Wang, T. C. Scherer, C. Wright, H. Bhaskaran, and W. E. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9, 725–732 (2015).
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Steinberg, D.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Steinkraus, D.

P. Simard, D. Steinkraus, and J. Platt, “Best practices for convolutional neural networks applied to visual document analysis,” in Proceedings of the Seventh International Conference on Document Analysis and Recognition (2003), Vol. 343, pp. 958–963.

Stenger, N.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24, 2710–2714 (2012).
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Stewart, T. C.

A. Neckar, S. Fok, B. V. Benjamin, T. C. Stewart, N. N. Oza, A. R. Voelker, C. Eliasmith, R. Manohar, and K. Boahen, “Braindrop: a mixed-signal neuromorphic architecture with a dynamical systems-based programming model,” Proc. IEEE 107, 144–164 (2019).
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Sun, X.

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).
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Swing, A.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Tait, A. N.

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Tan, M.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Thiel, M.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24, 2710–2714 (2012).
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G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
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D. Choudhury, D. K. McNicholl, A. RepettI, I. Gris-Sanchez, T. A. Birks, Y. Wiaux, and R. R. Thomson, “Compressive optical imaging with a photonic lantern,” arXiv:1903.01288 (2019).

Thorson, G.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Tian, B.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Toma, H.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Tuttle, E.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Van der Sande, G.

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6, 561–576 (2017).
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Van Vaerenbergh, T.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 1–6 (2014).
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Vandoorne, K.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 1–6 (2014).
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Vasudevan, V.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Venkatadri, V.

V. Venkatadri, B. Sammakia, K. Srihari, and D. Santos, “A review of recent advances in thermal management in three dimensional chip stacks in electronic systems,” J. Electron. Packag. 133, 041011 (2011).
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Verstraeten, D.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 1–6 (2014).
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Voelker, A. R.

A. Neckar, S. Fok, B. V. Benjamin, T. C. Stewart, N. N. Oza, A. R. Voelker, C. Eliasmith, R. Manohar, and K. Boahen, “Braindrop: a mixed-signal neuromorphic architecture with a dynamical systems-based programming model,” Proc. IEEE 107, 144–164 (2019).
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von Freymann, G.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
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M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
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Walter, R.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Wang, D. C.

C. Rios, M. Stegmaier, P. Hosseini, D. C. Wang, T. C. Scherer, C. Wright, H. Bhaskaran, and W. E. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9, 725–732 (2015).
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Wang, Q.

Wang, W.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Warner, J.

Y. Zhang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, C. Roberts, P. Robinson, B. Bohlin, C. Ríos, H. Lin, M. Kang, T. Gu, J. Warner, V. Liberman, K. Richardson, and J. Hu, “Broadband transparent optical phase change materials for high-performance nonvolatile photonics,” Nat. Commun. 10, 1–9 (2019).
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M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
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Wiaux, Y.

D. Choudhury, D. K. McNicholl, A. RepettI, I. Gris-Sanchez, T. A. Birks, Y. Wiaux, and R. R. Thomson, “Compressive optical imaging with a photonic lantern,” arXiv:1903.01288 (2019).

Wilcox, E.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

Wright, C.

C. Rios, M. Stegmaier, P. Hosseini, D. C. Wang, T. C. Scherer, C. Wright, H. Bhaskaran, and W. E. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9, 725–732 (2015).
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Y. Zhang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, C. Roberts, P. Robinson, B. Bohlin, C. Ríos, H. Lin, M. Kang, T. Gu, J. Warner, V. Liberman, K. Richardson, and J. Hu, “Broadband transparent optical phase change materials for high-performance nonvolatile photonics,” Nat. Commun. 10, 1–9 (2019).
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L. Yang, A. Münchinger, M. Kadic, V. Hahn, F. Mayer, E. Blasco, C. Barner-Kowollik, and M. Wegener, “On the Schwarzschild effect in 3D two-photon laser lithography,” Adv. Opt. Mater. 7, 1901040 (2019).
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Yoo, J.

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Young, C.

