Abstract

We develop and experimentally validate a practical artificial neural network (ANN) design framework for devices that can be used as building blocks in integrated photonic circuits. As case studies, we train ANNs to model both strip waveguides and chirped Bragg gratings using a small number of simple input and output parameters relevant to designers of integrated photonic circuits. Once trained, the ANNs decrease the computational cost relative to traditional design methodologies by more than 4 orders of magnitude. To illustrate the power of our new design paradigm, we develop and demonstrate both forward and inverse design tools enabled by the ANN. We use these tools to design and fabricate several integrated Bragg grating devices within a useful photonic circuit. The ANN’s predictions match the experimental measurements well and do not require any post-fabrication training adjustments.

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

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2019 (5)

F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82(1), 016001 (2019).
[Crossref]

T. Zhang, J. Wang, Q. Liu, J. Zhou, J. Dai, X. Han, Y. Zhou, and K. Xu, “Efficient spectrum prediction and inverse design for plasmonic waveguide systems based on artificial neural networks,” Photonics Res. 7(3), 368–380 (2019).
[Crossref]

A. M. Gabr, C. Featherston, C. Zhang, C. Bonfil, Q.-J. Zhang, and T. J. Smy, “Design and optimization of optical passive elements using artificial neural networks,” J. Opt. Soc. Am. B 36(4), 999–1007 (2019).
[Crossref]

D. Gostimirovic and N. Y. Winnie, “An open-source artificial neural network model for polarization-insensitive silicon-on-insulator subwavelength grating couplers,” IEEE J. Sel. Top. Quantum Electron. 25(3), 1–5 (2019).
[Crossref]

A. M. Hammond, E. Potokar, and R. M. Camacho, “Accelerating silicon photonic parameter extraction using artificial neural networks,” OSA Continuum 2(6), 1964–1973 (2019).
[Crossref]

2018 (10)

J. Peurifoy, Y. 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]

A. da Silva Ferreira, C. H. da Silva Santos, M. S. Gonçalves, and H. E. Hernández Figueroa, “Towards an integrated evolutionary strategy and artificial neural network computational tool for designing photonic coupler devices,” Appl. Soft Comput. 65, 1–11 (2018).
[Crossref]

S. Inampudi and H. Mosallaei, “Neural network based design of metagratings,” Appl. Phys. Lett. 112(24), 241102 (2018).
[Crossref]

Z. 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]

A. D. Silva Ferreira, G. N. Malheiros-Silveira, and H. E. Hernandez-Figueroa, “Computing Optical Properties of Photonic Crystals by Using Multilayer Perceptron and Extreme Learning Machine,” J. Lightwave Technol. 36(18), 4066–4073 (2018).
[Crossref]

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]

W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref]

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8(2), 021009 (2018).
[Crossref]

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, J. B. Wang, J. L. O’Brien, M. G. Thompson, and J. C. F. Matthews, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12(9), 534–539 (2018).
[Crossref]

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

2017 (1)

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor; EP,” Nat. Photonics 11(7), 447–452 (2017).
[Crossref]

2016 (3)

R. R. Andrawis, M. A. Swillam, M. A. El-Gamal, and E. A. Soliman, “Artificial neural network modeling of plasmonic transmission lines,” Appl. Opt. 55(10), 2780–2790 (2016).
[Crossref]

J. Wang, “Chip-scale optical interconnects and optical data processing using silicon photonic devices,” Photon. Netw. Commun. 31(2), 353–372 (2016).
[Crossref]

A. Orieux and E. Diamanti, “Recent advances on integrated quantum communications,” J. Opt. 18(8), 083002 (2016).
[Crossref]

2015 (1)

J. Schmidhuber, “Deep learning in neural networks: An overview,” Neural Networks 61, 85–117 (2015).
[Crossref]

2014 (1)

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: A Simple Way to Prevent Neural Networks from Overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

2012 (2)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

G. N. Malheiros-Silveira and H. E. Hernandez-Figueroa, “Prediction of Dispersion Relation and PBGs in 2-D PCs by Using Artificial Neural Networks,” IEEE Photonics Technol. Lett. 24(20), 1799–1801 (2012).
[Crossref]

