Abstract

We present a digital technique able to monitor and compensate for the mode-dependent losses (MDL) in space-division multiplexing (SDM) transmission systems. The working principle of the technique is based on the analysis of the received signal samples in the higher-order Poincaré spheres (HoPs). When an arbitrary pair of tributaries is represented in the respective HoPs, the effect of the MDL can be modeled as a simple shift of the constellation points in a such sphere. Therefore, the MDL can be estimated by computing those shifts over all the HoPs and the induced signal distortions can be compensated by re-centering all the constellations in the respective HoPs. It should be highlighted that the proposed technique is scalable with an arbitrary number of spatial channels, modulation format agonistic and free of training sequences. The HoPs-based MDL monitoring (compensation) technique allows the MDL estimation (compensation) up to values of ≈ 6 dB. The proposed technique can partially compensate the MDL distortion, making a MDL sensitive algorithm in an insensitive one. When the proposed technique assists a HoPs-based space-demultiplexing algorithm, it provides signal-to-noise ratio (SNR) enhancements of 2, 4 and 8 dB for PM-QPSK, PM-16QAM and PM-64QAM signals, respectively, for the particular case of a SDM-based transmission system with a spatial diversity of 2 and 2 dB of MDL.

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

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References

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  1. R. Ryf and N. K. Fontaine, “Space-division multiplexing and MIMO processing,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, eds. (John Wiley & Sons, Ltd, 2016), 547–608.
    [Crossref]
  2. A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
    [Crossref]
  3. G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
    [Crossref]
  4. K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
    [Crossref]
  5. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Topics Quantum Electron 16(5), 1164–1179 (2010).
    [Crossref]
  6. H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.
  7. N. J. Muga and A. N. Pinto, “Digital PDL compensation in 3D Stokes space,” J. Light. Technol. 31(13), 2122–2130 (2013).
    [Crossref]
  8. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
  9. Z. Yu, X. Yi, Q. Yang, M. Luo, J. Zhang, L. Chen, and K. Qiu, “Polarization demultiplexing in Stokes space for coherent optical PDM-OFDM,” Opt. Express 21(3), 3885–3890 (2013).
    [Crossref] [PubMed]
  10. S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
    [Crossref]
  11. G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.
  12. S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.
  13. N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Light. Technol. 32(19), 3290–3298 (2014).
    [Crossref]
  14. J. N. Damask, Polarization optics in telecommunications(Springer Science & Business Media, 2004).
  15. D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
    [Crossref]
  16. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
    [Crossref] [PubMed]
  17. A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19(10), 9714–9736 (2011).
    [Crossref] [PubMed]
  18. D. Aerts and M. Sassoli de Bianchi, “The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement,” J. Math. Phys. 57(12), 122110 (2016).
    [Crossref]
  19. G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 25(4), 3899–3915 (2017).
    [Crossref] [PubMed]
  20. G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Reduced-complexity algorithm for space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 26(10), 13506 (2018).
    [Crossref] [PubMed]
  21. C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express,  20(11) 11718–11733 (2012).
    [Crossref] [PubMed]
  22. F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.
  23. D. Soma, Y. Wakayama, K. Igarashi, and T. Tsuritani, “Weakly-coupled FMF transmission for reduction of MIMO complexity,” in IEEE Photonics Society Summer Topical Meeting Series, (2016), pp. 140–141.
  24. T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.
  25. D. L. Butler, “Space-division multiplexing (SDM) technology for short-reach fiber optic systems,” in European Conference on Optical Communication (ECOC), (2016), p. Tu3I.1.
  26. F. Mezzadri, “How to generate random matrices from the classical compact groups,” Notices AMS,  54(5), 592–604 (2007).
  27. K.-P. Ho and J. M. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Light. Technol. 32(4), 614–628 (2014).
    [Crossref]
  28. F. Buchal, H. Buelow, K. Schuh, and W. Idler, “4D-CMA: Enabling separation of channel compensation and polarization demultiplex,” in Optical Fiber Communications Conference and Exhibition (OFC), (2015), p. Th2A.15.
  29. B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Light. Technol. 31(4), 648–663 (2013).
    [Crossref]
  30. S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
    [Crossref]
  31. S. Ö. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Light. Technol. 32(10), 1841–1852 (2014).
    [Crossref]

