Abstract

We present a novel silicon photonic parameter extraction tool that uses artificial neural networks. While other parameter extraction methods are restricted to relatively simple devices whose responses are easily modeled by analytic transfer functions, this method is capable of extracting parameters for any device with a discrete number of design parameters. To validate the method, we design and fabricate integrated chirped Bragg gratings. We then estimate the actual device parameters by iteratively fitting the simultaneously measured group delay and reflection profiles to the artificial neural network output. The method is fast, accurate, and capable of modeling the complicated chirping and index contrast.

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

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References

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    [Crossref]
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  6. X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express 20(14), 15547–15558 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (2)

W. Bogaerts and L. Chrostowski, “Silicon Photonics Circuit Design: Methods, Tools and Challenges,” Laser Photonics Rev. 12(4), 1700237 (2018).
[Crossref]

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

2017 (1)

2016 (1)

2015 (1)

J. Schmidhuber, “Deep Learning in Neural Networks: An Overview,” Neural Networks 61, 85–117 (2015)..
[Crossref]

2014 (2)

2012 (1)

2011 (1)

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

2010 (3)

M. J. Strain and M. Sorel, “Design and Fabrication of Integrated Chirped Bragg Gratings for On-Chip Dispersion Control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref]

1999 (1)

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21(1), 1–23 (1999).
[Crossref]

1991 (1)

K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Networks 4(2), 251–257 (1991).
[Crossref]

Abadi, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Agarwal, A.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Aida, Y.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

Alippi, A.

Baehr-Jones, T.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

Barham, P.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Bogaerts, W.

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

W. Bogaerts and L. Chrostowski, “Silicon Photonics Circuit Design: Methods, Tools and Challenges,” Laser Photonics Rev. 12(4), 1700237 (2018).
[Crossref]

Bojko, R.

Bojko, R. J.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

Branch, M. A.

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21(1), 1–23 (1999).
[Crossref]

Brevdo, E.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Camacho, R. M.

A. M. Hammond and R. M. Camacho, “Designing Silicon Photonic Devices using Artificial Neural Networks,” arXiv:1812.03816 [physics] (2018).

Chen, X.

Chen, Z.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Chrostowski, L.

W. Bogaerts and L. Chrostowski, “Silicon Photonics Circuit Design: Methods, Tools and Challenges,” Laser Photonics Rev. 12(4), 1700237 (2018).
[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25(9), 9712 (2017).
[Crossref]

Y. Wang, X. Wang, J. Flueckiger, H. Yun, W. Shi, R. Bojko, N. A. Jaeger, and L. Chrostowski, “Focusing sub-wavelength grating couplers with low back reflections for rapid prototyping of silicon photonic circuits,” Opt. Express 22(17), 20652–20662 (2014).
[Crossref]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express 20(14), 15547–15558 (2012).
[Crossref]

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Fard, “Impact of Fabrication Non-Uniformity on Chip-Scale Silicon Photonic Integrated Circuits,” in Optical Fiber Communication Conference, (OSA, San Francisco, California, 2014), p. Th2A.37.

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems (Cambridge Univ. Press,, 2015).

Citro, C.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Coleman, T. F.

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21(1), 1–23 (1999).
[Crossref]

Corrado, G. S.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Davis, A.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Dean, J.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Devin, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Dong, J.

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

Dwivedi, S.

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

Fard, S. T.

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Fard, “Impact of Fabrication Non-Uniformity on Chip-Scale Silicon Photonic Integrated Circuits,” in Optical Fiber Communication Conference, (OSA, San Francisco, California, 2014), p. Th2A.37.

Flueckiger, J.

Ghemawat, S.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Goodfellow, I.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Grist, S.

Hammond, A. M.

A. M. Hammond and R. M. Camacho, “Designing Silicon Photonic Devices using Artificial Neural Networks,” arXiv:1812.03816 [physics] (2018).

Harp, A.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Haykin, S. S.

S. S. Haykin, Neural Networks and Learning Machines (Prentice Hall, 2009).

He, L.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

Helan, R.

R. Helan, Comparison of Methods for Fiber Bragg Gratings Simulation (IEEE, 2006), pp. 161–166.

Hochberg, M.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems (Cambridge Univ. Press,, 2015).

Hornik, K.

K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Networks 4(2), 251–257 (1991).
[Crossref]

Irving, G.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Isard, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Jaeger, N. A.

Jaeger, N. A. F.

Jhoja, J.

Jia, Y.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Jones, E.

E. Jones, T. Oliphant, and P. Peterson, “SciPy: Open source scientific tools for Python,” (2001).

Jozefowicz, R.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Kaiser, L.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Khan, U.

