Abstract

A machine learning assisted modal power analyzing scheme designed for optical modes in integrated multi-mode waveguides is proposed and studied in this work. Convolutional neural networks (CNNs) are successfully trained to correlate the far-field diffraction intensity patterns of a superposition of multiple waveguide modes with its modal power distribution. In particular, a specialized CNN is trained to analyze thin optical waveguides, which are single-moded along one axis and multi-moded along the other axis. A full-scale CNN is also trained to cross-validate the results obtained from this specialized CNN model. Prediction accuracy for modal power is benchmarked statistically with square error and absolute error distribution. It is found that the overall accuracy of our trained specialized CNN is very satisfactory for thin optical waveguides while that of our trained full-scale CNN remains nearly unchanged but the training time doubles. This approach is further generalized and applied to a waveguide that is multi-moded along both horizontal and vertical axes and the influence of noise on our trained network is studied. Overall, we find that the performance in this general condition keeps nearly unchanged. This new concept of analyzing modal power may open the door for high fidelity information recovery in far field and holds great promise for potential applications in both integrated and fiber-based spatial-division demultiplexing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Machine learning approach to OAM beam demultiplexing via convolutional neural networks

Timothy Doster and Abbie T. Watnik
Appl. Opt. 56(12) 3386-3396 (2017)

Transform- and multi-domain deep learning for single-frame rapid autofocusing in whole slide imaging

Shaowei Jiang, Jun Liao, Zichao Bian, Kaikai Guo, Yongbing Zhang, and Guoan Zheng
Biomed. Opt. Express 9(4) 1601-1612 (2018)

Dynamic mitigation of EDFA power excursions with machine learning

Yishen Huang, Craig L. Gutterman, Payman Samadi, Patricia B. Cho, Wiem Samoud, Cédric Ware, Mounia Lourdiane, Gil Zussman, and Keren Bergman
Opt. Express 25(3) 2245-2258 (2017)

References

  • View by:
  • |
  • |
  • |

  1. V. A. Sleiffer, Y. Jung, V. Veljanovski, R. G. van Uden, M. Kuschnerov, H. Chen, B. Inan, L. G. Nielsen, Y. Sun, D. J. Richardson, S. U. Alam, F. Poletti, J. K. Sahu, A. Dhar, A. M. Koonen, B. Corbett, R. Winfield, A. D. Ellis, and H. de Waardt, “73.7 Tb/s (96 x 3 x 256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA,” Opt. Express 20(26), B428–B438 (2012).
    [Crossref] [PubMed]
  2. T. Uematsu, Y. Ishizaka, Y. Kawaguchi, K. Saitoh, and M. Koshiba, “Design of a compact two-mode multi/demultiplexer consisting of multimode interference waveguides and a wavelength-insensitive phase shifter for mode-division multiplexing transmission,” J. Lightwave Technol. 30(15), 2421–2426 (2012).
    [Crossref]
  3. D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects (invited review),” Prog. Electromagnetics Res. 143, 773–819 (2013).
    [Crossref]
  4. H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013).
    [Crossref] [PubMed]
  5. L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
    [Crossref] [PubMed]
  6. R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
    [Crossref]
  7. H. Zhou, J. Dong, L. Shi, D. Huang, and X. Zhang, “Hybrid coding method of multiple orbital angular momentum states based on the inherent orthogonality,” Opt. Lett. 39(4), 731–734 (2014).
    [Crossref] [PubMed]
  8. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
    [Crossref] [PubMed]
  9. D. Dai, J. Wang, and Y. Shi, “Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013).
    [Crossref] [PubMed]
  10. J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
    [Crossref]
  11. R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
    [Crossref]
  12. Y. Ding, J. Xu, F. Da Ros, B. Huang, H. Ou, and C. Peucheret, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21(8), 10376–10382 (2013).
    [Crossref] [PubMed]
  13. J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
    [Crossref] [PubMed]
  14. P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
    [Crossref]
  15. C. Yang, Y. Wang, and C. Q. Xu, “A novel method to measure modal power distribution in multimode fibers using tilted fiber Bragg gratings,” IEEE Photonics Technol. Lett. 17(10), 2146–2148 (2005).
    [Crossref]
  16. L. Yan, R. Barankov, P. Steinvurzel, and S. Ramachandran, “Modal-weight measurements with fiber gratings,” J. Lightwave Technol. 33(13), 2784–2790 (2015).
    [Crossref]
  17. H. Zhou, Q. Zhu, W. Liang, G. Zhu, Y. Xue, S. Chen, L. Shen, M. Liu, J. Dong, and X. Zhang, “Mode measurement of few-mode fibers by mode-frequency mapping,” Opt. Lett. 43(7), 1435–1438 (2018).
    [Crossref] [PubMed]
  18. L. Li, J. Leng, P. Zhou, and J. Chen, “Multimode fiber modal decomposition based on hybrid genetic global optimization algorithm,” Opt. Express 25(17), 19680–19690 (2017).
    [Crossref] [PubMed]
  19. G. Stepniak, “Application of the error reduction algorithm to measurement of modal power distribution in a multimode fiber,” Proc. SPIE 9290, 929007 (2014).
    [Crossref]
  20. D. M. Nguyen, S. Blin, T. N. Nguyen, S. D. Le, L. Provino, M. Thual, and T. Chartier, “Modal decomposition technique for multimode fibers,” Appl. Opt. 51(4), 450–456 (2012).
    [Crossref] [PubMed]
  21. J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
    [Crossref]
  22. K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems(Curran Associates Inc, 2010), pp. 1090–1098.
  23. A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Proceedings of Advances in Neural Information Processing Systems (Curran Associates Inc, 2012), pp. 1097–1105.
  24. C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
    [Crossref] [PubMed]
  25. C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich, “Going deeper with convolutions,” https://arxiv.org/abs/1409.4842 (2014).
  26. M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
    [Crossref] [PubMed]
  27. I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep Learning (MIT press Cambridge, 2016).
  28. D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.
  29. Z. Zhu and T. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002).
    [Crossref] [PubMed]
  30. R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
    [Crossref] [PubMed]
  31. N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
    [Crossref]
  32. D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” https://arxiv.org/abs/1412.6980 (2014).
  33. S. Ioffe and C. Szegedy, “Batch normalization: accelerating deep network training by reducing internal covariate shift,” https://arxiv.org/abs/1502.03167 (2015).