2011 (1)

M. J. Heck, H.-W. Chen, A. W. Fang, B. R. Koch, D. Liang, H. Park, M. N. Sysak, and J. E. Bowers, “Hybrid silicon photonics for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17(2), 333–346 (2011).
[Crossref]

2010 (3)

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

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]

D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1(1), 116 (2010).
[Crossref]

2008 (1)

2007 (1)

2001 (1)

2000 (1)

N. M. L. B. J. Eggleton and G. Lenz, “Optical Pulse Compression Schemes That Use Nonlinear Bragg Gratings,” Fiber Integr. Opt. 19(4), 383–421 (2000).
[Crossref]

1999 (1)

M. Rochette, M. Guy, S. LaRochelle, J. Lauzon, and F. Trepanier, “Gain equalization of EDFA’s with Bragg gratings,” IEEE Photonics Technol. Lett. 11(5), 536–538 (1999).
[Crossref]

1997 (2)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[Crossref]

R. Storn and K. Price, “Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim. 11(4), 341–359 (1997).
[Crossref]

1991 (1)

K. Hornik, “Approximation Capabilities of Multilayer Feedforward Networks,” Neural Networks 4(2), 251–257 (1991).
[Crossref]

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[Crossref]

1963 (1)

D. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963).
[Crossref]

Andrawis, R. R.

B. J. Eggleton, N. M. L.

N. M. L. B. J. Eggleton and G. Lenz, “Optical Pulse Compression Schemes That Use Nonlinear Bragg Gratings,” Fiber Integr. Opt. 19(4), 383–421 (2000).
[Crossref]

Baehr-Jones, T.

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor; EP,” Nat. Photonics 11(7), 447–452 (2017).
[Crossref]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Barwicz, T.

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bogaerts, W.

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

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bonfil, C.

Bowers, J. E.

M. J. Heck, H.-W. Chen, A. W. Fang, B. R. Koch, D. Liang, H. Park, M. N. Sysak, and J. E. Bowers, “Hybrid silicon photonics for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17(2), 333–346 (2011).
[Crossref]

Boynton, N.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8(2), 021009 (2018).
[Crossref]

Bunandar, D.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8(2), 021009 (2018).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor; EP,” Nat. Photonics 11(7), 447–452 (2017).
[Crossref]

Buyya, R.

C. Vecchiola, S. Pandey, and R. Buyya, High-Performance Cloud Computing: A View of Scientific Applications (IEEE, New York, 2009).

Byun, H.

Cai, H.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8(2), 021009 (2018).
[Crossref]

Cai, W.

Z. 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]

Camacho, R.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8(2), 021009 (2018).
[Crossref]

Camacho, R. M.

A. M. Hammond, E. Potokar, and R. M. Camacho, “Accelerating silicon photonic parameter extraction using artificial neural networks,” OSA Continuum 2(6), 1964–1973 (2019).
[Crossref]

A. M. Hammond and R. M. Camacho, “Designing silicon photonic devices using artificial neural networks,” arXiv preprint arXiv:1812.03816 (2018).

Cano-Renteria, F.

J. Peurifoy, Y. 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]

Chen, C.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8(2), 021009 (2018).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor; EP,” Nat. Photonics 11(7), 447–452 (2017).
[Crossref]

Chen, H.-W.

M. J. Heck, H.-W. Chen, A. W. Fang, B. R. Koch, D. Liang, H. Park, M. N. Sysak, and J. E. Bowers, “Hybrid silicon photonics for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17(2), 333–346 (2011).
[Crossref]

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“TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems”.

