Abstract

The ultimate limits introduced by polarization dependent loss (PDL) in coherent polarization multiplexed systems using advanced signal processing are studied. An analytical framework for effectively assessing the penalties is established and applied to systems with and without dynamically optimized launch polarization control. In systems with no launch polarization control, the PDL induced penalty is described by a simple formula and it is independent of the choice of constellation, or modulation format. The gain from optimizing launch polarizations is studied numerically and the mechanisms limiting it are described.

© 2008 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. 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).
  3. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O�??Sullivan, "WDM Performance and PMD Tolerance of a Coherent 40-Gbit/s Dual-Polarization QPSK Transceiver," J. Lightwave Technol. 26, 168-175 (2008).
    [CrossRef]
  4. 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]
  5. 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. 221856-1871 (2004).
    [CrossRef]
  6. M. Shtaif and A. Mecozzi, "Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems," IEEE Photon. Technol. Lett. 16, 671-673 (2004).
    [CrossRef]
  7. I.T. Lima, A.O Lima,Yu Sun, Hua Jiao,J. Zweck, C.R. Menyuk, G.M. Carter,"A receiver model for optical fiber communication systems with arbitrarily polarized noise," J. Lightwave Technol. 23, 1478-1490 (2004).
    [CrossRef]
  8. A. Mecozzi and M. Shtaif, "The statistics of polarization dependent loss in optical communication systems," IEEE Photon. Technol. Lett. 14, 313-315 (2002).
    [CrossRef]
  9. J. P. Gordon and H. Kogelnik, "PMD fundamentals," Proc. Natl. Acad. Sci. 97, 4541-4550 (2000).
    [CrossRef] [PubMed]
  10. A. Galtarossa and L. Palmieri, "Spatially Resolved PMD Measurements," J. Lightwave Technol. 22, 1103-1105 (2004).
    [CrossRef]
  11. Q1. B. Huttner, C. Geiser, and N. Gisin, Polarization-induced distortions in optical fiber networks with polarizationmode dispersion and polarization-dependent losses," IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
    [CrossRef]
  12. This is what happens when each channel passes through different optical routes before being multiplexed into the transmission fiber.

2008 (3)

2004 (4)

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]

2000 (2)

J. P. Gordon and H. Kogelnik, "PMD fundamentals," Proc. Natl. Acad. Sci. 97, 4541-4550 (2000).
[CrossRef] [PubMed]

Q1. B. Huttner, C. Geiser, and N. Gisin, Polarization-induced distortions in optical fiber networks with polarizationmode dispersion and polarization-dependent losses," IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
[CrossRef]

Bigo, S.

Carter, G.M.

Charlet, G.

Galtarossa, A.

Geiser, C.

Q1. B. Huttner, C. Geiser, and N. Gisin, Polarization-induced distortions in optical fiber networks with polarizationmode dispersion and polarization-dependent losses," IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
[CrossRef]

Gisin, N.

Q1. B. Huttner, C. Geiser, and N. Gisin, Polarization-induced distortions in optical fiber networks with polarizationmode dispersion and polarization-dependent losses," IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, "PMD fundamentals," Proc. Natl. Acad. Sci. 97, 4541-4550 (2000).
[CrossRef] [PubMed]

Huttner, B.

Q1. B. Huttner, C. Geiser, and N. Gisin, Polarization-induced distortions in optical fiber networks with polarizationmode dispersion and polarization-dependent losses," IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
[CrossRef]

Jiao, Hua

Kogelnik, H.

J. P. Gordon and H. Kogelnik, "PMD fundamentals," Proc. Natl. Acad. Sci. 97, 4541-4550 (2000).
[CrossRef] [PubMed]

Laperle, C.

Lima, A.O

Lima, I.T.

Mardoyan, H.

McGhan, D.

Meccozzi, A.

Mecozzi, A.

M. Shtaif and A. Mecozzi, "Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems," IEEE Photon. Technol. Lett. 16, 671-673 (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]

Menyuk, C.R.

O???Sullivan, M.

Palmieri, L.

Pardo, O.B.

Renaudier, J.

Roberts, K.

Salsi, M.

Shtaif, M.

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. 221856-1871 (2004).
[CrossRef]

M. Shtaif and A. Mecozzi, "Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems," IEEE Photon. Technol. Lett. 16, 671-673 (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]

Sun, H.

Sun, Yu

Tran, P.

Villeneuve, B.

Wu, K.-T.

Zhang, Z.

Zweck, J.

