Abstract

We study long-haul Quasi-Single-mode (QSM) systems in which signals are transmitted in the fundamental modes of a few-mode fiber (FMF) while keeping other system components such as amplifiers and receivers are kept single-moded. The large-effective-area nature of the FMF fundamental modes improves system nonlinear tolerance in the expense of mode coupling along FMF transmissions which induces multi-path interference (MPI) and needs to be compensated. We analytically investigate 6-spatial-polarization mode QSM transmission systems in presence of MPI and show that in the weak coupling regime, the QSM channel is a Gaussian random process in frequency. MPI compensation filters are derived and performance penalties due to MPI and signal loss from higher-order modes are characterized. We also experimentally demonstrate 256 Gb/s polarization multiplexed (PM)-16-QAM QSM transmissions over a record distance of 2600 km with 100-km span using decision directed least mean square (DD-LMS) algorithm for MPI compensation.

© 2015 Optical Society of America

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References

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    [Crossref]
  10. J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems,” Proceedings of ECOC 2011, Paper Tu.5.B.2 (2011).
    [Crossref]
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    [Crossref]
  12. P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
    [Crossref]
  13. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
    [Crossref]
  14. F. M. Gardner, “A BPSK/QPSK Timing-Error Detector for Sampled Receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
    [Crossref]
  15. A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
    [Crossref]
  16. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
    [Crossref]
  17. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
    [Crossref]

2012 (2)

2011 (1)

2010 (3)

2008 (1)

2007 (1)

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

1997 (1)

D. Marcuse, C. R. Manyuk, 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(9), 1735–1746 (1997).
[Crossref]

1996 (2)

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

1986 (1)

F. M. Gardner, “A BPSK/QPSK Timing-Error Detector for Sampled Receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
[Crossref]

Bai, N.

Bolle, C.

Burrows, E. C.

Chen, Y.-K.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Corless, R. M.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

Downie, J. D.

Esmaeelpour, M.

Essiambre, R.-J.

Gardner, F. M.

F. M. Gardner, “A BPSK/QPSK Timing-Error Detector for Sampled Receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
[Crossref]

Gnauck, A. H.

Gonnet, G. H.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

Hare, D. E. G.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

Huang, M. F.

Huang, Y. K.

Hurley, J. E.

Ip, E.

Jeffrey, D. J.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

Kahn, J. M.

Kaneda, N.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Knuth, D. E.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

Koc, U.-V.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Korolev, A. E.

Kuksenkov, D. V.

Leven, A.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

Li, G.

Lingle, R.

Lynn, C. M.

Manyuk, C. R.

D. Marcuse, C. R. Manyuk, 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(9), 1735–1746 (1997).
[Crossref]

Marcuse, D.

D. Marcuse, C. R. Manyuk, 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(9), 1735–1746 (1997).
[Crossref]

McCurdy, A. H.

Menyak, C. R.

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Mumtaz, S.

Nazarov, V. N.

Peckham, D. W.

Randel, S.

Ryf, R.

Sierra, A.

Wai, P. K. A.

D. Marcuse, C. R. Manyuk, 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(9), 1735–1746 (1997).
[Crossref]

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Wang, T.

Winzer, P. J.

Xia, C.

Yaman, F.

Zhou, X.

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
[Crossref]

Zhu, B.

Adv. Comput. Math. (1)

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5(1), 329–359 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[Crossref]

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
[Crossref]

IEEE Trans. Commun. (1)

F. M. Gardner, “A BPSK/QPSK Timing-Error Detector for Sampled Receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
[Crossref]

J. Lightwave Technol. (4)

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
[Crossref]

D. Marcuse, C. R. Manyuk, 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(9), 1735–1746 (1997).
[Crossref]

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Opt. Express (4)

Other (5)

Q. Sui, H. Zhang, J. D. Downie, W. A. Wood, J. Hurley, S. Mishra, A. P. T. Lau, C. Lu, H.-Y. Tam, and P. K. A. Wai, “256 Gb/s PM-16-QAM Quasi-Single-Mode Transmission over 2600 km using Few-Mode Fiber with Multi-Path Interference Compensation,” in Proc. Opt. Fiber Commun. Conf. (OFC)2014, paper M3C.5.

