Abstract

An approximate explicit condition for the achievement of zero differential group delay (DGD) in a homogeneous multicore fiber (MCF) is presented and verified numerically for a step-index three-core fiber. This condition is explored for the study of compact three-core fibers with low DGDs. To achieve an ultra-low DGD in the C-band, a three-core fiber with a central refractive-index dip in each core is proposed and analyzed in detail. A specific design with three touching cores and a core-cladding index difference of 0.3% yields a maximum DGD smaller than 3.2 ps/km in the C-band. The fiber is suitable for broadband mode-division multiplexing applications and the design approach could be applied to MCFs with more cores.

© 2015 Optical Society of America

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References

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2015 (2)

2014 (6)

F. M. Ferreira, D. Fonseca, and H. J. A. da Silva, “Design of few-mode fibers with M-modes and low differential mode delay,” J. Lightwave Technol. 32(3), 353–360 (2014).
[Crossref]

N. Bai and G. Li, “Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling,” Opt. Express 22(4), 4247–4255 (2014).
[Crossref] [PubMed]

P. Sillard, M. Bigot-Astruc, and D. Molin, “Few-mode fibers for mode-division-multiplexed systems,” J. Lightwave Technol. 32(16), 2824–2829 (2014).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three‐dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

2013 (2)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

S. O. Arik and J. M. Kahn, “Coupled-core multi-core fibers for spatial multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
[Crossref]

2012 (2)

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. J. M. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

2009 (1)

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

1995 (1)

1989 (1)

H. S. Huang and H. C. Chang, “Guided vector modes of equilateral three-core fibres,” Electron. Lett. 25(1), 55–56 (1989).
[Crossref]

1988 (1)

N. Kishi and E. Yamashita, “A simple coupled-mode analysis method for multiple-core optical fiber and coupled dielectric waveguide structures,” IEEE Trans. Microw. Theory Tech. 36(12), 1861–1868 (1988).
[Crossref]

1972 (1)

Adhikari, S.

Alvarado, J. C.

Amezcua-Correa, R.

A. M. Velazquez-Benitez, J. C. Alvarado, G. Lopez-Galmiche, J. E. Antonio-Lopez, J. Hernández-Cordero, J. Sanchez-Mondragon, P. Sillard, C. M. Okonkwo, and R. Amezcua-Correa, “Six mode selective fiber optic spatial multiplexer,” Opt. Lett. 40(8), 1663–1666 (2015).
[Crossref] [PubMed]

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Antonio-Lopez, E.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Antonio-Lopez, J. E.

Arik, S. O.

S. O. Arik and J. M. Kahn, “Coupled-core multi-core fibers for spatial multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
[Crossref]

Arrioja, D. M.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Bai, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

N. Bai and G. Li, “Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling,” Opt. Express 22(4), 4247–4255 (2014).
[Crossref] [PubMed]

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

C. Xia, N. Bai, I. Ozdur, X. Zhou, and G. Li, “Supermodes for optical transmission,” Opt. Express 19(17), 16653–16664 (2011).
[Crossref] [PubMed]

F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010).
[Crossref] [PubMed]

Bigot-Astruc, M.

Chang, H. C.

H. S. Huang and H. C. Chang, “Guided vector modes of equilateral three-core fibres,” Electron. Lett. 25(1), 55–56 (1989).
[Crossref]

Chiang, K. S.

Correa, R. A.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

da Silva, H. J. A.

de Waardt, H.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Downie, J. D.

Ferreira, F.

Ferreira, F. M.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fonseca, D.

Gross, S.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three‐dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

Hanik, N.

Hernández-Cordero, J.

Huang, H. S.

H. S. Huang and H. C. Chang, “Guided vector modes of equilateral three-core fibres,” Electron. Lett. 25(1), 55–56 (1989).
[Crossref]

Huang, M. F.

Huang, Y. K.

Huijskens, F. M.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Hurley, J.

Inan, B.

Jansen, S. L.

Kahn, J. M.

S. O. Arik and J. M. Kahn, “Coupled-core multi-core fibers for spatial multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
[Crossref]

Kishi, N.

N. Kishi and E. Yamashita, “A simple coupled-mode analysis method for multiple-core optical fiber and coupled dielectric waveguide structures,” IEEE Trans. Microw. Theory Tech. 36(12), 1861–1868 (1988).
[Crossref]

Kokubun, Y.

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

Koonen, A. M. J.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Koshiba, M.

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

Kuschnerov, M.

Lau, A. P. T.

Li, G.

N. Bai and G. Li, “Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling,” Opt. Express 22(4), 4247–4255 (2014).
[Crossref] [PubMed]

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

C. Xia, N. Bai, I. Ozdur, X. Zhou, and G. Li, “Supermodes for optical transmission,” Opt. Express 19(17), 16653–16664 (2011).
[Crossref] [PubMed]

F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010).
[Crossref] [PubMed]

Liñares, J.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Lobato, A.

Lopez, E. A.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Lopez-Galmiche, G.

Love, J. D.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three‐dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

Lu, C.

