Abstract

In this paper we evaluate experimentally and model theoretically the nonlinear crosstalk random process in multi-core fiber. The experimental results indicate that mode coupling in multi-core fibers is reduced in presence of fiber Kerr nonlinearities. An analytical study of the inter-core crosstalk probability density function in nonlinear regime is performed, where the theoretical distribution, derived from the nonlinear coupled-mode equation, is experimentally validated in homogeneous four-core fiber. The herein presented analysis includes the evaluation of the inter-core crosstalk probability density function, mean and variance evolution considering the optical power launched into the fiber.

© 2015 Optical Society of America

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Corrections

16 October 2015: A correction was made to Ref. 10.


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References

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2015 (1)

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

2013 (3)

2012 (2)

2011 (2)

2010 (2)

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]

1996 (1)

K. Yasumoto, H. Maeda, and N. Maekawa, “Coupled-Mode Analysis of an Asymmetric Nonlinear Directional Coupler,” J. Lightwave Technol. 14(4), 628–633 (1996).
[Crossref]

1994 (2)

W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. 11(3), 963–983 (1994).
[Crossref]

L.-P. Yuan, “A unified approach for the coupled-mode analysis of nonlinear optical couplers,” IEEE J. Quantum Electron. 30(1), 126–133 (1994).
[Crossref]

1990 (1)

1982 (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microw. Theory Tech. 30(10), 1568–1571 (1982).
[Crossref]

Abedin, K. S.

Andrekson, P. A.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

Assanto, G.

Awaji, Y.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

Eriksson, T. A.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

Essiambre, R.-J.

Fini, J. M.

Foschini, G. J.

Fraile-Pelaez, F. J.

Goebel, B.

Hayashi, T.

Huang, W.-P.

W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. 11(3), 963–983 (1994).
[Crossref]

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microw. Theory Tech. 30(10), 1568–1571 (1982).
[Crossref]

Karlsson, M.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[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.

Kramer, G.

Li, H.

Luís, R. S.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

Maeda, H.

K. Yasumoto, H. Maeda, and N. Maekawa, “Coupled-Mode Analysis of an Asymmetric Nonlinear Directional Coupler,” J. Lightwave Technol. 14(4), 628–633 (1996).
[Crossref]

Maekawa, N.

K. Yasumoto, H. Maeda, and N. Maekawa, “Coupled-Mode Analysis of an Asymmetric Nonlinear Directional Coupler,” J. Lightwave Technol. 14(4), 628–633 (1996).
[Crossref]

Mafi, A.

Matsuo, S.

Nazemosadat, E.

Ogusu, K.

Puttnam, B. J.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

Saitoh, K.

Sasaki, T.

Sasaoka, E.

Shimakawa, O.

Takenaga, K.

Taru, T.

Taunay, T. F.

Wada, N.

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

Winzer, P. J.

Yan, M. F.

Yasumoto, K.

K. Yasumoto, H. Maeda, and N. Maekawa, “Coupled-Mode Analysis of an Asymmetric Nonlinear Directional Coupler,” J. Lightwave Technol. 14(4), 628–633 (1996).
[Crossref]

Yuan, L.-P.

L.-P. Yuan, “A unified approach for the coupled-mode analysis of nonlinear optical couplers,” IEEE J. Quantum Electron. 30(1), 126–133 (1994).
[Crossref]

Zhu, B.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

L.-P. Yuan, “A unified approach for the coupled-mode analysis of nonlinear optical couplers,” IEEE J. Quantum Electron. 30(1), 126–133 (1994).
[Crossref]

IEEE Photonics J. (1)

T. A. Eriksson, B. J. Puttnam, R. S. Luís, M. Karlsson, P. A. Andrekson, Y. Awaji, and N. Wada, “Experimental investigation of crosstalk penalties in multicore fiber transmission systems,” IEEE Photonics J. 7(1), 1943–1950 (2015).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microw. Theory Tech. 30(10), 1568–1571 (1982).
[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]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. (1)

W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. 11(3), 963–983 (1994).
[Crossref]

Opt. Express (6)

Other (9)

H. P. Hsu, Probability, Random Variables, & Random Processes, (McGraw-Hill, 1997), Chaps. 4 and 5.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Elsevier, 2013), Chaps. 2 and 9.

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Elsevier, 2006), Chap. 4.

T. Hayashi, “Multi-core Optical Fibers,” in Optical Fiber Telecommunications VIA: Components and Subsystems, I. P. Kaminow, T. Li, and A. E. Willner (Eds), 6th ed. (Elsevier, 2013), Chap. 9.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007), Chap. 21.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Elsevier, 2008), Chap. 1.

