Abstract

The equalizer tap length requirement is investigated analytically and numerically for differential modal group delay (DMGD) compensated fiber link with weakly random mode coupling. Each span of the DMGD compensated link comprises multiple pairs of fibers which have opposite signs of DMGD. The result reveals that under weak random mode coupling, the required tap length of the equalizer is proportional to modal group delay of a single DMGD compensated pair, instead of the total modal group delay (MGD) of the entire link. By using small DMGD compensation step sizes, the required tap length (RTL) can be potentially reduced by 2 orders of magnitude.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Bai, G. Li, “Adaptive frequency-domain equalization for mode-division multiplexed transmission,” Photonics Technology Letters 24(21), 1918–1921 (2012).
    [CrossRef]
  2. K. Ho, J. M. Kahn, “Statistics of group delays in multimode fiber with strong mode coupling,” J. Lightwave Technol. 29(21), 3119–3128 (2011).
    [CrossRef]
  3. F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
    [CrossRef]
  4. M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
    [CrossRef]
  5. T. Mori, T. Sakamoto, M. Wada, T. Yamamoto, and F. Yamamoto, “Low DMD Four LP Mode Transmission Fiber for Wide-band WDM-MIMO System,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, (Optical Society of America, 2013), paper OTh3K.1.
    [CrossRef]
  6. T. Sakamoto, T. Mori, T. Yamamoto, S. Tomita, “Differential Mode Delay Managed Transmission Line for WDM-MIMO System Using Multi-Step Index Fiber,” J. Lightwave Technol. 30(17), 2783–2787 (2013).
    [CrossRef]
  7. S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6×20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper PDP5C.5.
  8. C. Antonelli, A. Mecozzi, M. Shtaif, P. J. Winzer, “Random coupling between groups of degenerate fiber modes in mode multiplexed transmission,” Opt. Express 21(8), 9484–9490 (2013).
    [CrossRef] [PubMed]
  9. F. Yaman, E. Mateo, and T. Wang, “Impact of Modal Crosstalk and Multi-Path Interference on Few-Mode Fiber Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1D.2.
    [CrossRef]
  10. F. Ferreira, D. Fonseca, H. Silva, “Design of few-mode fibers with arbitrary and flattened differential mode delay,” Photonics Technology Letters 25(5), 438–441 (2013).
    [CrossRef]
  11. L. Grüner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, B. Pálsdóttir, “Few mode transmission fiber with low DGD, low mode coupling, and low loss,” J. Lightwave Technol. 30(23), 3693–3698 (2012).
    [CrossRef]

2013 (4)

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

F. Ferreira, D. Fonseca, H. Silva, “Design of few-mode fibers with arbitrary and flattened differential mode delay,” Photonics Technology Letters 25(5), 438–441 (2013).
[CrossRef]

T. Sakamoto, T. Mori, T. Yamamoto, S. Tomita, “Differential Mode Delay Managed Transmission Line for WDM-MIMO System Using Multi-Step Index Fiber,” J. Lightwave Technol. 30(17), 2783–2787 (2013).
[CrossRef]

C. Antonelli, A. Mecozzi, M. Shtaif, P. J. Winzer, “Random coupling between groups of degenerate fiber modes in mode multiplexed transmission,” Opt. Express 21(8), 9484–9490 (2013).
[CrossRef] [PubMed]

2012 (2)

2011 (1)

Antonelli, C.

Bai, N.

N. Bai, G. Li, “Adaptive frequency-domain equalization for mode-division multiplexed transmission,” Photonics Technology Letters 24(21), 1918–1921 (2012).
[CrossRef]

Bickham, S.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Ferreira, F.

F. Ferreira, D. Fonseca, H. Silva, “Design of few-mode fibers with arbitrary and flattened differential mode delay,” Photonics Technology Letters 25(5), 438–441 (2013).
[CrossRef]

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

Fonseca, D.

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

F. Ferreira, D. Fonseca, H. Silva, “Design of few-mode fibers with arbitrary and flattened differential mode delay,” Photonics Technology Letters 25(5), 438–441 (2013).
[CrossRef]

Grüner-Nielsen, L.

Ho, K.

Hoover, B.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Huang, Y.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Inan, B.

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

Ip, E.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Jakobsen, D.

Jespersen, K. G.

Kahn, J. M.

Li, G.

N. Bai, G. Li, “Adaptive frequency-domain equalization for mode-division multiplexed transmission,” Photonics Technology Letters 24(21), 1918–1921 (2012).
[CrossRef]

Li, M.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Li, S.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Lingle, R.

Lobato, A.

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

Mateo, E.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Mecozzi, A.

Mori, T.

Nicholson, J. W.

