## Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend |

Optics Express, Vol. 21, Issue 5, pp. 5401-5412 (2013)

http://dx.doi.org/10.1364/OE.21.005401

Acrobat PDF (1539 KB)

### 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

## 1. Introduction

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. Express **6**(2), 98–103 (2009). [CrossRef]

10. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express **19**(26), B102–B111 (2011). [CrossRef] [PubMed]

*et al.*derived a closed-form expression of the average power-coupling coefficient between cores in the MCF [11

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]

## 2. Review and clarification of previous derivation of power-coupling coefficient

*A*is the complex amplitude,

*κ*the mode coupling coefficient from Core

_{nm}*n*to Core

*m*,

*β*= 2π

*n*

_{eff}/

*λ*the propagation constant,

*n*

_{eff}the effective refractive index, and

*λ*the wavelength. Subscripts c and v of

*β*represent

*constant*and

*variable*perturbed parts of

*β*, respectively

*z*

_{1},

*z*

_{2}] can be expressed asby usingAccordingly, the average crosstalk increase in power within the segment [

*z*

_{1},

*z*

_{2}] can be expressed as

*R*is the autocorrelation function (ACF) of

_{ff}*f*(

*z*), Δ

*z*is

*z*

_{2}−

*z*

_{1}, and the correlation length

*l*

_{c}of

*R*is assumed to be adequately shorter than Δ

_{ff}*z*.

*ζ*after the coupling. For example, where

*ζ*>>

*l*

_{c}, the coupled and non-coupled lights becomes incoherent even if the lights are very coherent. Based on the Wiener–Khinchin theorem, the power spectrum density (PSD) is the Fourier transform of the ACF:where

*β*is the angular wave number. Note that

*n*

_{eff}, and

*β*have common subscripts, e.g.,

*β*with common expressions, we would like to define the PSD with respect to

*β*, whose total power is equivalent to Eq. (5). From the Parseval’s theorem, the average power of

*f*(

*z*), or expected value of |

*f*(

*z*)|

^{2}, is equivalent to the integral of the PSD over whole

*f*(

*z*) and the PSDs of

*f*(

*z*):where E[·] represents the expected value. Therefore, in this paper, the PSD

*β*(the angular wave number in the medium) is defined as:From Eqs. (4)–(7), the power-coupling coefficient can be expressed as

*β*, or how

*β*

_{v}can vary. As shown in Figs. 1(a) and 1(b), the bend and the structure fluctuation can induce a slight change in

*β*

_{v}in one core, which can occur ether in the single-core fiber or in the MCF. In the single-core fiber, by assuming proper

*R*or

_{ff}*S*for the perturbations shown in Figs. 1(a) and 1(b), Eq. (8) is utilized for analyzing the power coupling between modes in the multi-mode fiber, microbend loss—power coupling from the core modes to the cladding modes, and so on. In the MCF, as shown in Fig. 1(c), the bend can induce relatively large

_{ff}*β*

_{v}in a core when assuming another core as a reference of the propagation constant. Fini

*et al.*[4

4. J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Statistics of crosstalk in bent multicore fibers,” Opt. Express **18**(14), 15122–15129 (2010). [CrossRef] [PubMed]

*et al.*[5

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]

*β*

_{v}in the MCF is induced by the macrobend and twist of the MCF asand investigated the crosstalk characteristics of the MCFs. Here, (

*x*,

_{n}*y*) and (

_{n}*r*,

_{n}*θ*) are the local Cartesian and polar coordinates of Core

_{n}*n*in a fiber cross-section, respectively,

*θ*= 0 is the radial direction of the macrobend,

_{n}*θ*

_{f}the angle between the

*x*-axis and the radial direction of the macrobend, and

*R*

_{b}the macrobend radius of the MCF—that is, the distance between the center of the macrobend and the origin of the local coordinates.

