Abstract

We investigate the bending and twisting-induced longitudinal variation of the inter-core coupling coefficient (ICCC) and its effect on inter-core crosstalk (ICXT) in weakly coupled multi-core fibers (MCFs) with an arbitrary core layout. An analytical discrete changes model (DCM) for ICXT field propagation under those conditions is proposed for the first time, providing very fast and rather accurate mean ICXT power estimates. The analytical mean ICXT power estimates are validated through numerical simulation. It is predicted that the mean ICXT power between adjacent cores of the outer ring of the 19-core MCF can be more than 10 dB higher than the one between adjacent cores of the inner ring. It is also predicted that the difference between the mean ICXT power of cores in the inner and outer rings can be much smaller by decreasing the core pitch and increasing the bending radius. This behavior is attributed to the ICXT dependence on the bending and twisting-induced longitudinal variation of the ICCCs. In particular, larger bending and twisting-induced fluctuations of the ICCCs along the longitudinal coordinate are observed in the cores of the outer ring, but the fluctuations become smaller for smaller core pitches and larger bending radii. Furthermore, it is shown that, if the ICCCs’ longitudinal variation is neglected, the mean ICXT power estimates between two adjacent cores are very similar despite the location of those cores. This means that neglecting the longitudinal variation of the ICCCs can lead to misleading estimates of the mean ICXT power, with an error exceeding 15 dB.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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2018 (2)

R. Soeiro, T. Alves, and A. Cartaxo, “Impact of longitudinal variation of the coupling coefficient due to bending and twisting on inter-core crosstalk in weakly coupled MCFs,” J. Lightw. Technol. 36(18), 3898–3911 (2018).
[Crossref]

T. Alves and A. Cartaxo, “Characterization of the stochastic time evolution of short-term average intercore crosstalk in multicore fibers with multiple interfering cores,” Opt. Express 26(4), 4605–4620 (2018).
[Crossref] [PubMed]

2017 (4)

T. Alves and A. Cartaxo, “Intercore crosstalk in homogeneous multicore fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. 35(12), 2398–2408 (2017).
[Crossref]

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightwave Technol. 35(6), 1157–1167 (2017).
[Crossref]

2016 (4)

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

A. Macho, M. Morant, and R. Llorente, “Unified model of linear and nonlinear crosstalk in multi-core fiber,” J. Lightw. Technol. 34(13), 3035–3046 (2016).
[Crossref]

A. Macho, C. García-Meca, F. Fraile-Peláez, M. Morant, and R. Llorente, “Birefringence effects in multi-core fiber: coupled local-mode theory,” Opt. Express 24(19), 21415–21434 (2016).
[Crossref] [PubMed]

2014 (3)

2013 (5)

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photon. 7, 354–362 (2013).
[Crossref]

T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of inter-core crosstalk in multi-core fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express,  21(5), 5401–5412 (2013).
[Crossref] [PubMed]

S. Mumtaz, R.-J. Essiambre, and G. Agrawal, “Nonlinear propagation in multimode and multi-core fibers: generalization of the Manakov equations,” J. Lightw. Technol. 31(3), 398–406 (2013).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Random coupling between groups of degenerate fiber modes in mode multiplexed transmission,” Opt. Express 21(8), 9484–9490 (2013).
[Crossref] [PubMed]

2012 (2)

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(4), 15157–15170 (2012).
[Crossref]

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

2011 (2)

2010 (1)

1982 (1)

1976 (1)

D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Amer. 66(4), 311–320 (1976).
[Crossref]

Agrawal, G.

S. Mumtaz, R.-J. Essiambre, and G. Agrawal, “Nonlinear propagation in multimode and multi-core fibers: generalization of the Manakov equations,” J. Lightw. Technol. 31(3), 398–406 (2013).
[Crossref]

Agrell, E.

Alves, T.

R. Soeiro, T. Alves, and A. Cartaxo, “Impact of longitudinal variation of the coupling coefficient due to bending and twisting on inter-core crosstalk in weakly coupled MCFs,” J. Lightw. Technol. 36(18), 3898–3911 (2018).
[Crossref]

T. Alves and A. Cartaxo, “Characterization of the stochastic time evolution of short-term average intercore crosstalk in multicore fibers with multiple interfering cores,” Opt. Express 26(4), 4605–4620 (2018).
[Crossref] [PubMed]

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. 35(12), 2398–2408 (2017).
[Crossref]

T. Alves and A. Cartaxo, “Intercore crosstalk in homogeneous multicore fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

Amaya, N.

