Abstract

In this paper, we propose a new method to mitigate the mode partition noise (MPN) in VCSEL-MMF based links by using wavefront shaping technique. The noise characteristic of the VCSEL-MMF links is theoretically studied and the impacts of coupling coefficients between VCSEL and MMF on the MPN and the system performance are investigated via simulation and experiment. The simulation results show that for 25-Gb/s OOK signal after 300-m MMF transmission, five orders of magnitude improvement of BER can be observed and the standard deviation of the received signal, which is the characterization of the MPN, is reduced for about an order when wavefront shaping is applied. With the help of wavefront shaping, we show that the DSP complexity has been profoundly reduced in order to achieve reliable 56-Gb/s and 112-Gb/s PAM-4 transmission by simulation. We perform experiment for 25-Gb/s OOK signal transmission over 300-m OM3 MMF with the launching optical power of −4 dBm to the fiber. About 1-dB power penalty improvement has been achieved at 7% FEC threshold after 300-m MMF transmission and the noise in the eye diagram is mitigated. The results of our simulation and experiment show the effectiveness of wavefront shaping to mitigate the MPN, therefore reduce the DSP complexity and improve transmission performance for the VCSEL and MMF based high speed short reach optical interconnects.

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

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References

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  1. IEEE 802.3 Ethernet working group, “IEEE 802.3 400 Gb/s over Multimode Fiber Task Force,” http://www.ieee802.org/3/NGMMF/index.html .
  2. J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
    [Crossref]
  3. J. Carpenter, B. J. Eggleton, and J. Schröder, “Principal modes in 50μm graded-index multimode fiber,” in Specialty Optical Fibers, (2016), pp. SoM4G–1.
    [Crossref]
  4. J. Carpenter, “Principal modes in multimode fibre,” in European Conference on Optical Communication (ECOC), (2017), pp. 1–3.
  5. J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The interaction of modal and chromatic dispersion in VCSEL based multimode fiber channel links and its effect on mode partition noise,” Proc. 61 IWCS 2012 (2008).
  6. J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
    [Crossref]
  7. S. K. Pavan, J. Lavrencik, and S. E. Ralph, “New model for mode partition noise in VCSEL-MMF links based on langevin-driven spatio-temporal rate equations,” J. Light. Technol. 34, 3733–3751 (2016).
    [Crossref]
  8. J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
    [Crossref]
  9. G. Stepniak, “Comparison of PAM and CAP modulations robustness against mode partition noise in optical links,” in Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017, vol. 10445 (2017), p. 1044514.
    [Crossref]
  10. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21, 12881–12887 (2013).
    [Crossref] [PubMed]
  11. O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
    [Crossref]
  12. X. Shen, J. M. Kahn, and M. A. Horowitz, “Compensation for multimode fiber dispersion by adaptive optics,” Opt. Lett. 30, 2985–2987 (2005).
    [Crossref] [PubMed]
  13. J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
    [Crossref]
  14. G. P. Agrawal, P. J. Anthony, and T.-M. Shen, “Dispersion penalty for 1.3 mu m lightwave systems with multimode semiconductor lasers,” J. Light. Technol. 6, 620–625 (1988).
    [Crossref]
  15. M. X. Jungo, D. Erni, and W. Bachtold, “VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model,” J. Sel. Top. Quantum Electron. 9, 939–948 (2003).
    [Crossref]
  16. M. X. Jungo, “VISTAS Matlab source code,” https://sourceforge.net/projects/vistas/files/OldFiles/VISTAS_expert.zip/download .
  17. C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.
  18. R. A. Panicker, J. M. Kahn, and S. P. Boyd, “Compensation of multimode fiber dispersion using adaptive optics via convex optimization,” J. Light. Technol. 26, 1295–1303 (2008).
    [Crossref]
  19. C. Liang, W. Zhang, and Z. He, “Opto-Electrical Hybrid Equalization for VCSEL-MMF Based Links,” in IEEE Optical Interconnets, (2018), p. WC3.
  20. Keysight 86100 Infiniium DCA Online Help Archive, https://www.keysight.com/main/editorial.jspx?cc=GB&lc=eng&ckey=98996&nid=-32528.1150402.00&id=98996 .
  21. J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
    [Crossref]

2018 (1)

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

2017 (2)

J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
[Crossref]

J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
[Crossref]

2016 (1)

S. K. Pavan, J. Lavrencik, and S. E. Ralph, “New model for mode partition noise in VCSEL-MMF links based on langevin-driven spatio-temporal rate equations,” J. Light. Technol. 34, 3733–3751 (2016).
[Crossref]

2013 (2)

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21, 12881–12887 (2013).
[Crossref] [PubMed]

