Abstract

This paper investigates the applicability of a model of a cladding-pumped multicore erbium-doped fiber amplifier (CP-MC-EDFA) that employs the average inversion level of an erbium ion. The model is modified to include the effects of multiple cores for modifications of the background loss coefficient of the pump light. The model is validated experimentally by measurements of the pump power, gain transient, and intercore cross-gain modulation of a cladding-pumped 12-core EDFA in which the pump light is uniformly distributed in the inner cladding. The calculated and measured pump power, gain transient response, and gain change caused by the intercore cross-gain modulation agree well, suggesting the modified model is useful for characterizing a CP-MC-EDFA.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (1)

2015 (2)

C. Jin, B. Ung, Y. Messaddeq, and S. LaRochelle, “Annular-cladding erbium doped multicore fiber for SDM amplification,” Opt. Express 23, 29647–29659 (2015).
[Crossref]

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (1)

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

2004 (1)

1998 (1)

A. Bertoni and G. C. Reali, “A model for the optimization of double-clad fiber laser operation,” Appl. Phys. B66, 547–554 (1998).
[Crossref]

1997 (1)

Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average inversion level, modeling, and physics of erbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 991–1007 (1997).
[Crossref]

1991 (3)

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9, 147–154 (1991).
[Crossref]

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

R. M. Jopson and A. A. M. Saleh, “Modeling of gain and noise in erbium-doped fiber amplifiers,” Proc. SPIE 1581, 114–119 (1991).
[Crossref]

1990 (2)

M. Peroni and M. Tamburrini, “Gain in erbium-doped fiber amplifiers: a simple analytical solution for the rate equations,” Opt. Lett. 15, 842–844 (1990).
[Crossref]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[Crossref]

1981 (1)

1980 (1)

Abe, Y.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Abedin, K. S.

Aikawa, K.

Alam, S.

M. Nooruzzaman, S. Jain, Y. Jung, S. Alam, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Power consumption in multi-core fibre networks,” in The 43rd European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2017), paper Tu.2.F.

Amma, Y.

Aspell, J.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[Crossref]

Awaji, Y.

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

Bansal, L.

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers Fundamentals and Technology (Academic, 1999), Chap. 5.

Bertoni, A.

A. Bertoni and G. C. Reali, “A model for the optimization of double-clad fiber laser operation,” Appl. Phys. B66, 547–554 (1998).
[Crossref]

Bohn, M.

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9, 147–154 (1991).
[Crossref]

DiGiovanni, D. J.

Evankow, J. D.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[Crossref]

Fini, J. M.

Fragnito, H. L.

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9, 147–154 (1991).
[Crossref]

Goodman, J. W.

Hill, K. O.

Hiraga, K.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Hosokawa, T.

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

Ichii, K.

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

Igarashi, K.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Imamura, K.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Ishida, I.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Jain, S.

M. Nooruzzaman, S. Jain, Y. Jung, S. Alam, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Power consumption in multi-core fibre networks,” in The 43rd European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2017), paper Tu.2.F.

Jin, C.

Jopson, R. M.

R. M. Jopson and A. A. M. Saleh, “Modeling of gain and noise in erbium-doped fiber amplifiers,” Proc. SPIE 1581, 114–119 (1991).
[Crossref]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[Crossref]

Jung, Y.

Kawakami, H.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Kawasaki, B. S.

Kobayashi, T.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

LaRochelle, S.

Maeda, K.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Masuda, H.

H. Ono, M. Yamada, and H. Masuda, “Pump power reduction in optical fiber amplifier for WDM-interleaved multi-core/multi-fiber system,” IEEE Photon. Technol. Lett. 29, 1163–1166 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

Matsuo, S.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Messaddeq, Y.

Miyamoto, Y.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

M. Nooruzzaman, S. Jain, Y. Jung, S. Alam, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Power consumption in multi-core fibre networks,” in The 43rd European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2017), paper Tu.2.F.

Mizuno, T.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Monberg, E. M.

Mori, A.