2019 (1)

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

2018 (2)

K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
[Crossref]

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Reduced-complexity algorithm for space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 26(10), 13506 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (2)

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

D. Aerts and M. Sassoli de Bianchi, “The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement,” J. Math. Phys. 57(12), 122110 (2016).
[Crossref]

2015 (1)

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

2014 (5)

N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Light. Technol. 32(19), 3290–3298 (2014).
[Crossref]

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

S. Ö. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Light. Technol. 32(10), 1841–1852 (2014).
[Crossref]

K.-P. Ho and J. M. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Light. Technol. 32(4), 614–628 (2014).
[Crossref]

2013 (3)

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Light. Technol. 31(4), 648–663 (2013).
[Crossref]

N. J. Muga and A. N. Pinto, “Digital PDL compensation in 3D Stokes space,” J. Light. Technol. 31(13), 2122–2130 (2013).
[Crossref]

Z. Yu, X. Yi, Q. Yang, M. Luo, J. Zhang, L. Chen, and K. Qiu, “Polarization demultiplexing in Stokes space for coherent optical PDM-OFDM,” Opt. Express 21(3), 3885–3890 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (2)

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19(10), 9714–9736 (2011).
[Crossref] [PubMed]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

2010 (2)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Topics Quantum Electron 16(5), 1164–1179 (2010).
[Crossref]

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
[Crossref] [PubMed]

2007 (1)

F. Mezzadri, “How to generate random matrices from the classical compact groups,” Notices AMS,  54(5), 592–604 (2007).

Aerts, D.

D. Aerts and M. Sassoli de Bianchi, “The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement,” J. Math. Phys. 57(12), 122110 (2016).
[Crossref]

Aiello, A.

Akiyama, Y.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Andrusier, A.

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
[Crossref]

Antonelli, C.

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express,  20(11) 11718–11733 (2012).
[Crossref] [PubMed]

Arik, S. Ö.

K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
[Crossref]

S. Ö. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Light. Technol. 32(10), 1841–1852 (2014).
[Crossref]

Askarov, D.

S. Ö. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Light. Technol. 32(10), 1841–1852 (2014).
[Crossref]

Bai, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Bosco, G.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

Buchal, F.

F. Buchal, H. Buelow, K. Schuh, and W. Idler, “4D-CMA: Enabling separation of channel compensation and polarization demultiplex,” in Optical Fiber Communications Conference and Exhibition (OFC), (2015), p. Th2A.15.

Buelow, H.

F. Buchal, H. Buelow, K. Schuh, and W. Idler, “4D-CMA: Enabling separation of channel compensation and polarization demultiplex,” in Optical Fiber Communications Conference and Exhibition (OFC), (2015), p. Th2A.15.

Butler, D. L.

D. L. Butler, “Space-division multiplexing (SDM) technology for short-reach fiber optic systems,” in European Conference on Optical Communication (ECOC), (2016), p. Tu3I.1.

Carena, A.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

Chen, H.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Chen, L.

Choutagunta, K.

K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
[Crossref]

Damask, J. N.

J. N. Damask, Polarization optics in telecommunications(Springer Science & Business Media, 2004).

Dudley, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Essiambre, R.-J.

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Fernandes, G. M.

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Reduced-complexity algorithm for space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 26(10), 13506 (2018).
[Crossref] [PubMed]

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 25(4), 3899–3915 (2017).
[Crossref] [PubMed]

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

Ferreira, R.

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Ferreira, R. M.

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

Fontaine, N. K.

R. Ryf and N. K. Fontaine, “Space-division multiplexing and MIMO processing,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, eds. (John Wiley & Sons, Ltd, 2016), 547–608.
[Crossref]

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Forbes, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Forghieri, F.

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

Gabriel, C.

Goeger, G.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Guiomar, F. P.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Hayashi, T.

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Ho, K.

K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
[Crossref]

Ho, K.-P.

K.-P. Ho and J. M. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Light. Technol. 32(4), 614–628 (2014).
[Crossref]

Holleczek, A.