A. P. T. Lau, Q. Sui, H. Y. Tam, C. Lu, P. K. A. Wai, J. D. Downie, W. A. Wood, J. Hurley, and S. Mishra, “Long-haul Quasi-Single-Mode Transmission using Few-Mode Fiber with Multi-Path Interference Compensation” in Proc. of International Conference on Optical Internet (COIN)2014, paper FB3–1.
[Crossref]

F. Yaman, E. Mateo, and T. Wang, “Impact of Modal Crosstalk and Multi-Path Interference on Few-Mode Fiber Transmission,” in Proc. Opt. Fiber Commun. Conf. (OFC) 2012, paper OTu1D.2.
[Crossref]

J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems,” Proceedings of ECOC 2011, Paper Tu.5.B.2 (2011).
[Crossref]

S. Randel, “Space Division Multiplexed Transmission,” in Proc. Opt. Fiber Commun. Conf. (OFC) 2013, paper OW4F.

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Figures (12)

Fig. 1
Fig. 1 The 2-mode coupling model for one span of QSM transmission.
Fig. 2
Fig. 2 Theoretical and simulation results for (a) Expected impulse response power E[ | h xx(yy) (t) | 2 ] and (b) pdf of transfer function Hxx(yy)(ω) for a 32 Gbaud polarization-multiplexed QSM system. The link consists of 20 spans of 100-km fiber with κL = 0.1, DMD Δτ = 1.28 ns/km and ∆α = 0.1 dB/km.
Fig. 3
Fig. 3 The MPI length τMPI for various DMD Δτ and DML Δα for a 32 Gbaud polarization-multiplexed QSM transmission system.
Fig. 4
Fig. 4 (a) A sample realization of Hxx/yy(ω) and (b) pdf of the amplitude |Hxx/yy(ω)| for a 20-span QSM system with 100-km span length, κL = 0.1, Δα = 1 dB/km and ∆τ = 1.28 ns/km.
Fig. 5
Fig. 5 Q vs. OSNR for 32Gbaud-PM-16-QAM transmissions with and without MPI compensation for a 20-span QSM system with a random realization of the transfer function H(ω). The span length is 100 km, coupling strength κL = 0.1, DMD Δτ = 1.28 ns/km and DML Δα = 0.1 dB/km.
Fig. 6
Fig. 6 PDF of the overall performance gain Goverall of a 20-span QSM transmission system in presence of mode-coupling-induced penalties ΛMPI and ΛHOM and an effective area Aeff,FMF 2.5 times that of a standard single mode fiber. The span length is 100 km, DMD Δτ = 1.28 ns/km and the DML Δα = 0.5 dB/km.
Fig. 7
Fig. 7 Experimental setup for QSM transmission and MPI compensation. GEF: gain equalization filter; LSPS: loop synchronous polarization scrambler.
Fig. 8
Fig. 8 (a) Q vs. OSNR for segments of span no. 1 with different lengths in linear transmission. (b) Q vs. channel power of central channel for standard single mode fiber and QSM transmission over 600 km using DD-LMS for MPI compensation.
Fig. 9
Fig. 9 BER vs. number of taps of the DD-LMS filter used to compensate MPI for a single-span 50-km QSM link in which the relative symbol delay between the x- and y-polarization is 280 symbols. When the number of taps exceed 560, the DD-LMS double counts the signal and result in an abrupt BER reduction.
Fig. 10
Fig. 10 Q vs. distance at optimal launch power using DD-LMS for MPI compensation.
Fig. 11
Fig. 11 (a) Q vs. OSNR at optimal signal launched power with DD-LMS for QSM and standard fiber systems and (b) Q vs. distance at −1 and 3 dBm signal launched power with and without DD-LMS filter.
Fig. 12
Fig. 12 Estimated magnitude squared of self-polarization and cross polarization impulse responses for (a) 600, (b) 1200 and (c) 2400 km of QSM transmission in the presence of MPI.