Morioka, T.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

M. Nooruzzaman, S. Jain, Y. Jung, S. Alam, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Power consumption in multi-core fibre networks,” in The 43rd European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2017), paper Tu.2.F.

Morita, I.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Nasu, H.

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

Nooruzzaman, M.

M. Nooruzzaman, S. Jain, Y. Jung, S. Alam, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Power consumption in multi-core fibre networks,” in The 43rd European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2017), paper Tu.2.F.

Norton, R. E.

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers Fundamentals and Technology (Academic, 1999), Chap. 5.

Ono, H.

H. Ono, M. Yamada, and H. Masuda, “Pump power reduction in optical fiber amplifier for WDM-interleaved multi-core/multi-fiber system,” IEEE Photon. Technol. Lett. 29, 1163–1166 (2017).
[Crossref]

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

H. Ono, T. Watanabe, K. Suzuki, A. Mori, T. Takahashi, and T. Sakamoto, “Wide-range variable gain fiber amplifier with erbium-doped fiber switching,” J. Lightwave Technol. 31, 1965–1972 (2013).
[Crossref]

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Peroni, M.

Poletti, F.

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

Pulverer, K.

Rawson, E. G.

Reali, G. C.

A. Bertoni and G. C. Reali, “A model for the optimization of double-clad fiber laser operation,” Appl. Phys. B66, 547–554 (1998).
[Crossref]

Richardson, D.

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

Richardson, D. J.

Rieznik, A. A.

Ryf, R.

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

Saito, T.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Saitoh, K.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Sakamoto, T.

Saleh, A. A. M.

R. M. Jopson and A. A. M. Saleh, “Modeling of gain and noise in erbium-doped fiber amplifiers,” Proc. SPIE 1581, 114–119 (1991).
[Crossref]

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[Crossref]

Sano, A.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Sasa, T.

Sasaki, Y.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Shibahara, K.

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers Fundamentals and Technology (Academic, 1999), Chap. 5.

Srivastava, A. K.

Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average inversion level, modeling, and physics of erbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 991–1007 (1997).
[Crossref]

Sugizaki, R.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Sun, Y.

Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average inversion level, modeling, and physics of erbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 991–1007 (1997).
[Crossref]

Supradeepa, V. R.

Suzuki, K.

Suzuki, M.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Tadakuma, M.

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Takahashi, T.

H. Ono, T. Watanabe, K. Suzuki, A. Mori, T. Takahashi, and T. Sakamoto, “Wide-range variable gain fiber amplifier with erbium-doped fiber switching,” J. Lightwave Technol. 31, 1965–1972 (2013).
[Crossref]

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

Takara, H.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Takenaga, K.

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

Takeshima, K.

Tamburrini, M.

Thierry, T. F.

Tremblay, Y.

Tsuchida, Y.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Tsuritani, T.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Ung, B.

Wada, M.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Watanabe, K.

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

Watanabe, T.

Winzer, P.

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

Yamada, M.

H. Ono, M. Yamada, and H. Masuda, “Pump power reduction in optical fiber amplifier for WDM-interleaved multi-core/multi-fiber system,” IEEE Photon. Technol. Lett. 29, 1163–1166 (2017).
[Crossref]

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

Yan, M. F.

Ye, F.

Zhu, B.

Zyskind, J. L.

Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average inversion level, modeling, and physics of erbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 991–1007 (1997).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (1)

A. Bertoni and G. C. Reali, “A model for the optimization of double-clad fiber laser operation,” Appl. Phys. B66, 547–554 (1998).
[Crossref]

IEEE Commun. Mag. (1)

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average inversion level, modeling, and physics of erbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 991–1007 (1997).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2, 714–717 (1990).
[Crossref]

H. Ono, M. Yamada, and H. Masuda, “Pump power reduction in optical fiber amplifier for WDM-interleaved multi-core/multi-fiber system,” IEEE Photon. Technol. Lett. 29, 1163–1166 (2017).
[Crossref]

