Abstract

A statistical theory for crosstalk in multicore fibers is derived from coupled-mode equations including bend-induced perturbations. Bends are shown to play a crucial role in crosstalk, explaining large disagreement between experiments and previous calculations. The average crosstalk of a fiber segment is related to the statistics of the bend radius and orientation, including spinning along the fiber length. This framework allows efficient and accurate estimates of cross-talk for realistic telecommunications links.

© 2010 OSA

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References

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  1. S. Iano, T. Sato, S. Sentsui, T. Kuroha, and Y. Nishimura, “Multicore optical fiber,” in Optical Fiber Communication, 1979 OSA Technical Digest Series (Optical Society of America, 1979), paper WB1.
  2. B. Rosinski, J. W. D. Chi, P. Grosso, and J. Le Bihan, “Multichannel Transmission of a Multicore Fiber Coupled with Vertical-Cavity Surface-Emitting Lasers,” J. Lightwave Technol. 17(5), 807–810 (1999).
    [CrossRef]
  3. R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [CrossRef]
  4. G. Le Noane, P. Grosso, and I. Hardy, “Small, high precision, multicore optical guides and process for the production of said guides,” US Patent 5519801 (1996).
  5. 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.
  6. J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Low cross-talk design of multi-core fibers,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuAA3.
  7. J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Bends in the design of low-crosstalk multicore fiber communications links,” to be published in the 15th OptoElectronics and Communications Conference 2010.
  8. S. Kumar, U. H. Manyam, and V. Srikant, “Optical fibers having cores with different propagation constants, and methods of manufacturing same,” US Patent 6611648 (2003).
  9. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982).
    [CrossRef] [PubMed]
  10. K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. 4(1), 2–7 (1986).
    [CrossRef]
  11. J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of bend-induced nonlinearities in large-mode-area fibers,” Opt. Lett. 32(17), 2562–2564 (2007).
    [CrossRef] [PubMed]
  12. K. S. Shanmugan, and A. M. Breipohl, Random Signals (John Wiley and Sons, 1988).

2010

2007

1999

1986

K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. 4(1), 2–7 (1986).
[CrossRef]

1982

Chi, J. W. D.

Essiambre, R. J.

Feder, K.

Fini, J. M.

Foschini, G. J.

Goebel, B.

Grosso, P.

Headley, C.

Kramer, G.

Kuhne, R.

K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. 4(1), 2–7 (1986).
[CrossRef]

Le Bihan, J.

Marcuse, D.

Nicholson, J. W.

Petermann, K.

K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. 4(1), 2–7 (1986).
[CrossRef]

Rosinski, B.

Westbrook, P. S.

Winzer, P. J.

Yablon, A. D.

Appl. Opt.

J. Lightwave Technol.

Opt. Lett.

Other

K. S. Shanmugan, and A. M. Breipohl, Random Signals (John Wiley and Sons, 1988).

G. Le Noane, P. Grosso, and I. Hardy, “Small, high precision, multicore optical guides and process for the production of said guides,” US Patent 5519801 (1996).

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.

J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Low cross-talk design of multi-core fibers,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuAA3.

J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Bends in the design of low-crosstalk multicore fiber communications links,” to be published in the 15th OptoElectronics and Communications Conference 2010.

S. Kumar, U. H. Manyam, and V. Srikant, “Optical fibers having cores with different propagation constants, and methods of manufacturing same,” US Patent 6611648 (2003).

S. Iano, T. Sato, S. Sentsui, T. Kuroha, and Y. Nishimura, “Multicore optical fiber,” in Optical Fiber Communication, 1979 OSA Technical Digest Series (Optical Society of America, 1979), paper WB1.

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Figures (5)

Fig. 1
Fig. 1

A schematic link illustrates that real deployed fibers contain segments with very different bend characteristics. This link has short bend-challenged spans and a much longer span with carefully managed bends.

Fig. 2
Fig. 2

The six outer cores have alternating positive and negative skew (Δnm eff = ± Δnskew) relative to the center core in the fiber design (a). Transfer-matrix simulation results show the fraction of power coupled from the center core for an over-simplified model with no bends (b), and for an improved model including a 1m bend radius (c). Skew in effective index is given by the legend, and illustrated in the inset.

Fig. 3
Fig. 3

Intermittent resonant coupling is illustrated schematically. Two neighboring cores (blue and red) have an effective index mismatch caused by slight core size difference. Lower plots show bent-fiber equivalent index profile (black) and mode effective index for the two cores (blue and red lines). As bend orientation drifts, the bend perturbation to this mismatch oscillates. If the bend is tight enough, each pair of cores sees index matched resonance twice for each 2π of orientation drift. Coupling between cores is frustrated at other orientations (grey arrows), but is efficient near the index-matched orientation.

Fig. 4
Fig. 4

Calculations illustrating the statistical model: Two curvature (a) and bend orientation functions (b) were randomly generated from the same statistics and plotted versus length for Rb0 = 0.5m. Broad oscillations common to both orientation curves are the gulp, while differences between the traces are the random orientation drift. Average cross-talk (c) between two neighboring cores [Eq. (13)] is plotted as a function of effective index mismatch for several nominal bend radii.

Fig. 5
Fig. 5

The statistical average cross-talk expression, Eq. (12) (dashed), is validated by comparison with brute-force transfer-matrix propagation (solid). Asymptotic agreement is reached for each of the neighboring-core pairs, represented by different colors.

Equations (17)

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v ( L ) = T ( L , 0 ) v ( 0 ) = T ( L , z N 1 ) ... T ( z 2 , z 1 ) T ( z 1 , 0 ) v ( 0 )
d d z T = i 2 π λ ( A + B + C ) T .
B m , m = γ n c o r e R b e n d ( x m cos θ + y m sin θ ) .
d d z P i 2 π λ ( A + B ) P
T = P U
d d z U = i 2 π λ P 1 C P U
U n , m ( z p + 1 , z p ) δ n , m + i 2 π λ C n m z p z p + 1 d z P n , n 1 P m , m
U n , m ( z p + 1 , z p ) i 2 π λ C n m z p z p + 1 d z exp ( i Δ β m , n ( z z p ) ) exp ( z p z i 2 π λ ( B m , m B n , n ) ) ,
Δ β m , n = 2 π λ ( A m , m A n , n ) .
f ( z ) exp ( z p z i 2 π λ ( B m , m B n , n ) ) .
| U n , m | 2 | 2 π C n m λ | 2 z p z p + 1 d z z p z p + 1 d z exp ( i Δ β m , n ( z z ) ) f ( z ) f * ( z ) ,
| U n , m | 2 | 2 π C n m λ | 2 z p z p + 1 d z z p z p + 1 d z exp ( i Δ β m , n ( z z ) ) R f f ( z z ) .
| U n , m | 2 | 2 π C n m λ | 2 ( z p + 1 z p ) S f f ( Δ β m , n )
f ( z ) exp ( z 1 z i 2 π λ γ n c o r e R b e n d a cos ( θ θ m , n ) )
1 / R b = 1 / R b 0 + g 1
R b 0 | g 1 | 2 1 / 2 = 0.2.
d θ / d z = K 0 ( z ) + g 2 ( z )

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