Abstract

We study the performance of a simple optical receiver for use with polarization multiplexed transmission in the presence of polarization dependent loss (PDL). The receiver is based upon filtering of each of the channels with a polarizer that is orthogonal to the other channel, such that interference due to loss of orthogonality is avoided at the expense of a reduction in the detected signal to noise ratio. In spite of its simplicity, this receiver is shown to perform almost as well as the optimal maximum likelihood receiver, and much better than receivers that are based on conventional polarization splitting.

© 2009 Optical Society of America

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  1. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, S. Bigo, "Linear Fiber Impairments Mitigation of 40-Gbit/s Polarization-Multiplexed QPSK by Digital Processing in a Coherent Receiver," J. Lightwave Technol. 26, 36-42 (2008).
    [CrossRef]
  2. H. Sun, K.-T. Wu, and K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Express 16, 873-879 (2008)
    [CrossRef] [PubMed]
  3. L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D, Hanson, D. McGhan, H. Sun, M. Moyer, M. O’Sullivan, "Performance of a 46Gbps dual polarization QPSK transceiver in a high-PMD fiber transmission experiment," Optical Fiber Communications Conference, Paper PDP9, OFC San Diego (2008).
  4. A. Meccozzi and M. Shtaif, "Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization," J. Lightwave Technol. 22,1856-1871 (2004).
    [CrossRef]
  5. C. Xie and L. F. Mollenauer, "Performance degradation induced by polarization dependent loss in optical fiber transmission systems with and without polarization mode dispersion," J. Lightwave Technol. 21, 1953-1957 (2003).
    [CrossRef]
  6. T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, "Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK, Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).
  7. M. Shtaif, "Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss," Opt. Express. 16, 13918-13932 (2008).
    [CrossRef] [PubMed]
  8. M. Yoshida, H. Goto, K. Kasai, and M. Nakazawa, "64 and 128 coherent QAM optical transmission over 150 km using frequency-stabilized laser and heterodyne PLL detection," Opt. Express 16, 829-840 (2008).
    [CrossRef] [PubMed]
  9. A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
    [CrossRef]
  10. Z. Wang and C. Xie, "PMD and PDL Tolerance of Polarization Division Multiplexed Signals with Direct Detection," European Conf. on Opt. Comm. Paper We.3.E.2, ECOC 2008, Brussels, Belgium
  11. S. J. Savory, "Digital filters for coherent optical receivers," Opt. Express 16, 804-817 (2008).
    [CrossRef] [PubMed]
  12. A. Mecozzi and M. Shtaif, "The statistics of polarization dependent loss in optical communication systems," IEEE Photon. Technol. Lett. 14, 313-315 (2002).
    [CrossRef]
  13. The term (1−g′) was omitted mistakenly from the optimal detection case in [7]. Since its average is 0 (see appendix A), it does not affect the final result

2008 (5)

2004 (1)

2003 (1)

2002 (1)

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

1996 (1)

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Bigo, S.

Charlet, G.

Chraplyvy, A. R.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Derosier, R. M.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Forghieri, F.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Gnauck, A. H.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Goto, H.

Jopson, R. M.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Kasai, K.

Lucero, A. J.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Mardoyan, H.

McCormick, A. R.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Meccozzi, A.

Mecozzi, A.

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

Mollenauer, L. F.

Nakazawa, M.

Pardo, O. B.

Renaudier, J.

Roberts, K.

Salsi, M.

Savory, S. J.

Shtaif, M.

M. Shtaif, "Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss," Opt. Express. 16, 13918-13932 (2008).
[CrossRef] [PubMed]

A. Meccozzi and M. Shtaif, "Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization," J. Lightwave Technol. 22,1856-1871 (2004).
[CrossRef]

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

Sulhoff, J. W.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Sun, H.

Sun, Y.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Tkach, R.W.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Tran, P.

Wolf, C.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

Wu, K.-T.

Xie, C.

Yoshida, M.

Zyskind, J. L.

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. R. Chraplyvy, A. H. Gnauck, R.W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, A. R. McCormick, "1-Tb/s transmission experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

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

J. Lightwave Technol. (3)

Opt. Express (3)

Opt. Express. (1)

M. Shtaif, "Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss," Opt. Express. 16, 13918-13932 (2008).
[CrossRef] [PubMed]

Other (4)

The term (1−g′) was omitted mistakenly from the optimal detection case in [7]. Since its average is 0 (see appendix A), it does not affect the final result

Z. Wang and C. Xie, "PMD and PDL Tolerance of Polarization Division Multiplexed Signals with Direct Detection," European Conf. on Opt. Comm. Paper We.3.E.2, ECOC 2008, Brussels, Belgium

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D, Hanson, D. McGhan, H. Sun, M. Moyer, M. O’Sullivan, "Performance of a 46Gbps dual polarization QPSK transceiver in a high-PMD fiber transmission experiment," Optical Fiber Communications Conference, Paper PDP9, OFC San Diego (2008).