J. Lightwave Technol. (6)

H. Ono, T. Watanabe, K. Suzuki, A. Mori, T. Takahashi, and T. Sakamoto, “Wide-range variable gain fiber amplifier with erbium-doped fiber switching,” J. Lightwave Technol. 31, 1965–1972 (2013).
[Crossref]

T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer, H. Ono, Y. Abe, M. Yamada, K. Saitoh, S. Matsuo, K. Aikawa, M. Bohn, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Long-haul dense space-division multiplexed transmission over low-crosstalk heterogeneous 32-core transmission line using a partial recirculating loop system,” J. Lightwave Technol. 35, 488–498 (2017).
[Crossref]

K. Takeshima, T. Tsuritani, Y. Tsuchida, K. Maeda, T. Saito, K. Watanabe, T. Sasa, K. Imamura, R. Sugizaki, K. Igarashi, I. Morita, and M. Suzuki, “51.1-Tbit/s MCF transmission over 2520 km using cladding-pumped seven-core EDFAs,” J. Lightwave Technol. 34, 761–767 (2016).
[Crossref]

K. S. Abedin, J. M. Fini, T. F. Thierry, V. R. Supradeepa, B. Zhu, M. F. Yan, L. Bansal, E. M. Monberg, and D. J. DiGiovanni, “Multicore erbium doped fiber amplifiers for space division multiplexing systems,” J. Lightwave Technol. 32, 2800–2808 (2014).
[Crossref]

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9, 147–154 (1991).
[Crossref]

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

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

Opt. Express (1)

Opt. Express. (1)

H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, H. Nasu, and M. Yamada, “2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber,” Opt. Express. 23, 27405–27418 (2015).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (1)

R. M. Jopson and A. A. M. Saleh, “Modeling of gain and noise in erbium-doped fiber amplifiers,” Proc. SPIE 1581, 114–119 (1991).
[Crossref]

Other (5)

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers Fundamentals and Technology (Academic, 1999), Chap. 5.

H. Ono, K. Takenaga, K. Ichii, S. Matsuo, T. Takahashi, H. Masuda, and M. Yamada, “12-core double-clad Er/Yb-doped fiber amplifier employing free-space coupling pump/signal combiner module,” in The 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), paper We.4.A.4.

M. Nooruzzaman, S. Jain, Y. Jung, S. Alam, D. J. Richardson, Y. Miyamoto, and T. Morioka, “Power consumption in multi-core fibre networks,” in The 43rd European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2017), paper Tu.2.F.

T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, and T. Morioka, “2×344Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.4.

K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, and M. Suzuki, “1.03-Exabit/s⋅km super-Nyquist-WDM transmission over 7,326-km seven-core fiber,” in 39th European Conference and Exhibition on Optical Communication (ECOC), Technical Digest (2013), Postdeadline paper PD.3.E.3.

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Figures (12)

Fig. 1.
Fig. 1. Configuration of CP 12-core erbium-doped fiber amplifier.
Fig. 2.
Fig. 2. (a)–(c) Pump intensity distribution images in the inner cladding. (d)–(f) Probability density distribution of pump intensity in inner cladding. (a) and (d)  0.3 , (b) and (e)  6 , and (c) and (f) 24-m-long EDF outputs.
Fig. 3.
Fig. 3. Experimental setup for measuring the pump power.
Fig. 4.
Fig. 4. (a) Input signal power dependence of the experimentally obtained and calculated pump powers and (b) experimental and calculated gain spectra for C-band.
Fig. 5.
Fig. 5. (a) Input signal power dependence of the experimentally obtained and calculated pump powers and (b) experimental and calculated gain spectra for L-band.
Fig. 6.
Fig. 6. Experimental setup for measuring the gain transient response.
Fig. 7.
Fig. 7. Gain transient response for the C-band. Surviving channel wavelengths are (a) 1531.0, (b) 1548.5, and (c) 1561.4 nm.
Fig. 8.
Fig. 8. Gain transient response for the L-band. Surviving channel wavelengths are (a) 1572.0, (b) 1587.9, and (c) 1600.4 nm.
Fig. 9.
Fig. 9. (a) Calculated and (b) measured gains of the core of interest for the C-band.
Fig. 10.
Fig. 10. (a) Calculated and (b) measured gains of the core of interest for the L-band.
Fig. 11.
Fig. 11. Calculated transient response of the intercore cross-gain modulation for the C-band and L-band.
Fig. 12.
Fig. 12. Measured transients response of the intercore cross-gain modulation for (a) C-band and (b) L-band.

