Abstract

We designed and fabricated a multi-core fiber (MCF) in which seven identical trench-assisted pure-silica cores were arranged hexagonally. To design MCF, the relation among the crosstalk, fiber parameters, and fiber bend was derived using a new approximation model based on the coupled-mode theory with the equivalent index model. The mean values of the statistical distributions of the crosstalk were observed to be extremely low and estimated to be less than −30 dB even after 10,000-km propagation because of the trench-assisted cores and utilization of the fiber bend. The attenuation of each core was very low for MCFs (0.175–0.181 dB/km at 1550 nm) because of the pure-silica cores. Both the crosstalk and attenuation values are the lowest achieved in MCFs.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
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  17. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Ultra-low-crosstalk multi-core fiber feasible to ultra-long-haul transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPC2.
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    [CrossRef]
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  22. V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
    [CrossRef]
  23. B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fini, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, “Seven-core multicore fiber transmissions for passive optical network,” Opt. Express 18(11), 11117–11122 (2010).
    [CrossRef] [PubMed]
  24. M. Wandel and P. Kristensen, “Fiber designs for high figure of merit and high slope dispersion compensating fibers,” in Fiber Based Dispersion Compensation, S. Ramachandran, ed. (Springer, 2007).
  25. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: application to photonic crystal fibers,” J. Quantum Electron. 38(7), 927–933 (2002).
    [CrossRef]
  26. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier, 2005).

2011 (1)

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

2010 (4)

2009 (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[CrossRef]

2002 (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: application to photonic crystal fibers,” J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

1982 (1)

1972 (1)

Arakawa, Y.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

Bosco, G.

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
[CrossRef]

Carena, A.

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
[CrossRef]

Curri, V.

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
[CrossRef]

Dimarcello, F. V.

Essiambre, R.-J.

Fini, J. M.

Fishteyn, M.

Forghieri, F.

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
[CrossRef]

Foschini, G. J.

Goebel, B.

Guan, N.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

Kokubun, Y.

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[CrossRef]

Koshiba, M.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[CrossRef]

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: application to photonic crystal fibers,” J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

Kramer, G.

Marcuse, D.

Matsuo, S.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

Monberg, E. M.

Poggiolini, P.

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
[CrossRef]

Saitoh, K.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[CrossRef]

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: application to photonic crystal fibers,” J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

Snyder, A. W.

Takenaga, K.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

Tanigawa, S.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

Taunay, T. F.

Winzer, P. J.

Yan, M. F.

Zhu, B.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 111 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010).
[CrossRef]

IEICE Electron. Express (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[CrossRef]

IEICE Trans. Commun. E (1)

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun. E 94-B, 409–416 (2011).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Quantum Electron. (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: application to photonic crystal fibers,” J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

Opt. Express (2)

Other (17)

M. Wandel and P. Kristensen, “Fiber designs for high figure of merit and high slope dispersion compensating fibers,” in Fiber Based Dispersion Compensation, S. Ramachandran, ed. (Springer, 2007).

D. Marcuse, Theory of Dielectric Optical Waveguides Second Edition (Academic Press, 1991)

K. Saitoh, T. Matsui, T. Sakamoto, M. Koshiba, and S. Tomita, “Multi-core hole-assisted fibers for high core density space division multiplexing,” in Proceedings of 15th OptoElectronics and Communications Conference (Institute of Electrical and Electronics Engineers, 2010), paper 7C2–1.

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of 36th European Conference and Exhibition on Optical Communication (Institute of Electrical and Electronics Engineers, 2010), paper We.8.F.6.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-crosstalk and low-loss multi-core fiber utilizing fiber bend,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWJ3.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Ultra-low-crosstalk multi-core fiber feasible to ultra-long-haul transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPC2.

T. Morioka, “New generation optical infrastructure technologies: “EXAT initiative” towards 2020 and beyond,” in Proceedings of 14th OptoElectronics and Communications Conference (Institute of Electrical and Electronics Engineers, 2009), paper FT4.

M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over two modes of 40km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB9.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB10.

J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, and M. Watanabe, “109-Tb/s (7x97x172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB6.

B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB7.

Y. Kokubun and M. Koshiba, “Novel fibers for space/mode-division multiplexing—proposal of homogeneous and heterogeneous multi-core fibres—,” presented at the International Symposium on Global Optical Infrastructure Technologies towards the Next Decades (EXAT2008), Tokyo, Japan, 12 Sept. 2008.

K. Imamura, K. Mukasa, and T. Yagi, “Investigation on multi-core fibers with large Aeff and low micro bending loss,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWK6.

D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB5.