Mateo, E.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Mishra, S.

Molin, D.

Montero, C.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Okonkwo, C. M.

A. M. Velazquez-Benitez, J. C. Alvarado, G. Lopez-Galmiche, J. E. Antonio-Lopez, J. Hernández-Cordero, J. Sanchez-Mondragon, P. Sillard, C. M. Okonkwo, and R. Amezcua-Correa, “Six mode selective fiber optic spatial multiplexer,” Opt. Lett. 40(8), 1663–1666 (2015).
[Crossref] [PubMed]

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Ozdur, I.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Richardson, M.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Riesen, N.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three‐dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

Sanchez-Mondragon, J.

Schulzgen, A.

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

Schülzgen, A.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Sillard, P.

Sleiffer, V. A. J. M.

Snyder, A. W.

Spinnler, B.

Sui, Q.

Tam, H. Y.

van den Borne, D.

van Uden, R. G. H.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Velazquez-Benitez, A. M.

Wai, P. K.

Wang, T.

Withford, M. J.

S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three‐dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev. 8(5), L81–L85 (2014).
[Crossref]

Wood, W. A.

Xia, C.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja, A. Schulzgen, M. Richardson, J. Liñares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photonics Technol. Lett. 24(21), 1914–1917 (2012).
[Crossref]

C. Xia, N. Bai, I. Ozdur, X. Zhou, and G. Li, “Supermodes for optical transmission,” Opt. Express 19(17), 16653–16664 (2011).
[Crossref] [PubMed]

Yaman, F.

Yamashita, E.

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Figures (8)

Fig. 1
Fig. 1 A homogeneous MCF with N identical step-index single-mode cores of radius a and core separation s.
Fig. 2
Fig. 2 The normalized frequency V required for achieving zero DGD as a function of the normalized core separation s/a calculated by the coupled-mode theory (CMT) for a homogeneous MCF and by the finite-element method for a step-index three-core fiber that includes (with Dm) or excludes (without Dm) material dispersion, where the zero-DGD conditions for the three-core fiber are calculated for different mode pairs. The V curves for zero DGDs between the 1e mode and any of the 2e, 2o, and 3e modes are almost indistinguishable, either with or without material dispersion.
Fig. 3
Fig. 3 (a) A homogenous step-index three-core fiber with radius a and core separation s supports (b) six vector modes, which can be labeled as the 1e, 1o, 2e, 2o, 3e, and 3o modes with the number representing the mode order and the letter (“e” or “o”) indicating the symmetry of the electric-field distribution (even or odd) with respect to the y axis. The arrows associated with the mode patterns indicate the directions of the electric fields.
Fig. 4
Fig. 4 (a) Effective indices of the six vector modes of a step-index three-core fiber with a = 3.59 μm, s/a = 2, n1 = 1.4484, and n2 = 1.4440 (Δ = 0.3%). (b) DGDs among the 1e, 2e, 2o, and 3e modes of the fiber.
Fig. 5
Fig. 5 (a) A touching-core three-core fiber with a central refractive-index dip in each core and (b) the electric-field distributions of the first six vector modes of the fiber, where the arrows indicate the directions of the electric fields.
Fig. 6
Fig. 6 Dependence of the DGD between the 1e and 2e modes of a touching-core three-core fiber (Δ = 0.3%) with a central index dip in each core on (a) the core radius a for p = 0.5 and d/a = 0.75, (b) the normalized dip index p for a = 6 μm and d/a = 0.75, and (c) the normalized dip radius d/a for a = 6 μm and p = 0.5. The vertical dashed lines in (a) mark the cutoff wavelengths of the higher-order mode beyond the first six modes.
Fig. 7
Fig. 7 (a) Effective indices of the first six vector modes of a touching-core three-core fiber with a central index dip in each core with Δ = 0.3%, a = 6.40 μm, p = 0.462, and d/a = 0.77, (b) DGDs among the modes, and (c) variations of the DGD between the 1e and 2e modes with ± 5% changes in p and d/a.
Fig. 8
Fig. 8 DGDs among the modes of a touching-core three-core fiber with a central dip in each core with Δ = 0.5%, a = 4.97 µm, p = 0.462, and d/a = 0.77.

Equations (7)

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β i = β 0 +2Ccos[ 2π N (i1) ]= β 0 + w i C, i=1,2,...,N,
C= 2Δ a U 2 V 3 K 0 ( Ws/a ) K 1 2 ( W ) ,
DG D ij = d( β i β j ) dω =( w i w j ) dC dω ,
dC dω = 1 ω CG=0,
G=[ 2+2W K 0 ( W ) K 1 ( W ) Ws a K 1 ( Ws/a ) K 0 ( Ws/a ) ][ 1+ U 2 W 2 K 0 2 ( W ) K 1 2 ( W ) ][ 1+2 K 0 2 ( W ) K 1 2 ( W ) ].
DGD= 1 c [ Δ n eff λ d( Δ n eff ) dλ ],
p= n d 2 n 2 2 n 1 2 n 2 2 .

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