Abstract

We propose a configuration of signal multiplexing with four polarization states, and investigate its transmission performance over single-mode-fiber links. Assisted by coherent detection and digital signal processing (DSP), the demodulation of four-polarization multiplexed (4PM) on-off-keying (OOK) and phase-shift-keying (PSK) signals are achieved. We then discuss the impact of the crosstalk from polarization mode dispersion (PMD) on 4PM systems. The transmission distance is extended from ~50-km to ~80 km by employing feedback-decision-equalizers. We also compare the back-to-back characteristics of the 40-Gbit/s 4PM-OOK system and 40-Gbit/s PDM-QPSK system with the same spectral efficiency. The results show that the performance of 4PM systems is comparable to that of PDM-QPSK systems, which indicates that the proposed scheme is a potentially promising candidate for future optical networks.

© 2013 OSA

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2012 (4)

2011 (3)

2010 (5)

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010).
[CrossRef]

F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express18(20), 21342–21349 (2010).
[CrossRef] [PubMed]

E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron.12, 1129–1131 (2010).

F. Grassi, J. Mora, B. Ortega, and J. Capmany, “Centralized light-source optical access network based on polarization multiplexing,” Opt. Express18(5), 4240–4245 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (3)

2006 (1)

2005 (2)

2003 (1)

2002 (1)

L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett.14(2), 224–226 (2002).
[CrossRef]

2001 (1)

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett.13(7), 738–740 (2001).
[CrossRef]

2000 (2)

L. E. Nelson and H. Kogelnik, “Coherent crosstalk impairments in polarization multiplexed transmission due to polarization mode dispersion,” Opt. Express7(10), 350–361 (2000).
[CrossRef] [PubMed]

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett.12(12), 1627–1629 (2000).
[CrossRef]

1999 (1)

1993 (1)

S. Chen, B. Mulgrew, and S. Mclaughlin, “Adaptive Bayesian equalizer with decision feedback,” IEEE Trans. Signal Process.41(9), 2918–2927 (1993).
[CrossRef]

1971 (1)

D. George, R. Bowen, and J. Storey, “An adaptive decision feedback equalizer,” IEEE Trans. Commun. Technol.19(3), 281–293 (1971).
[CrossRef]

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Antonelli, C.

Bai, N.

Basch, E. B.

E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron.12, 1129–1131 (2010).

Bickham, S.

Bosco, G.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

Bowen, R.

D. George, R. Bowen, and J. Storey, “An adaptive decision feedback equalizer,” IEEE Trans. Commun. Technol.19(3), 281–293 (1971).
[CrossRef]

Capmany, J.

Carena, A.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

Chandrasekhar, S.

Chen, S.

S. Chen, B. Mulgrew, and S. Mclaughlin, “Adaptive Bayesian equalizer with decision feedback,” IEEE Trans. Signal Process.41(9), 2918–2927 (1993).
[CrossRef]

Chen, X.

Chen, Z. Y.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Cheng, K. S.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett.12(12), 1627–1629 (2000).
[CrossRef]

Chowdhury, D.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett.12(12), 1627–1629 (2000).
[CrossRef]

Coskun, O.

Curri, V.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

De Man, E.

de Waardt, H.

Dimarcello, F. V.

Djordjevic, I. B.

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Duthel, T.

Egorov, R.

E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron.12, 1129–1131 (2010).

Elby, S.

E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron.12, 1129–1131 (2010).

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Fini, J. M.

Fischer, G.

Fishteyn, M.

Fludger, C. R. S.

Forghieri, F.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

Gandhi, A.

George, D.

D. George, R. Bowen, and J. Storey, “An adaptive decision feedback equalizer,” IEEE Trans. Commun. Technol.19(3), 281–293 (1971).
[CrossRef]

Geyer, J.

Gliese, U.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett.12(12), 1627–1629 (2000).
[CrossRef]

Gnauck, A. H.

Gottwald, E.

Grassi, F.

Gringeri, S.

E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron.12, 1129–1131 (2010).

Gungener, C.

Guo, Y. H.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Haase, W.

Hinz, S.

Hu, J. Q.

Huang, H.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Huang, M. F.

Huang, Y. K.

Ip, E.

Jansen, S. L.