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Figures (10)

Fig. 1.
Fig. 1. The process overview describing the new design methodology. First, datasets are generated using traditional numerical methods (described in Methods). From this dataset, a neural network is trained to characterize the device under consideration. Figures 2 & 3 illustrate this process for a strip waveguide and a chirped grating respectively. Often, the designer iterates between these two steps until an appropriate model is developed. Once the model is ready, several design applications, like circuit simulations and inverse design solutions, are available. The designs are then fabricated to validate the model’s results. From here, the model can be shared and extended.
Fig. 2.
Fig. 2. Waveguide artificial neural network training results demonstrated by the training convergence with reference to the mean square error (a), the coefficient of determination (b), and the residual errors after training (c). Panel (d) compares the computational cost for the ANN and the eigenmode solver that is used to simulate the mode profiles (e). Panel (f) exhibits the effective index profiles as a function of a waveguide geometry at 1550 nm for the first TE and TM modes.
Fig. 3.
Fig. 3. Bragg grating artificial neural network training results demonstrated by the training convergence with reference to the mean square error (a), the coefficient of determination (b), and the absolute error after training (c). (d) illustrates the different adjustable grating parameters and (e) illustrates the interrogation circuit used to extract the reflection, transmission, and group delay profiles simultaneously from the chirped Bragg grating. A grating coupler (GC) feeds light into various Y-branches (YB) and directional couplers (DC) such that the transmission and reflection spectra can both be extracted from the chirped Bragg grating (BG). Half of the reflected signal is sent through a Mach-Zehner Interferometer (MZI). The output of which is used to extract the group delay.
Fig. 4.
Fig. 4. Fabrication data compared to corresponding ANN predictions. (a1)-(a4) Measured transmission responses for gratings with a period chirp of 5 nm (a1), 10 nm (a2), 15 nm (a3), and 20 nm (a4). (b1)-(b2) Transmission and reflection responses for two different Bragg gratings. Both gratings share the same design parameters, and have an identical but opposite linear chirp. The result of the mirrored chirping is seen in both the normalized MZI interference patterns (c1) and (c2) and the extracted group delay responses (d1), and (c2).
Fig. 5.
Fig. 5. Graphical user interface used to explore the design space of a chirped Bragg grating. The slider bars on the left control physical parameters like grating length (NG), grating corrugation (dw), and the grating chirp (a1) and (a2). Any time the user adjusts these parameters, the program calls the ANN and reproduces the expected reflection and group delay profiles for that particular grating. Due to the ANN’s speed, the program is extremely responsive.
Fig. 6.
Fig. 6. ANN-assisted design of a monolithic temporal pulse compressor using a silicon photonic chirped Bragg grating. A truncated Newton algorithm was tasked with constructing a grating that compressed an arbitrary chirped pulse by a factor of 2. After 340 grating simulations, the optimizer sufficiently minimized a cost function (right) that compared the new pulse’s width to the old pulse. The resulting grating is demonstrated in the bottom left panel and the input, output, and desired pulses for iterations 1, 140, and 288 are demonstrated on the left. The final compressed pulse predicted by the ANN (red) is compared to the target pulse (green) and the result simulated using the LDMTMM method (blue) in the lower right panel. The results show that the ANN accurately predicts the pulse width.
Fig. 7.
Fig. 7. Reflection profile for an integrated chirped Bragg grating with no apodization (blue), a Gaussian apodization (orange), and a raised cosine apodization. Different apodization functions reduce the response’s ringing.
Fig. 8.
Fig. 8. Demonstration of the fitting algorithm for a Bragg grating with no chirp (column one), a postive chirp (column two) and a negative chirp (column three). The chirp patterns themselves are illustrated in the first row, the reflection profiles are depicted in the second row, and the respective group delay responses are found in the third row. The modified Gaussian function accounts for the wider bandwidths, skewness, and overall shape of the responses will “filter” out the apodization dependent ringing.
Fig. 9.
Fig. 9. The normalization process for the integrated Bragg gratings. Data points outside of the stop band are fitted to a fifth degree polynomial to capture the response of the grating couplers and other devices within the circuit (top). The polynomial is then normalized from the data (bottom).
Fig. 10.
Fig. 10. The group delay extraction process. First, the low frequency carrier is removed by using a fifth order polynomial fit (top). Next, the oscillation peaks are tracked and the FSR is estimated (middle). Finally, the group delay is calculated using the transfer function of the MZI (bottom).

Equations (2)

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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 )

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