Equations (35)

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E out (ω)=[ 1 0 ] k=1 K ( G(ω)R k )[ E in (ω) 0 ]
G(ω)=[ 1 0 0 e (jωΔτ+ 1 2 Δα)ΔL ]
R k =[ 1 η k η k e j θ k η k e j θ k 1 η k ]
H 1span (ω)=[ 1 0 ] k=1 K ( G(ω)R k )[ 1 0 ]
E[ | h 1span (t) | 2 ] F E[ H 1span * (ω') H 1span (ω'+ω) ].
E[ | h 1span (t) | 2 ]={ e κL δ(t)+ e κL κ 2 L Δτ e Δαt Δτ ( 1 t ΔτL ) E[ | h MPI,1span (t) | 2 ] , 0tΔτL 0 otherwise ,
h(t)=( δ(t)+ h MPI,1 (t) )( δ(t)+ h MPI,2 (t) )...( δ(t)+ h MPI,N (t) ) ( δ(t)+ n=1 N h MPI,n (t) )
E[ | h(t) | 2 ]δ(t)+ n=1 N E[ | h MPI,n (t) | 2 ] ={ δ(t)+ N κ 2 L Δτ e Δαt Δτ ( 1 t ΔτL ) E[ | h MPI (t) | 2 ] 0tΔτL 0 otherwise
P MPI = 0 ΔτL E[ | h MPI (t) | 2 ]dt =N κ 2 ΔαL+ e ΔαL 1 Δ α 2 .
[ E out,x (ω) E out,y (ω) ]=H(ω) E in (ω)+V(ω)=[ H xx (ω) H xy (ω) H yx (ω) H xx (ω) ][ E in,x (ω) E in,y (ω) ]+[ V x (ω) V y (ω) ],
E[ | h xx (t) | 2 ]=E[ | h yy (t) | 2 ]=δ(t)+ 1 4 E[ | h MPI (t) | 2 ]
E[ | h xy (t) | 2 ]=E[ | h yx (t) | 2 ]= 1 4 E[ | h MPI (t) | 2 ].
H xx(yy) ( ω )N( 1, 1 8 P MPI I ) and H xy(yx) ( ω )N( 0, 1 8 P MPI I ),
0 τ MPI | h MPI (t) | 2 dt= 0 τ MPI ( 1 t ΔτL ) e Δαt Δτ dt =0.99 0 ΔτL ( 1 t ΔτL ) e Δαt Δτ dt
τ MPI = Δτ Δα ( ΔαLW( ( 0.01( ΔαL1 )0.99 e ΔαL ) e ΔαL1 )1 ) ΔαL large Δτ Δα ln100
W( ω )= ( H ( ω )H( ω ) S S ( ω )+ N 0 I ) 1 H ( ω ) S S ( ω ),
[ R out,x (ω) R out,y (ω) ]=W(ω)H(ω) E in (ω)+W(ω)V(ω)=U(ω) E in (ω)+W(ω)V(ω)
Λ MPI = ( | u 12 ( ω ) | 2 + | u 21 ( ω ) | 2 ) S S ( ω )dω + ( | w 11 ( ω ) | 2 + | w 12 ( ω ) | 2 + | w 21 ( ω ) | 2 + | w 22 ( ω ) | 2 ) N 0 dω 2 N 0 dω ( | u 11 ( ω ) | 2 + | u 22 ( ω ) | 2 ) S S ( ω )dω
Λ HOM lim K k=1 K ( 1 η k )= e κL
G OSNR = A eff,FMF / A eff,Std.fiber .