Hoshida, T.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Huang, G.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Huchard, M.

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

Idler, W.

F. Buchal, H. Buelow, K. Schuh, and W. Idler, “4D-CMA: Enabling separation of channel compensation and polarization demultiplex,” in Optical Fiber Communications Conference and Exhibition (OFC), (2015), p. Th2A.15.

Igarashi, K.

D. Soma, Y. Wakayama, K. Igarashi, and T. Tsuritani, “Weakly-coupled FMF transmission for reduction of MIMO complexity,” in IEEE Photonics Society Summer Topical Meeting Series, (2016), pp. 140–141.

Kahn, J. M.

K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
[Crossref]

K.-P. Ho and J. M. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Light. Technol. 32(4), 614–628 (2014).
[Crossref]

S. Ö. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Light. Technol. 32(10), 1841–1852 (2014).
[Crossref]

Leuchs, G.

Li, G.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Li, H.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Litvin, I.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Luo, M.

Marquardt, C.

Marrucci, L.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Marshall, T.

Marshall, T. S.

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Light. Technol. 31(4), 648–663 (2013).
[Crossref]

Mecozzi, A.

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express,  20(11) 11718–11733 (2012).
[Crossref] [PubMed]

Mezzadri, F.

F. Mezzadri, “How to generate random matrices from the classical compact groups,” Notices AMS,  54(5), 592–604 (2007).

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Muga, N. J.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Reduced-complexity algorithm for space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 26(10), 13506 (2018).
[Crossref] [PubMed]

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 25(4), 3899–3915 (2017).
[Crossref] [PubMed]

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Light. Technol. 32(19), 3290–3298 (2014).
[Crossref]

N. J. Muga and A. N. Pinto, “Digital PDL compensation in 3D Stokes space,” J. Light. Technol. 31(13), 2122–2130 (2013).
[Crossref]

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Naidoo, D.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Nebendahl, B.

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Light. Technol. 31(4), 648–663 (2013).
[Crossref]

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
[Crossref] [PubMed]

Nespola, A.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Oda, S.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Piccirillo, B.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Pinto, A. N.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Reduced-complexity algorithm for space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 26(10), 13506 (2018).
[Crossref] [PubMed]

G. M. Fernandes, N. J. Muga, and A. N. Pinto, “Space-demultiplexing based on higher-order Poincaré spheres,” Opt. Express 25(4), 3899–3915 (2017).
[Crossref] [PubMed]

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Light. Technol. 32(19), 3290–3298 (2014).
[Crossref]

N. J. Muga and A. N. Pinto, “Digital PDL compensation in 3D Stokes space,” J. Light. Technol. 31(13), 2122–2130 (2013).
[Crossref]

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Pittala, F.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Poggiolini, P.

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

Qiu, K.

Randel, S.

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Rosenkranz, W.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Roux, F. S.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Ryf, R.

R. Ryf and N. K. Fontaine, “Space-division multiplexing and MIMO processing,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, eds. (John Wiley & Sons, Ltd, 2016), 547–608.
[Crossref]

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Sasaki, T.

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Sassoli de Bianchi, M.

D. Aerts and M. Sassoli de Bianchi, “The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement,” J. Math. Phys. 57(12), 122110 (2016).
[Crossref]

Savory, S. J.

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Topics Quantum Electron 16(5), 1164–1179 (2010).
[Crossref]

Schuh, K.

F. Buchal, H. Buelow, K. Schuh, and W. Idler, “4D-CMA: Enabling separation of channel compensation and polarization demultiplex,” in Optical Fiber Communications Conference and Exhibition (OFC), (2015), p. Th2A.15.

Shahpari, A.

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Shtaif, M.

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express,  20(11) 11718–11733 (2012).
[Crossref] [PubMed]

Soma, D.

D. Soma, Y. Wakayama, K. Igarashi, and T. Tsuritani, “Weakly-coupled FMF transmission for reduction of MIMO complexity,” in IEEE Photonics Society Summer Topical Meeting Series, (2016), pp. 140–141.

Szafraniec, B.

