Abstract

An analytical expression for the mode coupling coefficient in homogeneous trench-assisted multi-core fibers is derived, which has a simple relationship with the one in normal step-index structures. The amount of inter-core crosstalk reduction (in dB) with trench-assisted structures compared to the one with normal step-index structures can then be written by a simple expression. Comparison with numerical simulations confirms that the obtained analytical expression has very good accuracy for crosstalk estimation. The crosstalk properties in trench-assisted multi-core fibers, such as crosstalk dependence on core pitch and wavelength-dependent crosstalk, can be obtained by this simple analytical expression.

© 2014 Optical Society of America

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References

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  1. T. Morioka, “New generation optical infrastructure technologies: ‘EXAT initiative’ towards 2020 and beyond,” in Proc. OECC (2009), paper FT4.
  2. S. Matsuo, M. Ikeda, and K. Himeno, “Bend-insensitive and low-splice-loss optical fiber for indoor wiring in FTTH,” in Proc. OFC (2004), paper ThI3.
  3. 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 Proc. OFC (2011), paper OWJ4.
  4. J. Sakaguchi, B. J. 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. Lightwave Technol. 31, 554–562 (2013).
    [Crossref]
  5. H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.
  6. K. Saitoh, T. Matsui, T. Sakamoto, M. Koshiba, and S. Tomita, “Multi-core hole-assisted fibers for high core density space division multiplexing,” in Proc. OECC (2010), paper 7C2-1.
  7. B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.
  8. K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.
  9. S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
    [Crossref] [PubMed]
  10. S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
    [Crossref] [PubMed]
  11. F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Theoretical investigation of inter-core crosstalk properties in homogeneous trench-assisted multi-core fibers,” in IEEE Photonics Society Summer Topicals Meeting Series (2014), paper TuE4.2.
  12. F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.
  13. K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, 2006).
  14. 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, 15157–15170 (2012).
    [Crossref] [PubMed]
  15. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.
  16. A. Snyder and J. D. Love, Optical Waveguide Theory, 1st ed. (Springer, 1983).
  17. K. Imamura, K. Mukasa, and T. Yagi, “Effective space division multiplexing by multi-core fibers,” in Proc. ECOC (2010), paper P1.09.

2013 (1)

2012 (2)

2011 (1)

Abe, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Akamatsu, T.

Arakawa, Y.

S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
[Crossref] [PubMed]

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 Proc. OFC (2011), paper OWJ4.

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

Awaji, Y.

Fukuzato, K.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Goto, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Guan, N.

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 Proc. OFC (2011), paper OWJ4.

Hayashi, T.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.

Himeno, K.

S. Matsuo, M. Ikeda, and K. Himeno, “Bend-insensitive and low-splice-loss optical fiber for indoor wiring in FTTH,” in Proc. OFC (2004), paper ThI3.

Hongo, A.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Ikeda, M.

S. Matsuo, M. Ikeda, and K. Himeno, “Bend-insensitive and low-splice-loss optical fiber for indoor wiring in FTTH,” in Proc. OFC (2004), paper ThI3.

Imamura, K.

Inaba, H.

Ishida, I.

S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
[Crossref] [PubMed]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Kanno, A.

Kawakami, H.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Kawanishi, T.

Klaus, W.

Kobayashi, T.

J. Sakaguchi, B. J. 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. Lightwave Technol. 31, 554–562 (2013).
[Crossref]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Koshiba, M.

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, 15157–15170 (2012).
[Crossref] [PubMed]

S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
[Crossref] [PubMed]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

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

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

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 Proc. OFC (2011), paper OWJ4.

Kosihba, M.

Kubota, H.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Love, J. D.

A. Snyder and J. D. Love, Optical Waveguide Theory, 1st ed. (Springer, 1983).

Matsui, T.

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

Matsuo, S.

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, 15157–15170 (2012).
[Crossref] [PubMed]

S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
[Crossref] [PubMed]

S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
[Crossref] [PubMed]

S. Matsuo, M. Ikeda, and K. Himeno, “Bend-insensitive and low-splice-loss optical fiber for indoor wiring in FTTH,” in Proc. OFC (2004), paper ThI3.