R. H. Stolen, “Nonlinear properties of optical fibers,” in S. E. Miller and A. G. Chynoweth (Eds), Optical Fiber Telecommunications, pp. 125–150, Academic Press, 1979.

J. M. Senior, Optical Fiber Communications Principles and Practice, 3rd ed. (Prentice Hall, 2009), Chap. 3.

B. Chomycz, Planning Fiber Optic Networks, 1st ed. (McGraw-Hill, 2009), Chap. 7.

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Figures (3)

Fig. 1
Fig. 1 Experimental set-up for nonlinear inter-core crosstalk evaluation.
Fig. 2
Fig. 2 Measured inter-core crosstalk temporal profile in linear and nonlinear regimes using different optical power levels launched into a multi-core fiber Fibercore SM-4C1500(8.0/125).
Fig. 3
Fig. 3 Statistical analysis of nonlinear inter-core crosstalk. (a) Probability density function (p.d.f) measured for 0 dBm optical power launch, (b) p.d.f. for 17 dBm optical power launch. (c) Measured IC-XT variance and (d) IC-XT mean as a function of power launch.

Equations (22)

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

j d A n ( z ) d z = q n | A n ( z ) | 2 A n ( z ) + k n m exp [ j ( β m β n ) z ] A m ( z )
k n m = ω ε 0 + + ( N 2 N m 2 ) e m e n * d x d y + + z ^ ( e n * × h n + e n × h n * ) d x d y
q n = ω ε 0 + + α | e n | 4 d x d y + + z ^ ( e n * × h n + e n × h n * ) d x d y
Δ β e q , m n ( z ) = β m + β B + S , m ( z ) β n β B + S , n ( z )
j d A n ( z ) d z = q n | A n ( z ) | 2 A n ( z ) + m n M k n m exp [ j 0 z Δ β e q , m n ( τ ) d τ ] A m ( z )
d d z E ¯ ( z ) = j ( q ¯ ¯ P e ¯ ¯ + β e q ¯ ¯ + k ¯ ¯ ) E ¯ ( z )
E ¯ ( z ) = exp [ j 0 z β e q ¯ ¯   d τ ] A ¯ ( z )
X n m P n ( z = N ) P m ( z = N )
X n m N L P n ( z = N ) P L = | A n ( z = N ) | 2 P L
A n ( z = N ) A n ( z = N 1 ) j q n L N 1 | A n ( z = N 1 ) | 2 A n ( z = N 1 ) j K n m A m ( z = N 1 ) e j ϕ m n ( z = N )                                     A n ( z = 0 ) j q n l = 1 N L l 1 | A n ( z = l 1 ) | 2 A n ( z = l 1 ) j K n m l = 1 N A m ( z = l 1 ) e j ϕ m n ( z = l )
q n ( L L N L 0 ) | A n ( z = N ) | 2 A n ( z = N ) q n L | A n ( z = N ) | 2 A n ( z = N )
A n ( z = N ) j q n L P n ( z = N ) A n ( z = N ) j A m ( z = 0 ) K n m l = 1 N e j ϕ m n ( z = l )
A n ( z = N ) j A m ( z = 0 ) K n m l = 1 N e j ϕ m n ( z = l ) 1 + j L q n P n ( z = N )
P n ( z = N ) = | A n ( z = N ) | 2 | A m ( z = 0 ) | 2 1 + L 2 q n 2 P n 2 ( z = N ) | K n m l = 1 N e j ϕ m n ( z = l ) | 2
X n m N L 1 1 + L 2 q n 2 P L 2 ( X n m N L ) 2 X n m L X n m L L 2 q n 2 P L 2 ( X n m N L ) 3 + X n m N L
f X N L ( x N L ) = f X L ( h ( x N L ) ) | d h ( x N L ) d x N L |
f X n m L ( x L ) = 4 x L N 2 | K n m | 4 exp ( 2 x L N | K n m | 2 ) u ( x L )
f X n m N L ( x N L ) = g ( x N L ) 1 N 2 | K n m | 4 exp ( 2 x N L N | K n m | 2 ) u ( x N L )
g ( x N L ) = ( 12 L 4 q n 4 P L 4 x N L 5 + 16 L 2 q n 2 P L 2 x N L 3 + 4 x N L ) exp ( 2 L q n 2 P L 2 x N L 3 N | K n m | 2 )
P L ( d B m ) α a t t ( d B / k m ) L N L ( k m ) P c ( d B m ) L N L P L P c α a t t
P c = 1 2 ε 0 c 0 A e f f E a t 2 1.58 mW 2 dBm
P t h , S B S 21 A e f f g B L e f f

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