A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and extended L-band transmission over 240 Km using PDM-16-QAM modulation and digital coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB7.

J. Cai, Y. Cai, C. Davidson, A. Lucero, H. Zhang, D. Foursa, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s capacity transmission over 6,860 km,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB4.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier, 2005).

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Figures (15)

Fig. 1
Fig. 1

Power conversions between coupled waveguides with the same coupling coefficients. (a) Propagation constants of the waveguides are the same. (b) Propagation constants of the waveguides are different.

Fig. 2
Fig. 2

Relative refractive index differences between equivalent and intrinsic indices.

Fig. 3
Fig. 3

Longitudinal variations of simulated coupled power [15].

Fig. 4
Fig. 4

Relationship between the bending radius and the crosstalk of a heterogeneous MCF [15].

Fig. 5
Fig. 5

Difference of XTμ between Eqs. (22) and (27). The former is based on the assumption that the crosstalk linearly accumulates and the latter on the coupled-power equation.

Fig. 6
Fig. 6

Designed refractive index profile of each MCF core [16].

Fig. 7
Fig. 7

Relationship between the core pitch Λ and the crosstalk for the designed core.

Fig. 8
Fig. 8

Relationship between the cladding diameter and the attenuation degradation of the outer core for the designed MCF [16].

Fig. 9
Fig. 9

Cross section of the fabricated MCF [16].

Fig. 10
Fig. 10

Attenuation spectra of cores of the fabricated MCF.

Fig. 11
Fig. 11

An example of crosstalk distribution [17].

Fig. 12
Fig. 12

Mean crosstalk of the fabricated MCF after 17.4-km propagation for R = 140 mm [17]. (a) Measured values. (b) Simulated wavelength dependence.

Fig. 13
Fig. 13

Bending radius dependence of the mean crosstalk of the fabricated MCF after 17.4-km propagation for λ = 1625 nm. (a) Between Cores 1 & 4. (b) Between Cores 1 & 5. (c) Between Cores 4 & 5.

Fig. 14
Fig. 14

Relationship between the propagation length L, the bending radius R, and the mean crosstalk XTμ of the center core of the MCF (a) at λ = 1550 nm and (b) at λ = 1625 nm [17]. The shaded diamond symbols represent L and R where XTμ was measured. Contour lines represent the estimated XTμ from the measurement values and Eq. (22).

Fig. 15
Fig. 15

Comparison between values of |Κ nm | obtained using the analytically derived Eq. (12) and those simulated numerically using Eqs. (30)(32).

Tables (2)

Tables Icon

Table 1 Designed Optical Properties of Each MCF Core at λ = 1550 nm

Tables Icon

Table 2 Optical Properties of Each Core of the Fabricated MCF

Equations (41)