2018 (1)

2017 (1)

2015 (1)

2014 (7)

G. Stepniak, “Application of the error reduction algorithm to measurement of modal power distribution in a multimode fiber,” Proc. SPIE 9290, 929007 (2014).
[Crossref]

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

H. Zhou, J. Dong, L. Shi, D. Huang, and X. Zhang, “Hybrid coding method of multiple orbital angular momentum states based on the inherent orthogonality,” Opt. Lett. 39(4), 731–734 (2014).
[Crossref] [PubMed]

2013 (6)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

D. Dai, J. Wang, and Y. Shi, “Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013).
[Crossref] [PubMed]

D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects (invited review),” Prog. Electromagnetics Res. 143, 773–819 (2013).
[Crossref]

H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013).
[Crossref] [PubMed]

Y. Ding, J. Xu, F. Da Ros, B. Huang, H. Ou, and C. Peucheret, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21(8), 10376–10382 (2013).
[Crossref] [PubMed]

C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
[Crossref] [PubMed]

2012 (3)

2009 (1)

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
[Crossref]

2007 (2)

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[Crossref]

N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
[Crossref]

2005 (1)

C. Yang, Y. Wang, and C. Q. Xu, “A novel method to measure modal power distribution in multimode fibers using tilted fiber Bragg gratings,” IEEE Photonics Technol. Lett. 17(10), 2146–2148 (2005).
[Crossref]

2003 (1)

M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
[Crossref] [PubMed]

2002 (1)

2000 (1)

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

Alam, S. U.

Barankov, R.

Bergmen, K.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Blin, S.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Brown, T.

Chartier, T.

Chen, C. P.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Chen, H.

Chen, J.

Chen, P.

Chen, S.

Ciresan, D. C.

D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.

Corbett, B.

Correa, R. A.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Couprie, C.

C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
[Crossref] [PubMed]

Da Ros, F.

Dai, D.

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects (invited review),” Prog. Electromagnetics Res. 143, 773–819 (2013).
[Crossref]

D. Dai, J. Wang, and Y. Shi, “Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013).
[Crossref] [PubMed]

De Waardt, H.

Dhar, A.

Ding, Y.

Dong, J.

Douglas, R. J.

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

Ellis, A. D.

Farabet, C.

