Learning to decompose the modes in few-mode fibers with deep convolutional neural network

Yi An; Liangjin Huang; Jun Li; Jinyong Leng; Lijia Yang; Pu Zhou

doi:10.1364/OE.27.010127

Optics Express
Vol. 27,
Issue 7,
pp. 10127-10137
(2019)
•https://doi.org/10.1364/OE.27.010127

Learning to decompose the modes in few-mode fibers with deep convolutional neural network

Yi An, Liangjin Huang, Jun Li, Jinyong Leng, Lijia Yang, and Pu Zhou

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Yi An, Liangjin Huang, Jun Li, Jinyong Leng, Lijia Yang, and Pu Zhou, "Learning to decompose the modes in few-mode fibers with deep convolutional neural network," Opt. Express 27, 10127-10137 (2019)

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Abstract

We introduce a deep-learning technique to perform complete mode decomposition for few-mode optical fibers for the first time. Our goal is to learn a fast and accurate mapping from near-field beam patterns to the complete mode coefficients, including both modal amplitudes and phases. We train the convolutional neural network with simulated beam patterns and evaluate the network on both the simulated beam data and the real beam data. In simulated beam data testing, the correlation between the reconstructed and the ideal beam patterns can achieve 0.9993 and 0.995 for 3-mode case and 5-mode case, respectively. While in the real 3-mode beam data testing, the average correlation is 0.9912 and the mode decomposition can be potentially performed at 33 Hz frequency on a graphic processing unit, indicating real-time processing ability. The quantitative evaluations demonstrate the superiority of our deep learning–based approach.

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Year
Author
Publication

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[Crossref]
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[Crossref]
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J. Demas and S. Ramachandran, “Sub-second mode measurement of fibers using C2 imaging,” Opt. Express 22(19), 23043–23056 (2014).
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N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]
Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry,” Appl. Phys. B 96(2-3), 345–353 (2009).
[Crossref]
T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
[Crossref] [PubMed]
M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]
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[Crossref] [PubMed]
R. Brüning, P. Gelszinnis, C. Schulze, D. Flamm, and M. Duparré, “Comparative analysis of numerical methods for the mode analysis of laser beams,” Appl. Opt. 52(32), 7769–7777 (2013).
[Crossref] [PubMed]
L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]
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]
S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]
Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]
N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]
M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]
A. Liu, T. Lin, H. Han, X. Zhang, Z. Chen, F. Gan, H. Lv, and X. Liu, “Analyzing modal power in multi-mode waveguide via machine learning,” Opt. Express 26(17), 22100–22109 (2018).
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[Crossref]

2018 (5)

T. Qiu, I. Ashry, A. Wang, and Y. Xu, “Adaptive Mode Control in 4-and 17-Mode Fibers,” IEEE Photonics Technol. Lett. 30(11), 1036–1039 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]

A. Liu, T. Lin, H. Han, X. Zhang, Z. Chen, F. Gan, H. Lv, and X. Liu, “Analyzing modal power in multi-mode waveguide via machine learning,” Opt. Express 26(17), 22100–22109 (2018).
[Crossref] [PubMed]

2017 (5)

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]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

L. Huang, T. Yao, J. Leng, S. Guo, R. Tao, P. Zhou, and X. Cheng, “Mode instability dynamics in high-power low-numerical-aperture step-index fiber amplifier,” Appl. Opt. 56(19), 5412–5417 (2017).
[Crossref] [PubMed]

2016 (1)

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

2015 (4)

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

L. Huang, H. Lü, P. Zhou, J. Leng, S. Guo, and X. Cheng, “Modal analysis of fiber laser beam by using stochastic parallel gradient descent algorithm,” IEEE Photonics Technol. Lett. 27(21), 2280–2283 (2015).
[Crossref]

L. Huang, J. Leng, P. Zhou, S. Guo, H. Lü, and X. Cheng, “Adaptive mode control of a few-mode fiber by real-time mode decomposition,” Opt. Express 23(21), 28082–28090 (2015).
[Crossref] [PubMed]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

2014 (3)

J. Demas and S. Ramachandran, “Sub-second mode measurement of fibers using C2 imaging,” Opt. Express 22(19), 23043–23056 (2014).
[Crossref] [PubMed]

J. Carpenter, B. J. Eggleton, and J. Schröder, “110X110 Optical Mode Transfer Matrix Inversion,” Opt. Express 22(1), 96–101 (2014).
[Crossref] [PubMed]

C. Jollivet, A. Mafi, D. Flamm, M. Duparré, K. Schuster, S. Grimm, and A. Schülzgen, “Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser,” Opt. Express 22(24), 30377–30386 (2014).
[Crossref] [PubMed]

2013 (6)

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21(3), 3170–3181 (2013).
[Crossref] [PubMed]

D. Flamm, K. C. Hou, P. Gelszinnis, C. Schulze, S. Schröter, and M. Duparré, “Modal characterization of fiber-to-fiber coupling processes,” Opt. Lett. 38(12), 2128–2130 (2013).
[Crossref] [PubMed]