Antonelli, C.

Awaji, Y.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightwave Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

N. Amaya, S. Yan, M. Channegowda, B. R. Rofoee, Y. Shu, M. Rashidi, Y. Ou, E. Hugues-Salas, G. Zervas, R. Nejabati, D. Simeonidou, B. Puttnam, W. Klaus, J. Sakaguchi, T. Miyazawa, Y. Awaji, H. Harai, and N. Wada, “Software defined networking (SDN) over space division multiplexing (SDM) optical networks: features, benefits and experimental demonstration,” Opt. Express 22(3), 3638–3647 (2014).
[Crossref] [PubMed]

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Cartaxo, A.

T. Alves and A. Cartaxo, “Characterization of the stochastic time evolution of short-term average intercore crosstalk in multicore fibers with multiple interfering cores,” Opt. Express 26(4), 4605–4620 (2018).
[Crossref] [PubMed]

R. Soeiro, T. Alves, and A. Cartaxo, “Impact of longitudinal variation of the coupling coefficient due to bending and twisting on inter-core crosstalk in weakly coupled MCFs,” J. Lightw. Technol. 36(18), 3898–3911 (2018).
[Crossref]

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. 35(12), 2398–2408 (2017).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

T. Alves and A. Cartaxo, “Intercore crosstalk in homogeneous multicore fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

Channegowda, M.

Delgado-Mendinueta, J.

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

Essiambre, R.-J.

S. Mumtaz, R.-J. Essiambre, and G. Agrawal, “Nonlinear propagation in multimode and multi-core fibers: generalization of the Manakov equations,” J. Lightw. Technol. 31(3), 398–406 (2013).
[Crossref]

R.-J. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

Fini, J.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photon. 7, 354–362 (2013).
[Crossref]

Foschini, G.

Fraile-Peláez, F.

Fu, S.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Galtarossa, A.

L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” Photon. J. 6(6), 1–8 (2014).

Gan, L.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

García-Meca, C.

Goebel, B.

Harai, H.

Hayashi, T.

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of inter-core crosstalk in multi-core fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express,  21(5), 5401–5412 (2013).
[Crossref] [PubMed]

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]

Hugues-Salas, E.

Imamura, K.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Inaba, H.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Kanno, A.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Kawanishi, T.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Ke, C.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Klaus, W.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightwave Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

N. Amaya, S. Yan, M. Channegowda, B. R. Rofoee, Y. Shu, M. Rashidi, Y. Ou, E. Hugues-Salas, G. Zervas, R. Nejabati, D. Simeonidou, B. Puttnam, W. Klaus, J. Sakaguchi, T. Miyazawa, Y. Awaji, H. Harai, and N. Wada, “Software defined networking (SDN) over space division multiplexing (SDM) optical networks: features, benefits and experimental demonstration,” Opt. Express 22(3), 3638–3647 (2014).
[Crossref] [PubMed]

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Kobayashi, T.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Koshiba, M.

Kramer, G.

Liu, D.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Llorente, R.

A. Macho, M. Morant, and R. Llorente, “Unified model of linear and nonlinear crosstalk in multi-core fiber,” J. Lightw. Technol. 34(13), 3035–3046 (2016).
[Crossref]

A. Macho, C. García-Meca, F. Fraile-Peláez, M. Morant, and R. Llorente, “Birefringence effects in multi-core fiber: coupled local-mode theory,” Opt. Express 24(19), 21415–21434 (2016).
[Crossref] [PubMed]

Luís, R.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightwave Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

Macho, A.

A. Macho, M. Morant, and R. Llorente, “Unified model of linear and nonlinear crosstalk in multi-core fiber,” J. Lightw. Technol. 34(13), 3035–3046 (2016).
[Crossref]

A. Macho, C. García-Meca, F. Fraile-Peláez, M. Morant, and R. Llorente, “Birefringence effects in multi-core fiber: coupled local-mode theory,” Opt. Express 24(19), 21415–21434 (2016).
[Crossref] [PubMed]

Marcuse, D.

