Abstract

Direct detection is traditionally regarded as a detection method that recovers only the optical intensity. Compared with coherent detection, it owns a natural advantage–the simplicity–but lacks a crucial capability of field recovery that enables not only the multi-dimensional modulation, but also the digital compensation of the fiber impairments linear with the optical field. Full-field detection is crucial to increase the capacity-distance product of optical transmission systems. A variety of methods have been investigated to directly detect the optical field of the single polarization mode, which normally sends a carrier traveling with the signal for self-coherent detection. The crux, however, is that any optical transmission medium supports at least two propagating modes (e.g. single mode fiber supports two polarization modes), and until now there is no direct detection that can recover the complete set of optical fields beyond one polarization, due to the well-known carrier fading issue after mode demultiplexing induced by the random mode coupling. To avoid the fading, direct detection receivers should recover the signal in an intensity space isomorphic to the optical field without loss of any degrees of freedom, and a bridge should be built between the field and its isomorphic space for the multi-mode field recovery. Based on this thinking, we propose, for the first time, the direct detection of dual polarization modes by a novel receiver concept, the Stokes-space field receiver (SSFR) and its extension, the generalized SSFR for multiple spatial modes. The idea is verified by a dual-polarization field recovery of a polarization-multiplexed complex signal over an 80-km single mode fiber transmission. SSFR can be applied to a much wider range of fields beyond optical communications such as coherent sensing and imaging, where simple field recovery without an extra local laser is desired for enhanced system performance.

© 2018 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 (1)

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: methods and potential Gain,” J. Lightw. Tech. 35, 903 (2017).

2016 (3)

2015 (1)

2014 (1)

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

2013 (2)

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

Q. Hu and W. Shieh, “Autocorrelation function of channel matrix in few-mode fibers with strong mode coupling,” Opt. Express 21(19), 22153–22165 (2013).
[Crossref] [PubMed]

2012 (3)

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]

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2010 (1)

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Tech. 28(4), 484–493 (2010).
[Crossref]

2009 (2)

2008 (1)

2007 (3)

E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightw. Tech. 25(8), 2033–2043 (2007).
[Crossref]

W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express 15(16), 9936–9947 (2007).
[Crossref] [PubMed]

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightw. Tech. 25(9), 2675–2692 (2007).
[Crossref]

2006 (1)

2005 (1)

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

1984 (1)

G. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. 20(10), 1208–1216 (1984).
[Crossref]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Amezcua Correa, R.

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

Antonelli, C.

Antonio Lopez, E.

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

Arbab, V. R.

Armstrong, J.

Bolle, C.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Burrows, E. C.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Cable, A. E.

Che, D.

W. Shieh, H. Khodakarami, and D. Che, “Polarization diversity and modulation for high-speed optical communications: architectures and capacity,” APL Photonics 1(4), 040801 (2016).
[Crossref]

D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conference, p. Tu3G.7 (2014).
[Crossref]

Chen, L.

Chen, X.

D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conference, p. Tu3G.7 (2014).
[Crossref]

Chi, S.

Christen, L. C.

Cvijetic, N.

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Tech. 28(4), 484–493 (2010).
[Crossref]

Dar, R.

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: methods and potential Gain,” J. Lightw. Tech. 35, 903 (2017).

de Waardt, H.

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

Doerr, C.

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Esmaeelpour, M.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Essiambre, R.-J.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Feng, K. M.

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]

Fujimoto, J. G.

Gnauck, A. H.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Han, Y.

He, J.

D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conference, p. Tu3G.7 (2014).
[Crossref]

Hoffmann, S.

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightw. Tech. 27(8), 989–999 (2009).
[Crossref]

Hu, J.

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Tech. 28(4), 484–493 (2010).
[Crossref]

Hu, Q.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Huijskens, F. M.

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

Ip, E.

E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightw. Tech. 25(8), 2033–2043 (2007).
[Crossref]

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightw. Tech. 25(9), 2675–2692 (2007).
[Crossref]

Jayaraman, V.

Kahn, J. M.

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightw. Tech. 25(9), 2675–2692 (2007).
[Crossref]

E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightw. Tech. 25(8), 2033–2043 (2007).
[Crossref]

Khodakarami, H.

W. Shieh, H. Khodakarami, and D. Che, “Polarization diversity and modulation for high-speed optical communications: architectures and capacity,” APL Photonics 1(4), 040801 (2016).
[Crossref]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Koonen, A. M. J.

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

Lee, H.-C.

Li, A.

A. Li, Y. Wang, Q. Hu, and W. Shieh, “Few-mode fiber based optical sensors,” Opt. Express 23(2), 1139–1150 (2015).
[Crossref] [PubMed]

D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conference, p. Tu3G.7 (2014).
[Crossref]

Li, G.

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

Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express 13(19), 7527–7534 (2005).
[Crossref] [PubMed]

Lingle, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Lowery, A.

Ma, Y.