N. P. Jouppi, C. Young, N. Patil, D. Patterson, G. Agrawal, R. Bajwa, S. Bates, S. Bhatia, N. Boden, A. Borchers, R. Boyle, P.-L. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, and D. H. Yoon, “In-datacenter performance analysis of a tensor processing unit,” arXiv:1704.04760 (2017), pp. 1–17.

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Yuan, M.

Zhang, Y.

Y. Zhang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, C. Roberts, P. Robinson, B. Bohlin, C. Ríos, H. Lin, M. Kang, T. Gu, J. Warner, V. Liberman, K. Richardson, and J. Hu, “Broadband transparent optical phase change materials for high-performance nonvolatile photonics,” Nat. Commun. 10, 1–9 (2019).
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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).
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Y. Zhang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, C. Roberts, P. Robinson, B. Bohlin, C. Ríos, H. Lin, M. Kang, T. Gu, J. Warner, V. Liberman, K. Richardson, and J. Hu, “Broadband transparent optical phase change materials for high-performance nonvolatile photonics,” Nat. Commun. 10, 1–9 (2019).
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Y. Zhang, J. B. Chou, J. Li, H. Li, Q. Du, A. Yadav, S. Zhou, M. Y. Shalaginov, Z. Fang, H. Zhong, C. Roberts, P. Robinson, B. Bohlin, C. Ríos, H. Lin, M. Kang, T. Gu, J. Warner, V. Liberman, K. Richardson, and J. Hu, “Broadband transparent optical phase change materials for high-performance nonvolatile photonics,” Nat. Commun. 10, 1–9 (2019).
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L. Yang, A. Münchinger, M. Kadic, V. Hahn, F. Mayer, E. Blasco, C. Barner-Kowollik, and M. Wegener, “On the Schwarzschild effect in 3D two-photon laser lithography,” Adv. Opt. Mater. 7, 1901040 (2019).
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C. Rios, M. Stegmaier, P. Hosseini, D. C. Wang, T. C. Scherer, C. Wright, H. Bhaskaran, and W. E. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9, 725–732 (2015).
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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. (a) Topology of a deep neural network. Links between layers of neurons correspond to large-scale interconnects. (b) Crossbar arrays link input and output channels (IO-channels, black dots) in parallel in 2D; IO-channels are arranged along a line. (c) In three dimensions, IO-channels can be arranged in an array, while connections are implemented in the third dimensions. (d) The number of IO-channels of a parallel interconnect scales linearly with size in 3D. In 2D, scalability is significantly worse.
Fig. 2.
Fig. 2. (a) Design principle of an optical coupler with a fractal geometry. Numerous layers of branching connections can be cascaded, and distances from one layer to the next scale with $\sqrt b$, where $b$ is the branching ratio. (b) 3D illustration of a small network hosting simple couplers. Chirality of the connections avoids the intersection of individual waveguides between the input and output ports.
Fig. 3.
Fig. 3. (a) SEM micrograph (15 kV, 40°) of an array of $1 \times 9$ couplers hosting nine elements, including an inset with higher magnification showing the low surface roughness. (b) SEM micrograph (10 kV, 40°) image of nine parallel $1 \times 81$ couplers featuring two bifurcation layers. (c) SEM micrograph (10 kV, 40°) of a large-scale array of $1 \times 81$ couplers, showing an area containing $15 \times 15$ units.
Fig. 4.
Fig. 4. (a) Optical transmission through a single bifurcation layer $1 \times 9$ coupler, with intensity color-coded on a logarithmic scale. Histograms of the relative output intensity distribution for the $1 \times 9$ (b) and $1 \times 81$ (c) coupler. Statistical information obtained from three couplers each.
Fig. 5.
Fig. 5. Schematic illustration of the input–output mapping of nine Haar filters (F1–F9) with Kernel width and stride three. A 3D-printed waveguide architecture realizing all nine filters in parallel is shown on the left, with filter F2 highlighted in orange. The highlighted structure implements filter F2.
Fig. 6.
Fig. 6. (a) SEM micrograph (10 kV, 40°) of a single Haar filter. (b) Full micrograph (5 kV, 0°) of a large array hosting spatial filtering for connecting layers of a convolutional neural network. (c) Optical characterization of the filter’s connection topology, injection at the output port, and recording the input ports emission.

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