D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982).
[Crossref] [PubMed]

D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Amer. 66(4), 311–320 (1976).
[Crossref]

Matsuo, S.

Mecozzi, A.

Miyazawa, T.

Morant, M.

A. Macho, C. García-Meca, F. Fraile-Peláez, M. Morant, and R. Llorente, “Birefringence effects in multi-core fiber: coupled local-mode theory,” Opt. Express 24(19), 21415–21434 (2016).
[Crossref] [PubMed]

A. Macho, M. Morant, and R. Llorente, “Unified model of linear and nonlinear crosstalk in multi-core fiber,” J. Lightw. Technol. 34(13), 3035–3046 (2016).
[Crossref]

Morioka, T.

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Simple analytical expression for crosstalk estimation in homogeneous trench-assisted multi-core fibers,” Opt. Express,  22(19), 23007–23018 (2014).
[Crossref] [PubMed]

T. Morioka, “New generation optical infrastructure technologies: “EXAT Initiative” towards 2020 and beyond,” in OptoElectronics and Communications Conference, Technical Digest Series (CD) (2009), paper FT4.

Mukasa, K.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Mumtaz, S.

S. Mumtaz, R.-J. Essiambre, and G. Agrawal, “Nonlinear propagation in multimode and multi-core fibers: generalization of the Manakov equations,” J. Lightw. Technol. 31(3), 398–406 (2013).
[Crossref]

Nakanishi, T.

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

Nejabati, R.

Nelson, L.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photon. 7, 354–362 (2013).
[Crossref]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

Ou, Y.

Palmieri, L.

L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” Photon. J. 6(6), 1–8 (2014).

Puttnam, B.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightwave Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

N. Amaya, S. Yan, M. Channegowda, B. R. Rofoee, Y. Shu, M. Rashidi, Y. Ou, E. Hugues-Salas, G. Zervas, R. Nejabati, D. Simeonidou, B. Puttnam, W. Klaus, J. Sakaguchi, T. Miyazawa, Y. Awaji, H. Harai, and N. Wada, “Software defined networking (SDN) over space division multiplexing (SDM) optical networks: features, benefits and experimental demonstration,” Opt. Express 22(3), 3638–3647 (2014).
[Crossref] [PubMed]

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Rademacher, G.

Rashidi, M.

Richardson, D.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photon. 7, 354–362 (2013).
[Crossref]

Rofoee, B. R.

Saitoh, K.

Sakaguchi, J.

Saridis, G.

Sasaki, T.

Sasaoka, E.

Shen, L.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Shimakawa, O.

Shtaif, M.

Shu, Y.

Simeonidou, D.

Soeiro, R.

R. Soeiro, T. Alves, and A. Cartaxo, “Impact of longitudinal variation of the coupling coefficient due to bending and twisting on inter-core crosstalk in weakly coupled MCFs,” J. Lightw. Technol. 36(18), 3898–3911 (2018).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

Sugizaki, R.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Takenaga, K.

Tang, M.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Taru, T.

Tong, W.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Tu, J.

Wada, N.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightwave Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

N. Amaya, S. Yan, M. Channegowda, B. R. Rofoee, Y. Shu, M. Rashidi, Y. Ou, E. Hugues-Salas, G. Zervas, R. Nejabati, D. Simeonidou, B. Puttnam, W. Klaus, J. Sakaguchi, T. Miyazawa, Y. Awaji, H. Harai, and N. Wada, “Software defined networking (SDN) over space division multiplexing (SDM) optical networks: features, benefits and experimental demonstration,” Opt. Express 22(3), 3638–3647 (2014).
[Crossref] [PubMed]

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Watanabe, M.

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

Winzer, P.

Xing, C.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Yan, S.

Yang, C.

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

Ye, F.

Zervas, G.

