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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 4 — Feb. 24, 2014
  • pp: 4247–4255
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Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling

Neng Bai and Guifang Li  »View Author Affiliations


Optics Express, Vol. 22, Issue 4, pp. 4247-4255 (2014)
http://dx.doi.org/10.1364/OE.22.004247


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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

1. Introduction

2. Theory

2.1 Impulse response of a DMGD uncompensated link

The two straight lines symbolize the F and the S modes. At location z, signal in the S mode is coupled to that in the F mode with a coupling coefficientκsf(z)wherez[0,L]. The statistics ofκsf(z)is assumed to obey normal distribution with zero mean [8

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

] and variance of σκ2which equals to mode scattering coefficient (MSC) defined in [9

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]

]. The path delay (Tp(z)) of the coupling light via coupling location z can be calculated
Tp(z)=Δτz+ΔτfL
(5)
The impulse response functionhsf therefore can be obtained by integrating over all possible coupling paths from beginning to end as
hsf(t)=0Lδ(tΔτzΔτfL)κsf(z)exp(jΔβsfz+jβfL)dz=1Δτκsf(tΔτfLΔτ)exp(jΔβsfΔτtjΔτfβsΔτsβfΔτL)
(6)
where βsand βfare the propagation constants of the two modes, respectively; Δβsfis the difference between them. Because κ(z) is nonzero for 0zL, the range of t can be calculated as ΔτfLtΔτsL. Inside the integral, the expression describes a decomposed impulse response induced by a single coupling event at location z with coupling strength κsf(z). The exponential term denotes an accumulated phase of the selected path. Since the equalizer needs to cover the non-zero range of the impulse response, the required tap length (RTL) of DMGD uncompensated link, assuming oversampling rate of 2, can be expressed as following
Ntaps=2ΔτLRs
(7)
where Rs is the symbol rate.

2.2 Impulse Response of a DMGD compensated pair

Figure 3(a)
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).
-3(b) shows a fiber span with one DMGD compensation pair.

2.3 Impulse Response of DMGD compensated link

3. Simulation

For simplicity, P-type and N-type FMFs which can guide two LP modes are designed and simulated. In P-type fiber, the faster LP01 mode is labeled as mode 1. the slower LP11 mode is labeled as mode 2. Trench assisted graded index profile is used as in [10

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

]. By adjusting the power indexα, DMGDs can be tuned to be 100 ps/km for P-type FMF and −100ps/km for N-type across the C-band. The index profile and the design parameters are shown in Fig. 4
Fig. 4 Trench assisted graded index profile of P type (α=2.079) or N type (α=2.196).
. The effective index differences between the two LP modes are 2.9 × 10−3 and the chromatic dispersion coefficients are 21 ps/nm/km for both types of fiber.

Multi-section field propagation model was used to simulate two-mode transmission in FMF [9

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]

]. The section length was set to be 200m as same as [10

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

]. For other section lengths such as 100m or 500m, negligible difference was observed. MSC was set to be −35dB/km which is slightly higher than the fiber with similar index profile used in [11

11. L. Grüner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle Jr, and B. Pálsdóttir, “Few mode transmission fiber with low DGD, low mode coupling, and low loss,” J. Lightwave Technol. 30(23), 3693–3698 (2012). [CrossRef]

] (−25dB crosstalk for 30km fiber, or −39.8dB/km). Losses were 0.2dB/km for both modes. No crosstalk was assumed from mode MUX/DEMUX or splicing.

To rigorously analyze the RTL for the link, the receiving data are processed by equalizers with various tap lengths. The Q2 factor as a function of tap length is plotted in Fig. 6
Fig. 6 Q2 (dB) Vs. Tap number used in LMS equalizer when MSC = −35dB/km for 10 spans.
. As the tap length increases, more distributed mode couplings or interferences are canceled leading to higher Q2. When the tap length exceeds the CIRS, Q2 converges to the maximum value determined by the OSNR at the receiver. Figure 6 also shows Q2 curves for various compensation step size. For each curve, the RTL can be defined as the minimum tap length of the equalizer to achieve a 0.1dB Q2 penalty compared to maximum achievable Q2. Therefore, RTL as a function of compensation step-size can be plotted and is shown in Fig. 7
Fig. 7 Required tap number Vs. compensation step-size for various MSCs.
for different MSCs.

4. Conclusion

Acknowledgement

This research was supported in part by the National Basic Research Programme of China (973) Project #2014CB340100.

References and links

1.

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

2.

K. Ho and 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, and 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, and 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, and 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, and 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, and 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 Jr, and B. Pálsdóttir, “Few mode transmission fiber with low DGD, low mode coupling, and low loss,” J. Lightwave Technol. 30(23), 3693–3698 (2012). [CrossRef]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.4230) Fiber optics and optical communications : Multiplexing

ToC Category:
Optical Communications

History
Original Manuscript: November 12, 2013
Revised Manuscript: December 31, 2013
Manuscript Accepted: January 27, 2014
Published: February 18, 2014

Citation
Neng Bai and Guifang Li, "Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling," Opt. Express 22, 4247-4255 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4247


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References

  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]

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