Abstract

We investigate the evolution of the decorrelation bandwidth of intercore crosstalk (IC-XT) based on the modified mode-coupled equations (MCEs) in homogeneous weakly coupled multicore fibers (WC-MCFs). The modified MCEs are numerically solved by combining the fourth order Runge-Kutta method with the compound Simpson integral method. It can be theoretically and numerically observed that the decorrelation bandwidth of IC-XT decreases with transmission distance by fractional linear function. The evolution rule of IC-XT’s decorrelation bandwidth is further confirmed by experiments, which can be used as an evaluation criterion for the channel model. Finally, we propose a new channel model with the coupling matrix of IC-XT generated directly from the phase transfer function (PTF), which is in good agreement with the above evaluation criterion. We believe the proposed channel model can provide a good simulation platform for homogeneous WC-MCF based communication systems.

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

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2018 (1)

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

2017 (10)

W. Klaus, B. J. Puttnam, R. S. Luís, J. Sakaguchi, J.-M. D. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

T. Mizuno and Y. Miyamoto, “High-capacity dense space division multiplexing transmission,” Opt. Fiber Technol. 35, 108–117 (2017).
[Crossref]

K. Kitayama and N. P. Diamantopoulos, “Few-Mode Optical Fibers: Original Motivation and Recent Progress,” IEEE Commun. Mag. 55(8), 163–169 (2017).
[Crossref]

T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
[Crossref]

T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
[Crossref]

A. V. T. Cartaxo and T. M. F. Alves, “Discrete Changes Model of Inter-core Crosstalk of Real Homogeneous Multi-core Fibers,” J. Lightwave Technol. 35(12), 2398–2408 (2017).
[Crossref]

R. O. J. Soeiro, T. M. F. Alves, and A. V. T. Cartaxo, “Dual Polarization Discrete Changes Model of Inter-Core Crosstalk in Multi-Core Fibers,” IEEE Photonics Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

T. M. F. Alves and A. V. T. Cartaxo, “Inter-core Crosstalk in Homogeneous Multi-core Fibers: Theoretical Characterization of Stochastic Time Evolution,” J. Lightwave Technol. 35(21), 4613–4623 (2017).
[Crossref]

G. Rademacher, R. S. Luís, B. J. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

I. S. Chekhovskoy, V. I. Paasonen, O. V. Shtyrina, and M. P. Fedoruk, “Numerical approaches to simulation of multi-core fibers,” J. Comput. Phys. 334, 31–44 (2017).
[Crossref]

2016 (15)

B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The Role of Effective Area in the Design of Weakly Coupled MCF: Optimization Guidance and OSNR Improvement,” IEEE J. Sel. Top. Quantum Electron. 22(2), 81–87 (2016).
[Crossref]

J. He, B. Li, L. Deng, M. Tang, L. Gan, S. Fu, P. P. Shum, and D. Liu, “Experimental investigation of inter-core crosstalk tolerance of MIMO-OFDM/OQAM radio over multicore fiber system,” Opt. Express 24(12), 13418–13428 (2016).
[Crossref] [PubMed]

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
[Crossref] [PubMed]

A. Macho, M. Morant, and R. Llorente, “Unified Model of Linear and Nonlinear Crosstalk in Multi-Core Fiber,” J. Lightwave Technol. 34(13), 3035–3046 (2016).
[Crossref]

A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
[Crossref]

C. Antonelli, M. Shtaif, and A. Mecozzi, “Modeling of nonlinear propagation in space-division multiplexed fiber-optic transmission,” J. Lightwave Technol. 34(1), 36–54 (2016).
[Crossref]

A. B. Khalifa, R. Cherif, A. B. Salem, and M. Zghal, “Propagation in few modes fiber with strongly coupled groups of modes,” Proc. SPIE 9886, 98860D (2016).

