Abstract

A deep-learning artificial neural network (NN) combined with the particle swarm optimization (PSO) method has been proposed to inversely design the semiconductor laser with high accuracy and computational speed. This method is exempt from the single-solution problem of tandem NN and can be highly useful to extract the possible problematic parameters in the failure analysis of a device. The light-current curves and small signal responses have been tested against the benchmarks calculated by the traveling-wave model to demonstrate the NN’s robustness and efficiency in simulating the laser behavior for further use in the inverse design by PSO.

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

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  1. X. Li, Optoelectronic devices: design, modeling, and simulation. (Cambridge University, 2009).
  2. R. S. Hegde, “Photonics inverse design: pairing deep neural networks with evolutionary algorithms,” IEEE J. Sel. Top. Quantum Electron. 26(1), 1–8 (2020).
    [Crossref]
  3. S. F. Shu, “Evolving ultrafast laser information by a learning genetic algorithm combined with a knowledge base,” IEEE Photonics Technol. Lett. 18(2), 379–381 (2006).
    [Crossref]
  4. P. H. Fu, T. Y. Huang, K. W. Fan, and D. W. Huang, “Optimization for ultrabroadband polarization beam splitters using a genetic algorithm,” IEEE Photonics J. 11(1), 1–11 (2019).
    [Crossref]
  5. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
    [Crossref]
  6. S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, “Simulated annealing in ocular adaptive optics,” Opt. Lett. 31(7), 939–941 (2006).
    [Crossref]
  7. J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proc. of IEEE Int. Conf. on Neural Networks 4, 1942–1948 (1995).
    [Crossref]
  8. J. Robinson and Y. R. Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52(2), 397–407 (2004).
    [Crossref]
  9. S. W. Piche, “Steepest descent algorithms for neural network controllers and filters,” IEEE Trans. Neural Netw. 5(2), 198–212 (1994).
    [Crossref]
  10. N. A. Ahmad, “A globally convergent stochastic pairwise conjugate gradient-based algorithm for adaptive filtering,” IEEE Signal Process. Lett. 15, 914–917 (2008).
    [Crossref]
  11. M. G. Davis and R. F. O’Dowd, “A transfer matrix method based large-signal dynamic model for multielectrode DFB lasers,” IEEE J. Quantum Electron. 30(11), 2458–2466 (1994).
    [Crossref]
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    [Crossref]
  13. Y. Li, Y. P. Xi, X. Li, and W. P. Huang, “Design and analysis of single mode Fabry-Perot lasers with high speed modulation capability,” Opt. Express 19(13), 12131–12140 (2011).
    [Crossref]
  14. P. Yeh, Optical waves in layered media (Wiley, 1988).
  15. Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
    [Crossref]
  16. J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. B. Hu, B. Wu, D. Tan, J. Xu, and Y. Chen, “Robust inverse-design of scattering spectrum in core-shell structure using modified denoising autoencoder neural network,” Opt. Express 27(25), 36276–36285 (2019).
    [Crossref]
  21. D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
    [Crossref]
  22. D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
    [Crossref]
  23. Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
    [Crossref]

2020 (2)

R. S. Hegde, “Photonics inverse design: pairing deep neural networks with evolutionary algorithms,” IEEE J. Sel. Top. Quantum Electron. 26(1), 1–8 (2020).
[Crossref]

D. Zibar, A. M. R. Brusin, U. C. de Moura, F. D. Ros, V. Curri, and A. Carena, “Inverse system design using machine learning: the Raman amplifier case,” J. Lightwave Technol. 38(4), 736–753 (2020).
[Crossref]

2019 (5)

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

G. P. P. Pun, R. Batra, R. Ramprasad, and Y. Mishin, “Physically informed artificial neural networks for atomistic modeling of materials,” Nat. Commun. 10(1), 2339 (2019).
[Crossref]

B. Hu, B. Wu, D. Tan, J. Xu, and Y. Chen, “Robust inverse-design of scattering spectrum in core-shell structure using modified denoising autoencoder neural network,” Opt. Express 27(25), 36276–36285 (2019).
[Crossref]

P. H. Fu, T. Y. Huang, K. W. Fan, and D. W. Huang, “Optimization for ultrabroadband polarization beam splitters using a genetic algorithm,” IEEE Photonics J. 11(1), 1–11 (2019).
[Crossref]

Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
[Crossref]

2018 (3)

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

2017 (1)

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

2011 (1)

2008 (1)

N. A. Ahmad, “A globally convergent stochastic pairwise conjugate gradient-based algorithm for adaptive filtering,” IEEE Signal Process. Lett. 15, 914–917 (2008).
[Crossref]

