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.

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

Full Article  |  PDF Article
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References

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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]

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[Crossref] [PubMed]

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[Crossref]

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[Crossref] [PubMed]

2016 (1)

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)

2013 (6)

2012 (3)

2011 (1)

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.

Bartelt, H.

Barthélémy, A.

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]

Borhani, N.

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.

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.

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.

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]

Demas, J.

Deng, M.

Duparré, M.

Eggleton, B. J.

Fabert, M.

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]

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.

Forbes, A.

Gaida, C.

Gan, F.

Gelszinnis, P.

Ghalmi, S.

Grimm, S.

Guo, S.

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.

Jansen, F.

Jauregui, C.

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.

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.

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]

Lee, J.

Leng, J.

Leuchs, G.

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]

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.

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]

Li, L.

Li, S.

Li, Y.

Limpert, J.

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.

Lv, H.

Lyu, M.

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]

Ma, Y. Z.

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]

Mafi, A.

Millot, G.

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]

Moser, C.

Naidoo, D.

Nelson, L. E.

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

Nicholson, J. W.

Onishchukov, G.

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]

Otto, H.-J.

Peschel, U.

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]

Psaltis, D.

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.

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.

Renninger, W. H.

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

Richardson, D. J.

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

Schmauss, B.

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]

Schmidt, O. A.

Schröder, J.

Schröter, S.

Schulze, C.

Schülzgen, A.

Schuster, K.

Shalaby, B. M.

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]

Shapira, O.

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]

Sinha, A.

Situ, 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]

Stutzki, F.

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.

Sych, Y.

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]

Tao, R.

Theeg, T.

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]

Thomsen, B. C.

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

Tian, L.

Tonello, A.

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]

Tünnermann, A.

Wabnitz, S.

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]

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).
[Crossref]

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).
[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]

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).
[Crossref] [PubMed]

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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).
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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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J. Light Technol. (1)

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[Crossref]

Nat. Commun. (1)

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Supplementary Material (4)

NameDescription
» 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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Figures (8)

Fig. 1
Fig. 1 Illustration of our network.
Fig. 2
Fig. 2 Illustration of our testing procedure.
Fig. 3
Fig. 3 Averaged correlation as a function of epochs for two cases. (a) 3-mode case; (b) 5-mode case.
Fig. 4
Fig. 4 Typical MD examples for two cases. (a) 3-mode case; (b) 5-mode case.
Fig. 5
Fig. 5 The relation between the mode number and (a) correlation; (b) weights and phase error.
Fig. 6
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.
Fig. 7
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.
Fig. 8
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.

Tables (4)

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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

Equations (4)

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U(r,φ)= n=1 N ρ n e i θ n ψ n (r,φ)
n=1 N ρ n 2 =1 θ n [π,π]
Loss= 1 M i=1 M j=1 2N1 ( y o (i) [j] y l (i) [j] ) 2
C=| Δ I r (r,φ)Δ I m (r,φ)rdrdφ Δ I r 2 (r,φ)rdrdφ Δ I m 2 (r,φ)rdrdφ |

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