Jiang, H. Y.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Kanter, G. S.

Kazovsky, L. G.

Khoe Giok-Djan,

Kogelnik, H.

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett.13(7), 738–740 (2001).
[CrossRef]

L. E. Nelson and H. Kogelnik, “Coherent crosstalk impairments in polarization multiplexed transmission due to polarization mode dispersion,” Opt. Express7(10), 350–361 (2000).
[CrossRef] [PubMed]

Lau, A. P.

Li, G.

Li, M. J.

Li, W.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Liñares, J.

Liu, J. G.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Liu, X.

Lu, C.

Luo, B.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Luo, Y.

Man Chung, K.

Marhic, M. E.

Mateo, E.

Mclaughlin, S.

S. Chen, B. Mulgrew, and S. Mclaughlin, “Adaptive Bayesian equalizer with decision feedback,” IEEE Trans. Signal Process.41(9), 2918–2927 (1993).
[CrossRef]

Mecozzi, A.

Mirvoda, V.

Monberg, E. M.

Montero, C.

Mora, J.

Moreno, V.

Morita, I.

Mulgrew, B.

S. Chen, B. Mulgrew, and S. Mclaughlin, “Adaptive Bayesian equalizer with decision feedback,” IEEE Trans. Signal Process.41(9), 2918–2927 (1993).
[CrossRef]

Nelson, L. E.

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett.13(7), 738–740 (2001).
[CrossRef]

L. E. Nelson and H. Kogelnik, “Coherent crosstalk impairments in polarization multiplexed transmission due to polarization mode dispersion,” Opt. Express7(10), 350–361 (2000).
[CrossRef] [PubMed]

Nielsen, T. N.

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett.13(7), 738–740 (2001).
[CrossRef]

Noe, R.

Ortega, B.

Pan, W.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Pan, Y.

Peng, G. D.

Poggiolini, P.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

Prieto, X.

Qian, D. Y.

Ren, X.

Ren, Y. X.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Rhee, J. K.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett.12(12), 1627–1629 (2000).
[CrossRef]

Samal, A. K.

Sandel, D.

Scheerer, C.

Schenk, T. C. W.

Schmidt, E. D.

Schopflin, A.

Schulien, C.

Shao, Y.

Shieh, W.

L. S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J.3(2), 325–330 (2011).
[CrossRef]

Shtaif, M.

Storey, J.

D. George, R. Bowen, and J. Storey, “An adaptive decision feedback equalizer,” IEEE Trans. Commun. Technol.19(3), 281–293 (1971).
[CrossRef]

Takeda, N.

Tam, H. Y.

Tanaka, H.

Taunay, T. F.

Ten, S.

Tse, V.

Tur, M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

van den Borne, D.

Vasic, B.

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Wang, T.

Wang, Z.

Weyrauch, T.

Willner, A. E.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett.14(2), 224–226 (2002).
[CrossRef]

Winzer, P. J.

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Wuth, T.

Xie, C.

Xie, Y.

L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett.14(2), 224–226 (2002).
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Yan, L.-S.

L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett.14(2), 224–226 (2002).
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Yan, M. F.

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

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L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

Yoshida-Dierolf, M.

Yu, Q.

L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett.14(2), 224–226 (2002).
[CrossRef]

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
[CrossRef]

Zhu, B.

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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012).
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Opt. Express (12)

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express20(11), 11718–11733 (2012).
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N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express20(3), 2668–2680 (2012).
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F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express18(20), 21342–21349 (2010).
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I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express14(9), 3767–3775 (2006).
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Other (8)

S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PDPB2.3.
[CrossRef]

W. Shieh, “High spectral efficiency coherent optical OFDM for 1 Tb/s Ethernet transport,” presented at Optical Fiber Communication Conference 2009 (OFC’2009), paper OWW1.
[CrossRef]

S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PD2.3.
[CrossRef]

D. O. Captan, B. S. Robinson, R. J. Murphy, and M. L. Stevens, “Demonstration of 2.5-Gsloth ptically-preamplified M-PPM with 4 photonbit receiver sensitivity,” presented at Optical Fiber Communication Conference 2005 (OFC’2005), paper PDP32.

A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432×171-Gb/s) C- and extended L-band transmission over 240 km using PDM-16-QAM,” presented at Optical Fiber Communication Conference 2010 (OFC’2010), paper PDPB7.