G overall = G OSNR ( dB ) Λ MPI ( dB ) Λ HOM ( dB ).
E[ H 1span * (ω') H 1span (ω'+ω) ]=E[ [ 1 0 ] k=0 K1 ( R Kk * G * (ω') ) [ 1 0 0 0 ] k=1 K ( G(ω'+ω) R k ) [ 1 0 ] ].
E[ H 1span * (ω') H 1span (ω'+ω) ]=E[ [ 1 0 ] k=0 K2 R Kk * G * (ω') E[ R 1 * G * (ω')[ 1 0 0 0 ]G(ω'+ω) R 1 ] k=2 K G(ω'+ω) R k [ 1 0 ] ],
E[ R 1 * G * (ω')[ 1 0 0 0 ]G(ω'+ω) R 1 ]=E[ [ 1 η 1 η 1 (1 η 1 ) e j θ 1 η 1 (1 η 1 ) e j θ 1 η 1 ] ]=[ 1κΔL 0 0 κΔL ].
E[ R 2 * G * (ω') R 1 * G * (ω')[ 1 0 0 0 ]G(ω'+ω) R 1 G(ω'+ω) R 2 ] =E[ R 2 * G * (ω')[ 1κΔL 0 0 κΔL ]G(ω'+ω) R 2 ] . =[ (1κΔL) 2 + κ 2 Δ L 2 ξ 0 0 (1κΔL)κΔL( ξ+ ξ 2 ) ]
E[ R 3 * G * (ω') R 2 * G * (ω') R 1 * G * (ω')[ 1 0 0 0 ]G(ω'+ω) R 1 G(ω'+ω) R 2 G(ω'+ω) R 3 ] =[ (1κΔL) 3 +(1κΔL) κ 2 Δ L 2 (2ξ+ ξ 2 ) 0 0 (1κΔL)κΔL( ξ+ ξ 2 + ξ 3 ) ]
E[ k=0 K1 ( R Kk * G * (ω') ) [ 1 0 ][ 1 0 ] k=1 K ( G(ω'+ω) R k ) ] [ (1κΔL) K + (1κΔL) K2 κ 2 Δ L 2 p=1 K (Kp) ξ p 0 0 (1κΔL)κΔL p=1 K ξ p ]
E[ H 1span * (ω') H 1span (ω'+ω)]= (1κΔL) K + (1κΔL) K2 κ 2 Δ L 2 p=1 K (Kp) ξ p
E[ | h 1span (t) | 2 ]= (1κΔL) K ( δ(t)+ ( κΔL 1κΔL ) 2 p=1 K (Kp) e pΔαΔL δ(tpΔτΔL) ).
lim K E[ | h 1span (t) | 2 ]= e κL ( δ(t)+ κ 2 L Δτ e Δαt Δτ ( 1 t ΔτL ) ).
H 1span (ω)= k=1 K 1 η k + k=1 K 1 η k m=1 K1 l=1 Km η l η m+l (1 η l )(1 η m+l ) e mΔαΔL+j( θ m+l θ l +mΔτΔLω) = k=1 K 1 η k + k=1 K 1 η k m=1 K1 l=1 Km η l η m+l (1 η l )(1 η m+l ) e mΔαΔL+j q=l m+l1 x q ,
Var( H 1span (ω) )= E[ | h MPI,1span (t) | 2 ]dt = 1 N P MPI .
Y n = m=1 K1 l=1 Km η l η m+l (1 η l )(1 η m+l ) e mΔαΔL+j q=l m+l1 x q
H(ω)= n=1 N ( 1+ Y n ) ( 1+ n=1 N Y n ) N large N( 1, 1 2 P MPI I )
H xx(yy) ( ω )N( 1, 1 8 P MPI I ) and H xy(yx) ( ω )N( 0, 1 8 P MPI I )

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