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 Proc. OFC (2011), paper OWJ4.

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Matsuura, A.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Miyamoto, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Morioka, T.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

T. Morioka, “New generation optical infrastructure technologies: ‘EXAT initiative’ towards 2020 and beyond,” in Proc. OECC (2009), paper FT4.

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Theoretical investigation of inter-core crosstalk properties in homogeneous trench-assisted multi-core fibers,” in IEEE Photonics Society Summer Topicals Meeting Series (2014), paper TuE4.2.

F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.

Mukasa, K.

Ohsono, K.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, 2006).

Okuyama, K.

Ono, H.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Puttnam, B. J.

Saito, K.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Saitoh, K.

S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
[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, 15157–15170 (2012).
[Crossref] [PubMed]

S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
[Crossref] [PubMed]

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

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

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Theoretical investigation of inter-core crosstalk properties in homogeneous trench-assisted multi-core fibers,” in IEEE Photonics Society Summer Topicals Meeting Series (2014), paper TuE4.2.

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 Proc. OFC (2011), paper OWJ4.

Sakaguchi, J.

Sakamoto, T.

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

Sano, A.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Sasaki, T.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.

Sasaki, Y.

S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
[Crossref] [PubMed]

S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
[Crossref] [PubMed]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

Sasaoka, E.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.

Sekiya, E. H.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Shiina, N.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Shikama, K.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Shimakawa, O.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.

Snyder, A.

A. Snyder and J. D. Love, Optical Waveguide Theory, 1st ed. (Springer, 1983).

Sugizaki, R.

Takara, H.

F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Takenaga, K.

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, 15157–15170 (2012).
[Crossref] [PubMed]

S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20, 28398–28408 (2012).
[Crossref] [PubMed]

S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200μm,” Opt. Lett. 36, 4626–4628 (2011).
[Crossref] [PubMed]

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 Proc. OFC (2011), paper OWJ4.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

Taniagwa, S.

Tanigawa, S.

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 Proc. OFC (2011), paper OWJ4.

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

Taru, T.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.

Tomita, S.

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

Tsujikawa, K.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

Tu, J.

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, 15157–15170 (2012).
[Crossref] [PubMed]

F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Theoretical investigation of inter-core crosstalk properties in homogeneous trench-assisted multi-core fibers,” in IEEE Photonics Society Summer Topicals Meeting Series (2014), paper TuE4.2.

Wada, N.

Watanabe, M.

Yagi, T.

K. Imamura, K. Mukasa, and T. Yagi, “Effective space division multiplexing by multi-core fibers,” in Proc. ECOC (2010), paper P1.09.

Yao, B.

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

Ye, F.

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Theoretical investigation of inter-core crosstalk properties in homogeneous trench-assisted multi-core fibers,” in IEEE Photonics Society Summer Topicals Meeting Series (2014), paper TuE4.2.

F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.

J. Lightwave Technol. (1)

Opt. Express (2)

Opt. Lett. (1)

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S. Matsuo, M. Ikeda, and K. Himeno, “Bend-insensitive and low-splice-loss optical fiber for indoor wiring in FTTH,” in Proc. OFC (2004), paper ThI3.

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 Proc. OFC (2011), paper OWJ4.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. ECOC (2012), paper Mo.1.F.3.

A. Snyder and J. D. Love, Optical Waveguide Theory, 1st ed. (Springer, 1983).

K. Imamura, K. Mukasa, and T. Yagi, “Effective space division multiplexing by multi-core fibers,” in Proc. ECOC (2010), paper P1.09.

F. Ye, J. Tu, K. Saitoh, and T. Morioka, “Theoretical investigation of inter-core crosstalk properties in homogeneous trench-assisted multi-core fibers,” in IEEE Photonics Society Summer Topicals Meeting Series (2014), paper TuE4.2.

F. Ye, J. Tu, K. Saitoh, H. Takara, and T. Morioka, “Wavelength-dependent crosstalk in trench-assisted multi-core fibers,” in Proc. OECC/ACOFT (2014), paper TU5C1.

