Abstract

We investigated the relationships between the capacity limit and various figures of merit (spatial channel density, aggregate effective area ratio to cladding area, and bandwidth density) of few-mode multi-core fibers (FM-MCFs) where the modes in each core are weakly coupled. The capacity limit was estimated based on the Gaussian noise model for nonlinear impairment of single-mode fibers by neglecting crosstalk and intermodal nonlinear effects for simplicity; therefore, the estimated capacity can be the upper bound of the weakly-coupled FM-MCF capacity. When we take account of the transmission wavelength band of the FM-MCFs and the wavelength band where efficient amplification is available, the bandwidth density had a good correlation to the estimated capacity, but the spatial channel density and the aggregate effective area ratio often overestimate the FM-MCF capacity. Thus, we propose the bandwidth density for the figure of merit of FM-MCFs rather than the spatial channel density or the aggregate effective area ratio. We also investigated the relationship between the bandwidth density and fiber design, and found that the supporting transmission bandwidth and the core count are the dominant factors for the bandwidth density, and the mode count per core has a small impact for the bandwidth density, when the core Δ is fixed.

© 2017 Optical Society of America

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References

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2017 (2)

2016 (2)

2015 (1)

P. J. Winzer, “Scaling Optical Fiber Networks: Challenges and Solutions,” Opt. Photonics News 26(3), 28–35 (2015).
[Crossref]

2013 (2)

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations,” J. Lightwave Technol. 31(3), 398–406 (2013).
[Crossref]

2012 (1)

2011 (2)

Abe, Y.

Agrawal, G. P.

Aikawa, K.

Antonelli, C.

Aozasa, S.

Arakawa, Y.

Awaji, Y.

Borui, L.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Bosco, G.

Carena, A.

Chraplyvy, A. R.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Curri, V.

Essiambre, R.-J.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations,” J. Lightwave Technol. 31(3), 398–406 (2013).
[Crossref]

Forghieri, F.

Fu, S.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Gan, L.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Gnauck, A. H.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Hayashi, T.

Igarashi, K.

Jiang, X.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Klaus, W.

Kobayashi, T.

Kokubun, Y.

Koshiba, M.

Lingle, R.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Liu, D.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Luis, R. S.

Matsui, T.

Matsuo, S.

Mecozzi, A.

Mendinueta, J.-M. D.

Mestre, M. A.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Miyamoto, Y.

Mizuno, T.

Mumtaz, S.

Nagashima, T.

Nakajima, K.

Nakanishi, T.

Poggiolini, P.

Puttnam, B. J.

Ryf, R.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Saitoh, K.

Saitoh, S.

Sakaguchi, J.

Sakamoto, T.

Sasaki, T.

Sasaki, Y.

Sasaoka, E.

Shibahara, K.

Shimakawa, O.

Shtaif, M.

Shum, P. P.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Soma, D.

Sun, Y.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Takahata, T.

Takenaga, K.

Tang, M.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Tanigawa, S.

Taru, T.

Tkach, R. W.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

Tobita, Y.

Tsuritani, T.

Wada, N.

Wakayama, Y.

Watanabe, T.

Winzer, P. J.

P. J. Winzer, “Scaling Optical Fiber Networks: Challenges and Solutions,” Opt. Photonics News 26(3), 28–35 (2015).
[Crossref]

Xu, Z.

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

Yonezawa, K.

IEEE Photonics Technol. Lett. (1)

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25(6), 535–538 (2013).
[Crossref]

J. Lightwave Technol. (5)

Opt. Express (3)

Opt. Photonics News (1)

P. J. Winzer, “Scaling Optical Fiber Networks: Challenges and Solutions,” Opt. Photonics News 26(3), 28–35 (2015).
[Crossref]

Other (3)

L. Borui, S. Fu, L. Gan, M. Tang, Z. Xu, P. P. Shum, and D. Liu, “Figure of Merit (FOM) for Multicore Fiber-based Long-haul Transmission Assessment,” in Asia Commun. Photon. Conf. (ACP) (Optical Society of America, 2015), p. AS4E.3.
[Crossref]

A. Carena, V. Curri, G. Bosco, R. Cigliutti, E. Torrengo, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “A novel figure of merit to compare fibers in coherent detection systems with uncompensated links,” in Eur. Conf. Opt. Commun. (ECOC) (2011), p. Th.12.LeCervin.5.
[Crossref]

Y. Awaji, K. Saitoh, and S. Matsuo, “Chapter 13 - Transmission Systems Using Multicore Fibers,” in Optical Fiber Telecommunications (Sixth Edition), Optics and Photonics (Academic Press, 2013), pp. 617–651.

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Figures (7)

Fig. 1
Fig. 1 The relationships between the various FoMs ( B agg, N SDM, and A eff,agg) vs. the normalized fiber capacity C fib, where C fib was calculated using Eq. (6) by assuming the Aeff of the reference SMF is 80 µm2 and the SNR (SNRref) in the reference SMF system is (a) 5 dB, (b) 10 dB, (c) 15 dB, or (d) 20 dB. No significant difference was observed due to the SNRref difference.
Fig. 2
Fig. 2 The correlation coefficients between the normalized fiber capacity C fib and the various FoMs ( B agg, N SDM, or A eff,agg), whose dependence on the SNRref is little.
Fig. 3
Fig. 3 The aggregate bandwidths of various FM-MCFs. Horizontal axis shows the wavelength band, mode count in a core, and core count in a fiber, from the bottom.
Fig. 4
Fig. 4 Designed refractive index profiles of (blue) 3-mode and (orange) 6-mode cores.
Fig. 5
Fig. 5 The core layouts employed for FM-MCF designs.
Fig. 6
Fig. 6 The relationships between the normalized aggregate BW and the cladding diameter for the designed FM-MCFs.
Fig. 7
Fig. 7 The relationships between the normalized BW density and the cladding diameter for the designed FM-MCFs. The BW densities were calculated with (a) bare fibers, or (b) coated fibers with a 60-µm coating thickness.

Tables (2)

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Table 1 Designed optical properties of the few-mode cores.

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Table 2 The dimensions of the designed FM-MCFs.

Equations (6)

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D SC = N SDM / A CS ,
R EA = A eff,agg / A CS ,
SE agg = n 2 log 2 ( 1 + S N R n ) ,
Max ( SE agg ) = 2 N SDM log 2 ( 1 + ( | β 2 | L eff ) 1 3 ( e α L span 1 ) 2 3 ( γ L eff ) 2 3 C system N span ) ,
Max ( SE agg ) = 2 N SDM log 2 ( 1 + A eff 2 3 C par ) ,
C fib = B n 2 log 2 ( 1 + A eff , n 2 3 C par ) ,

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