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

Klein, J.

Kudlur, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Lecn, Y.

Y. Lecn, “A Theoretical Framework for Back-Propagation,” in Proceedings of the 1988 Connectionist Models Summer School (1988), pp. 21–28.

Levenberg, J.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Li, J.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

Li, Y.

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21(1), 1–23 (1999).
[Crossref]

Li, Z.

Liu, A.

Lu, Z.

Mane, D.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Melati, D.

Melloni, A.

Mickelson, A. R.

Mohamed, M.

Monga, R.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Moore, S.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Murray, D.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Olah, C.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Oliphant, T.

E. Jones, T. Oliphant, and P. Peterson, “SciPy: Open source scientific tools for Python,” (2001).

Pan, S. J.

S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

Peterson, P.

E. Jones, T. Oliphant, and P. Peterson, “SciPy: Open source scientific tools for Python,” (2001).

Pond, J.

Schmidhuber, J.

J. Schmidhuber, “Deep Learning in Neural Networks: An Overview,” Neural Networks 61, 85–117 (2015)..
[Crossref]

Schuster, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Selvaraja, S. K.

S. K. Selvaraja, “Wafer-scale fabrication technology for silicon photonic integrated circuits,” Ph.D. thesis (Ghent University, 2011).

Shang, L.

Shi, W.

Shlens, J.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Sorel, M.

M. J. Strain and M. Sorel, “Design and Fabrication of Integrated Chirped Bragg Gratings for On-Chip Dispersion Control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

Steiner, B.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Strain, M. J.

M. J. Strain and M. Sorel, “Design and Fabrication of Integrated Chirped Bragg Gratings for On-Chip Dispersion Control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

Sutskever, I.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Talwar, K.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Trotter, D. C.

Tucker, P.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Vanhoucke, V.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Vasudevan, V.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Viegas, F.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Vinyals, O.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Wang, X.

Wang, Y.

Y. Wang, X. Wang, J. Flueckiger, H. Yun, W. Shi, R. Bojko, N. A. Jaeger, and L. Chrostowski, “Focusing sub-wavelength grating couplers with low back reflections for rapid prototyping of silicon photonic circuits,” Opt. Express 22(17), 20652–20662 (2014).
[Crossref]

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Fard, “Impact of Fabrication Non-Uniformity on Chip-Scale Silicon Photonic Integrated Circuits,” in Optical Fiber Communication Conference, (OSA, San Francisco, California, 2014), p. Th2A.37.

Warden, P.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Wattenberg, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Watts, M. R.

Wicke, M.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Wu, Y.

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Fard, “Impact of Fabrication Non-Uniformity on Chip-Scale Silicon Photonic Integrated Circuits,” in Optical Fiber Communication Conference, (OSA, San Francisco, California, 2014), p. Th2A.37.

Xing, Y.

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

Yang, Q.

S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

Yu, Y.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Yun, H.

Zheng, X.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

Zortman, W. A.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. J. Strain and M. Sorel, “Design and Fabrication of Integrated Chirped Bragg Gratings for On-Chip Dispersion Control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

IEEE Trans. Knowl. Data Eng. (1)

S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

J. Lightwave Technol. (1)

J. Vac. Sci. Technol. B (1)

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B 29(6), 06F309 (2011).
[Crossref]

Laser Photonics Rev. (1)

W. Bogaerts and L. Chrostowski, “Silicon Photonics Circuit Design: Methods, Tools and Challenges,” Laser Photonics Rev. 12(4), 1700237 (2018).
[Crossref]

Neural Networks (2)

K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Networks 4(2), 251–257 (1991).
[Crossref]

J. Schmidhuber, “Deep Learning in Neural Networks: An Overview,” Neural Networks 61, 85–117 (2015)..
[Crossref]

Opt. Express (4)

Photonics Res. (1)

Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate extraction of fabricated geometry using optical measurement,” Photonics Res. 6(11), 1008 (2018).
[Crossref]

SIAM J. Sci. Comput. (1)

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21(1), 1–23 (1999).
[Crossref]

Other (9)

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems (Cambridge Univ. Press,, 2015).

S. S. Haykin, Neural Networks and Learning Machines (Prentice Hall, 2009).

Y. Lecn, “A Theoretical Framework for Back-Propagation,” in Proceedings of the 1988 Connectionist Models Summer School (1988), pp. 21–28.

S. K. Selvaraja, “Wafer-scale fabrication technology for silicon photonic integrated circuits,” Ph.D. thesis (Ghent University, 2011).

