Abstract

We show that polarization modulated and polarization multiplexed transmission may be significantly impaired by the polarization scattering induced by intra-channel cross-phase modulation and four-wave mixing. In polarization multiplexed transmission, channel interleaving may be used to mitigate the effect when two-pulse collisions are dominant.

© 2011 OSA

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References

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  1. L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton-soliton collisions,” Opt. Lett. 20, 2060–2062 (1995).
    [CrossRef] [PubMed]
  2. A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
    [CrossRef]
  3. D. Marcuse, C. R. Menyuk, and P. K. A. Wai“Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
    [CrossRef]
  4. J. P. Gordon and H. Kogelnik“PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA97, 4541–4550 (2000).
    [CrossRef] [PubMed]

2011

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
[CrossRef]

1997

D. Marcuse, C. R. Menyuk, and P. K. A. Wai“Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

1995

Gordon, J. P.

L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton-soliton collisions,” Opt. Lett. 20, 2060–2062 (1995).
[CrossRef] [PubMed]

J. P. Gordon and H. Kogelnik“PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA97, 4541–4550 (2000).
[CrossRef] [PubMed]

Heismann, F.

Kogelnik, H.

J. P. Gordon and H. Kogelnik“PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA97, 4541–4550 (2000).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai“Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

Matera, F.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
[CrossRef]

Mecozzi, A.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
[CrossRef]

Menyuk, C. R.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai“Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

Mollenauer, L. F.

Settembre, M.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
[CrossRef]

Tabacchiera, M.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
[CrossRef]

Wai, P. K. A.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai“Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

J. Lightwave Technol.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai“Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

Opt. Expr.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Expr. 19, 3990–3995 (2011).
[CrossRef]

Opt. Lett.

Other

J. P. Gordon and H. Kogelnik“PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA97, 4541–4550 (2000).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Depolarization on the Poincaré sphere when two-pulse collisions are dominant, for 3 dBm (plot a), 7 dBm (plot b) and 13 dBm (plot c) average input power (per polarization).

Fig. 2
Fig. 2

a) Standard deviation of the first component of the Stokes vector, 〈[Δs⃗0(L) · e⃗1]21/2, for 7 dBm input power, vs. the pre-compensated length of fiber. Red dot-dashed curve: two-pulse collisions only; purple dashed curve, four pulse collisions only; blue solid curve, complete polarization jitter. The purple curve is also the standard deviation of the third component of the Stokes vector, 〈[Δs0(L) · e3]21/2, because the two-pulse contribution does not give fluctuations along e⃗3. b) Standard deviation of the first component of the Stokes vector, [ Δ s 0 ( L ) e 1 ] 2 2 pulse 1 / 2, for 3 dBm (lower solid curve and triangles), 7 dBm (intermediate solid curve and squares), and 13 dBm (upper solid curve and circles) average input power, vs. the dispersion pre-compensation z* in km of precompensated fiber, with no interleaving. Scattered symbols are the results of simulations, solid lines the prediction of the theory. In the three lower curves, dotted lines connect the results of simulations with channel interleaving under the same conditions of the solid lines.

Equations (11)

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E z = i β 2 2 E t 2 + i 8 9 γ f ( z ) ( E E ) E .
E 0 z = i β 2 2 E 0 t 2 + i 8 9 γ f ( z ) k = j + l , j , l E k E j E l ,
d d z [ d t | E 0 | 2 s 0 ( z , t ) ] = d t 2 Re [ i β 2 E 0 σ 2 E 0 t 2 + i 8 9 γ f ( z ) j , l ( E 0 σ E l ) ( E j + l E j ) ] .
d d z [ d t | E 0 | 2 s 0 ( z , t ) ] = 8 9 γ f ( z ) d t Re [ 2 i j , l E 0 * E j + l * E l E j s 0 | σ | s l s j + l | s j ] .
d s 0 ( z ) d z + s 0 d ln U 0 ( z ) d z = 8 9 γ f ( z ) Re [ 2 i j , l ( 1 U 0 d t E 0 * E j + l * E l E j s 0 | σ | s l s j + l | s j ) ] .
d s 0 ( z ) d z + s 0 d ln U 0 ( z ) d z = 8 9 γ f ( z ) l ( 1 U 0 d t | E l | 2 | E 0 | 2 ) s l × s 0 .
d s 0 ( z ) d z + s 0 d ln U 0 d z = 8 9 γ f ( z ) 2 π τ 2 j , l A j + l A l A j A 0 Re [ 2 i G ( T l , T j , z ) s 0 | σ | s l s j + l | s j ] ,
d s 0 ( z ) d z + s 0 d ln U 0 d z = 8 9 γ f ( z ) 2 π τ 2 l A l 2 G ( l T , 0 , z ) s l × s 0 ,
G ( T 1 , T 2 ; z ) = 1 2 π τ 2 1 ρ 2 ( z ) exp { T 1 2 + T 2 2 + 2 ρ ( z ) T 1 T 2 2 τ 2 [ 1 ρ 2 ( z ) ] } .
[ Δ s 0 ( z ) e 1 ] 2 2 pulse = ( 8 9 γ π A 2 τ 2 ) 2 l 0 [ 0 z d z f ( z ) G ( l T , 0 , z ) ] 2 ,
[ Δ s 0 ( z ) e 1 , 3 ] 2 4 pulse = ( 8 9 γ π A 2 τ 2 ) 2 k = j + l , j 0 , l 0 | 0 z d z f ( z ) G ( T l , T j , z ) | 2 .

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