S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval CO-OFDM superchannel over 7200-km of ultra-large-area fiber,” in 35th European Conference on Optical Communication,2009 (ECOC '09), paper PDPB2.6.

X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, and R. Lingle, “32 (320×114Gb/s) PDM-RZ-8QAM transmission over 580km of SMF-28 ultra-low-loss fiber,” presented at Optical Fiber Communication Conference 2009 (OFC'2009), paper PDPB4.

X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, P. Magill, M. Cvijetic, L. Nelson, M. Birk, G. Zhang, S. Ten, H. B. Mishra, and K. Snigdharaj, “64-Tb/s (640×107-Gb/s) PDM-36QAM transmission over 320km using both pre- and post-transmission digital equalization,” presented at Optical Fiber Communication Conference 2010 (OFC'2010), paper PDPB9.

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Figures (13)

Fig. 1
Fig. 1

(a) Setup for four SOPs multiplexing, transmission and demodulation. (b) Receiver configuration for 4PM-OOK signal. OC: optical coupler; PC: polarization controller; VOA: variable optical attenuator; SMF: single-mode fiber; PBS: polarization beam splitter; LO: local oscillator laser; PD: photodetector; ADC: analog to digital converter; DSP: digital signal processing; CHn: channel n, (n = 1-4).

Fig. 2
Fig. 2

Phase synchronization scheme for 4PM-OOK signal. Re{X}: real part of X.

Fig. 3
Fig. 3

Demodulation scheme for PSK signal. BPD: balance photodetector.

Fig. 4
Fig. 4

Demodulated model of a 4PM system. PC1 and PC2 control the launch angle into fiber and PBS, respectively. CHx: channel x; CHy: channel y.

Fig. 5
Fig. 5

Back-to-back eye-diagrams for one typical input and four demodulated outputs.

Fig. 6
Fig. 6

Crosstalk coupled form CH1 (a), CH2 (b) or CH3(c) to CH4 in the absence of CH4. Dash line in (a)-(c) is the bit patterns of the channel 1, 2 and 3; solid line is the bit patterns of channel 4 when there is only one input (CH1 (a), CH2 (b) or CH3 (c)). (d) Coupled spectral power density from CH1 to CH4 in absence of CH2, CH3 and CH4.

Fig. 7
Fig. 7

Back-to-back BER versus received power before PBS3.

Fig. 8
Fig. 8

Second demodulated scheme for 4PM-OOK systems (4PM-OOK-2).

Fig. 9
Fig. 9

Back-to-back eye-diagrams for the second demodulation scheme for OOK signal (4PM-OOK-2).

Fig. 10
Fig. 10

Eye closure performance versus different DGD values. The inserts are the eye-diagrams for different multiplexing signals in the presence of 10.2-ps DGD.

Fig. 11
Fig. 11

(a) BER versus received power before PBS3 (with and without compensation); (b) Q-factor versus transmission distance with and without the FDE. W/: with; W/O: without; Comp.: compensation; FDE: feedback decision equalizer; DCF: dispersion compensation fiber. Insert: dispersion compensation by using DCF.

Fig. 12
Fig. 12

Back to back BER of the 4PM-OOK-2 systems and the PDM-QPSK systems.

Fig. 13
Fig. 13

(a) Back-to-back eye-diagrams (5-ps/div) and (b) BER performance for 4 × 40Gbit/s 4PM-OOK signals when using the second demodulation scheme.

Equations (48)