S. Ö. Arık, K. P. Ho, and J. M. Kahn, “Group Delay management and multiinput multioutput signal processing in mode-division multiplexing systems,” J. Lightwave Technol. 34(11), 2867–2880 (2016).
[Crossref]

T. Mizuno, H. Takara, K. Shibahara, A. Sano, and Y. Miyamoto, “Dense space division multiplexed transmission over multicore and multimode fiber for long-haul transport systems,” J. Lightwave Technol. 34(6), 1484–1493 (2016).
[Crossref]

J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
[Crossref]

K. Igarashi, D. Soma, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, and M. Suzuki, “Ultra-dense spatial-division-multiplexed optical fiber transmission over 6-mode 19-core fibers,” Opt. Express 24(10), 10213–10231 (2016).
[Crossref] [PubMed]

B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
[Crossref]

K. Saitoh and S. Matsuo, “Multicore Fiber Technology,” J. Lightwave Technol. 34(1), 55–66 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (3)

2012 (4)

2011 (3)

1978 (1)

C. Moler and C. V. Loan, “Nineteen dubious ways to compute the exponential of a matrix,” SIAM Rev. 20(4), 801–836 (1978).
[Crossref]

Abedin, K. S.

Agrawal, G. P.

Aikawa, K.

T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
[Crossref]

Alves, T. M. F.

Amma, Y.

T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
[Crossref]

Antonelli, C.

Antonio-Lopez, J. E.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

Arik, S. O.

S. O. Arik and J. M. Kahn, “Coupled-Core Multi-Core Fibers for Spatial Multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
[Crossref]

Arik, S. Ö.

Awaji, Y.

G. Rademacher, R. S. Luís, B. J. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

W. Klaus, B. J. Puttnam, R. S. Luís, J. Sakaguchi, J.-M. D. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
[Crossref]

R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
[Crossref]

B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
[Crossref]

A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

Bolle, C.

Bolle, C. A.

Burrows, E. C.

Cartaxo, A. V. T.

Chekhovskoy, I. S.

I. S. Chekhovskoy, V. I. Paasonen, O. V. Shtyrina, and M. P. Fedoruk, “Numerical approaches to simulation of multi-core fibers,” J. Comput. Phys. 334, 31–44 (2017).
[Crossref]

Chen, Z.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Cherif, R.

A. B. Khalifa, R. Cherif, A. B. Salem, and M. Zghal, “Propagation in few modes fiber with strongly coupled groups of modes,” Proc. SPIE 9886, 98860D (2016).

Christodoulides, D.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

Cohen, E.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
[Crossref] [PubMed]

Correa, R. A.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

Delgado Mendinueta, J. M.

B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
[Crossref]

J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
[Crossref]

Deng, L.

Diamantopoulos, N. P.

K. Kitayama and N. P. Diamantopoulos, “Few-Mode Optical Fibers: Original Motivation and Recent Progress,” IEEE Commun. Mag. 55(8), 163–169 (2017).
[Crossref]

Eftekhar, M. A.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
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B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
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Essiambre, R. J.

Essiambre, R.-J.

Fedoruk, M. P.

I. S. Chekhovskoy, V. I. Paasonen, O. V. Shtyrina, and M. P. Fedoruk, “Numerical approaches to simulation of multi-core fibers,” J. Comput. Phys. 334, 31–44 (2017).
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T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
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B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The Role of Effective Area in the Design of Weakly Coupled MCF: Optimization Guidance and OSNR Improvement,” IEEE J. Sel. Top. Quantum Electron. 22(2), 81–87 (2016).
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A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
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J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
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R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
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T. Hayashi, T. Sasaki, and E. Sasaoka, “Behavior of Inter-Core Crosstalk as a Noise and Its Effect on Q-Factor in Multi-Core Fiber,” IEICE Trans. Commun. E97B(5), 936–944 (2014).
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T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express 21(5), 5401–5412 (2013).
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T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Characterization of Crosstalk in Ultra-Low-Crosstalk Multi-Core Fiber,” J. Lightwave Technol. 30(4), 583–589 (2012).
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A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
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Kawaguchi, Y.

