Abstract

We investigate theoretically nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate the case where linear coupling among spatial modes of the fiber is weak and derive new Manakov equations after averaging over random birefringence fluctuations. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms vanish. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We verify the accuracy of new Manakov equations by simulating the transmission of multiple 114-Gb/s bit streams in the PDM-QPSK format over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equations. The agreement is excellent in all cases studied. A major benefit of the new Manakov equations is that they typically reduce the computation time by more than a factor of 10. Our results show that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. The extent of improvement depends on the fiber design and how many spatial modes are used for SDM transmission. We also consider the case where all spatial modes experience strong random linear coupling modeled using a random matrix. We derive new Manakov equations in this regime and show that the impact of some nonlinear effects can be reduced relatively to single-modes fibers. Finally, we extend our analysis to multicore fibers and show that the Manakov equations obtained in the strong- and weak-coupling regimes can still be used depending on the extent of coupling among fiber cores.

© 2012 IEEE

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  27. F. Mezzadri, "How to generate random matrices from the classical compact groups," Notices of AMS 54, 592-604 (2007).
  28. A. M. Tulino, S. Verdú, "Random matrix theory and wireless communications," Commun. Inf. Theory 1, 1-182 (2004).

2012 (5)

R.-J. Essiambre, R. W. Tkach, "Capacity trends and limits of optical communication networks," Proc. IEEE 100, 1035-1055 (2012).

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, R. Lingle, "Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing," J. Lightw. Technol. 30, 521-531 (2012).

A. Mecozzi, R.-J. Essiambre, "Nonlinear shannon limit in pseudo-linear coherent systems," J. Lightw. Technol. 30, 2010-2024 (2012).

A. Mecozzi, C. Antonelli, M. Shtaif, "Nonlinear propagation in multi-mode fiber in the strong coupling regime," Opt. Express 20, 11673-11678 (2012).

S. Mumtaz, R.-J. Essiambre, G. P. Agrawal, "Reduction of nonlinear penalties due to linear coupling in multicore optical fibers," IEEE Photon. Technol. Lett. 24, 1574-1576 (2012).

2011 (4)

R. Ryf, R.-J. Essiambre, S. Randel, A. H. Gnauck, P. J. Winzer, T. Hayashi, T. Taru, T. Sasaki, "MIMO-based crosstalk suppression in spatially multiplexed 3 56-Gb/s PDM-QPSK signals for strongly coupled three-core fiber," IEEE Photon. Technol. Lett. 23, 1469-1471 (2011).

C. Koebele, M. Salsi, G. Charlet, S. Bigo, "Nonlinear effects in mode-division-multiplexed transmission over few-mode optical fiber," IEEE Photon. Technol. Lett. 23, 1316-1318 (2011).

K. Ho, J. Kahn, "Statistics of group delays in multimode fiber with strong mode coupling," J. Lightw. Technol. 29, 3119-3128 (2011).

K. Ho, J. Kahn, "Mode-dependent loss and gain: Statistics and effect on mode-division multiplexing," Opt. Express 19, 16612-16635 (2011).

2010 (2)

R. W. Tkach, "Scaling optical communications for the next decade and beyond," Bell Labs Tech. J. 14, 3-9 (2010).

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).

2009 (1)

M. B. Shemirani, W. Mao, R. A. Panicker, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).

2008 (1)

2007 (1)

F. Mezzadri, "How to generate random matrices from the classical compact groups," Notices of AMS 54, 592-604 (2007).

2004 (1)

A. M. Tulino, S. Verdú, "Random matrix theory and wireless communications," Commun. Inf. Theory 1, 1-182 (2004).

1997 (2)

P. K. A. Wai, C. R. Menyuk, "Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence," J. Lightw. Technol. 14, 148-157 (1997).

D. Marcuse, C. R. Manyuk, P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightw. Technol. 15, 1735-1746 (1997).

1992 (1)

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, "Polarization multiplexing with solitons," J. Lightw. Technol. 10, 28-35 (1992).

