Abstract

Two-dimensional statistics and Q-penalty performance under the combination of two major impairments induced by polarization-dependent loss, namely level imbalance and loss of orthogonality between polarization-multiplexed tributaries, for a polarization-division-multiplexing digital coherent transmission at over 100-Gb/s are presented for the first time to estimate the outage probability needed for designing the system.

© 2011 OSA

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References

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  1. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008).
    [Crossref] [PubMed]
  2. L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OFC/NFOEC, OMT2 (2009).
  3. C. Xie and S. Chandrasekhar, “Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver,” OFC/NFOEC, OMK (2010).
  4. Y. Fukada, “Probability density function of polarization dependent loss (PDL) in optical transmission system composed of passive devices and connecting fibers,” J. Lightwave Technol. 20(6), 953–964 (2002).
    [Crossref]
  5. ITU-T Recommendation G.680, “Physical transfer function of optical network elements,” July 2007.
  6. A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002).
    [Crossref]
  7. T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” OFC/NFOEC OThU5 (2008).
  8. K. Mori, S. Kawai, and T. Kataoka, “Statistical investigation of polarization-dependent loss for polarization-division-multiplexing digital coherent transmission,” IEICE Technical Report OCS 2011.
  9. T. Kobayashi, S. Yamanaka, H. Kawakami, S. Yamamoto, A. Sano, H. Kubota, A. Matsuura, E. Yamazaki, M. Ishikawa, K. Ishihara, T. Sakano, E. Yoshida, Y. Miyamoto, M. Tomizawa, and S. Matsuoka, “8-Tb/s (80x127Gb/s) DP-QPSK L-band DWDM transmission over 457-km installed DSF links with EDFA-only amplification,” OECC postdeadline paper PD2 (2010).

2008 (1)

2002 (2)

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002).
[Crossref]

Y. Fukada, “Probability density function of polarization dependent loss (PDL) in optical transmission system composed of passive devices and connecting fibers,” J. Lightwave Technol. 20(6), 953–964 (2002).
[Crossref]

Fukada, Y.

Mecozzi, A.

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002).
[Crossref]

Shtaif, M.

M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008).
[Crossref] [PubMed]

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (1)

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (1)

Other (6)

ITU-T Recommendation G.680, “Physical transfer function of optical network elements,” July 2007.

T. Duthel, C.R.S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” OFC/NFOEC OThU5 (2008).

K. Mori, S. Kawai, and T. Kataoka, “Statistical investigation of polarization-dependent loss for polarization-division-multiplexing digital coherent transmission,” IEICE Technical Report OCS 2011.

T. Kobayashi, S. Yamanaka, H. Kawakami, S. Yamamoto, A. Sano, H. Kubota, A. Matsuura, E. Yamazaki, M. Ishikawa, K. Ishihara, T. Sakano, E. Yoshida, Y. Miyamoto, M. Tomizawa, and S. Matsuoka, “8-Tb/s (80x127Gb/s) DP-QPSK L-band DWDM transmission over 457-km installed DSF links with EDFA-only amplification,” OECC postdeadline paper PD2 (2010).

L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” OFC/NFOEC, OMT2 (2009).

C. Xie and S. Chandrasekhar, “Two-stage constant modulus algorithm equalizer for singularity free operation and optical performance monitoring in optical coherent receiver,” OFC/NFOEC, OMK (2010).

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Figures (8)

Fig. 1
Fig. 1

Two types of transmission systems including PDL devices: (a) a single-polarization transmission and (b) a polarization-division multiplexing (PDM) transmission where Tmax and Tmin are the maximum and minimum transmission ratios, respectively, X' and Y' are the optical fields of the X- and Y-tributaries, respectively, and θ is their polarization angle after transmission. The models are used for performing numerical simulations in this paper.

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Fig. 2
Fig. 2

Histograms (blue dots) of the calculated (a) system PDL and (b) the level imbalance caused by PDL (LIP) where the device PDLs are set to 0.5 dB, and there are 20 spans, and 100,000 trials. The red curves are the fitting curves: (a) Maxwellian function and (b) Gaussian function. The horizontal axes are both in decibels.

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Fig. 3
Fig. 3

Histograms (blue dots) of (a) LOP (loss of orthogonality induced by PDL) and (b) PXP (polarization crosstalk induced by PDL) under the same conditions as in Fig. 1. The red curve in (b) is a fitting curve, which is a Rayleigh function.

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Fig. 4
Fig. 4

Two-dimensional histograms of LIP and LOP under various conditions where (a), (b) and (c) are for the same device PDL of 0.5 dB and spans of 5, 10, 20, respectively. (d), (e) and (f) are for 20 spans and different device PDLs of 0.2, 0.3 and 0.4 dB, respectively. There were 100,000 trials.

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Fig. 5
Fig. 5

Experimental setup for investigating Q-penalty vs. LIP and LOP where VOA: variable optical attenuator for setting LIP, PC1: polarization controller for setting LOP, CPL: optical coupler, PC2: polarization controller for scrambling polarization, ASE: optical noise source consisting of an erbium-doped fiber amplifier. PDM-QPSK-TX and -RX are a polarization-division-multiplexing QPSK transmitter and receiver, respectively.

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Fig. 6
Fig. 6

Contour maps of Q-penalty vs. LIP and LOP obtained from (a) experimental data and (b) numerical simulation data. The Q-penalty data were interpolated as a quadratic function of LIP and LOP to calculate the contours. The OSNR of the received signal was set at 18 dB.

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Fig. 7
Fig. 7

Calculation of outage probability for a given Q-penalty. The two-dimensional histogram over the LIP-LOP plane is bounded by an equi-Q-penalty curve (dashed curve) for a given Q-penalty obtained from the Q-penalty map in Fig. 6. The hatched area is an integral region over which the outage probability is calculated.

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Fig. 8
Fig. 8

Resulting outage probability vs. Q-penalty under various conditions: (a) for the same device PDL of 0.5 dB and spans of 5, 10 and 20. (b) for 20 spans and different device PDLs of 0.2, 0.3, 0.4 and 0.5 dB. The solid and dotted curves indicate the outage probabilities obtained with the Q-penalty maps of the experimental result (Fig. 6(a)) and the simulation result (Fig. 6(b)), respectively.

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Equations (3)

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LIP=|  20 log| E Y ′ / E X ′ |  |
LOP=90°−θ= sin −1 | E x' ⋅ E y' | | E x' || E y' |
PXP= | E x' ⋅ E y' | | E x' | 2 = | E y' | | E x' | sin LOP.

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