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, 2006).

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. ECOC (2012), paper Th.3.C.1.

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

B. Yao, K. Ohsono, N. Shiina, K. Fukuzato, A. Hongo, E. H. Sekiya, and K. Saito, “Reduction of crosstalk by hole-walled multi-core fibers,” in Proc. OFC (2012), paper OM2D.5.

K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fibre with an optimised cladding thickness,” in Proc. ECOC (2011), paper Mo.1.LeCervin.2.

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Figures (5)

Fig. 1
Fig. 1 Refractive index profiles and cross-sectional dimensions for (a) a normal step-index structure and (b) a trench-assisted structure.
Fig. 2
Fig. 2 (a) Cross-sectional view of one-ring structured trench-assisted 12-core MCF and (b) refractive index profiles between adjacent cores with a sufficient large core pitch.
Fig. 3
Fig. 3 Crosstalk comparison among analytical calculation and numerical simulations (non integrable expression and FEM) in a trench-assisted MCF as a function of core pitch Λ at 1550 nm, where the trench width equals the core radius. The XT in a normal step-index MCF is included for comparison.
Fig. 4
Fig. 4 Crosstalk comparison among analytical calculation and numerical simulations (non integrable expression and FEM) in trench-assisted structure as a function of ratio of trench width to core radius Rtr = wtr/a1, at 1550 nm, with core pitch Λ of 45 μm and Δ2 = −0.70%.
Fig. 5
Fig. 5 Further reduction of XT by changing Δ2 from −0.70% to −1.40%, based on analytical expression in trench-assisted structure versus core pitch Λ, at 1550 nm with trench width equal to core radius.

Tables (2)

Tables Icon

Table 1 Approximations of W2 at Different Values of m

Tables Icon

Table 2 Structural Parameters for XT Calculation and Numerical Simulations

Equations (24)