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Light. Technol. 31(4), 648–663 (2013).
[Crossref]

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
[Crossref] [PubMed]

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Tafur Monroy, I.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Tao, Z.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Teixeira, A.

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Teixeira, A. L.

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

Tsuritani, T.

D. Soma, Y. Wakayama, K. Igarashi, and T. Tsuritani, “Weakly-coupled FMF transmission for reduction of MIMO complexity,” in IEEE Photonics Society Summer Topical Meeting Series, (2016), pp. 140–141.

Vaquero Caballero, F. J.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Visintin, M.

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

Wakayama, Y.

D. Soma, Y. Wakayama, K. Igarashi, and T. Tsuritani, “Weakly-coupled FMF transmission for reduction of MIMO complexity,” in IEEE Photonics Society Summer Topical Meeting Series, (2016), pp. 140–141.

Winzer, P. J.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express,  20(11) 11718–11733 (2012).
[Crossref] [PubMed]

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Xia, C.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

Yamauchi, T.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

Yang, Q.

Ye, Y.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Yi, X.

Yu, Z.

Zanaty, A.

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

Zhang, J.

Zhao, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Ziaie, S.

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

Adv. Opt. Photonics (1)

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

IEEE J. Sel. Topics Quantum Electron (1)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Topics Quantum Electron 16(5), 1164–1179 (2010).
[Crossref]

IEEE Photonic Tech. L (1)

S. Ziaie, F. P. Guiomar, N. J. Muga, A. Nespola, G. Bosco, A. Carena, and A. N. Pinto, “Adaptive Stokes-based polarization demultiplexing for long-haul multi-subcarrier systems,” IEEE Photonic Tech. L.,  31(10), 759–762 (2019).
[Crossref]

J. Light. Technol. (8)

S. Ö. Arik, D. Askarov, and J. M. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Light. Technol. 32(10), 1841–1852 (2014).
[Crossref]

K.-P. Ho and J. M. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Light. Technol. 32(4), 614–628 (2014).
[Crossref]

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Light. Technol. 31(4), 648–663 (2013).
[Crossref]

S. Ziaie, N. J. Muga, F. P. Guiomar, G. M. Fernandes, R. M. Ferreira, A. Shahpari, A. L. Teixeira, and A. N. Pinto, “Experimental assessment of the adaptive Stokes space-based polarization demultiplexing for optical metro and access networks,” J. Light. Technol. 33(23), 4968–4974 (2015).
[Crossref]

N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Light. Technol. 32(19), 3290–3298 (2014).
[Crossref]

N. J. Muga and A. N. Pinto, “Digital PDL compensation in 3D Stokes space,” J. Light. Technol. 31(13), 2122–2130 (2013).
[Crossref]

K. Choutagunta, S. Ö. Arik, K. Ho, and J. M. Kahn, “Characterizing mode-dependent loss and gain in multimode components,” J. Light. Technol. 36(18), 3815–3823 (2018).
[Crossref]

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Assessing the effects of mode-dependent loss in space-division multiplexed systems,” J. Light. Technol. 32(7), 1317–1322 (2014).
[Crossref]

J. Math. Phys. (1)

D. Aerts and M. Sassoli de Bianchi, “The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement,” J. Math. Phys. 57(12), 122110 (2016).
[Crossref]

Nat. Photonics (1)

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Notices AMS (1)

F. Mezzadri, “How to generate random matrices from the classical compact groups,” Notices AMS,  54(5), 592–604 (2007).

Opt. Express (6)

Phys. Rev. Lett. (1)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Other (10)

J. N. Damask, Polarization optics in telecommunications(Springer Science & Business Media, 2004).

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental demonstration of a novel update algorithm in Stokes space for adaptive equalization in coherent receivers,” in European Conference on Optical Communication (ECOC), (2014), pp. Tu.3.3.6.

S. Ziaie, R. Ferreira, N. J. Muga, F. P. Guiomar, A. Shahpari, A. Teixeira, and A. N. Pinto, “Coherent UDWDM transceivers based on adaptive Stokes space polarization de-multiplexing in real-time,” in European Conference on Optical Communication (ECOC), (2017), pp. Th.1.B.4.