2012 (1)

J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
[Crossref]

2008 (1)

R. A. Panicker, J. M. Kahn, and S. P. Boyd, “Compensation of multimode fiber dispersion using adaptive optics via convex optimization,” J. Light. Technol. 26, 1295–1303 (2008).
[Crossref]

2005 (1)

2003 (1)

M. X. Jungo, D. Erni, and W. Bachtold, “VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model,” J. Sel. Top. Quantum Electron. 9, 939–948 (2003).
[Crossref]

2002 (1)

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
[Crossref]

1988 (1)

G. P. Agrawal, P. J. Anthony, and T.-M. Shen, “Dispersion penalty for 1.3 mu m lightwave systems with multimode semiconductor lasers,” J. Light. Technol. 6, 620–625 (1988).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, P. J. Anthony, and T.-M. Shen, “Dispersion penalty for 1.3 mu m lightwave systems with multimode semiconductor lasers,” J. Light. Technol. 6, 620–625 (1988).
[Crossref]

Anthony, P. J.

G. P. Agrawal, P. J. Anthony, and T.-M. Shen, “Dispersion penalty for 1.3 mu m lightwave systems with multimode semiconductor lasers,” J. Light. Technol. 6, 620–625 (1988).
[Crossref]

Bachtold, W.

M. X. Jungo, D. Erni, and W. Bachtold, “VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model,” J. Sel. Top. Quantum Electron. 9, 939–948 (2003).
[Crossref]

Bengtsson, J.

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
[Crossref]

Boyd, S. P.

R. A. Panicker, J. M. Kahn, and S. P. Boyd, “Compensation of multimode fiber dispersion using adaptive optics via convex optimization,” J. Light. Technol. 26, 1295–1303 (2008).
[Crossref]

Caravaca-Aguirre, A. M.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21, 12881–12887 (2013).
[Crossref] [PubMed]

Carpenter, J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Principal modes in 50μm graded-index multimode fiber,” in Specialty Optical Fibers, (2016), pp. SoM4G–1.
[Crossref]

J. Carpenter, “Principal modes in multimode fibre,” in European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

Castro, J.

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
[Crossref]

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The interaction of modal and chromatic dispersion in VCSEL based multimode fiber channel links and its effect on mode partition noise,” Proc. 61 IWCS 2012 (2008).

Castro, J. M.

J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
[Crossref]

Conkey, D. B.

Eggleton, B. J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Principal modes in 50μm graded-index multimode fiber,” in Specialty Optical Fibers, (2016), pp. SoM4G–1.
[Crossref]

Erni, D.

M. X. Jungo, D. Erni, and W. Bachtold, “VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model,” J. Sel. Top. Quantum Electron. 9, 939–948 (2003).
[Crossref]

Gustavsson, J. S.

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
[Crossref]

He, Z.

C. Liang, W. Zhang, and Z. He, “Opto-Electrical Hybrid Equalization for VCSEL-MMF Based Links,” in IEEE Optical Interconnets, (2018), p. WC3.

C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.

Horowitz, M. A.

Jungo, M. X.

M. X. Jungo, D. Erni, and W. Bachtold, “VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model,” J. Sel. Top. Quantum Electron. 9, 939–948 (2003).
[Crossref]

Kahn, J. M.

R. A. Panicker, J. M. Kahn, and S. P. Boyd, “Compensation of multimode fiber dispersion using adaptive optics via convex optimization,” J. Light. Technol. 26, 1295–1303 (2008).
[Crossref]

X. Shen, J. M. Kahn, and M. A. Horowitz, “Compensation for multimode fiber dispersion by adaptive optics,” Opt. Lett. 30, 2985–2987 (2005).
[Crossref] [PubMed]

Kose, B.

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
[Crossref]

J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
[Crossref]

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The interaction of modal and chromatic dispersion in VCSEL based multimode fiber channel links and its effect on mode partition noise,” Proc. 61 IWCS 2012 (2008).

Lane, B.

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
[Crossref]

J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
[Crossref]

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The interaction of modal and chromatic dispersion in VCSEL based multimode fiber channel links and its effect on mode partition noise,” Proc. 61 IWCS 2012 (2008).

Larsson, A.

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
[Crossref]

Lavrencik, J.

J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
[Crossref]

J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
[Crossref]

S. K. Pavan, J. Lavrencik, and S. E. Ralph, “New model for mode partition noise in VCSEL-MMF links based on langevin-driven spatio-temporal rate equations,” J. Light. Technol. 34, 3733–3751 (2016).
[Crossref]

Liang, C.

C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.

