Abstract

We have derived an intuitively interpretable expression of the average power-coupling coefficient for estimating the inter-core crosstalk of the multicore fiber. Based on the derived expression, we discuss how the structure fluctuation and macrobend can affect the crosstalk, and organize previously reported methods for crosstalk suppression. We also discuss how the microbending can affect the crosstalk in homogeneous and heterogeneous MCFs, based on the derived expression and previously reported measurement results.

© 2013 OSA

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  1. T. Morioka, “New generation optical infrastructure technologies: EXAT initiative towards 2020 and beyond,” in OptoElectron. Commun. Conf. (OECC) (2009), paper FT4.
    [CrossRef]
  2. M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express6(2), 98–103 (2009).
    [CrossRef]
  3. K. Takenaga, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by quasi-homogeneous solid multi-core fiber,” in Opt. Fiber Commun. Conf. (OFC) (2010), paper OWK7.
  4. J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Statistics of crosstalk in bent multicore fibers,” Opt. Express18(14), 15122–15129 (2010).
    [CrossRef] [PubMed]
  5. T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Eur. Conf. Opt. Commun. (ECOC) (2010), paper We.8.F.6.
    [CrossRef]
  6. 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.E94-B(2), 409–416 (2011).
    [CrossRef]
  7. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-crosstalk and low-loss multi-core fiber utilizing fiber bend,” in Opt. Fiber Commun. Conf. (OFC) (2011), paper OWJ3.
  8. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Ultra-low-crosstalk multi-core fiber feasible to ultra-long-haul transmission,” in Opt. Fiber Commun. Conf. (OFC) (2011), paper PDPC2.
  9. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express19(17), 16576–16592 (2011).
    [CrossRef] [PubMed]
  10. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express19(26), B102–B111 (2011).
    [CrossRef] [PubMed]
  11. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012).
    [CrossRef]
  12. K. Petermann, “Microbending loss in monomode fibers,” Electron. Lett.12(4), 107–109 (1976).
    [CrossRef]
  13. J. M. Fini, B. Zhu, T. F. Taunay, M. F. Yan, and K. S. Abedin, “Crosstalk in multicore fibers with randomness: gradual drift vs. short-length variations,” Opt. Express20(2), 949–959 (2012).
    [CrossRef] [PubMed]
  14. K. Saitoh, T. Matsui, T. Sakamoto, M. Koshiba, and S. Tomita, “Multi-core hole-assisted fibers for high core density space division multiplexing,” in OptoElectron. Commun. Conf. (OECC) (2010), paper 7C2–1.
  15. K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Opt. Fiber Commun. Conf. (OFC) (2011), paper OWJ4.
  16. D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
    [CrossRef]
  17. K. Imamura, K. Mukasa, R. Sugizaki, Y. Mimura, and T. Yagi, “Multi-core holey fibers for ultra large capacity wide-band transmission,” in Eur. Conf. Opt. Commun. (ECOC) (2008), paper P.1.17.
    [CrossRef]
  18. K. Imamura, K. Mukasa, Y. Mimura, and T. Yagi, “Multi-core holey fibers for the long-distance (>100 km) ultra large capacity transmission,” in Opt. Fiber Commun. Conf. (OFC) (2009), paper OTuC3.
  19. G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.
  20. J. Sakaguchi, Y. Awaji, N. Wada, T. Hayashi, T. Nagashima, T. Kobayashi, and M. Watanabe, “Propagation characteristics of seven-core fiber for spatial and wavelength division multiplexed 10-Gbit/s channels,” in Opt. Fiber Commun. Conf. (OFC) (2011), paper OWJ2.
  21. K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE8284, 82840I, 82840I-8 (2012).
    [CrossRef]
  22. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express20(14), 15157–15170 (2012).
    [CrossRef] [PubMed]
  23. T. Hayashi, T. Sasaki, and E. Sasaoka, “Microbending-induced crosstalk increase in heterogeneous multi-core fiber,” in Eur. Conf. Opt. Commun. (ECOC) (2011), paper Mo.1.LeCervin.3.
  24. T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers and their crosstalk characteristics,” in IEEE Photonics Society Summer Topical Meeting Series (2012), paper TuC4.1.
  25. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A11(3), 963–983 (1994).
    [CrossRef]
  26. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Characterization of crosstalk in ultra-low-crosstalk multi-core fiber,” J. Lightwave Technol.30(4), 583–589 (2012).
    [CrossRef]