McCurdy, A. H.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Mecozzi, A.

Meslener, G.

G. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. 20(10), 1208–1216 (1984).
[Crossref]

Mumtaz, S.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

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]

Nielson, T.

Noé, R.

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightw. Tech. 27(8), 989–999 (2009).
[Crossref]

Okonkwo, C. M.

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

Peckham, D. W.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Peng, W.-R.

Pfau, T.

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightw. Tech. 27(8), 989–999 (2009).
[Crossref]

Potsaid, B.

Qian, D.

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Tech. 28(4), 484–493 (2010).
[Crossref]

Randel, S.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

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]

Ryf, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Savory, S. J.

Schülzgen, A.

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

Shamee, B.

Shieh, W.

W. Shieh, H. Khodakarami, and D. Che, “Polarization diversity and modulation for high-speed optical communications: architectures and capacity,” APL Photonics 1(4), 040801 (2016).
[Crossref]

A. Li, Y. Wang, Q. Hu, and W. Shieh, “Few-mode fiber based optical sensors,” Opt. Express 23(2), 1139–1150 (2015).
[Crossref] [PubMed]

Q. Hu and W. Shieh, “Autocorrelation function of channel matrix in few-mode fibers with strong mode coupling,” Opt. Express 21(19), 22153–22165 (2013).
[Crossref] [PubMed]

W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express 15(16), 9936–9947 (2007).
[Crossref] [PubMed]

D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conference, p. Tu3G.7 (2014).
[Crossref]

Shtaif, M.

Sierra, A.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

Swanson, E.

Tang, Y.

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

van Uden, R. G. H.

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

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, T.

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Tech. 28(4), 484–493 (2010).
[Crossref]

Wang, Y.

Wang, Z.

Willner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

W.-R. Peng, X. Wu, K. M. Feng, V. R. Arbab, B. Shamee, J. Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17(11), 9099–9111 (2009).
[Crossref] [PubMed]

Winzer, P. J.

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: methods and potential Gain,” J. Lightw. Tech. 35, 903 (2017).

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[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]

Wu, X.

Xia, C.

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

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J. Y.

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yi, X.

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

APL Photonics (1)

W. Shieh, H. Khodakarami, and D. Che, “Polarization diversity and modulation for high-speed optical communications: architectures and capacity,” APL Photonics 1(4), 040801 (2016).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. 20(10), 1208–1216 (1984).
[Crossref]

J. Lightw. Tech. (6)

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Tech. 30(4), 521–531 (2012).
[Crossref]

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightw. Tech. 27(8), 989–999 (2009).
[Crossref]

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightw. Tech. 25(9), 2675–2692 (2007).
[Crossref]

E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightw. Tech. 25(8), 2033–2043 (2007).
[Crossref]

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: methods and potential Gain,” J. Lightw. Tech. 35, 903 (2017).

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Tech. 28(4), 484–493 (2010).
[Crossref]

Nat. Photonics (3)

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

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

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Opt. Express (8)

Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express 13(19), 7527–7534 (2005).
[Crossref] [PubMed]

A. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14(6), 2079–2084 (2006).
[Crossref] [PubMed]

W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express 15(16), 9936–9947 (2007).
[Crossref] [PubMed]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

W.-R. Peng, X. Wu, K. M. Feng, V. R. Arbab, B. Shamee, J. Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17(11), 9099–9111 (2009).
[Crossref] [PubMed]

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]

Q. Hu and W. Shieh, “Autocorrelation function of channel matrix in few-mode fibers with strong mode coupling,” Opt. Express 21(19), 22153–22165 (2013).
[Crossref] [PubMed]

A. Li, Y. Wang, Q. Hu, and W. Shieh, “Few-mode fiber based optical sensors,” Opt. Express 23(2), 1139–1150 (2015).
[Crossref] [PubMed]

Optica (2)

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Other (9)

D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “160-Gb/s stokes vector direct detection for short reach optical communication,” Proc. Optical Fiber Communication Conference, Th5C.7 (2014).
[Crossref]

M. Morsy-Osman, M. Chagnon, M. Poulin, S. Lessard, and D. V. Plant, “1λ × 224 Gb/s 10 km transmission of polarization division multiplexed PAM-4 signals using 1.3 μm SiP intensity modulator and a direct-detection MIMO-based receiver,” Proc. European Conference on Optical Communication, PD.4.4 (2014).

M. Chagnon, M. Osman, D. Patel, V. Veerasubramanian, A. Samani, and D. Plant, “1 λ, 6 bits/symbol, 280 and 350 Gb/s direct detection transceiver using intensity modulation, polarization multiplexing, and inter-polarization phase modulation,” Proc. Optical Fiber Communication Conference, Th5C.2 (2015).
[Crossref]

D. Che, C. Sun, and W. Shieh, “Single-channel 480-Gb/s direct detection of POL-MUX IQ signal using single-sideband Stokes vector receiver,” Proc. Optical Fiber Communication Conference, Tu2C.7 (2018).