Pálsdóttir, B.

Sakamoto, T.

Shao, Y.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Shtaif, M.

Silva, H.

F. Ferreira, D. Fonseca, H. Silva, “Design of few-mode fibers with arbitrary and flattened differential mode delay,” Photonics Technology Letters 25(5), 438–441 (2013).
[CrossRef]

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

Sun, Y.

Ten, S.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Tomita, S.

Wang, T.

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

Winzer, P. J.

Yamamoto, T.

J. Lightwave Technol. (3)

Opt. Express (1)

Photonics Technology Letters (3)

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” Photonics Technology Letters 25(12), 1091–1094 (2013).
[CrossRef]

N. Bai, G. Li, “Adaptive frequency-domain equalization for mode-division multiplexed transmission,” Photonics Technology Letters 24(21), 1918–1921 (2012).
[CrossRef]

F. Ferreira, D. Fonseca, H. Silva, “Design of few-mode fibers with arbitrary and flattened differential mode delay,” Photonics Technology Letters 25(5), 438–441 (2013).
[CrossRef]

Other (4)

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6×20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper PDP5C.5.

F. Yaman, E. Mateo, and T. Wang, “Impact of Modal Crosstalk and Multi-Path Interference on Few-Mode Fiber Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1D.2.
[CrossRef]

M. Li, B. Hoover, S. Li, S. Bickham, S. Ten, E. Ip, Y. Huang, E. Mateo, Y. Shao, T. Wang, “Low delay and large effective area few-mode fibers for mode-division multiplexing,” In Opto-Electronics and Communications Conference (OECC),495–496 (2012).
[CrossRef]

T. Mori, T. Sakamoto, M. Wada, T. Yamamoto, and F. Yamamoto, “Low DMD Four LP Mode Transmission Fiber for Wide-band WDM-MIMO System,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, (Optical Society of America, 2013), paper OTh3K.1.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

A single span of DMGDC link.

Fig. 2
Fig. 2

A single span of DMGD uncompensated fiber.

Fig. 3
Fig. 3

A single span with one DMGD compensation pair with mode coupling in (a) P type section (Case I), (b) N type section (Case II).

Fig. 4
Fig. 4

Trench assisted graded index profile of P type ( α=2.079 ) or N type ( α=2.196 ).

Fig. 5
Fig. 5

Magnitude of impulse response Vs. number of tap periods for (a) h 21 of 10 × 128km P-type fiber link; (b) h 21 , (c) h 12 and (d) h 11 of 10 × (64km(P) + 64km(N)) DMGDC fiber link.

Fig. 6
Fig. 6

Q2 (dB) Vs. Tap number used in LMS equalizer when MSC = −35dB/km for 10 spans.

Fig. 7
Fig. 7

Required tap number Vs. compensation step-size for various MSCs.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Δ τ i = τ i 1 N j=1 N τ j .
Δ τ i ( P ) L P =Δ τ i ( N ) L N
y j = i=1 D h ij x i
ΔT=( Δ τ s Δ τ f )L
T p ( z )=Δτz+Δ τ f L
h sf ( t )= 0 L δ( tΔτzΔ τ f L ) κ sf ( z )exp( jΔ β sf z+j β f L )dz = 1 Δτ κ sf ( tΔ τ f L Δτ )exp( j Δ β sf Δτ tj Δ τ f β s Δ τ s β f Δτ L )
N taps =2ΔτL R s
h sf ( t )= h sf (I) ( t )+ h sf (II) ( t )
h sf (I) ( t )= 0 L P δ( tΔ τ (P) z ) κ sf (P) ( z ) exp( jΔ β sf (P) z+j( β f (P) L p + β s (N) L N ) )dz
h sf (II) ( t )= L P L P + L N δ( tΔ τ (N) ( z L N L P ) ) κ sf (N) ( z ) exp[ jΔ β sf (N) z+j( ( β s (P) Δ β sf (N) ) L p + β f (N) L N ) ]dz
h sf ( t )= 1 Δ τ (P) κ sf (P) ( t Δ τ (P) )exp( jΔ β sf (P) t Δ τ (P) +j( β s (P) L P + β f (N) L N ) ) + 1 Δ τ (N) κ sf (N) ( L P + L N + t Δ τ (N) )exp[ jΔ β sf (N) t Δ τ (N) +j( β s (P) Δ β sf (N) ) L P +j β f (N) L N ]
h sf ( t )= k=1 K h sf (k) ( t ) .
T p ( z )={ Δ τ (P) Δz 0<Δz< L P Δ τ (N) ( Δz L N L P ) L P <Δz< L P + L N
N taps =4Δ τ ( P ) L P R s

Metrics