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

F = [ 1 + ( β m β n 2 κ n m ) ] 1 .
n eq ( r , θ , R ) n ( r , θ ) ( 1 + r cos θ R ) ,       r cos θ R 1 ,
Δ eq ( r , θ , R ) = n eq 2 n 2 2 n eq 2 = ( 1 + r cos θ R ) 2 1 2 ( 1 + r cos θ R ) 2 .
n eqeff, n = n eff, n ( 1 + D n m cos θ n m R ) ,
β eq, n = 2 π λ n eqeff, n = 2 π λ n eff, n ( 1 + D n m R cos θ n m ) = β n ( 1 + D n m R cos θ n m ) ,
A n z = m n j κ n m exp { j [ ϕ m ( z ) ϕ n ( z ) ] } A m ,
ϕ ( z ) = 0 z β eq ( z ) d z ,
ϕ ( z ) = { β m z 0 z β n [ 1 + D n m R ( z ) cos θ n m ( z ) ] d z .
δ n eq, n m = n eqeff, m n eqeff, n = n eff, m n eff, n ( 1 + D n m R cos θ n m ) .
R pk = n eff, n | n eff, m n eff, n | D n m .
A n , N = A n , N 1 j K n m exp [ j ϕ rnd ( N ) ] A m , N 1 = A n , 0 j K n m l = 1 N exp [ j ϕ rnd ( l ) ] A m , l 1 ,
| K n m | = | K m n | = | K | κ 2 β R D n m 2 π γ ,     κ n m = κ m n = κ ,
σ 2 2 = κ 2 β R D n m L .
f 2 ( σ 2 2 ) ( X T ) = f 2 ( X T σ 2 2 ) | d d X T ( X T σ 2 2 ) | = 1 2 σ 2 2 exp ( X T 2 σ 2 2 ) ,
F 2 ( σ 2 2 ) ( X T ) = F 2 ( X T σ 2 2 ) = 1 exp ( X T 2 σ 2 2 ) ,
σ 4 2 = 1 2 κ 2 β R D n m L ,
f 4 ( σ 4 2 ) ( X T ) = f 4 ( X T σ 4 2 ) | d d X T ( X T σ 4 2 ) | = X T 4 σ 4 4 exp ( X T 2 σ 4 2 ) ,
F 4 ( σ 4 2 ) ( X T ) = F 4 ( X T σ 4 2 ) = 1 ( 1 + X T 2 σ 4 2 ) exp ( X T 2 σ 4 2 ) .
X T μ = 2 σ 2 2 = 4 σ 4 2 = 2 κ 2 β R D n m L = h L ,
X T Q = σ k 2 F k 1 ( Q ) = X T μ k F k 1 ( Q ) ,
X T Q ( dB ) = 10 log 10 σ k 2 + 10 log 10 F k 1 ( Q ) = 10 log 10 X T μ k + 10 log 10 F k 1 ( Q ) ,
X T μ = 6 2 κ 2 β R Λ L = 6 h L = X T coeff R L ,
P 1 , 1 ( z ) = 1 + 6 exp ( 7 h z ) 7 ,
P n , 1 ( z ) = 1 exp ( 7 h z ) 7 ,     n = 2 , 3 , , 7 ,
P 1 , 2 7 ( z ) = 6 6 exp ( 7 h z ) 7 ,
P n , 2 7 ( z ) = 6 + exp ( 7 h z ) 7 ,     n = 2 , 3 , , 7.
X T μ = P 1 , 2 7 ( L ) P 1 , 1 ( L ) = 6 6 exp ( 7 h L ) 1 + 6 exp ( 7 h L ) = 6 6 exp ( 7 2 κ 2 β R Λ L ) 1 + 6 exp ( 7 2 κ 2 β R Λ L ) .
A n , 1 = j K n m exp [ j ϕ rnd ( 1 ) ] .
K n m = A n , 1 j .
A n ( z ) = j 0 z κ n m exp { j [ ϕ m ( z ) ϕ n ( z ) ] } A m ( z ) d z ,
ϕ ( z ) = { β m z 0 z β n ( 1 + D n m R cos γ z ) d z .
K n m = A n ( π / γ ) j .
K n m = κ n m 0 π γ exp { j [ ϕ m ( z ) ϕ n ( z ) ] } d z = κ n m 0 π γ exp [ j ( β m β n ) z ] exp [ j β n D n m γ R sin ( γ z ) ] d z = κ n m 0 π γ exp [ j ( β m β n ) z ] ν J ν ( β n D n m γ R ) exp ( j ν γ z ) d z = κ n m ν J ν ( β n D n m γ R ) 0 π γ exp [ j ( β m β n ν γ ) z ] d z ,
exp ( j x sin θ ) = ν = J ν ( x ) exp ( j ν θ ) ,
K n m = κ { π γ J 0 ( β D n m γ R ) + j γ ν 0 ( 1 ) ν 1 ν J ν ( β D n m γ R ) } .
K n m κ 2 β R D n m 2 π γ [ cos ( β D n m γ R π 4 ) + j π ν 0 ( 1 ) ν 1 ν cos ( β D n m γ R ν π 2 π 4 ) ] ,
J ν ( x ) 2 π x cos [ x ( ν + 1 2 ) π 2 ] ,       ( 8 x 4 ν 2 1 ) .
ν 0 ( 1 ) ν 1 ν cos ( x ν π 2 π 4 )     = ν 0 ( 1 ) ν 1 ν [ cos ( x π 4 ) cos ( ν π 2 ) + sin ( x π 4 ) sin ( ν π 2 ) ]     = sin ( x π 4 ) ν 0 ( 1 ) ν 1 ν sin ( ν π 2 ) .
sin ( x π 4 ) ν 0 ( 1 ) ν 1 ν sin ( ν π 2 ) = 2 sin ( x π 4 ) ν = 1 ( 1 ) ν 1 ν sin ( ν π 2 ) = 2 sin ( x π 4 ) ν = 0 2 2 ν + 1 sin [ ( 2 ν + 1 ) π 2 ] = π sin ( x π 4 ) ,
ν = 0 sin ( 2 ν + 1 ) x 2 ν + 1 = { π / 4 , π / 4 ,     0 < x < π , π < x < 0.
K n m κ 2 β R D n m 2 π γ [ cos ( β D n m γ R π 4 ) j sin ( β D n m γ R π 4 ) ] κ 2 β R D n m 2 π γ exp [ j ( β D n m γ R π 4 ) ] .

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