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

R. Brüning, P. Gelszinnis, C. Schulze, D. Flamm, and M. Duparré, “Comparative analysis of numerical methods for the mode analysis of laser beams,” Appl. Opt. 52(32), 7769–7777 (2013).
[Crossref] [PubMed]

2012 (3)

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurement for fiber beams based on modal analysis,” Appl. Opt. 51(7), 987–993 (2012).
[Crossref] [PubMed]

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Light Technol. 30(24), 3946–3952 (2012).
[Crossref]

2011 (1)

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[Crossref] [PubMed]

2009 (2)

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry,” Appl. Phys. B 96(2-3), 345–353 (2009).
[Crossref]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
[Crossref] [PubMed]

2008 (2)

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008).
[Crossref] [PubMed]

2005 (1)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Abouraddy, A. F.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Andermahr, N.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Ashry, I.

T. Qiu, I. Ashry, A. Wang, and Y. Xu, “Adaptive Mode Control in 4-and 17-Mode Fibers,” IEEE Photonics Technol. Lett. 30(11), 1036–1039 (2018).
[Crossref]

Barbastathis, G.

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Bartelt, H.

Barthélémy, A.

Borhani, N.

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]

Brüning, R.

Carpenter, J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “110X110 Optical Mode Transfer Matrix Inversion,” Opt. Express 22(1), 96–101 (2014).
[Crossref] [PubMed]

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Light Technol. 30(24), 3946–3952 (2012).
[Crossref]

Chen, J.

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]

Chen, N.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

Chen, Z.

Cheng, X.

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Christodoulides, D. N.

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

Couderc, V.

Fabert, M.

Fallnich, C.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fink, Y.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Flamm, D.

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

Forbes, A.

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

Gaida, C.

Gan, F.

Gelszinnis, P.

Ghalmi, S.

Grimm, S.

Guo, S.

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Han, H.

Hartung, A.

He, K.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2016), 770–778.

Hou, K. C.

Huang, L.

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Jansen, F.

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Jollivet, C.

Kaiser, T.

Kakkava, E.

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]

Klein, R.

J. Li, R. Klein, and A. Yao, “A two-streamed network for estimating fine-scaled depth maps from single rgb images,” in Proceedings of the 2017 IEEE International Conference on Computer Vision, (IEEE, 2017), 3392–3400.
[Crossref]

Krupa, K.

Lee, J.

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Leng, J.

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]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Leuchs, G.

Li, G.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

Li, J.

Li, L.

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]

Li, S.

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Li, Y.

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

Limpert, J.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Lin, T.

Lin, Z.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Liu, A.

Liu, X.

Lorenz, A.

Lü, H.

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Lv, H.

Lyu, M.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Ma, Y. Z.

Mafi, A.

Millot, G.

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N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]

Naidoo, D.

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

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D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
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Onishchukov, G.

Otto, H.-J.

Peschel, U.

Psaltis, D.

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]

Qiu, T.

T. Qiu, I. Ashry, A. Wang, and Y. Xu, “Adaptive Mode Control in 4-and 17-Mode Fibers,” IEEE Photonics Technol. Lett. 30(11), 1036–1039 (2018).
[Crossref]

Ramachandran, S.

J. Demas and S. Ramachandran, “Sub-second mode measurement of fibers using C2 imaging,” Opt. Express 22(19), 23043–23056 (2014).
[Crossref] [PubMed]

Ren, S.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2016), 770–778.

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W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
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Schmidt, O. A.

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

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J. Carpenter, B. J. Eggleton, and J. Schröder, “110X110 Optical Mode Transfer Matrix Inversion,” Opt. Express 22(1), 96–101 (2014).
[Crossref] [PubMed]

Schröter, S.

Schulze, C.

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

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M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
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Sun, J.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2016), 770–778.

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Tao, R.

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Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
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Wang, A.

T. Qiu, I. Ashry, A. Wang, and Y. Xu, “Adaptive Mode Control in 4-and 17-Mode Fibers,” IEEE Photonics Technol. Lett. 30(11), 1036–1039 (2018).
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Wang, H.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
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Wang, W.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
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J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Light Technol. 30(24), 3946–3952 (2012).
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Wise, F. W.

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
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L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
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W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
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Wright, L. G.

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

Xu, Y.

T. Qiu, I. Ashry, A. Wang, and Y. Xu, “Adaptive Mode Control in 4-and 17-Mode Fibers,” IEEE Photonics Technol. Lett. 30(11), 1036–1039 (2018).
[Crossref]

Xue, Y.

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

Yablon, A. D.

Yao, A.

Yao, T.

Zhang, X.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2016), 770–778.

Zhou, P.

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]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Zhu, Z.