C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
[Crossref] [PubMed]

Fini, J. M.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
[Crossref]

Gabrielli, L. H.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Hahnloser, R. H.

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

He, S.

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects (invited review),” Prog. Electromagnetics Res. 143, 773–819 (2013).
[Crossref]

Hu, T.

Huang, B.

Huang, D.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Huijskens, F.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Inan, B.

Ishizaka, Y.

Jiang, G.

Jiang, X.

Jung, Y.

Kaneda, Y.

M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
[Crossref] [PubMed]

Kawaguchi, Y.

Kimerling, L.

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[Crossref]

Kirchain, R.

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[Crossref]

Koonen, A.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Koonen, A. M.

Koshiba, M.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Kuschnerov, M.

Le, S. D.

Lecun, Y.

C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
[Crossref] [PubMed]

Leng, J.

Li, G.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Li, L.

Liang, W.

Lipson, M.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Liu, M.

Lopez, E. A.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Luo, L. W.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Mahowald, M. A.

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

Maria Gambardella, L.

D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.

Masci, J.

D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.

Matsugu, M.

M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
[Crossref] [PubMed]

Meier, U.

D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.

Mermelstein, M. D.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
[Crossref]

Mitari, Y.

M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
[Crossref] [PubMed]

Mori, K.

M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
[Crossref] [PubMed]

Najman, L.

C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
[Crossref] [PubMed]

Nasrabadi, N. M.

N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
[Crossref]

Nguyen, D. M.

Nguyen, T. N.

Nicholson, J. W.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
[Crossref]

Nielsen, L. G.

Okonkwo, C.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Ophir, N.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Ou, H.

Peucheret, C.

Poitras, C. B.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Poletti, F.

Provino, L.

Qiu, H.

Ramachandran, S.

L. Yan, R. Barankov, P. Steinvurzel, and S. Ramachandran, “Modal-weight measurements with fiber gratings,” J. Lightwave Technol. 33(13), 2784–2790 (2015).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Richardson, D. J.

Sahu, J. K.

Saitoh, K.

Sarpeshkar, R.

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

Schmidhuber, J.

D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.

Schülzgen, A.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Seung, H. S.

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

Shao, H.

Shen, L.

Shi, L.

Shi, Y.

Sleiffer, V. A.

Steinvurzel, P.

Stepniak, G.

G. Stepniak, “Application of the error reduction algorithm to measurement of modal power distribution in a multimode fiber,” Proc. SPIE 9290, 929007 (2014).
[Crossref]

Sun, Y.

Thual, M.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Uematsu, T.

Van Uden, R.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

van Uden, R. G.

Veljanovski, V.

Wang, J.

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects (invited review),” Prog. Electromagnetics Res. 143, 773–819 (2013).
[Crossref]

D. Dai, J. Wang, and Y. Shi, “Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013).
[Crossref] [PubMed]

Wang, Y.

C. Yang, Y. Wang, and C. Q. Xu, “A novel method to measure modal power distribution in multimode fibers using tilted fiber Bragg gratings,” IEEE Photonics Technol. Lett. 17(10), 2146–2148 (2005).
[Crossref]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Winfield, R.

Winzer, P. J.

P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

Xia, C.

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Xu, C. Q.

C. Yang, Y. Wang, and C. Q. Xu, “A novel method to measure modal power distribution in multimode fibers using tilted fiber Bragg gratings,” IEEE Photonics Technol. Lett. 17(10), 2146–2148 (2005).
[Crossref]

Xu, J.

Xue, Y.

Yablon, A. D.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
[Crossref]

Yan, L.

Yang, C.

C. Yang, Y. Wang, and C. Q. Xu, “A novel method to measure modal power distribution in multimode fibers using tilted fiber Bragg gratings,” IEEE Photonics Technol. Lett. 17(10), 2146–2148 (2005).
[Crossref]

Yang, J.

Yu, H.

Yu, P.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Zhang, X.

Zhou, H.

Zhou, P.

Zhu, G.

Zhu, Q.

Zhu, Z.