2006 (2)

S. F. Shu, “Evolving ultrafast laser information by a learning genetic algorithm combined with a knowledge base,” IEEE Photonics Technol. Lett. 18(2), 379–381 (2006).
[Crossref]

S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, “Simulated annealing in ocular adaptive optics,” Opt. Lett. 31(7), 939–941 (2006).
[Crossref]

2004 (2)

J. Robinson and Y. R. Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52(2), 397–407 (2004).
[Crossref]

W. Li, X. Li, and W. P. Huang, “A traveling-wave model of laser diodes with consideration for thermal effects,” Opt. Quantum Electron. 36(8), 709–724 (2004).
[Crossref]

1995 (1)

J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proc. of IEEE Int. Conf. on Neural Networks 4, 1942–1948 (1995).
[Crossref]

1994 (2)

S. W. Piche, “Steepest descent algorithms for neural network controllers and filters,” IEEE Trans. Neural Netw. 5(2), 198–212 (1994).
[Crossref]

M. G. Davis and R. F. O’Dowd, “A transfer matrix method based large-signal dynamic model for multielectrode DFB lasers,” IEEE J. Quantum Electron. 30(11), 2458–2466 (1994).
[Crossref]

1983 (1)

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

Adler, J.

Ahmad, N. A.

N. A. Ahmad, “A globally convergent stochastic pairwise conjugate gradient-based algorithm for adaptive filtering,” IEEE Signal Process. Lett. 15, 914–917 (2008).
[Crossref]

Batra, R.

G. P. P. Pun, R. Batra, R. Ramprasad, and Y. Mishin, “Physically informed artificial neural networks for atomistic modeling of materials,” Nat. Commun. 10(1), 2339 (2019).
[Crossref]

Brusin, A. M. R.

Cai, W.

Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Cano-Renteria, F.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Carena, A.

Cheben, P.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Chen, H.

Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
[Crossref]

Chen, X.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Chen, Y.

Curri, V.

Davis, M. G.

M. G. Davis and R. F. O’Dowd, “A transfer matrix method based large-signal dynamic model for multielectrode DFB lasers,” IEEE J. Quantum Electron. 30(11), 2458–2466 (1994).
[Crossref]

de Moura, U. C.

DeLacy, B. G.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Dezfouli, M. K.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Eberhart, R.

J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proc. of IEEE Int. Conf. on Neural Networks 4, 1942–1948 (1995).
[Crossref]

Fan, K. W.

P. H. Fu, T. Y. Huang, K. W. Fan, and D. W. Huang, “Optimization for ultrabroadband polarization beam splitters using a genetic algorithm,” IEEE Photonics J. 11(1), 1–11 (2019).
[Crossref]

Fu, M.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Fu, P. H.

P. H. Fu, T. Y. Huang, K. W. Fan, and D. W. Huang, “Optimization for ultrabroadband polarization beam splitters using a genetic algorithm,” IEEE Photonics J. 11(1), 1–11 (2019).
[Crossref]

Gelatt, C. D.

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

Grinberg, Y.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Hegde, R. S.

R. S. Hegde, “Photonics inverse design: pairing deep neural networks with evolutionary algorithms,” IEEE J. Sel. Top. Quantum Electron. 26(1), 1–8 (2020).
[Crossref]

Hu, B.

Huang, D. W.

P. H. Fu, T. Y. Huang, K. W. Fan, and D. W. Huang, “Optimization for ultrabroadband polarization beam splitters using a genetic algorithm,” IEEE Photonics J. 11(1), 1–11 (2019).
[Crossref]

Huang, T. Y.

P. H. Fu, T. Y. Huang, K. W. Fan, and D. W. Huang, “Optimization for ultrabroadband polarization beam splitters using a genetic algorithm,” IEEE Photonics J. 11(1), 1–11 (2019).
[Crossref]

Huang, W. P.

Y. Li, Y. P. Xi, X. Li, and W. P. Huang, “Design and analysis of single mode Fabry-Perot lasers with high speed modulation capability,” Opt. Express 19(13), 12131–12140 (2011).
[Crossref]

W. Li, X. Li, and W. P. Huang, “A traveling-wave model of laser diodes with consideration for thermal effects,” Opt. Quantum Electron. 36(8), 709–724 (2004).
[Crossref]

Janz, S.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Jing, L.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Joannopoulos, J. D.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Kennedy, J.

J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proc. of IEEE Int. Conf. on Neural Networks 4, 1942–1948 (1995).
[Crossref]

Khoram, E.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Kirkpatrick, S.

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

Lee, K. T.

Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Li, J.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Li, W.

W. Li, X. Li, and W. P. Huang, “A traveling-wave model of laser diodes with consideration for thermal effects,” Opt. Quantum Electron. 36(8), 709–724 (2004).
[Crossref]

Li, X.

Y. Li, Y. P. Xi, X. Li, and W. P. Huang, “Design and analysis of single mode Fabry-Perot lasers with high speed modulation capability,” Opt. Express 19(13), 12131–12140 (2011).
[Crossref]

W. Li, X. Li, and W. P. Huang, “A traveling-wave model of laser diodes with consideration for thermal effects,” Opt. Quantum Electron. 36(8), 709–724 (2004).
[Crossref]

X. Li, Optoelectronic devices: design, modeling, and simulation. (Cambridge University, 2009).

Li, Y.

Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
[Crossref]

Y. Li, Y. P. Xi, X. Li, and W. P. Huang, “Design and analysis of single mode Fabry-Perot lasers with high speed modulation capability,” Opt. Express 19(13), 12131–12140 (2011).
[Crossref]

Li, Z.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Lipson, S. G.

Liu, D.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Liu, Z. C.

Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Long, Y.

Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
[Crossref]

Melati, D.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Mishin, Y.

G. P. P. Pun, R. Batra, R. Ramprasad, and Y. Mishin, “Physically informed artificial neural networks for atomistic modeling of materials,” Nat. Commun. 10(1), 2339 (2019).
[Crossref]

O’Dowd, R. F.

M. G. Davis and R. F. O’Dowd, “A transfer matrix method based large-signal dynamic model for multielectrode DFB lasers,” IEEE J. Quantum Electron. 30(11), 2458–2466 (1994).
[Crossref]

Peurifoy, J.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Piche, S. W.

S. W. Piche, “Steepest descent algorithms for neural network controllers and filters,” IEEE Trans. Neural Netw. 5(2), 198–212 (1994).
[Crossref]

Pun, G. P. P.

G. P. P. Pun, R. Batra, R. Ramprasad, and Y. Mishin, “Physically informed artificial neural networks for atomistic modeling of materials,” Nat. Commun. 10(1), 2339 (2019).
[Crossref]

Ramprasad, R.

G. P. P. Pun, R. Batra, R. Ramprasad, and Y. Mishin, “Physically informed artificial neural networks for atomistic modeling of materials,” Nat. Commun. 10(1), 2339 (2019).
[Crossref]

Ren, J.

Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
[Crossref]

Ribak, E. N.

Robinson, J.

J. Robinson and Y. R. Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52(2), 397–407 (2004).
[Crossref]

Rodrigues, S. P.

Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Ros, F. D.

Samii, Y. R.

J. Robinson and Y. R. Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52(2), 397–407 (2004).
[Crossref]

Sanchez-Postigo, A.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Schmid, J. H.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Shen, Y. C.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Shu, S. F.

S. F. Shu, “Evolving ultrafast laser information by a learning genetic algorithm combined with a knowledge base,” IEEE Photonics Technol. Lett. 18(2), 379–381 (2006).
[Crossref]

Soljacic, M.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Song, C.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Tan, D.

Tan, Y.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Tegmark, M.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Vecchi, M. P.

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

Wang, D.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Wu, B.

Xi, Y. P.

Xu, D. X.

D. Melati, Y. Grinberg, M. K. Dezfouli, S. Janz, P. Cheben, J. H. Schmid, A. Sanchez-Postigo, and D. X. Xu, “Mapping the global design space of nanophotonic components using machine learning pattern recognition,” Nat. Commun. 10(1), 4775 (2019).
[Crossref]

Xu, J.

Yang, Y.

J. Peurifoy, Y. C. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 (2018).
[Crossref]

Yeh, P.

P. Yeh, Optical waves in layered media (Wiley, 1988).

Yu, Z.

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Zhang, M.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).
[Crossref]

Zhu, D.

Z. C. Liu, D. Zhu, S. P. Rodrigues, K. T. Lee, and W. Cai, “Generative model for the inverse design of metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018).
[Crossref]

Zibar, D.

Zommer, S.