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E m = E x + E y =[ x ^ ( 2 2 A 1 + 1 2 j A 3 1 2 j A 4 )+ y ^ ( 2 2 A 2 + 1 2 j A 3 + 1 2 j A 4 )]exp(j ω c t+ϕ),
{ E 1 = 2 2 { 2 2 A 1 exp[j( ω c t+ϕ)]+ 1 2 j A 3 exp[j( ω c t+ϕ)] 1 2 j A 4 exp[j( ω c t+ϕ)]+j A LO exp[j( ω c t+θ)]} = 2 2 { 2 2 A 1 exp[j( ω c t+ϕ)]+j B 1 expj( ω c t)}, E 2 = 2 2 { 2 2 A 1 exp[j( ω c t+ϕ)]+ 1 2 j A 3 exp[j( ω c t+ϕ)] 1 2 j A 4 exp[j( ω c t+ϕ)]j A LO exp[j( ω c t+θ)]} = 2 2 { 2 2 A 1 exp[j( ω c t+ϕ)]+j B 2 expj( ω c t)}, E 3 = 2 2 { 2 2 A 2 exp[j( ω c t+ϕ)]+ 1 2 j A 3 exp[j( ω c t+ϕ)]+ 1 2 j A 4 exp[j( ω c t+ϕ)]+j A LO exp[j( ω c t+θ)]} = 2 2 { 2 2 A 2 exp[j( ω c t+ϕ)]+j B 3 expj( ω c t)}, E 4 = 2 2 { 2 2 A 2 exp[j( ω c t+ϕ)]+ 1 2 j A 3 exp[j( ω c t+ϕ)]+ 1 2 j A 4 exp[j( ω c t+ϕ)]j A LO exp[j( ω c t+θ)]} = 2 2 { 2 2 A 2 exp[j( ω c t+ϕ)]+j B 4 expj( ω c t)},
[ B 1 B 2 B 3 B 4 ]=[ 1 2 A 3 exp(jϕ) 1 2 A 4 exp(jϕ)+ A LO exp(jθ) 1 2 A 3 exp(jϕ) 1 2 A 4 exp(jϕ) A LO exp(jθ) 1 2 A 3 exp(jϕ)+ 1 2 A 4 exp(jϕ)+ A LO exp(jθ) 1 2 A 3 exp(jϕ)+ 1 2 A 4 exp(jϕ) A LO exp(jθ) ].
i 1 = 2 [ 2 2 A 1 expj( ω c t+ϕ)+j B 1 expj( ω c t)][ 2 2 A 1 expj( ω c tϕ)j B 1 * expj( ω c t)] = 2 [ 1 2 A 1 2 + B 1 B 1 * 2 2 j A 1 B 1 * exp(jϕ)+ 2 2 j A 1 B 1 exp(jϕ)],
i 2 = 2 [ 1 2 A 1 2 + B 2 B 2 * 2 2 j A 1 B 2 * exp(jϕ)+ 2 2 j A 1 B 2 exp(jϕ)],
i 7 = 2 [ 1 2 A 2 2 + B 3 B 3 * 2 2 j A 2 B 3 * exp(jϕ)+ 2 2 j A 2 B 3 exp(jϕ)],
i 8 = 2 [ 1 2 A 2 2 + B 4 B 4 * 2 2 j A 2 B 4 * exp(jϕ)+ 2 2 j A 2 B 4 exp(jϕ)].
i 1 =[ 1 4 A 1 2 + ( 2 4 A 3 2 4 A 4 + 2 2 A LO ) 2 ],
i 2 =[ 1 4 A 1 2 + ( 2 4 A 3 2 4 A 4 2 2 A LO ) 2 ],
i 7 =[ 1 4 A 2 2 + ( 2 4 A 3 + 2 4 A 4 + 2 2 A LO ) 2 ],
i 8 =[ 1 4 A 2 2 + ( 2 4 A 3 + 2 4 A 4 2 2 A LO ) 2 ],
i 1 i 2 =( A 3 A LO A 4 A LO ),
i 7 i 8 =( A 3 A LO + A 4 A LO ).
A 1 = 1 2( i 1 + i 2 ) ( i 1 i 2 ) 2 2 A LO 2 2 A LO 2 ,
A 2 = 1 2( i 7 + i 8 ) ( i 7 i 8 ) 2 2 A LO 2 2 A LO 2 ,
