Abstract

We propose a polarization demultiplexing method for coherent optical PDM-OFDM based on Stokes space, without inserting training symbols. The proposed approach performs well for different modulation formats of OFDM subcarrier, and shows comparable performances with that of conventional methods, but with a fast convergence speed and reduced overhead. The OFDM signal in the time domain cannot satisfy the conditions of SS-PDM accurately. Therefore, we first digitally convert the received OFDM signals to the frequency domain using fast Fourier transform (FFT). Each subcarrier of the OFDM signal has a much lower speed and narrower bandwidth, the polarization effects that it experiences can be treated as flat. Consequently, we can apply the polarization demultiplexing in Stokes space (SS-PDM) on per subcarrier basis. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960km SSMF respectively. We also compare the results with those of training symbols. Finally, we analyze of the convergence speed of this method.

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  1. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
    [CrossRef]
  2. X. Yi, N. K. Fontaine, R. P. Scott, and S. J. B. Yoo, “Tb/s coherent optical OFDM systems enabled by optical frequency combs,” J. Lightwave Technol.28(14), 2054–2061 (2010).
    [CrossRef]
  3. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008).
    [CrossRef] [PubMed]
  4. C. Chen, Q. Zhuge, and D. V. Plant, “Zero-guard-interval coherent optical OFDM with overlapped frequency-domain CD and PMD equalization,” Opt. Express19(8), 7451–7467 (2011).
    [CrossRef] [PubMed]
  5. A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39.
  6. W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express16, 6378–6386 (2008).
    [CrossRef] [PubMed]
  7. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express14(9), 3767–3775 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008).
    [CrossRef] [PubMed]
  15. H. Sun, K. T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express16(2), 873–879 (2008).
    [CrossRef] [PubMed]
  16. K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express19(10), 9868–9880 (2011).
    [CrossRef] [PubMed]
  17. Y. Mori, C. Zhang, and K. Kikuchi, “Novel FIR-Filter Configuration Tolerant to Fast Phase Fluctuations in Digital Coherent Receivers for Higher-Order QAM Signals.” in Proc. OFC 2012, paper OTh4C.4.
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    [CrossRef]
  19. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express18(17), 17928–17939 (2010).
    [CrossRef] [PubMed]
  20. X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett.19(12), 919–921 (2007).
    [CrossRef]
  21. H. Kogelnik, at al. “Polarization-Mode Dispersion”, Optical Fiber Telecommunications IV B, I. Kaminow, T. Li, 725–861, Elsevier Science (USA), San Diego, CA, 2002.
  22. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach, (John Wiley & Sons, 1998), Chap. 4.
  23. G. H. Golub and C. Reinsch, “Singular Value Decomposition and Least Squares Solution,” Numer. Math.14(5), 403–420 (1970).
    [CrossRef]

2011

2010

2009

2008

2007

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett.19(12), 919–921 (2007).
[CrossRef]

2006

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express14(9), 3767–3775 (2006).
[CrossRef] [PubMed]

1970

G. H. Golub and C. Reinsch, “Singular Value Decomposition and Least Squares Solution,” Numer. Math.14(5), 403–420 (1970).
[CrossRef]

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

Bao, H.

Barros, D. J. F.

Buchali, F.

Chen, C.

Djordjevic, I. B.

Fontaine, N. K.

Golub, G. H.

G. H. Golub and C. Reinsch, “Singular Value Decomposition and Least Squares Solution,” Numer. Math.14(5), 403–420 (1970).
[CrossRef]

Ip, E.

Jansen, S. L.

Kahn, J. M.

Kikuchi, K.

Lau, A. P. T.

Liu, X.

Lowery, A. J.

Ma, Y.

Marshall, T.

Morita, I.

Nebendahl, B.

Plant, D. V.

Reinsch, C.

G. H. Golub and C. Reinsch, “Singular Value Decomposition and Least Squares Solution,” Numer. Math.14(5), 403–420 (1970).
[CrossRef]

Roberts, K.

Savory, S. J.

Schenk, T. C.

Schenk, T. C. W.