Appl. Opt. (1)

J. Lightw. Technol. (7)

J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightw. Technol. 31(4), 554–562 (2013).
[Crossref]

S. Mumtaz, R.-J. Essiambre, and G. Agrawal, “Nonlinear propagation in multimode and multi-core fibers: generalization of the Manakov equations,” J. Lightw. Technol. 31(3), 398–406 (2013).
[Crossref]

A. Macho, M. Morant, and R. Llorente, “Unified model of linear and nonlinear crosstalk in multi-core fiber,” J. Lightw. Technol. 34(13), 3035–3046 (2016).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Delgado-Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. 35(12), 2398–2408 (2017).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Impact of longitudinal variation of the coupling coefficient due to bending and twisting on inter-core crosstalk in weakly coupled MCFs,” J. Lightw. Technol. 36(18), 3898–3911 (2018).
[Crossref]

T. Alves and A. Cartaxo, “Intercore crosstalk in homogeneous multicore fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Amer. (1)

D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Amer. 66(4), 311–320 (1976).
[Crossref]

Nat. Photon. (1)

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photon. 7, 354–362 (2013).
[Crossref]

Opt. Express (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]

T. Alves and A. Cartaxo, “Characterization of the stochastic time evolution of short-term average intercore crosstalk in multicore fibers with multiple interfering cores,” Opt. Express 26(4), 4605–4620 (2018).
[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. Express 19(26), B102–B111 (2011).
[Crossref]

T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of inter-core crosstalk in multi-core fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express,  21(5), 5401–5412 (2013).
[Crossref] [PubMed]

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Simple analytical expression for crosstalk estimation in homogeneous trench-assisted multi-core fibers,” Opt. Express,  22(19), 23007–23018 (2014).
[Crossref] [PubMed]

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(4), 15157–15170 (2012).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Random coupling between groups of degenerate fiber modes in mode multiplexed transmission,” Opt. Express 21(8), 9484–9490 (2013).
[Crossref] [PubMed]

A. Macho, C. García-Meca, F. Fraile-Peláez, M. Morant, and R. Llorente, “Birefringence effects in multi-core fiber: coupled local-mode theory,” Opt. Express 24(19), 21415–21434 (2016).
[Crossref] [PubMed]

N. Amaya, S. Yan, M. Channegowda, B. R. Rofoee, Y. Shu, M. Rashidi, Y. Ou, E. Hugues-Salas, G. Zervas, R. Nejabati, D. Simeonidou, B. Puttnam, W. Klaus, J. Sakaguchi, T. Miyazawa, Y. Awaji, H. Harai, and N. Wada, “Software defined networking (SDN) over space division multiplexing (SDM) optical networks: features, benefits and experimental demonstration,” Opt. Express 22(3), 3638–3647 (2014).
[Crossref] [PubMed]

Photon. J. (2)

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

L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” Photon. J. 6(6), 1–8 (2014).

Photon. Technol. Lett. (2)

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

Other (3)

T. Morioka, “New generation optical infrastructure technologies: “EXAT Initiative” towards 2020 and beyond,” in OptoElectronics and Communications Conference, Technical Digest Series (CD) (2009), paper FT4.