A 3 = i 1 i 2 + i 7 i 8 2 A LO ,
A 4 = i 1 i 2 ( i 7 i 8 ) 2 A LO .
i 1 = 2 [ 1 2 A 1 2 + 1 4 A 3 2 + 1 4 A 4 2 + A LO 2 1 2 A 3 A 4 + A 3 A LO cos(ϕθ) A 4 A LO cos(ϕθ)+ 2 A 1 A LO sin(ϕθ)],
i 2 = 2 [ 1 2 A 1 2 + 1 4 A 3 2 + 1 4 A 4 2 + A LO 2 1 2 A 3 A 4 A 3 A LO cos(ϕθ) + A 4 A LO cos(ϕθ) 2 A 1 A LO sin(ϕθ)].
i 1 i 2 =[ A 3 A LO cos(ϕθ) A 4 A LO cos(ϕθ)+ 2 A 1 A LO sin(ϕθ)].
i 3 = 2 [ 1 2 A 1 2 + 1 4 A 3 2 + 1 4 A 4 2 + A LO 2 1 2 A 3 A 4 A 3 A LO sin(ϕθ) + A 4 A LO sin(ϕθ)+ 2 A 1 A LO cos(ϕθ)],
i 4 = 2 [ 1 2 A 1 2 + 1 4 A 3 2 + 1 4 A 4 2 + A LO 2 1 2 A 3 A 4 + A 3 A LO sin(ϕθ) A 4 A LO sin(ϕθ) 2 A 1 A LO cos(ϕθ)].
i 3 i 4 =[ A 3 A LO sin(ϕθ) A 4 A LO sin(ϕθ) 2 A 1 A LO cos(ϕθ)].
E A =[ A 3 A LO expj(ϕθ) A 4 A LO expj(ϕθ) 2 A 1 A LO expj(ϕθ+ π 2 )].
E B = E A exp[j(ϕθ)] =[ A 3 A LO A 4 A LO j 2 A 1 A LO ].
i out =( A 3 A LO A 4 A LO ).
E m =Aexp(j ω c t){ x ^ [ 2 2 exp(j ϕ 1 )+ 1 2 jexp(j ϕ 3 ) 1 2 jexp(j ϕ 4 )] + y ^ [ 2 2 exp(j ϕ 2 )+ 1 2 jexp(j ϕ 3 )+ 1 2 jexp(j ϕ 4 )] }.
{ i 1 (1) =( E x +j E LO ) ( E x +j E LO ) * =|A | 2 [ 2 2 sin( ϕ 1 ϕ 3 )+ 2 2 sin( ϕ 4 ϕ 1 )+ 2 sin( ϕ 1 ϕ LO ) 1 2 cos( ϕ 3 ϕ 4 ) +cos( ϕ 3 ϕ LO )cos( ϕ LO ϕ 4 )+2] i 1 (2) =( E x j E LO ) ( E x j E LO ) * =|A | 2 [ 2 2 sin( ϕ 1 ϕ 3 )+ 2 2 sin( ϕ 4 ϕ 1 ) 2 sin( ϕ 1 ϕ LO ) 1 2 cos( ϕ 3 ϕ 4 ) cos( ϕ 3 ϕ LO )+cos( ϕ LO ϕ 4 )+2] ,
{ i 2 (1) =( E x + E LO ) ( E x + E LO ) * =|A | 2 [ 2 2 sin( ϕ 1 ϕ 3 )+ 2 2 sin( ϕ 4 ϕ 1 )+ 2 cos( ϕ 1 ϕ LO ) 1 2 cos( ϕ 3 ϕ 4 ) sin( ϕ 3 ϕ LO )+sin( ϕ 4 ϕ LO )+2] i 2 (2) =( E x E LO ) ( E x E LO ) * =|A | 2 [ 2 2 sin( ϕ 1 ϕ 3 )+ 2 2 sin( ϕ 4 ϕ 1 ) 2 cos( ϕ 1 ϕ LO ) 1 2 cos( ϕ 3 ϕ 4 ) +sin( ϕ 3 ϕ LO )sin( ϕ 4 ϕ LO )+2] ,
{ i 3 (1) =( E y + E LO ) ( E y + E LO ) * =|A | 2 [ 2 2 sin( ϕ 2 ϕ 3 )+ 2 2 sin( ϕ 2 ϕ 4 )+ 2 cos( ϕ 2 ϕ LO )+ 1 2 cos( ϕ 3 ϕ 4 ) sin( ϕ 3 ϕ LO )sin( ϕ 4 ϕ LO )+2] i 3 (2) =( E y E LO ) ( E y E LO ) * =|A | 2 [ 2 2 sin( ϕ 2 ϕ 3 )+ 2 2 sin( ϕ 2 ϕ 4 ) 2 cos( ϕ 2 ϕ LO )+ 1 2 cos( ϕ 3 ϕ 4 ) +sin( ϕ 3 ϕ LO )+sin( ϕ 4 ϕ LO )+2] ,