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. B (2)

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (2)

T. Qiu, I. Ashry, A. Wang, and Y. Xu, “Adaptive Mode Control in 4-and 17-Mode Fibers,” IEEE Photonics Technol. Lett. 30(11), 1036–1039 (2018).
[Crossref]

J. Light Technol. (1)

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Light Technol. 30(24), 3946–3952 (2012).
[Crossref]

Nat. Commun. (1)

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

Nat. Photonics (4)

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Opt. Express (11)

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

J. Carpenter, B. J. Eggleton, and J. Schröder, “110X110 Optical Mode Transfer Matrix Inversion,” Opt. Express 22(1), 96–101 (2014).
[Crossref] [PubMed]

J. Demas and S. Ramachandran, “Sub-second mode measurement of fibers using C2 imaging,” Opt. Express 22(19), 23043–23056 (2014).
[Crossref] [PubMed]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

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]

Opt. Lett. (3)

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

Optica (3)

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5(8), 960–966 (2018).
[Crossref]

Phys. Rev. Lett. (1)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Sci. Rep. (2)

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref] [PubMed]

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Other (5)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” https://arxiv.org/abs/1409.1556 .

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems, F. Pereira, C. J. C. Burges and L. Bottou and K. Q. Weinberger, eds. (Curran Associates, 2012), 1097–1105.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2016), 770–778.

Supplementary Material (4)

Name	Description
Visualization 1	the results of processing simulated beam pattern through the network with GPU
Visualization 2	the results of processing simulated beam pattern through the network with GPU, slowing 10x
Visualization 3	the processing results through the network with GPU for real beam patterns
Visualization 4	the processing results through the network with GPU for real beam patterns, slowing 3x

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Fig. 1 Illustration of our network.

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Fig. 2 Illustration of our testing procedure.

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Fig. 3 Averaged correlation as a function of epochs for two cases. (a) 3-mode case; (b) 5-mode case.

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Fig. 4 Typical MD examples for two cases. (a) 3-mode case; (b) 5-mode case.

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Fig. 5 The relation between the mode number and (a) correlation; (b) weights and phase error.

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Fig. 6 The performance of CNN for noisy input patterns. (a) input patterns and reconstructed ones under different noise intensity levels. The pattern in the red rectangle is the ground truth. (b) averaged correlation between the reconstructed pattern and ground truth under different noise intensity. (c) averaged weights and phase prediction errors under different noise intensity.

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Fig. 7 Scheme of the experimental setup. SMF, single mode fiber; FMF, few-mode fiber; L, lens; HWP, half-wave plate; PBS, polarization beam splitter.

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Fig. 8 The correlation between the measured and the reconstructed intensity pattern of every frame. The insets depict measured (up), reconstructed (middle) and residual(down) intensity of the frame denoted with letters.

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Tables (4)

Table 1 Details of our network

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Table 2 Averaged error of modal weights

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Table 3 Averaged error of modal phase

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Table 4 Consuming time for the CNN

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Equations (4)

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

U (r, φ) = \sum_{n = 1}^{N} ρ_{n} e^{i θ_{n}} ψ_{n} (r, φ)

\sum_{n = 1}^{N} ρ_{n}^{2} =1 θ_{n} \in [- π, π]

L o s s = \frac{1}{M} • \sum_{i =1}^{M} \sum_{j = 1}^{2 N - 1} (y_{o}^{(i)} [j] - y_{l}^{(i)} [j])^{2}

C = | \frac{\iint Δ I_{r} (r, φ) Δ I_{m} (r, φ) r d r d φ}{\sqrt{\iint Δ I_{r}^{2} (r, φ) r d r d φ \iint Δ I_{m}^{2} (r, φ) r d r d φ}} |

Network	Block
Network	1	2	3	4	5	6	7
#conv size	2 64 × 64	2 32 × 32	3 16 × 16	3 8 × 8	3 4 × 4	1 1 × 1	1 1 × 1
#chan#	64	128	256	512	512	1024	2N-1

	$\bar{Δ ρ_{01}^{2}}$	$\bar{Δ ρ_{11 e}^{2}}$	$\bar{Δ ρ_{11 o}^{2}}$	$\bar{Δ ρ_{21 e}^{2}}$	$\bar{Δ ρ_{21 o}^{2}}$	$\bar{Δ ρ^{2}}$
3-mode case	0.55%	0.50%	0.45%	-	-	0.50%
5-mode case	0.82%	1.27%	1.37%	0.84%	0.87%	1.03%

	$\bar{Δ θ_{11 e}}$	$\bar{Δ θ_{11 o}}$	$\bar{Δ θ_{21 e}}$	$\bar{Δ θ_{21 o}}$	$\bar{Δ θ}$
3-mode case	0.71%	0.69%	-	-	0.70%
5-mode case	1.17%	1.24%	1.45%	1.46%	1.33%

	Total Time		Averaged Time
	CPU	GPU	CPU	GPU
3-mode case	71s	9s	71 ms	9ms
5-mode case	76 s	14 s	76 ms	14 ms

Network	Block
Network	1	2	3	4	5	6	7
#conv size	2 64 × 64	2 32 × 32	3 16 × 16	3 8 × 8	3 4 × 4	1 1 × 1	1 1 × 1
#chan#	64	128	256	512	512	1024	2N-1

Abstract

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