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

L. Gan, M. Tang, L. Shen, C. Xing, C. Ke, C. Yang, W. Tong, S. Fu, and D. Liu, “Realistic model for frequency-dependent crosstalk in weakly coupled multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Tu3B.6.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic illustration of a 19-core double-ring MCF cross-section. The cores comprising the inner and outer rings are identified. Two cores are chosen as an example, cores m and n, in order to illustrate the Cartesian coordinates of the center of the cores.
Fig. 2
Fig. 2 Contours of the relative error, in percentage, between: (a) κnm obtained from the formal definition (Eq. (2)) and approximated closed-form expression (Eq. (3)), (b) κnm obtained from the approximated closed-form expression and linearized expression (Eq. (7)), (c) κnm obtained from the formal definition and linearized expression. The intrinsic κnm, κ n m ( int ), used in the linearized expressions is obtained from Eq. (3). The MCF parameters considered in these results are shown in Table 1.
Fig. 3
Fig. 3 κnm obtained from Eq. (2), in logarithmic scale, with the parameters shown in Table 1. (a) as a function of Δ n eff , m ( N ) ( z ), with Δ n eff , n ( N ) ( z ) = { ( c 1 ) : 0.09 %; (c2) : 0; (c3) : 0.06%; (c4) : 0.08%; (c5) : 0.1%}, (b) as a function of Δ n eff , n ( N ) ( z ), with Δ n eff , m ( N ) ( z ) = { ( d 1 ) : 0.09 %; (d2) : 0; (d3) : 0.06%; (d4) : 0.08%; (d5) : 0.1%}.
Fig. 4
Fig. 4 Continuous lines: (κnm(z) + κmn(z))/2, obtained from Eq. (3). Dashed lines: neff,n(z) − neff,m(z). an = am = 4 μm, ym = 65 μm, yn = 20 μm, Rb = 0.05 m, γ = 4π rad/m and the remaining parameters are presented in Table 1. (a) xn = xm = 0, (b) xn = xm = 10 μm, (c) xn = xm = 40 μm.
Fig. 5
Fig. 5 Most of the mean ICXT power estimates are obtained considering an MCF structure obeying the 19-core MCF design (cases 1–4). Cases 1–3 consider a single interfering core, and case 4 considers multiple interfering cores. A variant of case 1, which does not obey the 19-core MCF design, is also studied. The Cartesian coordinates of cores m (xm and ym) and core n (xn and yn) are detailed for each case.
Fig. 6
Fig. 6 Mean ICXT power as a function of Δn(N), for cases 1–3 and the variant of case 1 (see Fig. 5), with Λnm = 45 μm. The z-dependent ICCCs and intrinsic ICCCs used in the simulated and analytical mean ICXT power estimates, respectively, are obtained from Eqs. (2) and (3), respectively. The following parameters are considered in the four cases: Rb = 0.1 m, γ = 4π rad/m, an = am = 4 μm, L = 200 m. The remaining parameters are shown in Table 1. (a): comparison between the mean ICXT power estimates obtained analytically and by numerical simulation (sim). (b): comparison between the analytical mean ICXT power estimates with and without z −variation of the ICCCs.
Fig. 7
Fig. 7 Mean ICXT power as a function of Δn(N), for a case of multiple interfering cores (case 4), which is a combination of cases 1 and 3. The MCF parameters are the same as the ones considered in Fig. 6.
Fig. 8
Fig. 8 Mean ICXT power as a function of the bending radius, using the parameters of Fig. 6, with Δn(N) = 0.02%. (a) comparison between analytical and simulation estimates of the mean ICXT power, (b) comparison of the analytical mean ICXT power estimates with and without z-dependent ICCCs.
Fig. 9
Fig. 9 Mean ICXT power estimates using the parameters of Fig. 6. (a) mean ICXT power as a function of γ /(2π), with Δn(N) = 0.02 %, (b) mean ICXT power as a function of the core pitch, with (c1) Δn(N) = −0.026 % and (c2) Δn(N) = 0 %.

Tables (1)

Tables Icon

Table 1 Main parameters of the MCF used to study the ICCC variation with Δneff,m(z) and Δneff,n(z).

Equations (26)