ACS Photonics (1)

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics 5(4), 1365–1369 (2018).
[Crossref]

Appl. Phys. Lett. (1)

Y. Long, J. Ren, Y. Li, and H. Chen, “Inverse design of photonic topological state via machine learning,” Appl. Phys. Lett. 114(18), 181105 (2019).
[Crossref]

IEEE J. Quantum Electron. (1)

M. G. Davis and R. F. O’Dowd, “A transfer matrix method based large-signal dynamic model for multielectrode DFB lasers,” IEEE J. Quantum Electron. 30(11), 2458–2466 (1994).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. The topology of forward NN with 7 input parameters and 200 output ports. The 7 inputs are the design parameters, while the 200 outputs represent the 80 output powers and 120 small signal responses, respectively.
Fig. 2.
Fig. 2. Training curves in terms of the mean square errors (MSE) for different neural networks with one/two/three hidden layers (each layer containing 50 neurons), where the 3-layer DLNN can converge to the lowest level of MSE of about 10−4.
Fig. 3.
Fig. 3. Dependency of the neural network accuracy and total computational time (blue-triangle straight-line, as is circled out and pointed to the right-side axis) on the dataset sizes, where the accuracy is shown in terms of MSE for the testing (black-squared dotted-line) and training sets (red-circled dash-dotted line, as are both circled out and pointed to the left-side axis), respectively.
Fig. 4.
Fig. 4. (a) L-I, and (b) SSR curves generated by the neural network, and compared with the TWM method. The SSR curves are under bias currents of 30/50/70 mA. The same for (c) L-I and (d) SSR for another sample. (e) Histogram of the normalized L-I / SSR values in the training dataset, with the corresponding NN prediction errors (i.e., difference between the NN predicted value and the benchmark TWM one) of the final-test dataset for each column of the L-I / SSR histogram. (f) The histogram of NN prediction errors for all the points in the final test-set.
Fig. 5.
Fig. 5. Comparison of the neural network predictions with the TWM benchmarks, for parameters X = [0.8, 7e8, 19, T, 111, 124, 34] at randomly-selected temperatures T = 302 K, 331 K and 354 K, respectively.
Fig. 6.
Fig. 6. (a) The working principle of NN-PSO method. (b) The flow chart. (c) The convergence curve of NN-PSO, for the original parameter set of X = [0.720, 5.373×108, 11.833, 359.673, 67.448, 331.619, 14.044].
Fig. 7.
Fig. 7. TWM verifications of the curves for S1 and S2 parameters, as compared to the original design.
Fig. 8.
Fig. 8. (a)-(g) Statistical distribution of one randomly selected group for the inverse design parameters calculated by the NN-PSO method. The blue dots represent the parameter values generated by NN-PSO, the dashed lines represent their statistical averages and the red solid lines are the original true values; (h) the fitness function distribution of PSO at Epoch 500 for 50 repeated rounds.
Fig. 9.
Fig. 9. Mean and standard deviation of the 7 parameters inversely designed by NN-PSO method, for 11 groups of data in the test dataset.

Tables (3)

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Table 1. Two groups of design parameters corresponding to one set of spectrum

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Table 2. Mean and standard deviation of the 7 parameters inversely designed by NN-PSO method, as compared to the original pre-set design parameters

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Table 3. Laser parameters

Equations (13)

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[ E f ( t + d t , k + 1 ) E b ( t , k + 1 ) ] = [ A k ( t ) ] [ E f ( t , k ) E b ( t + d t , k ) ] = [ a 11 ( t , k )   a 12 ( t , k ) a 21 ( t , k )   a 22 ( t , k ) ] [ E f ( t , k ) E b ( t + d t , k ) ] ,
P  =  [ e j β l   0 0   e j β l ]
T i j = 1 2 n j [ n j + n i   n j n i n j n i   n j + n i ] .
E f ( t + d t , 0 ) = r l E b ( t , 0 ) ,
E b ( t + d t , L ) = r r E f ( t , L ) ,
N ( t + d t , k ) = N ( t , k ) + d t [ η J ( t , k ) e d R s p ( N ( t , k ) ) v g g ( t , k ) S ( t , k ) ] ,
T ( z , t ) = K e + n = 0 t n 1 exp ( D n t ) [ I s 0 2 D n + 0 t exp ( D n τ ) I 2 ( z , τ ) d τ ] + n = 0 t n 2 exp ( D n t ) ( I s 0 X s 0 D n + 0 t exp ( D n τ ) [ I ( z , τ ) X ( τ ) ] d τ ) ,
D n = [ ( n + 1 2 ) π / h ] 2 D ,
t n 1 = ( 1 ) n 2 h 0 h R t ( x ) R s ( x ) sin [ ( n + 1 2 ) π x / h ]   d x ,
t n 2 = 2 E g d e h R t ( h ) ,
X ( t ) = e E g P o u t ( t ) ,
Δ T = T [ K e + f ( I 2 ) + g ( I a P o u t ) ] ,
g k ( N k , S k ) = d g d N e Δ T K g ln ( e Δ T K n N k / N t r ) 1 + ε S k ,

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