Abstract

Photonic neural networks benefit from both the high-channel capacity and the wave nature of light acting as an effective weighting mechanism through linear optics. Incorporating a nonlinear activation function by using active integrated photonic components allows neural networks with multiple layers to be built monolithically, eliminating the need for energy and latency costs due to external conversion. Interferometer-based modulators, while popular in communications, have been shown to require more area than absorption-based modulators, resulting in a reduced neural network density. Here, we develop a model for absorption modulators in an electro-optic fully connected neural network, including noise, and compare the network’s performance with the activation functions produced intrinsically by five types of absorption modulators. Our results show the quantum well absorption modulator–based electro-optic neuron has the best performance allowing for 96% prediction accuracy with 1.7×1012 J/MAC excluding laser power when performing MNIST classification in a 2 hidden layer feed-forward photonic neural network.

© 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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R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

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V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

R. Amin, J. B. Khurgin, and V. J. Sorger, “Waveguide based electro-absorption modulator performance: comparative performance,” Opt. Express 26, 15445–15470 (2018).
[Crossref] [PubMed]

2017 (3)

D. A. Miller, “Attojoule optoelectronics for low-energy information processing and communications,” J. Light. Technol. 35, 346–396 (2017).
[Crossref]

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

2015 (2)

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

C. Ye, K. Liu, R. Soref, and V. J. Sorger, “A compact plasmonic mos-based 2x2 electro-optic switch,” Nanophotonics 4, 261–268 (2015).
[Crossref]

2014 (1)

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Light. Technol. 32, 3427–3439 (2014).
[Crossref]

2013 (1)

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

1998 (1)

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

1964 (1)

W. E. Pruitt, “Eigenvalues of non-negative matrices,” Ann. Math. Statist. 35, 1797–1800 (1964).
[Crossref]

Agarwal, R.

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

Alloatti, L.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

Amin, R.

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

R. Amin, J. B. Khurgin, and V. J. Sorger, “Waveguide based electro-absorption modulator performance: comparative performance,” Opt. Express 26, 15445–15470 (2018).
[Crossref] [PubMed]

Atabaki, A. H.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

Baeuerle, B.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Bengio, Y.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Bottou, L.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Bruna, J.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

Chellapilla, K.

K. Chellapilla, S. Puri, and P. Simard, “High performance convolutional neural networks for document processing,” in Tenth International Workshop on Frontiers in Handwriting Recognition, (Suvisoft, 2006).

Dalir, H.

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

Dalton, L. R.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

de Cea, M.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

Duchi, J.

J. Duchi, E. Hazan, and Y. Singer, “Adaptive subgradient methods for online learning and stochastic optimization,” Tech. Rep. UCB/EECS-2010-24, EECS Department, University of California, Berkeley (2010).

Ducry, F.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, vol. 624 (Pearson-Prentice-Hall, 2004).

Elder, D. L.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Emboras, A.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Englund, D.

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

Erhan, D.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

Fedoryshyn, Y.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Fergus, R.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

Ferreira de Lima, T.

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

George, J. K.

J. K. George, H. Nejadriahi, and V. J. Sorger, “Towards on-chip optical ffts for convolutional neural networks,” in 2017 IEEE International Conference on Rebooting Computing (ICRC), (IEEE, 2017), pp. 1–4.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, vol. 624 (Pearson-Prentice-Hall, 2004).

Goodfellow, I.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

Haffner, C.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Haffner, P.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Hafner, C.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Harris, N. C.

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

Hazan, E.

J. Duchi, E. Hazan, and Y. Singer, “Adaptive subgradient methods for online learning and stochastic optimization,” Tech. Rep. UCB/EECS-2010-24, EECS Department, University of California, Berkeley (2010).

Heni, W.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Hillerkuss, D.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Hochberg, 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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

Hoessbacher, C.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Johnson, R.