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A. B. Khalifa, R. Cherif, A. B. Salem, and M. Zghal, “Propagation in few modes fiber with strongly coupled groups of modes,” Proc. SPIE 9886, 98860D (2016).

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K. Kitayama and N. P. Diamantopoulos, “Few-Mode Optical Fibers: Original Motivation and Recent Progress,” IEEE Commun. Mag. 55(8), 163–169 (2017).
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Kobayashi, T.

Kokubun, Y.

Koshiba, M.

T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
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T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express 21(5), 5401–5412 (2013).
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Li, G.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
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E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
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B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
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A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
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J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
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Luís, R. S.

Luo, B.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
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Malka, D.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
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T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
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K. Saitoh and S. Matsuo, “Multicore Fiber Technology,” J. Lightwave Technol. 34(1), 55–66 (2016).
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Mendinueta, J. M. D.

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Miyamoto, Y.

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C. Moler and C. V. Loan, “Nineteen dubious ways to compute the exponential of a matrix,” SIAM Rev. 20(4), 801–836 (1978).
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Morant, M.

Mori, T.

T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
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Morita, I.

Mumtaz, S.

Nakajima, K.

T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
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Nakanishi, T.

Paasonen, V. I.

I. S. Chekhovskoy, V. I. Paasonen, O. V. Shtyrina, and M. P. Fedoruk, “Numerical approaches to simulation of multi-core fibers,” J. Comput. Phys. 334, 31–44 (2017).
[Crossref]

Pan, W.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Pan, Y.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
[Crossref]

Peckham, D. W.

Puttnam, B. J.

W. Klaus, B. J. Puttnam, R. S. Luís, J. Sakaguchi, J.-M. D. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
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G. Rademacher, R. S. Luís, B. J. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
[Crossref]

J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
[Crossref]

B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
[Crossref]

A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

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Randel, S.

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Sakaguchi, J.

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T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
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A. B. Khalifa, R. Cherif, A. B. Salem, and M. Zghal, “Propagation in few modes fiber with strongly coupled groups of modes,” Proc. SPIE 9886, 98860D (2016).

Sano, A.

Sasaki, T.

Sasaki, Y.

T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
[Crossref]

Sasaoka, E.

Schülzgen, A.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

Shahmoon, A.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
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E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
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I. S. Chekhovskoy, V. I. Paasonen, O. V. Shtyrina, and M. P. Fedoruk, “Numerical approaches to simulation of multi-core fibers,” J. Comput. Phys. 334, 31–44 (2017).
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B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The Role of Effective Area in the Design of Weakly Coupled MCF: Optimization Guidance and OSNR Improvement,” IEEE J. Sel. Top. Quantum Electron. 22(2), 81–87 (2016).
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Shum, P. P.

Sierra, A.

Soeiro, R. O. J.

R. O. J. Soeiro, T. M. F. Alves, and A. V. T. Cartaxo, “Dual Polarization Discrete Changes Model of Inter-Core Crosstalk in Multi-Core Fibers,” IEEE Photonics Technol. Lett. 29(16), 1395–1398 (2017).
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Tong, W.

B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The Role of Effective Area in the Design of Weakly Coupled MCF: Optimization Guidance and OSNR Improvement,” IEEE J. Sel. Top. Quantum Electron. 22(2), 81–87 (2016).
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B. Li, Z. Feng, M. Tang, Z. Xu, S. Fu, Q. Wu, L. Deng, W. Tong, S. Liu, and P. P. Shum, “Experimental demonstration of large capacity WSDM optical access network with multicore fibers and advanced modulation formats,” Opt. Express 23(9), 10997–11006 (2015).
[Crossref] [PubMed]

Tsuritani, T.

Tu, J.

Wada, M.

T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
[Crossref]

Wada, N.

W. Klaus, B. J. Puttnam, R. S. Luís, J. Sakaguchi, J.-M. D. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

G. Rademacher, R. S. Luís, B. J. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
[Crossref]

J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
[Crossref]

B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
[Crossref]

A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

Wakayama, Y.