IEEE J. Sel. Top. Quantum Electron. (1)

Q1. B. Huttner, C. Geiser, and N. Gisin, Polarization-induced distortions in optical fiber networks with polarizationmode dispersion and polarization-dependent losses," IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Shtaif and A. Mecozzi, "Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems," IEEE Photon. Technol. Lett. 16, 671-673 (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]

J. Lightwave Technol. (5)

Opt. Express (1)

Proc. Natl. Acad. Sci. (1)

J. P. Gordon and H. Kogelnik, "PMD fundamentals," Proc. Natl. Acad. Sci. 97, 4541-4550 (2000).
[CrossRef] [PubMed]

Other (2)

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).

This is what happens when each channel passes through different optical routes before being multiplexed into the transmission fiber.

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Figures (4)

Fig. 1.
Fig. 1.

The assumed set-up and definition of indices.

Fig. 2.
Fig. 2.

(a) Probability density functions of η SNR . (b) The cumulated probability distributions. The solid curve represents the analytical result (16).

Fig. 3.
Fig. 3.

(a) Cumulated probability curves for two choices of Δ ^ in . In the curves labelled “choice 1”, Δ ^ in is orthogonal to the plain containing Γ⃗0 and Γ⃗† and in the curves labelled “choice 2” it is in that plane, but orthogonal to their difference. The mean PDL is 4dB. Figure (b) corresponds to only the first choice of Δ ^ in and shows results obtained with several PDL values. The dashed curves were obtained by neglecting pairs of constellation points differing in both polarizations.

Fig. 4.
Fig. 4.

(a) Allowed mean PDL for a specified system margin and for an outage probability of 4×10-5. The bottom curve is both analytical (Eq. (17)) and numerical (circles). The top two curves are numerical. (b) Comparison between the cumulated distribution of ηSNR corresponding to Q-PSK and to 8-PSK with optimized state launch.

Equations (19)

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s 1 ( t ) = ξ k a 1 ( k ) f ( t k T ) , and s 2 ( t ) = ξ e i Δ φ k a 2 ( k ) f ( t + Δ t k T )
( r 1 ( t ) r 2 ( t ) ) = T 0 ( s 1 ( t ) s 2 ( t ) ) + j = 1 N s T j ( n 1 ( j ) ( t ) n 2 ( j ) ( t ) )
( r 1 r 2 ) = η ξ T 0 ( a 1 e i Δ φ a 2 ) + j = 1 N s T j ( n 1 ( j ) n 2 ( j ) )
r = η ξ T 0 u + j = 1 N s T j n ( j )
Λ n = P n 2 N s j = 1 N s ( g j ( 0 ) + g j · σ ) = P n 2 g ( I + Γ · σ )
U Λ n U = P n 2 g ( 1 + Γ 0 0 1 Γ ) = P n 2 g ( I + Γ σ 1 ) .
r = 2 P n g ( 1 Γ 2 ) I Γ ' σ 1 U r
= 2 η ξ P n g ( 1 Γ 2 ) I Γ ' σ 1 U T 0 u + n
Δ r 2 = 2 η ξ P n g ( 1 Γ 2 ) Δ u T 0 U ( I Γ σ 1 ) U T 0 Δ u
Δ r 2 = 2 η ξ Δ in P n g 0 ( 1 + Γ 0 · Δ in ) Γ · Δ out Δ in g ( 1 Γ ' 2 )
η r Δ r 2 Δ r 0 2 = g 0 g ( 1 + Γ 0 · Δ in ) ( 1 Γ · Δ out ) 1 Γ 2 .
α 2 = 9 2 N s ln ( 2 9 γ 2 ρ 2 + 1 ) ρ 64 N s
η r 1 + ( Γ 0 Γ ) · Δ ̂ in Γ 0 · Γ + Γ 2 + O ( Γ 3 )
Γ 1 N s j = 1 N s 1 j α j
m r = 1 Γ 0 · Γ + Γ 2 = 1 N s 2 1 6 N s α j 2
σ r 2 = ( Γ 0 Γ ) 2 = [ 1 + ( N s 1 ) ( 2 N s 1 ) 6 N s ] α j 2 3
f η SNR ( η ) { 2 π σ r 2 e ( m r η ) 2 2 σ r 2 , η m r 1 0 η > m r .
M r = 10 log 10 [ m r σ r Q 1 ( P outage 2 ) ]
η SNR = min { η r ( Δ ̂ in = ± S ̂ 1 ) , 2 η r ( Δ ̂ in ( θ ) ) }

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