2012 (5)

2011 (3)

2010 (1)

2009 (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express6(2), 98–103 (2009).
[CrossRef]

2006 (1)

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

1994 (1)

1976 (1)

K. Petermann, “Microbending loss in monomode fibers,” Electron. Lett.12(4), 107–109 (1976).
[CrossRef]

Abedin, K. S.

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.E94-B(2), 409–416 (2011).
[CrossRef]

Bennett, C. R.

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

Bizeul, J. C.

G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.

Boscher, D.

G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.

Botton, C.

G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.

Fini, J. M.

Grosso, P.

G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.

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.E94-B(2), 409–416 (2011).
[CrossRef]

Hayashi, T.

Huang, W.-P.

Kokubun, Y.

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express6(2), 98–103 (2009).
[CrossRef]

Koshiba, M.

K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE8284, 82840I, 82840I-8 (2012).
[CrossRef]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012).
[CrossRef]

J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express20(14), 15157–15170 (2012).
[CrossRef] [PubMed]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express19(26), B102–B111 (2011).
[CrossRef] [PubMed]

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.E94-B(2), 409–416 (2011).
[CrossRef]

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express6(2), 98–103 (2009).
[CrossRef]

Le Noane, G.

G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.

Matsuo, S.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012).
[CrossRef]

K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE8284, 82840I, 82840I-8 (2012).
[CrossRef]

J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express20(14), 15157–15170 (2012).
[CrossRef] [PubMed]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express19(26), B102–B111 (2011).
[CrossRef] [PubMed]

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.E94-B(2), 409–416 (2011).
[CrossRef]

Michaille, L. F.

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

Nielsen, M. D.

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

Petermann, K.

K. Petermann, “Microbending loss in monomode fibers,” Electron. Lett.12(4), 107–109 (1976).
[CrossRef]

Saitoh, K.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012).
[CrossRef]

K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE8284, 82840I, 82840I-8 (2012).
[CrossRef]

J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express20(14), 15157–15170 (2012).
[CrossRef] [PubMed]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express19(26), B102–B111 (2011).
[CrossRef] [PubMed]

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.E94-B(2), 409–416 (2011).
[CrossRef]

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express6(2), 98–103 (2009).
[CrossRef]

Sasaki, T.

Sasaoka, E.

Shepherd, T. J.

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

Shimakawa, O.

Simonsen, H. R.

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

Takenaga, K.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012).
[CrossRef]

K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE8284, 82840I, 82840I-8 (2012).
[CrossRef]

J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express20(14), 15157–15170 (2012).
[CrossRef] [PubMed]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express19(26), B102–B111 (2011).
[CrossRef] [PubMed]

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.E94-B(2), 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.E94-B(2), 409–416 (2011).
[CrossRef]

Taru, T.

Taunay, T. F.

Taylor, D. M.

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

Tu, J.

Yan, M. F.

Zhu, B.

Electron. Lett. (2)

D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, “Demonstration of multi-core photonic crystal fibre in an optical interconnect,” Electron. Lett.42(6), 331–332 (2006).
[CrossRef]

K. Petermann, “Microbending loss in monomode fibers,” Electron. Lett.12(4), 107–109 (1976).
[CrossRef]

IEEE Photon. J. (1)

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012).
[CrossRef]

IEICE Electron. Express (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express6(2), 98–103 (2009).
[CrossRef]

IEICE Trans. Commun. (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.E94-B(2), 409–416 (2011).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Opt. Express (5)

Proc. SPIE (1)

K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE8284, 82840I, 82840I-8 (2012).
[CrossRef]

Other (13)

T. Hayashi, T. Sasaki, and E. Sasaoka, “Microbending-induced crosstalk increase in heterogeneous multi-core fiber,” in Eur. Conf. Opt. Commun. (ECOC) (2011), paper Mo.1.LeCervin.3.