Watanabe, T.

Winzer, P. J.

Wu, Q.

Xia, C.

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

Xu, Z.

B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The Role of Effective Area in the Design of Weakly Coupled MCF: Optimization Guidance and OSNR Improvement,” IEEE J. Sel. Top. Quantum Electron. 22(2), 81–87 (2016).
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B. Li, Z. Feng, M. Tang, Z. Xu, S. Fu, Q. Wu, L. Deng, W. Tong, S. Liu, and P. P. Shum, “Experimental demonstration of large capacity WSDM optical access network with multicore fibers and advanced modulation formats,” Opt. Express 23(9), 10997–11006 (2015).
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Yamamoto, F.

T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
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Yamamoto, T.

T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, F. Yamamoto, and K. Nakajima, “Strongly-coupled multi-core fiber and its optical characteristics for MIMO transmission systems,” Opt. Fiber Technol. 35, 8–18 (2017).
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Yan, L.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
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Yan, M. F.

Ye, F.

Yi, A.

A. Yi, L. Yan, Y. Pan, L. Jiang, Z. Chen, W. Pan, and B. Luo, “Transmission of multi-dimensional signals for next generation optical communication systems,” Opt. Commun. 408, 42–52 (2018).
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Yoshikane, N.

Zalevsky, Z.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6(1), 29080 (2016).
[Crossref] [PubMed]

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A. B. Khalifa, R. Cherif, A. B. Salem, and M. Zghal, “Propagation in few modes fiber with strongly coupled groups of modes,” Proc. SPIE 9886, 98860D (2016).

Zhu, B.

IEEE Commun. Mag. (1)

K. Kitayama and N. P. Diamantopoulos, “Few-Mode Optical Fibers: Original Motivation and Recent Progress,” IEEE Commun. Mag. 55(8), 163–169 (2017).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The Role of Effective Area in the Design of Weakly Coupled MCF: Optimization Guidance and OSNR Improvement,” IEEE J. Sel. Top. Quantum Electron. 22(2), 81–87 (2016).
[Crossref]

C. Xia, M. A. Eftekhar, R. A. Correa, J. E. Antonio-Lopez, A. Schülzgen, D. Christodoulides, and G. Li, “Supermodes in Coupled Multi-Core Waveguide Structures,” IEEE J. Sel. Top. Quantum Electron. 22(2), 196–207 (2016).
[Crossref]

IEEE Photonics J. (2)

B. J. Puttnam, R. S. Luis, T. A. Eriksson, W. Klaus, J. M. Delgado Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” IEEE Photonics J. 8(2), 1–9 (2016).
[Crossref]

T. Fujisawa, Y. Amma, Y. Sasaki, S. Matsuo, K. Aikawa, K. Saitoh, and M. Koshiba, “Crosstalk Analysis of Heterogeneous Multicore Fibers Using Coupled-Mode Theory,” IEEE Photonics J. 9(5), 1–8 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (3)

A. V. T. Cartaxo, R. S. Luis, B. J. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion Impact on the Crosstalk Amplitude Response of Homogeneous Multi-Core Fibers,” IEEE Photonics Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. O. J. Soeiro, T. M. F. Alves, and A. V. T. Cartaxo, “Dual Polarization Discrete Changes Model of Inter-Core Crosstalk in Multi-Core Fibers,” IEEE Photonics Technol. Lett. 29(16), 1395–1398 (2017).
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S. O. Arik and J. M. Kahn, “Coupled-Core Multi-Core Fibers for Spatial Multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
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IEICE Trans. Commun. (1)

T. Hayashi, T. Sasaki, and E. Sasaoka, “Behavior of Inter-Core Crosstalk as a Noise and Its Effect on Q-Factor in Multi-Core Fiber,” IEICE Trans. Commun. E97B(5), 936–944 (2014).
[Crossref]