R. Johnson and T. Zhang, “Accelerating stochastic gradient descent using predictive variance reduction,” in Advances in Neural Information Processing Systems, (2013), pp. 315–323.

Josten, A.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Juchli, L.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Kawaguchi, K.

K. Kawaguchi, “Deep learning without poor local minima,” in Advances in Neural Information Processing Systems, (2016), pp. 586–594.

Khan, S.

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

Khurgin, J. B.

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

R. Amin, J. B. Khurgin, and V. J. Sorger, “Waveguide based electro-absorption modulator performance: comparative performance,” Opt. Express 26, 15445–15470 (2018).
[Crossref] [PubMed]

Koch, U.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Kohl, M.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Larochelle, H.

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

LeCun, Y.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Leuthold, J.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Lima, T. F.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

Liu, K.

C. Ye, K. Liu, R. Soref, and V. J. Sorger, “A compact plasmonic mos-based 2x2 electro-optic switch,” Nanophotonics 4, 261–268 (2015).
[Crossref]

Ma, Z.

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

Melikyan, A.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Miller, D. A.

D. A. Miller, “Attojoule optoelectronics for low-energy information processing and communications,” J. Light. Technol. 35, 346–396 (2017).
[Crossref]

Nahmias, M. A.

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

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Light. Technol. 32, 3427–3439 (2014).
[Crossref]

Nejadriahi, H.

J. K. George, H. Nejadriahi, and V. J. Sorger, “Towards on-chip optical ffts for convolutional neural networks,” in 2017 IEEE International Conference on Rebooting Computing (ICRC), (IEEE, 2017), pp. 1–4.

Niegemann, J.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Peng, H.-T.

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

Popovic, M.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

Prabhu, 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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

Prucnal, P. R.

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

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Light. Technol. 32, 3427–3439 (2014).
[Crossref]

Pruitt, W. E.

W. E. Pruitt, “Eigenvalues of non-negative matrices,” Ann. Math. Statist. 35, 1797–1800 (1964).
[Crossref]

Puri, S.

K. Chellapilla, S. Puri, and P. Simard, “High performance convolutional neural networks for document processing,” in Tenth International Workshop on Frontiers in Handwriting Recognition, (Suvisoft, 2006).

Ram, R. J.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

Salamin, Y.

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Sarpkaya, I.

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

Shastri, B. J.

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

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Light. Technol. 32, 3427–3439 (2014).
[Crossref]

Shen, Y.

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

Simard, P.

K. Chellapilla, S. Puri, and P. Simard, “High performance convolutional neural networks for document processing,” in Tenth International Workshop on Frontiers in Handwriting Recognition, (Suvisoft, 2006).

Singer, Y.

J. Duchi, E. Hazan, and Y. Singer, “Adaptive subgradient methods for online learning and stochastic optimization,” Tech. Rep. UCB/EECS-2010-24, EECS Department, University of California, Berkeley (2010).

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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

Soref, R.

C. Ye, K. Liu, R. Soref, and V. J. Sorger, “A compact plasmonic mos-based 2x2 electro-optic switch,” Nanophotonics 4, 261–268 (2015).
[Crossref]

Sorger, V. J.

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

R. Amin, J. B. Khurgin, and V. J. Sorger, “Waveguide based electro-absorption modulator performance: comparative performance,” Opt. Express 26, 15445–15470 (2018).
[Crossref] [PubMed]

C. Ye, K. Liu, R. Soref, and V. J. Sorger, “A compact plasmonic mos-based 2x2 electro-optic switch,” Nanophotonics 4, 261–268 (2015).
[Crossref]

J. K. George, H. Nejadriahi, and V. J. Sorger, “Towards on-chip optical ffts for convolutional neural networks,” in 2017 IEEE International Conference on Rebooting Computing (ICRC), (IEEE, 2017), pp. 1–4.

Suer, C.

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

Sutskever, I.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” 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 1312, 6199 (2013).

Tait, A. N.

