Abstract

In this paper, the concept of supermode is introduced for long-distance optical transmission systems. The supermodes exploit coupling between the cores of a multi-core fiber, in which the core-to-core distance is much shorter than that in conventional multi-core fiber. The use of supermodes leads to a larger mode effective area and higher mode density than the conventional multi-core fiber. Through simulations, we show that the proposed coupled multi-core fiber allows lower modal dependent loss, mode coupling and differential modal group delay than few-mode fibers. These properties suggest that the coupled multi-core fiber could be a good candidate for both spatial division multiplexing and single-mode operation.

© 2011 OSA

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References

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  1. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
    [CrossRef] [PubMed]
  2. F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express 18(12), 13250–13257 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-12-13250 .
    [CrossRef] [PubMed]
  3. B. Zhu, T. Thierry, F. Michael, X. Liu, C. Sethumadhavan, Y. Man, F. John, M. Eric, and D. Frank, “Space-, Wavelength-, Polarization-Division Multiplexed Transmission of 56-Tb/s over a 76.8-km Seven-Core Fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPB7.
  4. S. Jun, A. Yoshinari, W. Naoya, K. Atsushi, K. Tetsuya, H. Tetsuya, T. Toshiki, K. Tetsuya, and W. Masayuki, “109-Tb/s (7x97x172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” in National Fiber Optic Engineers Conference (Optical Society of America, 2011), p. PDPB6.
  5. L. An, A. Abdullah Al, C. Xi, and S. William, “Reception of Mode and Polarization Multiplexed 107-Gb/s CO-OFDM Signal over a Two-Mode Fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPB8.
  6. S. Massimiliano, K. Clemens, S. Donato, T. Patrice, B. Patrick, M. Haik, B. Sébastien, B. Aurélien, V. Frederic, S. Pierre, B.-A. Marianne, P. Lionel, C. Frederic, and C. Gabriel, “Transmission at 2x100Gb/s, over Two Modes of 40km-long Prototype Few-Mode Fiber, using LCOS based Mode Multiplexer and Demultiplexer,” in National Fiber Optic Engineers Conference (Optical Society of America, 2011), p. PDPB9.
  7. R. Roland, R. Sebastian, H. G. Alan, B. Cristian, E. Rene-Jean, W. Peter, W. P. David, M. Alan, and L. Robert, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPB10.
  8. H. Tetsuya, T. Toshiki, S. Osamu, S. Takashi, and S. Eisuke, “Ultra-Low-Crosstalk Multi-Core Fiber Feasible to Ultra-Long-Haul Transmission,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPC2.
  9. 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]
  10. N. Kishi and E. Yamashita, “A simple coupled-mode analysis method for multiple-core optical fiber and coupled dielectric waveguide structures,” IEEE Trans. Micro. Theory Techn. 36(12), 1861–1868 (1988).
    [CrossRef]
  11. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. 62(11), 1267–1277 (1972).
    [CrossRef]
  12. G. P. Agrawal, Nonlinear fiber optics (Academic Press 1995).
  13. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. A 66(3), 216–220 (1976).
    [CrossRef]
  14. P. M. Krummrich and K. Petermann, “Evaluation of Potential Optical Amplifier Concepts for Coherent Mode Multiplexing” Proc. OFC 2011, Paper OMH5, Los Angeles, CA, USA (2011)
  15. H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
    [CrossRef]

2010 (2)

F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express 18(12), 13250–13257 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-12-13250 .
[CrossRef] [PubMed]

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

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]

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

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. Micro. Theory Techn. 36(12), 1861–1868 (1988).
[CrossRef]

1976 (1)

D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. A 66(3), 216–220 (1976).
[CrossRef]

1972 (1)

Bai, N.

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. Micro. Theory Techn. 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]

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]

Kubota, H.

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

Li, G.

Marcuse, D.

D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. A 66(3), 216–220 (1976).
[CrossRef]

Matsui, M.

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

Mitra, P. P.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

Morioka, T.

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

Nakagawa, T.

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

Snyder, W.

Stark, J. B.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

Takara, H.

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

Wang, T.

Yaman, F.

Yamashita, E.

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

Zhu, B.

IEEE Trans. Micro. Theory Techn. (1)

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

IEICE Electron. Express (2)

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]

H. Kubota, H. Takara, T. Nakagawa, M. Matsui, and T. Morioka, “Intermodal group velocity dispersion of few-mode fiber,” IEICE Electron. Express 7(20), 1552–1556 (2010).
[CrossRef]

J. Opt. Soc. A (1)

D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. A 66(3), 216–220 (1976).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Other (8)

B. Zhu, T. Thierry, F. Michael, X. Liu, C. Sethumadhavan, Y. Man, F. John, M. Eric, and D. Frank, “Space-, Wavelength-, Polarization-Division Multiplexed Transmission of 56-Tb/s over a 76.8-km Seven-Core Fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPB7.

S. Jun, A. Yoshinari, W. Naoya, K. Atsushi, K. Tetsuya, H. Tetsuya, T. Toshiki, K. Tetsuya, and W. Masayuki, “109-Tb/s (7x97x172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” in National Fiber Optic Engineers Conference (Optical Society of America, 2011), p. PDPB6.