J. Comput. Phys. (1)

I. S. Chekhovskoy, V. I. Paasonen, O. V. Shtyrina, and M. P. Fedoruk, “Numerical approaches to simulation of multi-core fibers,” J. Comput. Phys. 334, 31–44 (2017).
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J. Lightwave Technol. (14)

J. M. Fini, B. Zhu, T. F. Taunay, M. F. Yan, and K. S. Abedin, “Statistical Models of Multicore Fiber Crosstalk Including Time Delays,” J. Lightwave Technol. 30(12), 2003–2010 (2012).
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K. Saitoh and S. Matsuo, “Multicore Fiber Technology,” J. Lightwave Technol. 34(1), 55–66 (2016).
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T. Mizuno, H. Takara, K. Shibahara, A. Sano, and Y. Miyamoto, “Dense space division multiplexed transmission over multicore and multimode fiber for long-haul transport systems,” J. Lightwave Technol. 34(6), 1484–1493 (2016).
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J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-Mode Multicore Fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
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R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6*6 MIMO Processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
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T. M. F. Alves and A. V. T. Cartaxo, “Inter-core Crosstalk in Homogeneous Multi-core Fibers: Theoretical Characterization of Stochastic Time Evolution,” J. Lightwave Technol. 35(21), 4613–4623 (2017).
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R. S. Luis, B. J. Puttnam, A. V. T. Cartaxo, W. Klaus, J. M. D. 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. Lightwave Technol. 34(2), 441–447 (2016).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 Schematic diagram of seven core homogeneous WC-MCF.
Fig. 2
Fig. 2 (a)Numerical results without bending. (b)Numerical results with bending radius 105 mm.
Fig. 3
Fig. 3 Relative error of numerical simulation under different calculation step sizes.
Fig. 4
Fig. 4 (a) The evolution of XT under the first condition. (b) The evolution of XT under the second condition (with inherent propagation mismatch). (c) One realization of simulation under the third condition (with reasonable fluctuations added).
Fig. 5
Fig. 5 (a) Average XT power. (b) Probability distribution of XT. (c) The distribution of real part of XT. (d) The distribution of imaginary part of XT
Fig. 6
Fig. 6 (a) Power of frequency-dependent XT at transmission distance 400.0 m with twist (red line) or without twist (blue line). (b) Real and imaginary parts of XT without twist. (c) The evolution of XT’s period without twist.
Fig. 7
Fig. 7 Propagation constant and coupling coefficient change linearly with optical wavelength.
Fig. 8
Fig. 8 (a) Power of frequency-dependent XT with fluctuations. (b) Real and imaginary parts of XT with fluctuations. (c) The evolution of XT’s decorrelation bandwidth (BW).
Fig. 9
Fig. 9 Experimental scheme of XT measurement.
Fig. 10
Fig. 10 (a) Frequency-dependent XT from Core 1 to Core 7 at 11.004 km. (b) Variation of 1 dB decorrelation bandwidth of XT from Core 1 to Core 7 at 11.004 km
Fig. 11
Fig. 11 The evolution of decorrelation bandwidth of XT from Core1 to Core 2-7 changed with transmission length.
Fig. 12
Fig. 12 Frequency-dependent XT under three different conditions (blue dot line: only the propagation constant changes; red solid line: only the coupling coefficient changes, magenta solid line: both the propagation constant and the coupling coefficient change).
Fig. 13
Fig. 13 (a) The real part and imaginary part of the optical pulse. (b) The spectrum of the optical pulse.
Fig. 14
Fig. 14 The simulation results of proposed WC-MCF’s channel model: (a) The power of frequency-dependent XT. (b) The real and imaginary parts of XT. (c) The evolution of decorrelation bandwidth (BW).