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

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Light. Technol. 32, 3427–3439 (2014).
[Crossref]

Wade, M.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

Woods, R. E.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, vol. 624 (Pearson-Prentice-Hall, 2004).

Wu, A. X.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

Ye, C.

C. Ye, K. Liu, R. Soref, and V. J. Sorger, “A compact plasmonic mos-based 2x2 electro-optic switch,” Nanophotonics 4, 261–268 (2015).
[Crossref]

Zaremba, W.

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

Zhang, T.

R. Johnson and T. Zhang, “Accelerating stochastic gradient descent using predictive variance reduction,” in Advances in Neural Information Processing Systems, (2013), pp. 315–323.

Zhao, 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. Soljacić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441 (2017).
[Crossref]

Zhou, E.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

Ann. Math. Statist. (1)

W. E. Pruitt, “Eigenvalues of non-negative matrices,” Ann. Math. Statist. 35, 1797–1800 (1964).
[Crossref]

arXiv (1)

C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” arXiv 1312, 6199 (2013).

IEEE J. Sel. Top. Quantum Electron. (1)

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

J. Light. Technol. (2)

D. A. Miller, “Attojoule optoelectronics for low-energy information processing and communications,” J. Light. Technol. 35, 346–396 (2017).
[Crossref]

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Light. Technol. 32, 3427–3439 (2014).
[Crossref]

J. Opt. (1)

V. J. Sorger, R. Amin, J. B. Khurgin, Z. Ma, H. Dalir, and S. Khan, “Scaling vectors for attojoule per bit modulators,” J. Opt. 20, 014012 (2018).
[Crossref]

Nanophotonics (2)

C. Ye, K. Liu, R. Soref, and V. J. Sorger, “A compact plasmonic mos-based 2x2 electro-optic switch,” Nanophotonics 4, 261–268 (2015).
[Crossref]

R. Amin, C. Suer, Z. Ma, I. Sarpkaya, J. B. Khurgin, R. Agarwal, and V. J. Sorger, “Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance,” Nanophotonics 7, 455–472 (2018).

Nat. Photonics (2)

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

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic mach–zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9, 525–528 (2015).
[Crossref]

Opt. Express (1)

Proc. IEEE (1)

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86, 2278–2324 (1998).
[Crossref]

Sci. Reports (1)

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 7430 (2017).
[Crossref]

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K. Kawaguchi, “Deep learning without poor local minima,” in Advances in Neural Information Processing Systems, (2016), pp. 586–594.

J. K. George, H. Nejadriahi, and V. J. Sorger, “Towards on-chip optical ffts for convolutional neural networks,” in 2017 IEEE International Conference on Rebooting Computing (ICRC), (IEEE, 2017), pp. 1–4.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, vol. 624 (Pearson-Prentice-Hall, 2004).

Keras, “Keras: the python deep learning library,” https://keras.io (2015).

Y. LeCun and C. Cortes, “Mnist handwritten digit database,” http://yann.lecun.com/exdb/mnist/ (2010).

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems,” (2015). Software available from tensorflow.org .

K. Chellapilla, S. Puri, and P. Simard, “High performance convolutional neural networks for document processing,” in Tenth International Workshop on Frontiers in Handwriting Recognition, (Suvisoft, 2006).

R. Johnson and T. Zhang, “Accelerating stochastic gradient descent using predictive variance reduction,” in Advances in Neural Information Processing Systems, (2013), pp. 315–323.

J. Duchi, E. Hazan, and Y. Singer, “Adaptive subgradient methods for online learning and stochastic optimization,” Tech. Rep. UCB/EECS-2010-24, EECS Department, University of California, Berkeley (2010).