*β*

_{v},

*R*, or

_{ff}*S*that can include the perturbations of both the bend and the structure fluctuation. Therefore, by assuming that

_{ff}*R*includes only the effect of structure fluctuation and does not include that of macrobend and twist, Koshiba

_{ff}*et al.*investigated the effects of correlation length

*l*

_{c}and of the shape of the ACF

*R*on the average crosstalk

_{ff}*μ*[10

_{X}10. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express **19**(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]

*R*, and found that the exponential ACF (EAF)is proper for estimating actual

_{ff}*μ*of the MCFs. The EAF have been introduced to microbending loss analysis [12

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

10. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express **19**(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]

*β*´

_{c,}

*is*

_{nm}*β*´

_{c,}

*−*

_{n}*β*´

_{c,}

*, and*

_{m}*β*´

_{c}is redefined

*β*

_{c}that includes the effects of macrobend and twist:Average crosstalk

*μ*estimated using coupled-power equation with the power-coupling coefficient of Eq. (11) may be valid in cases where changes of

_{X}*R*

_{b}and

*θ*are gradual enough compared to

*l*

_{c}, since Δ

*β*´

_{c,}

*—which is variable and includes macrobend and twist— is substituted to Δ*

_{nm}*β*

_{c,}

*—which is constant— in Eq. (8).*

_{nm}*R*

_{b}and twist rate, Koshiba

*et al.*also analytically derived an average power-coupling coefficient

*h̅*, which is averaged over

*θ*, as [11

**4**(5), 1987–1995 (2012). [CrossRef]

*B*can be approximated as

_{nm}*β*

_{c,}

*if*

_{n}D_{nm}*β*

_{c,}

*/*

_{m}*β*

_{c,}

*≈1,*

_{n}*D*is the center-to-center distance between Core

_{nm}*m*and Core

*n*. They also reported that Eqs. (13)–(17) agreed well with measurement results. However, it is difficult to interpret physical meaning of Eqs. (13)–(17) intuitively.

## 3. Derivation of an intuitive expression of average power-coupling coefficient

*m*is taken as the origin of the local coordinate, and accordingly Δ

*β*´

_{c,}

*can be written as where*

_{nm}*θ*represents the angle between the radial direction of the bend and a line segment from Core

_{nm}*m*to Core

*n*, Δ

*β*

_{b,}

*the difference of*

_{nm}*β*variation between Core

*m*and Core

*n*from the macrobend, and

*β*

_{b,}

*.*

_{nm}*θ*and of

_{nm}*R*

_{b}, respectively, along the MCF; by assuming that

*μ*from Core

_{X,nm}*m*to Core

*n*can be expressed aswhere the average power-coupling coefficient isBy assuming that the twist of the MCF is random enough and the MCF is adequately long,

*θ*; therefore, by substituting

_{nm}*S*is the Lorentzian distribution as shown in Eq. (11). By using the arcsine distribution:which is the probability distribution of Δ

_{ff}*β*

_{b}, Eq. (23) can be rewritten aswhere the expression of

*f*and

*g*with respect to

*x*, and the expression with respect to

*S*in Eq. (8) includes both the effects of the structure fluctuation and the macrobend, the convolution term in Eq. (25) may be understood as the PSD

_{ff}*S*in Eq. (8).

_{ff}*β*

_{c,}

*| and the bandwidth of*

_{nm}*S*becomes a narrow delta-function-like distribution and the convolution contains only a gradually varying part of

_{ff}*β*

_{b}—shown in Eq. (24)— with constant

*R*

_{b}, as shown in [13

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. Express **20**(2), 949–959 (2012). [CrossRef] [PubMed]

*β*

_{c}

*= 0), Eq. (26) is reduced towhich coincides with Eq. (19) in [9*

_{,nm}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. Express **19**(17), 16576–16592 (2011). [CrossRef] [PubMed]

**4**(5), 1987–1995 (2012). [CrossRef]

*β*

_{c}< 0.21

*β*

_{c}

*D/R*

_{b}; therefore, Eq. (27) may be also used for estimating the crosstalk of a bent heterogeneous MCF with small Δ

*β*

_{c}.

*h̅*calculated by using Eq. (25) and

*h̅*calculated by using Eqs. (13)–(17). Figures 2(a) and 2(b) show the PSDs normalized with respect to the Lorentzian

*S*and to the arcsine distribution

_{ff}*h̅*calculated by using Eq. (25) and dashed lines represent

*h̅*calculated by using Eqs. (13)–(17); however, the solid lines and the dashed lines are overlapped, and we can only see the solid lines. Accordingly, it was clearly confirmed that Eq. (25) is equivalent to the expression of

*h̅*with Eqs. (13)–(17), and it can be also said that the set of Eqs. (13)–(17) is a closed-form solution of the convolution of the Lorentzian and the arcsine distribution.