Equations (24)

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d A d z = j κ ( λ ) B exp ( j Δ ϕ ( z , λ ) ) d B d z = j κ ( λ ) A exp ( + j Δ ϕ ( z , λ ) )
Δ ϕ ( z , λ ) = 0 z [ β eq , B ( z , , λ ) β e q , A ( z , , λ ) ] d z ,
β e q , n ( z , λ ) = β c , n ( λ ) ( 1 + r n cos θ n ( z ) R b ( z ) )
B N ( z ) = B 0 j | K | k = 1 N exp [ j ϕ r n d ( k ) ] A k 1 = j | K | k = 1 N exp [ j ϕ r n d ( k ) ]
| K | κ 2 β c R b D 2 π γ
X T a v e = 2 σ 2 2 = 4 σ 4 2 = 2 κ 2 β c R b D L = h L
X T ( ω ) = j | K | exp ( j β e q , B ( ω ) L ) k = 1 N exp ( j Δ β e q ( ω ) z k j ϕ r n d ( k ) )
Δ β e q ( ω ) = β e q , B ( ω ) β e q , A ( ω ) = ( β 0 , B β 0 , A ) ω 0 + ( β 1 , B β 1 , A ) ( ω ω 0 ) + 1 2 ( β 2 , B β 2 , A ) ( ω ω 0 ) 2 + ... = Δ β 0 ω 0 + Δ β 1 ( ω ω 0 ) + 1 2 Δ β 2 ( ω ω 0 ) 2 + ...
β e q , A ( z , ω ) = β c , A ( ω ) ( 1 + S β , A ( z ) )
β e q , B ( z , ω ) = β c , B ( ω ) ( 1 + B i a s β + S β , B ( z ) ) ( 1 + D cos θ ( z ) R b ( z ) )
R b ( z ) = R 0 ( 1 + S R ( z ) )
θ ( z ) = 0 z { γ [ 1 + S T ( z , ) ] z , + θ 0 } d z ,
[ A ( z ) B ( z ) ] = [ cos ( κ z ) j sin ( κ z ) j sin ( κ z ) cos ( κ z ) ] [ A ( 0 ) B ( 0 ) ]
B ( z ) = j κ q sin ( q z ) exp ( j δ z ) ; w h e r e q = κ 2 + δ 2 , δ = β e q , B β e q , A 2
| B ( z , λ ) | 2 = | κ q sin ( q z ) | 2 | κ q sin ( | δ | z ) | 2 = | κ q sin ( 1 2 D R b | Q λ + P | z ) | 2
T ( λ ) = | 2 π R b Q D z |
Δ ϕ ( z , ω ) = 0 z β c ( ω ) B i a s β d z + 0 z β c ( ω ) D cos θ ( z ) R b ( z ) ( 1 + B i a s β + S β , B ) d z + 0 z β c ( ω ) ( S β , B S β , A ) d z
A z = ( α 2 Δ β 1 T j β 2 , A 2 2 T 2 ) A + j γ A | A | 2 B z = ( α 2 + Δ β 1 T j β 2 , B 2 2 T 2 ) A + j γ B | B | 2
Δ β 1 = β 1 , B β 1 , A 2 = 1 2 ( 1 v g , B 1 v g , A )
γ n = 2 π n 2 f ω 0 c A e f f , n
[ A z ' ( z , ω ) B z ' ( z , ω ) ] = [ 1 | K | 2 j | K | exp ( j ϕ r n d ) j | K | exp ( + j ϕ r n d ) 1 | K | 2 ] [ A z ( z , ω ) B z ( z , ω ) ]
[ A z ' ( z , ω ) B z ' ( z , ω ) ] = [ 1 | K | 2 j | K | exp ( j Δ ϕ ( z , ω ) ) j | K | exp ( + j Δ ϕ ( z , ω ) ) 1 | K | 2 ] [ A z ( z , ω ) B z ( z , ω ) ]
Δ ϕ ( z , ω ) = ϕ B ( z , ω ) ϕ A ( z , ω ) + ϕ r n d ( ω 0 )
ϕ A ( z + h x t , ω ) = a n g l e ( A ( z + h x t , ω ) ) a n g l e ( A ( z , ω ) ) ϕ B ( z + h x t , ω ) = a n g l e ( B ( z + h x t , ω ) ) a n g l e ( B ( z , ω ) )

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