Appl. Opt. (1)

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

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009).
[Crossref]

IEEE Photonics Technol. Lett. (1)

C. Yang, Y. Wang, and C. Q. Xu, “A novel method to measure modal power distribution in multimode fibers using tilted fiber Bragg gratings,” IEEE Photonics Technol. Lett. 17(10), 2146–2148 (2005).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

C. Farabet, C. Couprie, L. Najman, and Y. Lecun, “Learning hierarchical features for scene labeling,” IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 1915–1929 (2013).
[Crossref] [PubMed]

J. Electron. Imaging (1)

N. M. Nasrabadi, “Pattern recognition and machine learning,” J. Electron. Imaging 16(4), 049901 (2007).
[Crossref]

J. Lightwave Technol. (2)

Laser Photonics Rev. (1)

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

Nat. Commun. (1)

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014).
[Crossref] [PubMed]

Nat. Photonics (3)

R. Van Uden, R. A. Correa, E. A. Lopez, F. Huijskens, C. Xia, G. Li, A. Schülzgen, H. De Waardt, A. Koonen, and C. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[Crossref]

P. J. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

Nature (1)

R. H. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, “Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit,” Nature 405(6789), 947–951 (2000).
[Crossref] [PubMed]

Neural Netw. (1)

M. Matsugu, K. Mori, Y. Mitari, and Y. Kaneda, “Subject independent facial expression recognition with robust face detection using a convolutional neural network,” Neural Netw. 16(5-6), 555–559 (2003).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (3)

Proc. SPIE (1)

G. Stepniak, “Application of the error reduction algorithm to measurement of modal power distribution in a multimode fiber,” Proc. SPIE 9290, 929007 (2014).
[Crossref]

Prog. Electromagnetics Res. (1)

D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects (invited review),” Prog. Electromagnetics Res. 143, 773–819 (2013).
[Crossref]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Other (7)

C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich, “Going deeper with convolutions,” https://arxiv.org/abs/1409.4842 (2014).

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems(Curran Associates Inc, 2010), pp. 1090–1098.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Proceedings of Advances in Neural Information Processing Systems (Curran Associates Inc, 2012), pp. 1097–1105.

I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep Learning (MIT press Cambridge, 2016).

D. C. Ciresan, U. Meier, J. Masci, L. Maria Gambardella, and J. Schmidhuber, “Flexible, high performance convolutional neural networks for image classification,” in Proceedings of International Joint Conference on Artificial Intelligence (Barcelona, Spain, 2011), pp. 1237–1242.

D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” https://arxiv.org/abs/1412.6980 (2014).

S. Ioffe and C. Szegedy, “Batch normalization: accelerating deep network training by reducing internal covariate shift,” https://arxiv.org/abs/1502.03167 (2015).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 SOI waveguide under consideration. (a) A schematic with a superimposed mode at the exit of the SOI waveguide and the corresponding far-field pattern that can be easily recorded by CCD and analyzed by CNN. (b) Pseudo-color images showing the calculated mode profile for the three quasi-TE modes of this SOI waveguide with w = 1.6µm, h = 0.22µm, and λ = 1.55µm.
Fig. 2
Fig. 2 Input data and the CNN architecture. (a) Far-field intensity distribution data is compressed by summing up all the intensity values along the vertical axis leaving behind a horizontal-position (or x'-axis) dependent grayscale map, I, and -log(I) is used as final input data to our CNN. (b) CNN architecture with two convolutional layers and three fully connected layers.
Fig. 3
Fig. 3 Histograms of square error distribution of 10000 testing samples. Insert: samples with square error larger than 1e-3.
Fig. 4
Fig. 4 Histogram of absolute error distribution of 10000 testing samples. Insert: samples with absolute error larger than 0.02.
Fig. 5
Fig. 5 (a) Structure of proposed CNN for predicting mode power distribution for waveguides with multiple mode orders in both vertical and horizontal directions. (b) Performance of this CNN with 10000 testing samples benchmarked with square error distribution. Insert: samples with square error larger than 1e-3. (c) Performance benchmarked with absolute error distribution. Insert: samples with absolute error larger than 0.02.
Fig. 6
Fig. 6 Prediction accuracy against different noise intensities with absolute error smaller than 0.02 as criteria.

Equations (4)

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

I(x',y')| E ff (x',y';a) | 2 =| i a i E i (x,y)exp(j2π( x' λz x+ y' λz y))dxdy | 2
J= 1 m i=1 m j=1 3 ( y p (i) [j] y l (i) [j] ) 2 .
SE(i)= j=1 3 ( y p (i) [j] y l (i) [j] ) 2
AE(i)=max(| y p (i) [j] y l (i) [j]|),j=1,2,3