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. T. Fard, “Impact of Fabrication Non-Uniformity on Chip-Scale Silicon Photonic Integrated Circuits,” in Optical Fiber Communication Conference, (OSA, San Francisco, California, 2014), p. Th2A.37.

E. Jones, T. Oliphant, and P. Peterson, “SciPy: Open source scientific tools for Python,” (2001).

A. M. Hammond and R. M. Camacho, “Designing Silicon Photonic Devices using Artificial Neural Networks,” arXiv:1812.03816 [physics] (2018).

R. Helan, Comparison of Methods for Fiber Bragg Gratings Simulation (IEEE, 2006), pp. 161–166.

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. Mane, 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. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015).

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Figures (7)

Fig. 1.
Fig. 1. Summary of the ICBG parameterization scheme and corresponding ANN architecture. (a) The ICBG is parameterized by the optical wavlength ($\lambda$) the length of the first period ($a_0$), the length of the last period ($a_1$), the corrugation width difference ($Delta w$), and the number of grating periods (NG). (b) The trained ANN architecture that models the ICBG’s inputs and the corresponding reflection (R) and group delay profiles (GD). The ANN consists of 8 deep layers with 32, 64, 128, 256, 128, 64, 32, and 16 neurons respectively. Each layer uses hyperbolic tangent activation functions. (c) The corresponding reflection and group delay profiles for the particular ICBG.
Fig. 2.
Fig. 2. ANN modeling process. First, several different ICBGs are discretized into individual dielectric layers (1). Then, the reflection and group delay profiles are simulated using the transfer matrix method (2). The apodization dependent ringing is then filtered by fitting the curves to modified Gaussians (3). This dataset is then fed into a ANN training algorithm (4). Often, this process must be repeated until the ANN can suitably express a large enough ICBG design space.
Fig. 3.
Fig. 3. Hyper-parameter optimization used to determine a suitable architecture for the ANN. We swept through various parameters like the activation function (a), the optimizer’s learning rate (b), the number of neurons (c), the number of layers (d), and the number of batches per epoch (e). Each box and whisker plot illustrates the distribution of a particular parameter with reference to its MSE after the final epoch. While some parameters showed little influence (number of layers, activation functions, etc) others greatly affected the MSE convergence (learning rate).
Fig. 4.
Fig. 4. Interrogation circuit used to extract the reflection, transmission, and group delay profiles of a single ICBG simaltaneously. First, light enters the chip via the second grating from the top. It continues through a Y-branch splitter and a directional coupler until it reaches the Bragg grating. The light transmitted through the Bragg grating leaves the chip via the fourth grating coupler (light path in red). The Light that is reflected by the Bragg grating returns through the directional coupler, where half of it is routed off the chip via the first grating coupler (light path in blue). The other half of the reflected light is interfered with the original transmission signal using the directional coupler and an additional Y-branch (light path in green). This interference pattern is routed off of the chip with the third grating coupler. The group delay is then extracted from this interference pattern.
Fig. 5.
Fig. 5. Calibration process used to extract the measured reflection and group delay responses. The reflection data is first fit to a fourth order polynomial outside of the expected bandwidth in order to remove the grating couplers’ transfer function (a1). Next, the data is once again fit to a fourth order polynomial outside of the device’s bandwidth to identify the noise floor (a2). The data is then normalized to unit power (a3). Similar to the reflection data, the group delay data is also fit to a fourth order polynomial to remove the grating couplers’ response (b1). Next, the FSR is approximated using a peaktracking algorithm (b2). From the FSR, the group delay is estimated (b3).
Fig. 6.
Fig. 6. Efficient and robust method to extract fabricated ICBG device parameters using ANNs and a nonlinear least-squares optimizer. First, the ANN simulates reflection and group delay spectra for the device’s initial design parameters (1). Then, the simulations are compared directly to the measured data (2). If the results are sufficiently similar, the optimizer returns the device parameters (3). If not, the optimizer strategically simulates a new set of device parameters based on the residual error (4).
Fig. 7.
Fig. 7. The extracted reflection (a1, a2, a3) and group delay (b1, b2, b3) profiles (yellow) compared to the initial design profiles (red) and the calibrated measurement data (blue).

Tables (1)

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Table 1. Parameter extraction results for three separate devices. The design parameters are compared directly to the algorithm’s extracted parameters for each device.

Equations (5)

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D i = f ( W k D k 1 + b i ) ,
f ( λ , λ 0 , σ , β , a , p , c ) = a σ γ e β | λ λ 0 | γ p + c
γ = 2 σ 1 + e β ( λ λ 0 )
τ ( λ ) = ( L r e f L ( λ ) ) n g ( λ ) c
L ( λ ) = λ 2 F S R n g ( λ )