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, "Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK, Optical Fiber Communications conference, Paper OThU5, OFC San Diego (2008).

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Figures (3)

Fig. 1
Fig. 1

The studied set-up. The polarizers (marked as “pol.”) are oriented so as to remove interference.

Fig. 2
Fig. 2

(a) Cumulative distributions of η for 3 values of average PDL. Blue diamonds represent the 2-polarizers configuration and the red circles show the optimal receiver case [7]. Solid curves represents the analytical expressions (b) Tolerable average PDL as a function of assigned system margin for 2-pol. configuration and for the brute-force method. Solid blue is the analytical result (11) and solid red is the result with an optimal receiver [7].

Fig. 3
Fig. 3

The cumulative distribution of the equivalent SNR penalty η for the 2-polarizers scheme of Fig. 1 and for brute force detection with 2-PSK and QPSK modulation. Figures (a) and (b) correspond to average PDL values of 1dB and 2dB, respectively.

Equations (26)

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s_(t)=ξ(e_1kak,1f(tkT)+e_2kak,2f(tkT)).
r_(t)=T0s_(t)+j=1NsTjn_(j)(t)
e_1,out=T0e_1e_1T0T0e_1ande_2,out=T0e_2e_2T0T0e_2,
rk,i=ξκ(p_iT0e_i)ak,i+p_ij=1NsTjn_(j)
Λn=Pn2g(1+Γσ)
n˜_Λn1/2p_ip_iΛn1/2n˜_=Pn2g(1+Γp^i)
r˜_=a˜_+n˜_
a˜i=2ξκPn(p_iT0e_ig(1+Γ.p^i))ai,
ηj=g0g(1+Γ0e^j)(1+p^je^j,out)2(1+Γp^j)=g0g1Γ02(1Γ0e^j)(1+Γp^j)
ηi1+(ΓΓ0)e^iΓ0Γ+Γ2((ΓΓ0))2+(1g)+O(Γ3)
fηSNR(η){2πσr2e(mrη)22σr2,ηmr10η>mr.
mr=17Ns2+6Ns118Ns|α|2
σr2=[1+(Ns1)(2Ns1)6Ns]|α|23
|α|2=92Nsln(πln2(10)4800ρ2+1)ρ264Ns
p^=e^1,oute^2,out2(1e^1,oute^2,out).
r˜j=a˜j+b˜j+n˜j=a˜j(1+b˜ja˜j)+n˜j
b˜1a˜1=(1Γ0e^11+Γ0e^1)1/2Γ01(Γ0e^1)2+1Γ02(a2a1)eiΔϕ
e^j,out=e^j+Γ0+O(Γ02)
ηj1+Γ0e^j+(Γ0e^j)2Γe^j+ΓΓ0Γ0e^jΓe^j+(Γe^j)2Γ02+(1g)=1+(Γ0Γ)e^jΓ.Γ0+Γ2((Γ0Γ))2+(1g).
Λn=Pn2Nsj=1NsTjTj=Pn2Nsj=1Ns(gj(0)+gjσ)
gj(0)=12Trace(TjTj)=12Trace(Jj1T0T0Jj1)=12Trace[(JjJj)1T0T0].
(JjJj)1T0T0=11Γj2(1Γjσ)(1+Γ0σ)
gj(0)=12Trace(TjTj)=1ΓjΓ01Γj21Γj(Γ0Γj)+O(Γ4).
1g=11Nsj=1Nsgj(0)=1Nsj=1NsΓj(Γ0Γj)
Λn1/2=Pn2g1+Γσ=Pn2g(1+Γ+1Γ2+Γσ1+Γ+1Γ)=Pn2gl(1+qσ),
n˜_Λn1/2p_1p_1Λn1/2n˜_=12n_˜Λn1/2(1+p^1σ)Λn1/2n˜_=gPn4l2n_˜(1+qσ)(1+p^σ)(1+qσ)n˜_=gPn2l2(1+2qp^1+q2)=gPn2(1+Γp^1),

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