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

d A n ( z ) d z = j m = 1 m n N c κ n m ( z ) e j [ θ m ( z ) θ n ( z ) ] A m ( z )
κ n m = NA n 2 k 0 2 n eff , n F n * ( r , ξ ) F m ( r , ξ ) d S n | F n ( r , ξ ) | 2 d S
κ n m ϒ n m k 0 NA n 2 n eff , n J 0 ( u m ) π a m 2 w m Λ n m e w m Λ n m a m a m [ a n w n J 0 ( u n ) I 1 ( a n w m a m ) + a m u n J 1 ( u n ) I 0 ( a n w m a m ) ] K 0 ( w m ) J 1 2 ( u n ) [ 1 + J 0 2 ( u n ) K 1 2 ( w n ) J 1 2 ( u n ) K 0 2 ( w n ) ] [ a n 2 w m 2 + a m 2 u n 2 ]
n eff , m ( z ) = n eff , m ( int ) [ 1 + x m cos ( γ z ) y m sin ( γ z ) R b ]
n eff , n ( z ) = n eff , n ( int ) [ 1 + x n cos ( γ z ) y n sin ( γ z ) R b ]
θ m ( z ) = k 0 n eff , m ( int ) z + ρ m [ x m sin ( γ z ) + y m cos ( γ z ) y m ] θ n ( z ) = k 0 n eff , n ( int ) z + ρ n [ x n sin ( γ z ) + y n cos ( γ z ) y n ]
κ n m ( z ) κ n m ( int ) e s n m ( m ) Δ n eff , m ( z ) + s n m ( n ) Δ n eff , n ( z )
κ m n ( z ) κ m n ( int ) e s m n ( m ) Δ n eff , m ( z ) + s m n ( n ) Δ n eff , n ( z ) .
A n ( L ) j A m ( 0 ) k = 1 N K n m , k e j ϕ n m , k
K n m , k = ( K ˜ n m , k + K ˜ m n , k ) / 2
K ˜ n m , k = z k 1 z k κ n m ( z ) e j [ θ m ( z ) θ n ( z ) ] d z
K ˜ m n , k = z k 1 z k κ m n ( z ) e j [ θ m ( z ) θ n ( z ) ] d z
X T = k = 1 N | K n m , k | 2 .
κ n m ( z ) = κ n m ( int ) e σ n m ( m ) [ x m cos ( γ z ) y m sin ( γ z ) ] e σ n m ( n ) [ x n cos ( γ z ) y n sin ( γ z ) ]
K ˜ n m , k = κ n m ( int ) z k 1 z k e σ n m ( m ) [ x m cos ( γ z ) y m sin ( γ z ) ] e σ n m ( n ) [ x n cos ( γ z ) y n sin ( γ z ) ] e j [ θ m ( z ) θ n ( z ) ] d z .
K ˜ n m , k = κ n m ( int ) e j [ Δ β m n z k 1 ρ m y m + ρ n y n ] 0 z k z k 1 e B n m cos [ γ ( z + z k 1 ) ] + A n m sin [ γ ( z + z k 1 ) ] e j Δ β m n z d z
K ˜ n m , k = κ n m ( int ) e j [ Δ β m n ( z k 1 z k ) ρ m y m + ρ n y n ] 0 z k z k 1 e B n m cos [ γ ( z + z k 1 ) ] + A n m sin [ γ ( z + z k 1 ) ] e j Δ β m n z d z
K ˜ n m , k = K ˜ n m , k e j Δ β m n z k
K ˜ n m , k = 2 γ κ n m ( int ) e j Δ β m n ( z k z k 1 ) / 2 e j ( ρ m y m ρ n y n ) × ν = + J ν ( A ¯ n m 2 + B ¯ n m 2 ) e j ν α n m e j ν γ ( z k + z k 1 ) / 2 × sin [ γ ( ν ς n m ) ( z k z k 1 ) / 2 ] ν ς n m
K ˜ n m , min max = 2 γ κ n m ( int ) e j π 2 ς n m e j ( ρ m y m ρ n y n ) × ν = + J ν ( A ¯ n m 2 + B ¯ n m 2 ) e j ν α n m e j ν π / 2 e j ν φ × sin [ π 2 ( ν ς n m ) ] ν ς n m
K ˜ n m , max min = 2 γ κ n m ( int ) e j π 2 ς n m e j ( ρ m y m ρ n y n ) × ν = + J ν ( A ¯ n m 2 + B ¯ n m 2 ) e j ν α n m e j ν π / 2 e j ν φ × sin [ π 2 ( ν ς n m ) ] ν ς n m .
X T = N 2 ( | K n m , min max | 2 + | K n m , max min | 2 )
K n m , min max = ( K ˜ n m , min max + K ˜ m n , min max ) / 2 K n m , max min = ( K ˜ n m , max min + K ˜ m n , max min ) / 2 .
X T = X T min max + X T max min
X T min max = N 2 γ 2 | ν = + [ κ n m ( int ) J ν ( A ¯ n m 2 + B ¯ n m 2 ) e j ν α n m + κ m n ( int ) J ν ( A ¯ m n 2 + B ¯ m n 2 ) e j ν α m n ] × e j ν ( π / 2 φ ) sin [ π 2 ( ν ς n m ) ] ν ς n m | 2
X T max min = N 2 γ 2 | ν = + [ κ n m ( int ) J ν ( A ¯ n m 2 + B ¯ n m 2 ) e j ν α n m + κ m n ( int ) J ν ( A ¯ m n 2 + B ¯ m n 2 ) e j ν α m n ] × e j ν ( π / 2 φ ) sin [ π 2 ( ν ς n m ) ] ν ς n m | 2

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