F. Buchal, H. Buelow, K. Schuh, and W. Idler, “4D-CMA: Enabling separation of channel compensation and polarization demultiplex,” in Optical Fiber Communications Conference and Exhibition (OFC), (2015), p. Th2A.15.

H. Li, G. Huang, Z. Tao, H. Chen, S. Oda, Y. Akiyama, T. Yamauchi, and T. Hoshida, “An accurate and robust PDL monitor by digital signal processing in coherent receiver,” in Optical Fiber Communications Conference and Exhibition (OFC), (2018), pp. M2F–6.

R. Ryf and N. K. Fontaine, “Space-division multiplexing and MIMO processing,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, eds. (John Wiley & Sons, Ltd, 2016), 547–608.
[Crossref]

F. J. Vaquero Caballero, A. Zanaty, F. Pittala, G. Goeger, Y. Ye, I. Tafur Monroy, and W. Rosenkranz, “Efficient SDM-MIMO Stokes-space equalization,” in European Conference on Optical Communication (ECOC), (2016), pp. 1–3.

D. Soma, Y. Wakayama, K. Igarashi, and T. Tsuritani, “Weakly-coupled FMF transmission for reduction of MIMO complexity,” in IEEE Photonics Society Summer Topical Meeting Series, (2016), pp. 140–141.

T. Hayashi, R. Ryf, N. K. Fontaine, C. Xia, S. Randel, R.-J. Essiambre, P. J. Winzer, and T. Sasaki, “Coupled-core multi-core fibers: High-spatial-density optical transmission fibers with low differential modal properties,” in European Conference on Optical Communication (ECOC), (2015), pp. 0318.

D. L. Butler, “Space-division multiplexing (SDM) technology for short-reach fiber optic systems,” in European Conference on Optical Communication (ECOC), (2016), p. Tu3I.1.

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Figures (9)

Fig. 1
Fig. 1 Upper row: schematic representation of two tributaries containing arbitrary modulation format in the Jones space without and with MDL, left and right, respectively. Lower row: schematic representation of two tributaries containing arbitrary modulation formats in the HoPs with and without MDL, left and right, respectively.
Fig. 2
Fig. 2 (a) Schematic of MDL monitoring and compensation technique. (b) Schematic of DSP subsystems considered at the optical coherent receiver.
Fig. 3
Fig. 3 (a) Estimated value of MDL as a function of the real value of MDL for a transmission system with two spatial channels, considering PM-QPSK, PM-16QAM, and PM-64QAM signal. (b) Components of the MDL vector as a function of the real ones. The four values of ρ are estimated from a PM-QPSK signal.
Fig. 4
Fig. 4 Stokes parameters histograms for a PM-QPSK signal transmitted through a SDM link with 3 dB of MDL. In black the B2B signal. In blue/green the received signal before/after the SpDemux stage without MDL compensation stage. In red the post-processed signal after MDL compensation plus SpDemux. Lines are used (instead of 500 bars) to smooth the representation of all data in the same plot. (a)-(f): parameter Ψ 1 ( f , g ), (g)-(l): parameter Ψ 2 ( f , g ) and (m)-(r): parameter Ψ 3 ( f , g ).
Fig. 5
Fig. 5 (a) Evolution of the absolute value of the filter coefficients for the NLMS and the HoPS-based SpDemux supported by the HoPS-based MDL equalizer. Dashed lines indicate the values of the inverse channel matrix. (b) Error estimation on the filter coefficients calculated by the HoPs-based SpDemux without MDL equalization. Sparse bars represents the filter coefficients calculated by the SpDemux algorithm without MDL equalization and the respective value of the inverse channel matrix. Parameter F denotes a given filter coefficient.
Fig. 6
Fig. 6 SNR penalty as a function of the MDLP-P for a (a) PM-QPSK, (b) PM-16QAM and (c) PM-64QAM signals after space-demultiplexing with and without MDL compensation. Insets show both constellations with and without MDL compensation. It is assumed that MDL is induced by a single element.
Fig. 7
Fig. 7 SNR penalty as a function of the MDLP-P for a (a) PM-QPSK, (b) PM-16QAM and (c) PM-64QAM signals after space-demultiplexing without MDL compensation, with a MDL compensation stage and with two MDL compensation stages. It is assumed that MDL is distributed along the transmission channel.
Fig. 8
Fig. 8 SNR penalty as a function of the ASE. It is assumed a SDM transmission system with 10 spans of fiber and MDLP-P of 3 dB.
Fig. 9
Fig. 9 SNR penalty as a function of the MDLP-P for a SDM transmission system based on 3-, 4-, 6- and 7-core CC-MCF, in which each spatial channel supports a PM-QPSK signal. In the calculations of the inverse channels matrix, it is assumed two MDL compensation stages placed after and before the SpDemux.