T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers and their crosstalk characteristics,” in IEEE Photonics Society Summer Topical Meeting Series (2012), paper TuC4.1.

K. Takenaga, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by quasi-homogeneous solid multi-core fiber,” in Opt. Fiber Commun. Conf. (OFC) (2010), paper OWK7.

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Eur. Conf. Opt. Commun. (ECOC) (2010), paper We.8.F.6.
[CrossRef]

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-crosstalk and low-loss multi-core fiber utilizing fiber bend,” in Opt. Fiber Commun. Conf. (OFC) (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 Opt. Fiber Commun. Conf. (OFC) (2011), paper PDPC2.

K. Saitoh, T. Matsui, T. Sakamoto, M. Koshiba, and S. Tomita, “Multi-core hole-assisted fibers for high core density space division multiplexing,” in OptoElectron. Commun. Conf. (OECC) (2010), paper 7C2–1.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Opt. Fiber Commun. Conf. (OFC) (2011), paper OWJ4.

K. Imamura, K. Mukasa, R. Sugizaki, Y. Mimura, and T. Yagi, “Multi-core holey fibers for ultra large capacity wide-band transmission,” in Eur. Conf. Opt. Commun. (ECOC) (2008), paper P.1.17.
[CrossRef]

K. Imamura, K. Mukasa, Y. Mimura, and T. Yagi, “Multi-core holey fibers for the long-distance (>100 km) ultra large capacity transmission,” in Opt. Fiber Commun. Conf. (OFC) (2009), paper OTuC3.

G. Le Noane, D. Boscher, P. Grosso, J. C. Bizeul, and C. Botton, “Ultra high density cables using a new concept of bunched multicore monomode fibers: A key for the future FTTH networks,” in Int. Wire Cable Symp. (IWCS) (1994), 203–210.

J. Sakaguchi, Y. Awaji, N. Wada, T. Hayashi, T. Nagashima, T. Kobayashi, and M. Watanabe, “Propagation characteristics of seven-core fiber for spatial and wavelength division multiplexed 10-Gbit/s channels,” in Opt. Fiber Commun. Conf. (OFC) (2011), paper OWJ2.

T. Morioka, “New generation optical infrastructure technologies: EXAT initiative towards 2020 and beyond,” in OptoElectron. Commun. Conf. (OECC) (2009), paper FT4.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematics of perturbations on the propagation constant. (a) a slight change of the propagation constant in a core due to bend, (b) a slight change of the propagation constant in a core due to structure fluctuation, and (c) a bend-induced change of the propagation constant in a core when assuming another core as a reference of the propagation constant.

Fig. 2
Fig. 2

Comparisons between calculated by using Eq. (25) and calculated by using Eqs. (13)(17). (a) normalized with respect to the Lorentzian, (b) normalized with respect to the arcsine distribution. Solid lines: calculated by using Eq. (25), dashed lines: calculated by using Eqs. (13)(17). The solid lines and the dashed lines are overlapped.

Fig. 3
Fig. 3

A schematic example of the average power-coupling coefficient , as a function of the propagation constant mismatch Δβc and the curvature 1/Rb, in case that twist of an MCF is gradual and random enough. (a) a 3-dimensional plot, (b) a contour map of log(). Thick solid lines in (b) are the thresholds between the phase-matching region and the non-phase-matching region.

Fig. 4
Fig. 4

Dependences of the microbend on the average crosstalk (average power-coupling coefficient) for MCF-A (heterogeneous) and MCF-B (homogeneous), measured by wavelength averaging [26] with 100-m fiber [23,24] at λ = 1550 nm.