K. Schuh, F. Buchali, W. Idler, T. A. Eriksson, L. Schmalen, W. Templ, R. Schmid, L. Altenhain, M. Moeller, and K. Engenhardt, “Single carrier 1.2 Tbit/s transmission over 300 km with PM-64 QAM at 100 Gbaud,” Proc. Optical Fiber Communication Conference, Th5B.5 (2017).
[Crossref]

B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “100 Gbit/s transmission using single-band direct-detection optical OFDM,” Proc. Optical Fiber Communication Conference, PDPC3 (2009).

D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conference, p. Tu3G.7 (2014).
[Crossref]

R. Ryf, N. K. Fontaine, B. Guan, R.-J. Essiambre, S. Randel, A. H. Gnauck, S. Chandrasekhar, A. Adamiecki, G. Raybon, B. Ercan, R. P. Scott, S. J. Ben Yoo, T. Hayashi, T. Nagashima, and T. Sasaki, “1705-km transmission over coupled-core fibre supporting 6 spatial modes,” Proc. European Conference on Optical Communication, PD.3.2 (2014).
[Crossref]

Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” Proc. Optical Fiber Communication Conference, PDP7 (2008).

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Figures (6)

Fig. 1
Fig. 1 Direct detection of single-polarization optical field. (a) Intensity receiver (a-1) with frequency gap [14] (a-2) without frequency gap [15,17]; (b) Coherent receiver with a single-carrier interleaving input [16]. Fig. (a) shows frequency domain while (b) shows time domain. C: carrier; S: signal; PD: photodiode; SSBN: signal-to-signal beat noise; COH: coherent; Rx: receiver; superscript *: conjugate.
Fig. 2
Fig. 2 Detection of dual-polarization optical field in SMF. (a) Coherent detection; self-coherent detection with (b) a complete carrier fading at Y-POL; (c) dual carriers [22]; (d) a pair of self-polarization-diversity carriers by polarization rotator. PBS: polarization beam splitter; LO: local oscillator; PC: polarization controller; C: carrier; DMUX: de-multiplexer; FRM: Faraday rotator mirror.
Fig. 3
Fig. 3 Direct detection in Stokes space. (a) Tx: 3-D intensity modulation (IM) in Stokes space [23]; Rx: Stokes-vector receiver with three intensity detections. (b) Tx: Dual-polarization gapless-SSB modulation in Jones space; Rx: Stokes-space field receiver with optical field recovery of dual polarization modes. In Fig. (a), the three polarizations (POL) at transmitter are 0-degree linear POL; 45-degree linear POL and left-circular (LC) POL; in (b), the transmitter sends complex-modulated signals along 0- and 90- degree linear POLs. PC: POL controller; SVR: Stokes-vector receiver; IQM: I/Q modulator; Δf: optical frequency shifter; PBC: polarization beam combiner; FR: field recovery.
Fig. 4
Fig. 4 Experiment setup for the field recovery of dual polarization modes. ECL: external cavity laser; IQ mod.: IQ modulator; PC: polarization controller; S/C: signal/carrier; PBC/PBS: polarization beam combiner/splitter; OSA: optical spectrum analyser; SW: optical switch; PD: photodiode; DSO: digital sampling oscilloscope.
Fig. 5
Fig. 5 Recovery of DP optical field using Stokes-space field receiver. (a) RF spectra of the received X-POL (port 1 of the SVR in Fig. 4) at various signal processing stages when X-POL suffers from severe carrier fading; (b) the recovered optical field of both polarizations (namely, the pair of 16-QAM constellations), and their SNR performance across the spectrum.
Fig. 6
Fig. 6 OSNR sensitivity of the 256-Gb/s POL-MUX 16-QAM system. The reference BER level is the 20% soft-decision (SD) forward error correction (FEC) threshold of 4 × 10−2, achieved by the spatially-coupled LDPC codes in [31]. B2B: back-to-back measurement.

Equations (8)

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

S Q (t)=HT[ S I (t)]
φ(t)=HT[logI(t)]
E: E H FE=0
E 1 H D E 1 =0 η 1 | E 1X | 2 + η 2 | E 1Y | 2 =0
|s=[ X Y ] s ^ =s| σ |s=[ X X * Y Y * X Y * + X * Y j(X Y * X * Y) ]
R σ = U H σ U
|s= [ | X |exp(i φ x +i2πΔft) | Y |exp(i φ y ) ] s ˜ =[ s 0 s 1 s 2 s 3 ]=[ | X | 2 + | Y | 2 | X | 2 | Y | 2 2| X || Y |Re(exp(i φ x i φ y +i2πΔft)) 2| X || Y |Im(exp(i φ x i φ y +i2πΔft)) ]
|v= [ E 1 E 2 E 3 E 4 ] T v ˜ = [ | E i | 2 2Re( E i E j * ) 2Im( E i E j * ) i,j{1,2,3,4}ji ] 16×1 T

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