Equations (24)

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| ψ = ( υ 1 , υ 2 , ... υ h , ... υ 2 n ) T ,
υ j ( z , t ) = a j ( z , t ) e i ( ω t + φ j ) ,
Ψ l ( f , g ) = ψ | Λ l ( f , g ) | ψ ,
Λ ( f , g ) = [ Λ 1 ( f , g ) , Λ 2 ( f , g ) , Λ 3 ( f , g ) ] T .
H = diag { ρ 1 , ρ 2 , ρ 3 , ρ 4 } ,
MDL P P = 10 log  ( max { Γ } / min { Γ } ) .
| ψ = ( 1 , r e θ , 1 , 1 ) T ,
Ψ 1 ( 1 , 2 ) = ψ | Λ 1 ( 1 , 2 ) | ψ = n [ ( 1 r 2 ) ρ ( 1 , 2 ) ( 1 + r 2 ) ] ,
Ψ 2 ( 1 , 2 ) = ψ | Λ 2 ( 1 , 2 ) | ψ = 2 r n 1 + ρ ( 1 , 2 ) 1 ρ ( 1 , 2 ) cos  ( δ 1 , 2 ) ,
Ψ 3 ( 1 , 2 ) = ψ | Λ 3 ( 1 , 2 ) | ψ = 2 r n 1 + ρ ( 1 , 2 ) 1 ρ ( 1 , 2 ) sin  ( δ 1 , 2 ) .
ρ ( 1 , 2 ) = d ( 1 , 2 ) 2 n ,
H = f = 1 n 1 g = f + 1 n T ( f , g ) ,
T ( f , g ) ( k , l )   =   { 1 ρ ( f , g ) if k = g , l = g 1 + ρ ( f , g ) if k = f , l = f 1 if k = l and k , l g , f 0 otherwise ,
ρ ( f , g ) = max { ρ f , ρ g } 2 min { ρ f , ρ g } 2 2 n k n ,
ρ ( f , g ) = D ( f , g ) 2 n k n a 2 ,
D ( f , g ) = P ( f , g ) O ¯ = ( d 1 ( f , g ) ) 2 + ( d 2 ( f , g ) ) 2 + ( d 3 ( f , g ) ) 2 ,
| ψ o u t = [ U 2 ( f , g ) ( θ ) T ( f , g ) ( d 3 ) U 2 ( f , g ) ( θ ) ] [ U 3 ( f , g ) ( θ ) T ( f , g ) ( d 2 ) U 3 ( f , g ) ( θ ) ] T ( f , g ) ( d 1 ) | ψ i n ,
U 3 ( θ ) ( g , f ) ( k , l ) = { cos  ( θ / 2 ) sin  ( θ / 2 ) sin  ( θ / 2 ) cos  ( θ / 2 ) 1 0 and U 2 ( θ ) ( g , f ) ( k , l ) = { cos  ( θ / 2 ) if k = g , l = g i sin  ( θ / 2 ) if k = g , l = f i sin  ( θ / 2 ) if k = f , l = g cos  ( θ / 2 ) if k = f , l = f 1 if k = l and k , l g , f 0 otherwise ,
M = k = 1 n s [ H k l = 1 n step V k l Θ U k l * ] ,
Θ = diag { e i ω τ 1 , ... , e i ω τ 2 n } ,
H k = diag { e ρ 1 k ( ω ) 2 , ... , e ρ 2 n k ( ω ) 2 } ,
Δ = SNR i n SNR o u t ,
N m = 9 n s + 1 ,
N s = 12 n s ,

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