Fig. 5
Fig. 5

Comparisons of the average power-coupling coefficient s obtained from the measurements and from Eqs. (13)(17). (a) The dependences of in MCF-A on the bending radius Rb and on the microbend. (b) The dependence of in MCF-A and MCF-B on the propagation constant mismatch Δβc and on the microbend at Rb = 140 mm. Closed-marks: measured without the microbend, open-marks: measured with the microbend, triangulars: measured by averaging the crosstalk by rewinding 2-m fiber 10 times [5], circles: measured by wavelength averaging [26] with 100-m fiber [23,24]. Solid lines: calculated at lc = 3 cm, dashed lines: at lc = 4 mm, dotted lines: at lc = 3 mm, dashed-dotted lines: at lc = 2 mm, dashed-two dotted lines: at lc = 1 mm,

Tables (1)

Tables Icon

Table 1 Characteristics of the Evaluated MCFs

Equations (32)

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

d A n dz =j κ nm exp[ j 0 z ( β m β n )dz ] A m =j κ nm exp[ j( β c,m β c,n )zj 0 z ( β v,m β v,n )dz ] A m ,
Δ x nm = Δ A n A m j κ nm z 1 z 2 exp[ j( β c,m β c,n )z ]f( z )dz ,
f( z )exp[ j 0 z [ β v,m ( z ) β v,n ( z ) ]d z ].
Δ X nm = | Δ x nm | 2 = Δ x nm Δ x nm * κ nm 2 z 1 z 2 z 1 z 2 exp[ j( β c,m β c,n )( z z ) ] f( z ) f * ( z ) dz d z κ nm 2 z 1 z 2 z 1 z z 2 z exp[ jΔ β c,nm ζ ] f( z +ζ ) f * ( z ) dζ d z κ nm 2 z 1 z 2 d z R ff ( ζ )exp( jΔ β c,nm ζ )dζ κ nm 2 Δz R ff ( ζ )exp( jΔ β c,nm ζ )dζ ,
S ff ( ν ˜ ) ( ν ˜ )= R ff ( ζ )exp( j2π ν ˜ ζ )dζ ,
S ff ( ν ˜ ) ( ν ˜ )d ν ˜ = S ff ( ν ˜ ) ( ν ˜ ) d ν ˜ dβ dβ =E[ | f( z ) | 2 ]=1,
S ff ( β ) ( β ) S ff ( ν ˜ ) ( ν ˜ ) d ν ˜ dβ = 1 2π S ff ( ν ˜ ) ( ν ˜ )= 1 2π R ff ( ζ )exp( jβζ )dζ .
h nm = Δ X nm Δz κ nm 2 S ff ( ν ˜ ) ( Δ n eff,c,nm λ )= κ nm 2 [ 2π S ff ( β ) ( Δ β c,nm ) ].
β v,n = β c,n x n cos θ f ( z ) y n sin θ f ( z ) R b ( z ) = β c,n r n cos θ n ( z ) R b ( z ) ,
R ff ( ζ )=exp( | ζ | / l c )
h nm ( z )= κ nm 2 1 π 1/ ( 2π l c ) 1/ ( 2π l c ) 2 + [ Δ n eff,c,nm ( z ) /λ ] 2 = κ nm 2 2π 1 π 1/ l c 1/ l c 2 + [ Δ β c,nm ( z ) ] 2 = κ nm 2 2 l c 1+ [ Δ β c,nm ( z ) l c ] 2 ,