{ i 4 (1) =( E y +j E LO ) ( E y +j E LO ) * =|A | 2 [ 2 2 sin( ϕ 2 ϕ 3 )+ 2 2 sin( ϕ 2 ϕ 4 )+ 2 sin( ϕ 2 ϕ LO )+ 1 2 cos( ϕ 3 ϕ 4 ) +cos( ϕ 3 ϕ LO )+cos( ϕ 4 ϕ LO )+2] i 4 (2) =( E y j E LO ) ( E y j E LO ) * =|A | 2 [ 2 2 sin( ϕ 2 ϕ 3 )+ 2 2 sin( ϕ 2 ϕ 4 ) 2 sin( ϕ 2 ϕ LO )+ 1 2 cos( ϕ 3 ϕ 4 ) cos( ϕ 3 ϕ LO )cos( ϕ 4 ϕ LO )+2] .
[ i 1 i 2 i 3 i 4 ]=[ i 1 (1) i 1 (2) i 2 (1) i 2 (2) i 3 (1) i 3 (2) i 4 (1) i 4 (2) ]=[ 2|A | 2 [ 2 sin( ϕ 1 ϕ LO )+cos( ϕ 3 ϕ LO )cos( ϕ 4 ϕ LO )] 2|A | 2 [ 2 cos( ϕ 1 ϕ LO )sin( ϕ 3 ϕ LO )+sin( ϕ 4 ϕ LO )] 2|A | 2 [ 2 cos( ϕ 2 ϕ LO ) sin( ϕ 3 ϕ LO )sin( ϕ 4 ϕ LO )] 2|A | 2 [ 2 sin( ϕ 2 ϕ LO ) +cos( ϕ 3 ϕ LO )+cos( ϕ 4 ϕ LO )] ].
I yx (ω)= A ˜ y A ˜ y * ( ω τ × s ^ Ey (0) 2 ) 2 ,
{ E x =[( 2 2 A 1 + 1 2 j A 3 1 2 j A 4 )+j Δτ ω c 2 ( 2 2 A ˙ 2 + 1 2 j A ˙ 3 + 1 2 j A ˙ 4 )]exp[j( ω c +ϕ)] E y =[( 2 2 A 2 + 1 2 j A 3 + 1 2 j A 4 )+j Δτ ω c 2 ( 2 2 A ˙ 1 + 1 2 j A ˙ 3 1 2 j A ˙ 4 )]exp[j( ω c +ϕ)] .
A 1 = A 1 2 2 2 Δτ ω c ( A 1 A ˙ 3 + A 1 A ˙ 4 ) ,
A 2 = A 2 2 2 2 Δτ ω c ( A 2 A ˙ 3 + A 2 A ˙ 4 ) ,
A 3 = A 3 + 2 4 Δτ ω c ( A ˙ 1 + A ˙ 2 ),
A 4 = A 4 + 2 4 Δτ ω c ( A ˙ 1 + A ˙ 2 ).
E xx = x ^ x ^ ( 2 2 j A 3 + 1 2 A 1 + 1 2 A 2 )exp(j ω c t+ϕ),
E yy = y ^ y ^ ( 2 2 j A 4 1 2 A 1 + 1 2 A 2 )exp(j ω c t+ϕ).
i 1 = 2 [( E xx + E LO ) ( E xx + E LO ) * ( E xx E LO ) ( E xx E LO ) * ]=( A 1 + A 2 ) A LO ,
i 2 = 2 [( E yy + E LO ) ( E yy + E LO ) * ( E yy E LO ) ( E yy E LO ) * ]=( A 2 A 1 ) A LO ,
i 3 = 2 [( E x +j E LO ) ( E x +j E LO ) * ( E x j E LO ) ( E x j E LO ) * ]=( A 3 A 4 ) A LO ,
i 4 = 2 [( E y +j E LO ) ( E y + E LO ) * ( E y E LO ) ( E y E LO ) * ]=( A 3 + A 4 ) A LO .
A 1 = i 1 i 2 2 A LO ,
A 2 = i 1 + i 2 2 A LO ,
A 3 = i 3 + i 4 2 A LO ,
A 4 = i 3 i 4 2 A LO .

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