L. An, A. Abdullah Al, C. Xi, and S. William, “Reception of Mode and Polarization Multiplexed 107-Gb/s CO-OFDM Signal over a Two-Mode Fiber,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPB8.

S. Massimiliano, K. Clemens, S. Donato, T. Patrice, B. Patrick, M. Haik, B. Sébastien, B. Aurélien, V. Frederic, S. Pierre, B.-A. Marianne, P. Lionel, C. Frederic, and C. Gabriel, “Transmission at 2x100Gb/s, over Two Modes of 40km-long Prototype Few-Mode Fiber, using LCOS based Mode Multiplexer and Demultiplexer,” in National Fiber Optic Engineers Conference (Optical Society of America, 2011), p. PDPB9.

R. Roland, R. Sebastian, H. G. Alan, B. Cristian, E. Rene-Jean, W. Peter, W. P. David, M. Alan, and L. Robert, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPB10.

H. Tetsuya, T. Toshiki, S. Osamu, S. Takashi, and S. Eisuke, “Ultra-Low-Crosstalk Multi-Core Fiber Feasible to Ultra-Long-Haul Transmission,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. PDPC2.

G. P. Agrawal, Nonlinear fiber optics (Academic Press 1995).

P. M. Krummrich and K. Petermann, “Evaluation of Potential Optical Amplifier Concepts for Coherent Mode Multiplexing” Proc. OFC 2011, Paper OMH5, Los Angeles, CA, USA (2011)

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Figures (7)

Fig. 1
Fig. 1

Schematic of a coupled four-core fiber structure.

Fig. 2
Fig. 2

Field distributions of the 1st (a), 2nd (b), 3rd (c) and 4th (d) supermodes for four-core CMCFs. (Black lines indicate the boundaries of the cores)

Fig. 3
Fig. 3

(a) A e f f and Δ N e f f vs. d/r for the fundamental mode of six-core CMCFs, (b) the field distribution of the fundamental mode in CMCF (black lines are the boundaries of cores) and (c) A e f f vs. Δ N e f f for six-core CMCFs and six-mode FMFs.

Fig. 4
Fig. 4

Field distributions of the 1st (a), 2nd (b), 3rd (c), 4th (d), 5th (e) and 6th (f) supermodes for the six-core CMCF. (Black lines indicate the boundaries of the cores)

Fig. 5
Fig. 5

(a) A e f f vs. Δ N e f f for CMCFs and FMFs ( Δ N e f f refers to the minimum Δ N e f f for one mode to any other mode). (b) Confinement factor vs. Δ N e f f for CMCFs and FMFs

Fig. 7
Fig. 7

(a) maximum DMGD vs. wavelength at V=1.707 @1.55μm and ∆=0.06%, (b) (c) (d) field distribution of the 1st, 2nd and 3rd supermode of a three-core CMCF

Fig. 6
Fig. 6

(a) (b) (c) d c d ω at V=1.6, 1.7 and 1.9. (d) d d λ ( d c d ω ) at V=1.7.

Tables (2)

Tables Icon

Table 1 Properties of Coupled Multi-Core Fiber and Few-Mode Fiber Design for Single-Mode Operation

Tables Icon

Table 2 Comparison of Next Generation Transmission Fibers for Spatial Division Multiplexing

Equations (13)

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

d d z A = - j M ¯ A ,
Q 1 M ¯ Q = Λ ,
Λ = ( β 1 0 0 0 0 β 2 0 0 0 0 β 3 0 0 0 0 β 4 )
B = Q 1 A
d d z B = j Λ Β .
c j = n 1 2 n 2 2 n 1 2 1 r U 2 V 3 K 0 ( W d j / r ) K 1 2 ( W )
β 1 = β 0 + 2 c 1 + c 2 ; β 2 = β 0 c 2 ; β 3 = β 0 c 2 ; β 4 = β 0 2 c 1 + c 2 .
A e f f = | + + I ( x , y ) d x d y | 2 + + I 2 ( x , y ) d x d y
Δ N e f f ( i , j ) = 1 k 0 ( β i β j ) = 1 k 0 n ( a n i a n j ) c n
DMGD(i,j) = d β i d ω d β j d ω = n = 1 2 ( a n i a n j ) d c n d ω
d c n d ω = 1 r { ω 1 n 2 2 ( ω ) n 1 2 ( ω ) [ U 2 V 3 K 0 ( W d n / r K 1 2 ( W ) ] + 1 n 2 2 n 1 2 ω } [ U ( ω ) 2 V ( ω ) 3 K 0 ( W ( ω ) d n / r ) K 1 2 ( ω ) ) ]
D M G D S (i,j) = d d λ ( d β i d ω d β j d ω ) = ( a 1 i a 1 j ) d d λ ( d c 1 d ω )
d d λ ( d C d ω ) = 1 r 1 n 2 2 n 1 2 2 λ ω [ U ( ω ) 2 V ( ω ) 3 K 0 ( W ( ω ) d / r ) K 1 2 ( W ( ω ) ) ]

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