## 4. Crosstalk suppression methods related to macrobend and structure fluctuation

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]

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. Express **19**(17), 16576–16592 (2011). [CrossRef] [PubMed]

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]

### 4.1 Utilization of the propagation constant mismatch

*β*

_{c}to suppress the phase matching [2

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

4. J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Statistics of crosstalk in bent multicore fibers,” Opt. Express **18**(14), 15122–15129 (2010). [CrossRef] [PubMed]

*β*

_{c}larger than

4. J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Statistics of crosstalk in bent multicore fibers,” Opt. Express **18**(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]

*adequately*larger than the critical bending radius

*R*

_{pk}[5

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]

**4**(5), 1987–1995 (2012). [CrossRef]

*R*

_{b}where Eq. (26) can be infinite, or the maximal

*R*

_{b}where the phase matching due to the macrobend can occur even if there is no structure fluctuation. Some margin from

*R*

_{pk}is needed for avoiding the phase matching induced by the spectral broadening of

*S*, due to the structural fluctuations. In heterogeneous MCFs, it is preferred if the correlation length

_{ff}*l*

_{c}of the structural fluctuation can be elongated, because the spectral broadening of

*S*can be narrowed and the PSD leakage into the non-phase-matching region can be suppressed, as shown in Figs. 2(b) and 3.

_{ff}**18**(14), 15122–15129 (2010). [CrossRef] [PubMed]

*R*

_{pk}less than 10 cm requires very large difference in core structure [5

*R*

_{pk}can be smaller than the bobbin radius of 140 mm.

*et al.*reported that up to two kinds of dissimilar step-index cores can be designed to achieve

*R*

_{pk}around 5 cm while achieving a similar

*A*

_{eff}of around 80 µm

^{2}at 1550 nm, and other good optical properties [21

21. K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Low-crosstalk multi-core fibers for long-haul transmission,” Proc. SPIE **8284**, 82840I, 82840I-8 (2012). [CrossRef]

*et al.*also reported that up to two kinds of dissimilar trench-assisted cores can be designed to achieve

*R*

_{pk}around 5 cm while achieving a similar

*A*

_{eff}of around 100 µm

^{2}[22

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. Express **20**(14), 15157–15170 (2012). [CrossRef] [PubMed]

### 4.2. Utilization of the bend-induced perturbation

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. Express **19**(17), 16576–16592 (2011). [CrossRef] [PubMed]

*β*

_{c}= 0). Identical core structure is rather desirable for suppressing the PSD. The PSD changes gradually with the bend radius, and there is no drastic PSD increase like that around

*R*

_{pk}in case of heterogeneous MCFs, since the PSD is suppressed in the phase-matching region. As shown in Eq. (27), the average crosstalk of a homogeneous MCF is proportional to the average bending radius, where |Δ

*β*

_{c,}

*| and the bandwidth of*

_{nm}### 4.3. Utilization of the longitudinal structural fluctuation

## 5. Applicability of the average power-coupling coefficient for estimating microbend-affected crosstalk

*S*only includes structure fluctuation, and

_{ff}*l*

_{c}, we may redefine the

*S*as the PSD of high frequency perturbations other than the macrobend perturbation, and thus

_{ff}*S*may include not only the effect of structure fluctuation but also the effect of microbend, in Eqs. (13)–(17) and Eq. (25). In this case, the increase of the microbend can be understood as the decrease of the correlation length

_{ff}*l*

_{c}of

*S*. The microbend may induce

_{ff}*β*perturbations both within a core (Fig. 1(a)) and between cores (Fig. 1(c)); and may be induced by various ways such as winding on a sandpaper-coated bobbin, winding on a wire mesh bobbin, and actual cabling. Therefore, the shape of

*S*for the structure fluctuation and the microbend could possibly be different from the Lorentzian—that is,

_{ff}*S*only for the structure fluctuation— and depend on how the microbend is induced. Thus, we need to investigate further details of the effect of the microbend on the crosstalk through experiment.

_{ff}*S*for the structure fluctuation and the microbend, in this paper.