C. Liang, W. Zhang, and Z. He, “Opto-Electrical Hybrid Equalization for VCSEL-MMF Based Links,” in IEEE Optical Interconnets, (2018), p. WC3.

Niv, E.

Panicker, R. A.

R. A. Panicker, J. M. Kahn, and S. P. Boyd, “Compensation of multimode fiber dispersion using adaptive optics via convex optimization,” J. Light. Technol. 26, 1295–1303 (2008).
[Crossref]

Pavan, S. K.

J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
[Crossref]

S. K. Pavan, J. Lavrencik, and S. E. Ralph, “New model for mode partition noise in VCSEL-MMF links based on langevin-driven spatio-temporal rate equations,” J. Light. Technol. 34, 3733–3751 (2016).
[Crossref]

Piestun, R.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21, 12881–12887 (2013).
[Crossref] [PubMed]

Pimpinella, R.

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
[Crossref]

J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
[Crossref]

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The interaction of modal and chromatic dispersion in VCSEL based multimode fiber channel links and its effect on mode partition noise,” Proc. 61 IWCS 2012 (2008).

Ralph, S. E.

J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
[Crossref]

J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
[Crossref]

S. K. Pavan, J. Lavrencik, and S. E. Ralph, “New model for mode partition noise in VCSEL-MMF links based on langevin-driven spatio-temporal rate equations,” J. Light. Technol. 34, 3733–3751 (2016).
[Crossref]

Schröder, J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Principal modes in 50μm graded-index multimode fiber,” in Specialty Optical Fibers, (2016), pp. SoM4G–1.
[Crossref]

Shen, T.-M.

G. P. Agrawal, P. J. Anthony, and T.-M. Shen, “Dispersion penalty for 1.3 mu m lightwave systems with multimode semiconductor lasers,” J. Light. Technol. 6, 620–625 (1988).
[Crossref]

Shen, X.

Stepniak, G.

G. Stepniak, “Comparison of PAM and CAP modulations robustness against mode partition noise in optical links,” in Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017, vol. 10445 (2017), p. 1044514.
[Crossref]

Thomas, V. A.

J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
[Crossref]

J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
[Crossref]

Tzang, O.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

Varughese, S.

J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
[Crossref]

Vukusic, J. A.

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
[Crossref]

Wagner, K.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

Wang, Q.

C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.

Yao, S.

C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.

Zhang, W.

C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.

C. Liang, W. Zhang, and Z. He, “Opto-Electrical Hybrid Equalization for VCSEL-MMF Based Links,” in IEEE Optical Interconnets, (2018), p. WC3.

IEEE J. Quantum Electron. (1)

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38, 203–212 (2002).
[Crossref]

J. Light. Technol. (7)

R. A. Panicker, J. M. Kahn, and S. P. Boyd, “Compensation of multimode fiber dispersion using adaptive optics via convex optimization,” J. Light. Technol. 26, 1295–1303 (2008).
[Crossref]

J. Lavrencik, V. A. Thomas, S. Varughese, and S. E. Ralph, “DSP-Enabled 100 Gb/s PAM-4 VCSEL MMF Links,” J. Light. Technol. 35, 3189–3196 (2017).
[Crossref]

J. Lavrencik, S. K. Pavan, V. A. Thomas, and S. E. Ralph, “Noise in VCSEL-based links: Direct measurement of VCSEL transverse mode correlations and implications for MPN and RIN,” J. Light. Technol. 35, 698–705 (2017).
[Crossref]

S. K. Pavan, J. Lavrencik, and S. E. Ralph, “New model for mode partition noise in VCSEL-MMF links based on langevin-driven spatio-temporal rate equations,” J. Light. Technol. 34, 3733–3751 (2016).
[Crossref]

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode partition noise and modal-chromatic dispersion interaction effects on random jitter,” J. Light. Technol. 31, 2629–2638 (2013).
[Crossref]

J. M. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the interaction of modal and chromatic dispersion in VCSEL–MMF channels,” J. Light. Technol. 30, 2532–2541 (2012).
[Crossref]

G. P. Agrawal, P. J. Anthony, and T.-M. Shen, “Dispersion penalty for 1.3 mu m lightwave systems with multimode semiconductor lasers,” J. Light. Technol. 6, 620–625 (1988).
[Crossref]

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

M. X. Jungo, D. Erni, and W. Bachtold, “VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model,” J. Sel. Top. Quantum Electron. 9, 939–948 (2003).
[Crossref]

Nat. Photonics (1)

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Other (9)

IEEE 802.3 Ethernet working group, “IEEE 802.3 400 Gb/s over Multimode Fiber Task Force,” http://www.ieee802.org/3/NGMMF/index.html .

