Abstract

Contrary to single mode fibers, where random imperfections are responsible for polarization-mode dispersion, modal dispersion (MD) in multi-mode fiber structures for space-division multiplexed (SDM) transmission, originates chiefly from the intrinsic non-degeneracy of the propagating modes, also known as modal birefringence. The presence of random imperfections in such fibers has a positive aspect, as it reduces the intrinsic MD, and in the limit of strong coupling it causes the signal delay spread to increase with the square root of the propagation distance, rather than linearly, as would be the case in an ideal fiber. In this paper we derive a formula that relates the signal delay spread to the fiber geometry and to the statistical properties of the structural fiber perturbations. The derived formula provides insight into the MD phenomenon and facilitates the design of low-MD multi-mode fiber structures.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Intensity impulse response of SDM links

Antonio Mecozzi, Cristian Antonelli, and Mark Shtaif
Opt. Express 23(5) 5738-5743 (2015)

Stokes-space analysis of modal dispersion in fibers with multiple mode transmission

Cristian Antonelli, Antonio Mecozzi, Mark Shtaif, and Peter J. Winzer
Opt. Express 20(11) 11718-11733 (2012)

Long distance crosstalk-supported transmission using homogeneous multicore fibers and SDM-MIMO demultiplexing

Ruben S. Luís, Georg Rademacher, Benjamin J. Puttnam, Yoshinari Awaji, and Naoya Wada
Opt. Express 26(18) 24044-24053 (2018)

References

  • View by:
  • |
  • |
  • |

  1. H. Kogelnik and P.J. Winzer, “Modal birefringence in weakly guiding fibers,” J. Lightwave Technol. 30, 2240–2243 (2012).
    [Crossref]
  2. C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express 20, 11718–11733 (2012).
    [Crossref] [PubMed]
  3. K-P. Ho and J.M Kahn, “Statistics of group delays in multi-mode fibers with strong mode coupling,” J. Lightwave Technol. 29, 3119–3128 (2011).
    [Crossref]
  4. R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).
  5. C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Random coupling between groups of degenerate fiber modes in mode multiplexed transmission,” Opt. Express 21, 9484–9490 (2013).
    [Crossref] [PubMed]
  6. L. Palmieri, “Coupling mechanism in multimode fibers,” SPIE OPTO (2013), Paper 90090G.
  7. J.P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
    [Crossref] [PubMed]
  8. A. Mecozzi, C. Antonelli, and M. Shtaif, “Intensity impulse response of SDM links,” to be published (2015).
  9. C. Xia, N. Bai, I. Ozdur, X. Zhou, and G. Li, “Supermodes for optical transmission,” Opt. Express 19, 16653–16664 (2011).
    [Crossref] [PubMed]
  10. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. 62, 1267–1277 (1972).
    [Crossref]
  11. A. Galtarossa and L. Palmieri, “Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments,” J. Lightwave Technol. 20, 1149–1159 (2002).
    [Crossref]

2013 (1)

2012 (2)

2011 (2)

2002 (1)

2000 (1)

J.P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref] [PubMed]

1972 (1)

Antonelli, C.

Bai, N.

Delbue, R.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Essiambre, R.-J.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Galtarossa, A.

Gnauck, A. H.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Gordon, J.P.

J.P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref] [PubMed]

Hayashi, T.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Ho, K-P.

Kahn, J.M

Kogelnik, H.

H. Kogelnik and P.J. Winzer, “Modal birefringence in weakly guiding fibers,” J. Lightwave Technol. 30, 2240–2243 (2012).
[Crossref]

J.P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref] [PubMed]

Li, G.

Mecozzi, A.

Mestre, M. A.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Ozdur, I.

Palmieri, L.

Pupalaikis, P.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Randel, S.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Ryf, R.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Sasaki, T.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Schmidt, C.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Shtaif, M.

Snyder, W.

Sureka, A.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Taru, T.

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

Winzer, P. J.

Winzer, P.J.

Xia, C.

Zhou, X.

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

Opt. Express (3)

Proc. Natl. Acad. Sci. USA (1)

J.P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref] [PubMed]

Other (3)

A. Mecozzi, C. Antonelli, and M. Shtaif, “Intensity impulse response of SDM links,” to be published (2015).

R. Ryf, R.-J. Essiambre, A. H. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “SDM transmission over 4200-km 3-core microstructured fiber,” OFC 2011, Paper PDP5C.2 (2011).

L. Palmieri, “Coupling mechanism in multimode fibers,” SPIE OPTO (2013), Paper 90090G.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 On the left is the schematic of the three-core fiber that we assume in our examples. The fiber parameters are taken from [4]: each core’s radius is r = 6.2 μm, the inter-core distance is d = 29.4μm, and the refractive index difference between cores and cladding is of 0.27%. In the middle we show the structure of the Jones vector for this fiber in the reference frame of the individual cores. On the right we show the deterministic coupling matrix B0, where the coupling coefficient b can be obtained as in [10].
Fig. 2
Fig. 2 a) The coupling coefficient b as a function of the inter-core distance d. Relative changes of b of the order of 20% can be seen to correspond to variations smaller than 1μm in the inter-core distance. b) The square delay spread T2 versus distance for the displayed perturbation parameters. The solid curve shows the results of Monte Carlo simulations with 104 fiber realizations; the dashed curve is based on Eq. (4). The asymptotic growth-rate κ2.
Fig. 3
Fig. 3 Theoretical and simulated values of the delay spread coefficient κ for various parameter settings. The first row coincides with the settings used in Fig. 2. In each of the rows from the second to the fifth only one parameter is varied.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E z = i B E ,
B 0 = b Λ 2 N , B n = n Λ 2 N ,
τ z = b ω + n ω + ( b + n ) + τ ,
T 2 = 2 4 N 2 b ω Q 1 [ Q 1 ( exp ( Q z ) I ) I z ] b ω κ z ,
Q = 1 Δ z Δ z exp ( z b × ) { i , j = 1 D e ^ i × [ 0 N i , j ( ζ ) exp ( ζ b × ) d ζ e ^ j ] × } exp ( z b × ) d z ,
Q = 1 Δ z Δ z exp ( z b × ) { i = 1 35 σ i 2 L C e ^ i × [ ( I L C b × ) 1 e ^ i ] × } exp ( z b × ) d z .
τ z = exp { z b × } b ω + n × τ ,
τ z = b ω + n × τ .
τ 2 z = 2 τ τ z = 2 b ω τ .
τ ( z + Δ z ) = τ ( z ) + b ω Δ z + z z + Δ z n ( z 1 ) × τ ( z 1 ) d z 1 .
Δ τ = b ω Δ z + Δ V × b ω + Δ W × τ ( z ) + z z + Δ z z z n ( z ) × n ( z ) × τ ( z ) d z d z ,
Δ W = z z + Δ z n ( z ) d z , Δ V = z z + Δ z ( z z ) n ( z ) d z .
Δ τ = b ω Δ z + Δ W × τ ( z ) + Q τ ( z ) Δ z , Q = 1 Δ z z z + Δ z z z n ( z ) × n ( z ) × d z d z .
Q Q = 1 Δ z z z + Δ z z z [ exp ( z b × ) n ( z ) ] × [ exp ( z b × ) n ( z ) ] × d z d z 1 Δ z z z + Δ z exp ( z b × ) { i , j = 1 D e ^ i × [ 0 N i , j ( ζ ) exp [ ζ b × ] d ζ e ^ j ] × } exp ( z b × ) d z .

Metrics