Abstract

In the strong mode-coupling regime, the model for mode-dependent gains and losses (collectively referred as MDL) of a multimode fiber is extended to the region with large MDL. The MDL is found to have the same statistical properties as the eigenvalues of the sum of two matrices. The first matrix is a random Gaussian matrix with its standard deviation proportional to the accumulated MDL. The other matrix is a deterministic matrix with uniform eigenvalues proportional to the square of the accumulated MDL. The results are analytically correct for fibers with two or very large number of modes, and also numerically verified for multimode fibers with other number of modes.

© 2012 IEEE

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2012 (1)

J. Carpenter, T. Wilkinson, "All optical mode-multiplexing using holography and multimode fiber couplers," J. Lightw. Technol. 30, 1978-1984 (2012).

2011 (6)

A. Al Amni, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP$_{{11}}$ mode 4$\,\times\,$4 MIMO-OFDM transmission over a two-mode fiber," Opt. Exp. 19, 16672-16678 (2011).

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Margoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2$\,\times\,$100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Exp. 19, 16593-16600 (2011).

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

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

P. J. Winzer, G. J. Foschini, "MIMO capacities and outage probabilities in spatially multiplexed optical transport systems," Opt. Exp. 19, 16680-16696 (2011).

K.-P. Ho, J. M. Kahn, "Frequency diversity in mode-division multiplexing systems," J. Lightw. Technol. 19, 3719-3726 (2011).

2010 (1)

F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, "Long distance transmission in few-mode fibers," Opt. Exp. 18, 13250-13257 (2010).

2008 (1)

S. Murshid, B. Grossman, P. Narakorn, "Spatial domain multiplexing: A new dimension in fiber optic multiplexing," Opt. Laser Technol. 40, 1030-1036 (2008).

2007 (1)

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, B. Jalali, "Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links," IEEE Commun. Mag. 45, 57-63 (2007).

2003 (2)

P. K. Pepeljugoski, D. M. Kuchta, "Design of optical communications data links," IBM J. Res. Dev. 47, 223-237 (2003).

A. Glatarossa, L. Palmieri, "The exact statistics of polarization-dependent loss in fiber-optic links," IEEE Photon. Technol. Lett. 15, 57-59 (2003).

2001 (2)

M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

P. Lu, L. Chen, X. Bao, "Statistical distribution of polarization dependent loss in the presence of polarization mode dispersion in single mode fibers," IEEE Photon. Technol. Lett. 13, 451-453 (2001).

2000 (1)

H. R. Stuart, "Dispersive multiplexing in multimode optical fiber," Science 289, 281-283 (2000).

1999 (1)

L. López, "Asymptotic expansions of the Whittaker functions for large order parameter," Methods Appl. Anal. 6, 249-256 (1999).

1995 (1)

J. Abad, J. Sesma, "Computation of the regular confluent hypergeometric function," Mathematica J. 5, 74-76 (1995).

1982 (1)

1975 (1)

R. Olshansky, "Mode-coupling effects in graded-index optical fibers," App. Opt. 14, 935-945 (1975).

1972 (1)

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1780 (1972).

App. Opt. (1)

R. Olshansky, "Mode-coupling effects in graded-index optical fibers," App. Opt. 14, 935-945 (1975).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1780 (1972).

IBM J. Res. Dev. (1)

P. K. Pepeljugoski, D. M. Kuchta, "Design of optical communications data links," IBM J. Res. Dev. 47, 223-237 (2003).

IEEE Commun. Mag. (1)

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, B. Jalali, "Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links," IEEE Commun. Mag. 45, 57-63 (2007).

IEEE Photon. Technol. Lett. (1)

A. Glatarossa, L. Palmieri, "The exact statistics of polarization-dependent loss in fiber-optic links," IEEE Photon. Technol. Lett. 15, 57-59 (2003).

IEEE Photon. Technol. Lett. (1)

P. Lu, L. Chen, X. Bao, "Statistical distribution of polarization dependent loss in the presence of polarization mode dispersion in single mode fibers," IEEE Photon. Technol. Lett. 13, 451-453 (2001).

J. Lightw. Technol. (2)

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

J. Carpenter, T. Wilkinson, "All optical mode-multiplexing using holography and multimode fiber couplers," J. Lightw. Technol. 30, 1978-1984 (2012).

J. Lightw. Technol. (3)

M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

K.-P. Ho, J. M. Kahn, "Frequency diversity in mode-division multiplexing systems," J. Lightw. Technol. 19, 3719-3726 (2011).

S. Ö. Arik, D. Askarov, J. M. Kahn, "Effect of mode coupling on signal processing complexity in mode-division multiplexing," J. Lightw. Technol. submitted for publication.

Mathematica J. (1)

J. Abad, J. Sesma, "Computation of the regular confluent hypergeometric function," Mathematica J. 5, 74-76 (1995).

Methods Appl. Anal. (1)

L. López, "Asymptotic expansions of the Whittaker functions for large order parameter," Methods Appl. Anal. 6, 249-256 (1999).

Opt. Exp. (2)

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

F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, "Long distance transmission in few-mode fibers," Opt. Exp. 18, 13250-13257 (2010).

Opt. Laser Technol. (1)

S. Murshid, B. Grossman, P. Narakorn, "Spatial domain multiplexing: A new dimension in fiber optic multiplexing," Opt. Laser Technol. 40, 1030-1036 (2008).

Opt. Exp. (3)

P. J. Winzer, G. J. Foschini, "MIMO capacities and outage probabilities in spatially multiplexed optical transport systems," Opt. Exp. 19, 16680-16696 (2011).

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Margoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2$\,\times\,$100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Exp. 19, 16593-16600 (2011).

A. Al Amni, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP$_{{11}}$ mode 4$\,\times\,$4 MIMO-OFDM transmission over a two-mode fiber," Opt. Exp. 19, 16672-16678 (2011).

Science (1)

H. R. Stuart, "Dispersive multiplexing in multimode optical fiber," Science 289, 281-283 (2000).

Other (9)

Y. Koike, S. Takahashi, Optical Fiber Telecommunications VB: Systems and Networks (Elsevier-Academic, 2008).

D. Voiculescu, K. Dykema, A. Nica, Free Random Variables (AMS, 1992).

A. Nica, R. Speicher, Lectures on the Combinatorics of Free Probability (Cambridge Univ. Press, 2006).

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. (2000) pp. 4541-4550.

E. T. Whittaker, G. N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, 1927).

K.-P. Ho, "Central limits for the products of free random variables," http://arxiv.org/abs/1101.5220.

J. G. Proakis, Digital Communications (McGraw-Hill, 2000).

M. L. Mehta, Random Matrices (Elsevier-Academic, 2004).

H. Buchholz, The Confluent Hypergeometric Function (Springer, 1969) pp. 97.

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