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Figures (5)

Fig. 1
Fig. 1 An electro-optic neuron taking an input from (a) a WDM bus and weighting by wavelength with rings or (b) from a parallel bus weighting with an interferometer network. The neuron sums the optical signal with a photodiode converting the signal to avoltage (c), optionally amplified by a TIA (d), drives an electro-optic modulator (e) modulating a CW laser (f), which produces a nonlinear transfer function at the output (g) of an photonic neural network (NN).
Fig. 2
Fig. 2 (a) Schematic of a charge carrier-driven electro-absorption modulator. The optical mode and its propagation direction are shown in red. The modulator’s nonlinearity use utilized in this work to provide the photonic perceptron’s activation. (b) Modulator transfer function (absorption vs. their drive voltage ( V in ) from the perceptron-summation photodiode. Color coded are five different electro-optic ’active’ materials, whose response and equation-set was derived in [12]). (c) The photonic perceptron’s nonlinearity varies by the type of tunable material used in the capacitively-biased modulator and translates into a voltage activation function ( V o u t) when a 100   μ m modulator with gate oxide thickness t o x = 10   n m is coupled through a 50 Ω current-to-voltage converting resistor to a photodiode (at the receiving neuron) with quantum efficiency of η = 0.6. These nonlinearities are used in the subsequent photonic neural network analysis below.
Fig. 3
Fig. 3 Inside the photonic neuron (i.e. perceptron model Fig. 1), the photodiode is coupled to the modulator with a reverse bias either by a current to voltage converting resistive load, R l o a d, (a), a TIA (b), or directly coupling to the modulator as a capacitive load (c). When coupled with load resistance R l o a d must be large enough to to produce a voltage in the operating range of the electro-absorption modulator, limiting the RC frequency response of the circuit. For the NN results presented below, capacitive coupling of (c) was selected.
Fig. 4
Fig. 4 The SNR of a neurons output after two NN layers for graphene (a), quantum dot (b), quantum well (c), three quantum well (d), and exciton (e) electro-absorption modulators against modulator device length over a range of optical powers from 0.01 mWto 50 mW shows low performance of graphene for low optical powers, almost no response for QD for optical power over 10 mW, a wide range of reasonable performance for QW, and a short region of peak performance for exciton, all for modulator lengths < 350 μ m.
Fig. 5
Fig. 5 Simulation of a 300 hidden node MNIST classification neural network with two hidden layers of 150 nodes each swept over range of laser optical powers from 0.01 mW to 50 mW show accuracy results (a) converging across modulator types, except exciton, to approach digital computer accuracy for a similar 300 hidden node network [19] as the optical power exceeds 30 mW. At lower power levels modulator types vary in performance with the quantum well modulator outperforms the others in terms of accuracy. Power dissipation, excluding electrical power to drive the CW laser and clocking overhead, (b) shows the quantum dot modulator consuming the least power. In energy per operation terms (c) QW performed at 93% accuracy using 6.3 × 10 14 J/MAC and QD at 92% accuracy using 6 × 10 14 J/MAC, both excluding laser power. Including laser power with wall plug efficiency of 50% (d) brings the J/MAC up significantly demonstrating that the power cost is dominated by laser efficiency. All results are with NN operating speed = 10 GHz (gated to 5 GHz), and training with 45 epochs of the Adagrad [23] method.

Equations (9)

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

P o u t = P c w exp ( α ( V i n ) L )
γ p = λ 0 f h c P i n
Δ V o u t = P p o i s s o n ( γ p ) q η C + V n o i s e _ c i r c u i t
Δ N o p t i c a l = γ p q η C ( G 1 )
Δ N a m p _ g a i n = G a m p ( N 0 ) N 0 + N a m p , N 0 = γ p q η C + N c i r c u i t
N a m p _ g a i n < γ p q η C ( G + N c i r c u i t ( 1 G ) )
V r m s = i = 1 n ( V i j = 1 n V j n ) 2 n
S N R d B = 20 log 10 ( V r m s _ s i g n a l V r m s _ n o i s e )
P t o t a l = k = 1 N n o d e s ( V k 2 ( C m o d + C p h o t o d i o d e ) + C g a t e V g 2 ) f 2 + N n o d e s P o η l a s e r

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