Scott, R. P.

Shieh, W.

Sun, H.

Szafraniec, B.

Tanaka, H.

Tang, Y.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express16(2), 841–859 (2008).
[CrossRef] [PubMed]

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett.19(12), 919–921 (2007).
[CrossRef]

Vasic, B.

Wu, K. T.

Yang, Q.

Yi, X.

Yoo, S. J. B.

Zhuge, Q.

Electron. Lett.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett.19(12), 919–921 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Netw.

Numer. Math.

G. H. Golub and C. Reinsch, “Singular Value Decomposition and Least Squares Solution,” Numer. Math.14(5), 403–420 (1970).
[CrossRef]

Opt. Express

I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express14(9), 3767–3775 (2006).
[CrossRef] [PubMed]

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008).
[CrossRef] [PubMed]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008).
[CrossRef] [PubMed]

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express16(2), 841–859 (2008).
[CrossRef] [PubMed]

A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express16(2), 860–865 (2008).
[CrossRef] [PubMed]

H. Sun, K. T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express16(2), 873–879 (2008).
[CrossRef] [PubMed]

W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express16, 6378–6386 (2008).
[CrossRef] [PubMed]

X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008).
[CrossRef] [PubMed]

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express18(17), 17928–17939 (2010).
[CrossRef] [PubMed]

C. Chen, Q. Zhuge, and D. V. Plant, “Zero-guard-interval coherent optical OFDM with overlapped frequency-domain CD and PMD equalization,” Opt. Express19(8), 7451–7467 (2011).
[CrossRef] [PubMed]

K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Express19(10), 9868–9880 (2011).
[CrossRef] [PubMed]

Other

H. Kogelnik, at al. “Polarization-Mode Dispersion”, Optical Fiber Telecommunications IV B, I. Kaminow, T. Li, 725–861, Elsevier Science (USA), San Diego, CA, 2002.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach, (John Wiley & Sons, 1998), Chap. 4.

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka; “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation,” OFC’07, post-deadline paper PDP15

A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39.

Y. Mori, C. Zhang, and K. Kikuchi, “Novel FIR-Filter Configuration Tolerant to Fast Phase Fluctuations in Digital Coherent Receivers for Higher-Order QAM Signals.” in Proc. OFC 2012, paper OTh4C.4.

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Figures (3)

Fig. 1
Fig. 1

Stokes vectors in Poincare sphere of one OFDM subcarrier with 4QAM modulation (a) before SS-PDM and (b) after SS-PDM; Constellations of one OFDM subcarrier (c) before and (d) after SS-PDM, and(c) after channel compensation and phase noise compensation, respectively.

Fig. 2
Fig. 2

Experimental setup. PBS/C: Polarization beam splitter/combiner; ECL: External cavity laser; SW: switch; OTF: optical tunable filter.

Fig. 3
Fig. 3

(a) BER results of 66.7-Gb/s TS-PDM-OFDM and SS-PDM-OFDM with 4QAM subcarrier modulation; (b) and (c) Constellations after transmission over 5440km with 4QAM subcarrier modulation vs. OSNR 18.42dB; (d) BER results of 133.3-Gb/s TS-PDM-OFDM and SS-PDM-OFDM with 16QAM subcarrier modulation; (e) and (f) Constellations after transmission over 960km with 16QAM subcarrier modulation vs. OSNR 23.82dB.

Equations (5)

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

s ki r =exp(j ϕ i )exp(j Φ k ) M k s ki t + n ki .
M(k)=( a(k) b(k) b * (k) a * (k) ).
S=( s 0 s 1 s 2 s 3 )= 1 2 ( s x s x * + s y s y * s x s x * s y s y * s x * s y + s x s y * j s x * s y +j s x s y * ).
M 1 =( cos(α/2)exp(jΔϕ/2) sin(α/2)exp(jΔϕ/2) sin(α/2)exp(jΔϕ/2) cos(α/2)exp(jΔϕ/2) ).
s ^ ki t =exp(j ϕ ^ i )exp(j Φ ^ k ) M k 1 s ki r .

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