Tables (1)

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Table 1. MFD, Cutoff-Wavelength, and Erbium Ion Absorption of the Double-Clad 12-Core EDF

Equations (12)

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N 2 ( z , t ) t = N 2 ( z , t ) τ j Γ j S P j ( z , t ) [ σ j e N 2 ( z , t ) σ j a N 1 ( z , t ) ] ,
P j ( z , t ) z = ρ Γ j [ ( σ j e N 2 ( z , t ) σ j a N 1 ( z , t ) ) P j ( z , t ) ] + 2 ρ Γ j σ j e Δ ν j N 2 ( z , t ) a j P j ( z , t ) ,
N ¯ 2 ( t ) = 1 L 0 L N 2 ( z , t ) d z ,
P j out ( t ) = P j in ( t ) e g ¯ j ( t ) L + 2 ρ Γ j σ j e Δ ν j N ¯ 2 ( t ) g ¯ j ( t ) ( e g ¯ j ( t ) L 1 ) ,
g ¯ j ( t ) = ρ Γ j [ ( σ j e + σ j a ) N ¯ 2 ( t ) σ j a ] a j , ( j = k , s , p ) ,
d d t N ¯ 2 ( t ) = N ¯ 2 ( t ) τ + 1 S k 2 Γ k σ k e Δ ν k N ¯ 2 ( t ) 1 ρ S L [ k 2 ρ Γ k σ k e Δ ν k N ¯ 2 ( t ) g ¯ k ( t ) · { ( 1 + a k g ¯ k ( t ) ) ( e g ¯ k ( t ) L 1 ) a k L } + k P k in ( 1 + a k g ¯ k ( t ) ) ( e g ¯ k ( t ) L 1 ) + s P s in ( 1 + a s g ¯ s ( t ) ) ( e g ¯ s ( t ) L 1 ) + p P p in ( 1 + a p g ¯ p ( t ) ) ( e g ¯ p ( t ) L 1 ) ] .
Γ j = 0 0 2 π ξ ( r , θ ) ψ ¯ j ( r , θ ) r d r d θ , ( j = k , s ) ,
Γ p = S S clad .
P p in = P p 0 ( 1 + a p / g ¯ p ss ) ( 1 e g ¯ p ss L ) ,
P p 0 = s P s in ( 1 + a s g ¯ s ss ) ( e g ¯ s s s L 1 ) + k P k in ( 1 + a k g ¯ k ss ) ( e g ¯ k s s L 1 ) + ρ S L τ N ¯ 2 ss L k 2 ρ Γ k σ k e Δ ν k N ¯ 2 ss + k 2 ρ Γ k σ k e Δ ν k N ¯ 2 ss g ¯ k s s [ ( 1 + a k g ¯ k ss ) ( e g ¯ k ss L 1 ) a k L ] .
P p ( z , t ) z = n = 1 M ρ n Γ p , n [ ( σ p e N 2 , n ( z , t ) σ p a N 1 , n ( z , t ) ) P p ( z , t ) + 2 σ p e h ν p Δ ν p N 2 ( z , t ) ] a p P p ( z , t ) = ρ m Γ p , m σ p a ( 1 N 2 , m ( z , t ) ) P p ( z , t ) [ n m ρ n Γ p , n σ p a ( 1 N 2 , n ( z , t ) ) + a p ] P p ( z , t ) ,
a p a p , m c = a p + n m ρ n Γ p , n σ p a ( 1 N ¯ 2 , n ( t ) ) ,

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