1974 (1)

S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves," Sov. Phys. JETP 38, 248-253 (1974).

Bell Labs Tech. J. (1)

R. W. Tkach, "Scaling optical communications for the next decade and beyond," Bell Labs Tech. J. 14, 3-9 (2010).

Commun. Inf. Theory (1)

A. M. Tulino, S. Verdú, "Random matrix theory and wireless communications," Commun. Inf. Theory 1, 1-182 (2004).

IEEE Photon. Technol. Lett. (3)

S. Mumtaz, R.-J. Essiambre, G. P. Agrawal, "Reduction of nonlinear penalties due to linear coupling in multicore optical fibers," IEEE Photon. Technol. Lett. 24, 1574-1576 (2012).

R. Ryf, R.-J. Essiambre, S. Randel, A. H. Gnauck, P. J. Winzer, T. Hayashi, T. Taru, T. Sasaki, "MIMO-based crosstalk suppression in spatially multiplexed 3 56-Gb/s PDM-QPSK signals for strongly coupled three-core fiber," IEEE Photon. Technol. Lett. 23, 1469-1471 (2011).

C. Koebele, M. Salsi, G. Charlet, S. Bigo, "Nonlinear effects in mode-division-multiplexed transmission over few-mode optical fiber," IEEE Photon. Technol. Lett. 23, 1316-1318 (2011).

J. Lightw. Technol. (8)

M. B. Shemirani, W. Mao, R. A. Panicker, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, "Polarization multiplexing with solitons," J. Lightw. Technol. 10, 28-35 (1992).

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, R. Lingle, "Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing," J. Lightw. Technol. 30, 521-531 (2012).

A. Mecozzi, R.-J. Essiambre, "Nonlinear shannon limit in pseudo-linear coherent systems," J. Lightw. Technol. 30, 2010-2024 (2012).

P. K. A. Wai, C. R. Menyuk, "Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence," J. Lightw. Technol. 14, 148-157 (1997).

D. Marcuse, C. R. Manyuk, P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightw. Technol. 15, 1735-1746 (1997).

K. Ho, J. Kahn, "Statistics of group delays in multimode fiber with strong mode coupling," J. Lightw. Technol. 29, 3119-3128 (2011).

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

Notices of AMS (1)

F. Mezzadri, "How to generate random matrices from the classical compact groups," Notices of AMS 54, 592-604 (2007).

Opt. Express (2)

Proc. IEEE (1)

R.-J. Essiambre, R. W. Tkach, "Capacity trends and limits of optical communication networks," Proc. IEEE 100, 1035-1055 (2012).

Sov. Phys. JETP (1)

S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves," Sov. Phys. JETP 38, 248-253 (1974).

Other (9)

A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge Univ. Press, 1998).

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, R. Lingle, "Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing," Proc. Opt. Fiber Commun. Conf. Expo./Nat. Fiber Opt. Eng. Conf. (2011) pp. 1-3.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, "88 × 3 × 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier," Proc. 37th Eur. Conf. Opt. Commun. (2011) pp. 1-3.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, G. Charlet, "40 km transmission of five mode division multiplexed data streams at 100 Gb/s with low MIMO-DSP complexity," Proc. 37th Eur. Conf. Opt. Commun. (2011) pp. 1-3.

R.-J. Essiambre, "Impact of fiber parameters on nonlinear fiber capacity," Proc. Opt. Fiber Commun. Conf. Expo./Nat. Fiber Opt. Eng. Conf. (2011).

R.-J. Essiambre, R. Ryf, M. A. Mestre, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, S. Randel, Y. Sun, X. Jiang, R. Lingle, Jr"Inter-modal nonlinear interactions between well separated channels in spatially-multiplexed fiber transmission," Proc. 38th Eur. Conf. Opt. Commun. (2012).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

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