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κ pq = ω ε 0 ( N 2 N q 2 ) E p * E q d x d y u z ( E p * × H p + E p × H p * ) d x d y ,
κ pq = Δ 1 a 1 U 1 2 V 1 3 K 1 2 ( W 1 ) π a 1 W 1 Λ exp ( W 1 a 1 Λ ) ,
0 2 π 0 a 1 J 0 ( U 1 a 1 r ) exp ( W 1 a 1 r cos θ ) r d r d θ = 2 π 0 a 1 J 0 ( U 1 a 1 r ) I 0 ( W 1 a 1 r ) r d r ,
κ pq = k ( n 1 2 n 0 2 ) W 1 2 n 1 a 1 2 V 1 2 J 1 2 ( U 1 ) J 0 ( U 1 ) K 0 ( W 1 ) π a 1 2 W 1 Λ exp ( W 1 a 1 Λ ) 0 a 1 J 0 ( U 1 a 1 r ) I 0 ( W 1 a 1 r ) r d r ,
κ pq = k ( n 1 2 n 0 2 ) W 1 U 1 L q n 1 a 1 2 V 1 2 J 1 2 ( U 1 ) π a 1 2 W 1 Λ exp ( W 1 a 1 Λ ) 0 a 1 J 0 ( U 1 a 1 r ) × I 0 [ ( W 1 a 1 + P 1 P 2 + Y 1 Y 2 Λ r ) r ] exp ( P 1 P 2 + Y 1 Y 2 Λ r Λ ) r d r ,
{ L q = J 1 ( U 1 ) K 1 ( W 1 a 2 / a 1 ) K 1 ( W 2 a 3 / a 1 ) K 1 ( W 1 ) K 1 ( W 2 a 2 / a 1 ) K 1 ( W 1 a 3 / a 1 ) , P 1 = W 1 Λ a 3 a 1 , P 2 = W 2 Λ a 3 a 1 , Y 1 = W 2 Λ a 2 a 1 , Y 2 = W 1 Λ a 2 a 1 , P 1 P 2 + Y 1 Y 2 = ( W 2 W 1 ) a 3 a 2 a 1 = ( W 2 W 1 ) w tr a 1 ,
κ pq κ pq = U 1 L q 0 a 1 J 0 ( U 1 a 1 r ) I 0 [ ( W 1 a 1 + P 1 P 2 + Y 1 Y 2 Λ r ) r ] exp ( P 1 P 2 + Y 1 Y 2 Λ r Λ ) r d r W 1 J 0 ( U 1 ) K 0 ( W 1 ) 0 a 1 J 0 ( U 1 a 1 r ) I 0 ( W 1 a 1 r ) r d r .
I 0 ( a x ) 1 2 π a x exp ( a x ) , I 0 [ ( a + b ) x ] 1 2 π ( a + b ) x exp [ ( a + b ) x ] ,
I 0 [ ( a + b ) x ] a a + b I 0 ( a x ) exp ( b x ) .
I 0 [ ( W 1 a 1 + P 1 P 2 + Y 1 Y 2 Λ r ) r ] Γ I 0 ( W 1 a 1 r ) exp ( P 1 P 2 + Y 1 Y 2 Λ r r ) ,
Γ = W 1 / a 1 W 1 / a 1 + ( P 1 P 2 + Y 1 Y 2 ) / Λ = W 1 W 1 + ( W 2 W 1 ) w tr / Λ ,
κ pq κ pq = U 1 L q 0 a 1 J 0 ( U 1 a 1 r ) Γ I 0 ( W 1 a 1 r ) exp ( P 1 P 2 + Y 1 Y 2 Λ r r ) exp ( P 1 P 2 + Y 1 Y 2 Λ r Λ ) r d r W 1 J 0 ( U 1 ) K 0 ( W 1 ) 0 a 1 J 0 ( U 1 a 1 r ) I 0 ( W 1 a 1 r ) r d r = Γ U 1 L q 0 a 1 J 0 ( U 1 a 1 r ) I 0 ( W 1 a 1 r ) exp [ ( P 1 P 2 + Y 1 Y 2 ) Λ r Λ r ] r d r W 1 J 0 ( U 1 ) K 0 ( W 1 ) 0 a 1 J 0 ( U 1 a 1 r ) I 0 ( W 1 a 1 r ) r d r = Γ U 1 L q exp [ ( P 1 P 2 + Y 1 Y 2 ) ] W 1 J 0 ( U 1 ) K 0 ( W 1 ) .
J 0 ( U 1 ) U 1 J 1 ( U 1 ) = K 0 ( W 1 ) W 1 K 1 ( W 1 ) .
κ pq κ pq = Γ L q exp [ ( P 1 P 2 + Y 1 Y 2 ) ] J 1 ( U 1 ) K 1 ( W 1 ) .
K 1 ( x ) K 0 ( x ) π 2 x exp ( x ) .
L q = J 1 ( U 1 ) K 1 ( W 1 ) exp [ ( W 2 W 1 ) w tr a 1 ] .
κ pq κ pq = Γ exp [ ( P 1 P 2 + Y 1 Y 2 ) ] exp [ ( W 2 W 1 ) w tr a 1 ] = Γ exp [ 2 ( W 2 W 1 ) w tr a 1 ] .
κ pq = Γ Δ 1 a 1 U 1 2 V 1 3 K 1 2 ( W 1 ) π a 1 W 1 Λ exp [ W 1 Λ + 2 ( W 2 W 1 ) w tr a 1 ] .
XT μ 2 κ pq 2 R b β Λ L ,
XT μ XT μ = ( κ pq κ pq ) 2 = Γ exp [ 4 ( W 2 W 1 ) w tr a 1 ] ,
XT dB XT dB = 10 log 10 { Γ exp [ 4 ( W 2 W 1 ) w tr a 1 ] } 10 log 10 Γ 17.4 ( W 2 W 1 ) w tr a 1 ,
V 1 = 2 π λ a 1 n 1 2 Δ 1 , V 2 = 2 π λ a 1 n 0 2 | Δ 2 | , W 2 = V 2 2 + W 1 2 .
W 2 m V 1 2 + W 1 2 = m V 1 2 + ( 1.1428 V 1 0.996 ) 2 .
XT dB = XT dB + 10 log 10 Γ 17.4 ( W 2 W 1 ) w tr a 1 .

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