_{ff}*h̅*on microbend conditions for a heterogeneous MCF-A [23] and for a homogeneous MCF-B [24]. Fiber properties of the MCFs are shown in Table 1 . For MCF-A,

*h̅*from the center core to an outer core was obtained. For MCF-B, the average of

*h̅*s between the three pairs of the neighboring cores was obtained. The values of

*h̅*were obtained from values of measured average crosstalk and fiber length by using coupled power equation. The microbend was applied by winding the MCFs on a 140-mm-radius bobbin with sandpaper (grade P240) at winding tension

*T*.

*h̅*at

*T*= 0 N was measured using a 140-mm-radius bobbin

*without*the sandpaper.

*h̅*of the heterogeneous MCF was increased by the microbend, but that of the homogeneous MCF was varied only slightly.

*l*

_{c}by using Eqs. (13)–(17) or Eq. (25). Figure 5 shows comparisons of the average power-coupling coefficients

*h̅*s obtained from the measurement results and those obtained from Eqs. (13)–(17). Figure 5(a) shows the dependences of

*h̅*in MCF-A on

*R*

_{b}, and on whether the microbend is applied or not—that is, difference of

*l*

_{c}— at

*R*

_{b}= 140 mm. When the microbend is not applied,

*l*

_{c}can be estimated to be around 3 cm for this measurement. When the microbend is applied,

*l*

_{c}can be estimated to be around 1–4 mm. Figure 5(b) shows the dependences of

*h̅*in MCF-A and MCF-B on the propagation constant mismatch Δ

*β*

_{c}and on whether the microbend is applied or not, at

*R*

_{b}= 140 mm. We can see that Δ

*β*

_{c}between dissimilar cores in MCF-A is in the non-phase-matching region and

*h̅*between dissimilar cores is increased by the decreasing of

*l*

_{c}, or by the broadening of the bandwidth of

*S*. On the other hand, Δ

_{ff}*β*

_{c}in MCF-B is designed to be zero and in the center of the phase-matching region; therefore,

*h̅*in MCF-B is hardly affected by the decreasing of

*l*

_{c}, at least if

*l*

_{c}is larger than 1 mm. Based on this evaluation,

*l*

_{c}was shortened from around 3 cm to around 1–4 mm by applying the microbend in these experiments. Though this shortening of

*l*

_{c}did not affect

*h̅*in MCF-B at

*R*

_{b}= 140 mm, the shortening of

*l*

_{c}may decrease

*h̅*in the (quasi-)homogeneous MCF if

*R*

_{b}is adequately large. Thus, we may consider that the microbend is possible to be utilized for suppressing the crosstalk in a very straight homogeneous MCF.

*S*for the structure fluctuation and the microbend as the Lorentzian. However, further investigation of the effect of the microbend on the crosstalk is necessary for elucidating the detailed characteristics of the effect, as we mentioned above.

_{ff}## 6. Conclusions

**4**(5), 1987–1995 (2012). [CrossRef]

## Appendix: Calculation of Eq. (25) for Figs. 2 and 3

*J*

_{0}(

*x*) is the Bessel function of the first kind of order zero, and functions

*F*and

*G*represents the Fourier transform of functions

*f*and

*g*respectively; we calculated Eq. (25) numerically by performing the fast Fourier transform (FFT) on the following relations:We calculated adequately broad bandwidths of the PSD so that the aliasing noise caused by the FFT can be suppressed in the plotted ranges.

## References and links

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. Express |

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. Express |

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. |

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. Express |

10. | M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express |

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. |

12. | K. Petermann, “Microbending loss in monomode fibers,” Electron. Lett. |

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. Express |

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. |

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. SPIE |

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. Express |

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. A |

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. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.2400) Fiber optics and optical communications : Fiber properties

(060.4005) Fiber optics and optical communications : Microstructured fibers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: December 27, 2012

Revised Manuscript: February 18, 2013

Manuscript Accepted: February 19, 2013

Published: February 26, 2013

**Citation**

Tetsuya Hayashi, Takashi Sasaki, Eisuke Sasaoka, Kunimasa Saitoh, and Masanori Koshiba, "Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend," Opt. Express **21**, 5401-5412 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5401

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### References

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