β c,n = β c,n ( 1+ x n cos θ f ( z ) y n sin θ f ( z ) R b ( z ) )= β c,n ( 1+ r n cos θ n ( z ) R b ( z ) ).
h ¯ nm = κ nm 2 2 l c [ 1/ a( b+ ac ) +1/ c( b+ ac ) ],
a=1+ ( Δ β c,nm l c B nm l c / R b ) 2 1+ l c ( Δ β c,nm l c β c,n D nm l c / R b ) 2 ,
b=1+ ( Δ β c,nm l c ) 2 ( B nm l c / R b ) 2 1+ ( Δ β c,nm l c ) 2 ( β c,n D nm l c / R b ) 2 ,
c=1+ ( Δ β c,nm l c + B nm l c / R b ) 2 1+ ( Δ β c,nm l c + β c,n D nm l c / R b ) 2 ,
B nm = ( β c,n x n β c,m x m ) 2 + ( β c,n y n β c,m y m ) 2 ,
Δ β c,nm ( R b , θ nm )=Δ β c,nm +Δ β b,nm ( R b , θ nm ),
Δ β b,nm ( R b , θ nm )=Δ β b,nm dev ( R b )cos θ nm ,
Δ β b,nm dev ( R b )= β c,n D nm R b ,
μ X,nm ( L ) 0 L h nm ( z )dz L[ 1 L 0 L h nm ( z )dz ]LE[ h nm ] L 0 p R b ( R b ) h ¯ nm ( R b )d R b ,
h ¯ nm ( R b )= 0 2π p θ nm ( θ nm ) h nm ( R b , θ nm )d θ nm .
h ¯ nm ( R b )= 0 2π 1 2π h nm ( R b , θ nm )d θ nm = 0 2π 1 2π κ nm 2 2π S ff ( β ) [ Δ β c,nm ( R b , θ nm ) ]d θ nm =2 0 π κ nm 2 S ff ( β ) [ Δ β c,nm +Δ β b,nm dev ( R b )cos θ nm ]d θ nm =2π Δ β b,nm dev Δ β b,nm dev κ nm 2 π [ Δ β b,nm dev ( R b ) ] 2 Δ β 2 S ff ( β ) ( Δ β c,nm Δβ )d( Δβ ) .
p Δ β b ( Δ β c,nm )={ 1 π ( Δ β b,nm dev ) 2 Δ β c,nm 2 , | Δ β c,nm |Δ β b,nm dev , 0, otherwise,
h ¯ nm ( Δ β c,nm , R b )= κ nm 2 2π ( p Δ β b S ff ( β ) ) Δβ ( Δ β c,nm )= κ nm 2 ( p Δ ν ˜ b S ff ( ν ˜ ) ) Δ ν ˜ ( Δ ν ˜ c,nm ),
h ¯ nm ( Δ β c,nm , R b ) κ nm 2 [ 2π p Δ β b ( Δ β c,nm ) ]= κ nm 2 p Δ ν ˜ b ( Δ ν ˜ c,nm ) κ nm 2 2 ( β c,n D nm R b ) 2 Δ β c,nm 2 = κ nm 2 λ π ( n eff,c,n D nm R b ) 2 Δ n eff,c,nm 2 ,
h ¯ nm ( R b ) κ nm 2 2 R b β c,n D nm = κ nm 2 λ R b π n eff,c,n D nm ,
R pk = B nm | Δ β c,nm | D nm β c,n | Δ β c,nm | = D nm n eff,c,n | Δ n eff,c,nm | ,
J 0 ( Δ β b ζ ) Fourier transform p Δ ν ˜ b ( Δ ν ˜ c )=2π p Δ β b ( Δ β c ),
R ff ( ζ ) Fourier transform S ff ( ν ˜ ) ( Δ ν ˜ c )=2π S ff ( β ) ( Δ β c ),
fg Fourier transform ( FG ) Δ ν ˜ = 1 2π ( FG ) Δβ ,
J 0 ( Δ β b ζ ) R ff ( ζ ) Fourier transform ( p Δ ν ˜ b S ff ( ν ˜ ) ) Δ ν ˜ b ( Δ ν ˜ c )=2π ( p Δ β b S ff ( β ) ) Δ β b ( Δ β c ).

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