M. X. Jungo, “VISTAS Matlab source code,” https://sourceforge.net/projects/vistas/files/OldFiles/VISTAS_expert.zip/download .

C. Liang, W. Zhang, S. Yao, Q. Wang, and Z. He, “Optical equalization using spatial phase manipulation for VCSEL-MMF based links,” in CLEO: Science and Innovations, (2018), pp. STh4B–2.

G. Stepniak, “Comparison of PAM and CAP modulations robustness against mode partition noise in optical links,” in Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017, vol. 10445 (2017), p. 1044514.
[Crossref]

J. Carpenter, B. J. Eggleton, and J. Schröder, “Principal modes in 50μm graded-index multimode fiber,” in Specialty Optical Fibers, (2016), pp. SoM4G–1.
[Crossref]

J. Carpenter, “Principal modes in multimode fibre,” in European Conference on Optical Communication (ECOC), (2017), pp. 1–3.

J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The interaction of modal and chromatic dispersion in VCSEL based multimode fiber channel links and its effect on mode partition noise,” Proc. 61 IWCS 2012 (2008).

C. Liang, W. Zhang, and Z. He, “Opto-Electrical Hybrid Equalization for VCSEL-MMF Based Links,” in IEEE Optical Interconnets, (2018), p. WC3.

Keysight 86100 Infiniium DCA Online Help Archive, https://www.keysight.com/main/editorial.jspx?cc=GB&lc=eng&ckey=98996&nid=-32528.1150402.00&id=98996 .

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Figures (11)

Fig. 1
Fig. 1 Fiber transmission simulation setup. Att: attenuator. PD: photodiode. TIA: trans-impedance amplifier.
Fig. 2
Fig. 2 (a) VCSEL output field. (b) Calculated phase pattern.
Fig. 3
Fig. 3 Coupling coefficients between each VCSEL mode and fiber modes.
Fig. 4
Fig. 4 Eye diagram at received optical power of 0 dBm (a) without wavefront shaping after 300-m MMF, (b) with wavefront shaping after 300-m MMF, (c) without wavefront shaping after 2-m MMF and (d) with wavefront shaping after 2-m MMF.
Fig. 5
Fig. 5 (a) BER of 25-Gb/s OOK signal after 300-m MMF transmission. (b) Calculated standard deviation of the received signal. (c) Zoomed-in of the marked region.
Fig. 6
Fig. 6 (a) BER of 56-Gb/s PAM-4 signal after 300-m MMF transmission. (b) BER of 112-Gb/s PAM-4 signal after 100-m MMF transmission. W.S.: wavefront shaping. FFE: feed-forward equalizer. VF: Volterra filter.
Fig. 7
Fig. 7 (a) Experimental setup. (b) Probing and coupling system of the VCSEL-MMF links. (c) Free space setup for wavefront shaping and coupling system to the MMF. AWG: arbitrary waveform generator. Pol.: polarizer. SLM: spatial light modulator. PR: photoreceiver. OSC: oscilloscope.
Fig. 8
Fig. 8 (a) LIV curve and (b) spectrum of the VCSEL used in our experiment
Fig. 9
Fig. 9 Final pixel information shown on the SLM
Fig. 10
Fig. 10 Eye diagram of 25-Gb/s OOK signal after 300-m OM3 MMF (a) before wavefront shaping and (b) after wavefront shaping. (c) SNR values before and after wavefront shaping. (d) BER curves of 25-Gb/s OOK signal after 300-m MMF transmission.
Fig. 11
Fig. 11 Eye diagram of 10-Gb/s fixed pattern after 300-m MMF transmission (a) without wavefront shaping and (b) with wavefront shaping. (200 ps/div)

Tables (1)

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Table 1 Fiber transmission simulation parameters

Equations (5)

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COV { a i } = [ var 1 cov 12 cov 1 M cov 21 var 2 cov 2 M cov M 1 cov M 2 var M ]
y ( t ) = P OMA i = 1 M F i ( t ) a i ( t ) + n ( t )
F i ( t ) = g = 1 N g C ig f i ( t L Δ t ig )
σ 2 ( t 0 ) = ( i = 1 M F i ( t 0 ) a i i = 1 M F i ( t 0 ) a i ¯ ) 2 ¯ = [ i = 1 M F i ( t 0 ) a i ] 2 ¯ ( i = 1 M F i ( t 0 ) a i ¯ ) 2 = i = 1 M F i 2 ( t 0 ) var i + 2 i j > i F i ( t 0 ) F j ( t 0 ) cov i j ( δ τ i j )
σ 2 ( t ) = k eff 2 [ i = 1 M F i 2 ( t ) a i ¯ ( i = 1 M F i ( t ) a i ¯ ) 2 ]

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