Abstract

In mode-division multiplexed (MDM) transmission systems, mode coupling is responsible for inter-modal crosstalk. We consider the transmission of modulated signals over a few-mode fiber (FMF) having low mode coupling and large differential mode group delay in the presence of a non-ideal fiber connection responsible for extra mode coupling. In this context, we first analytically derive the coupling matrix of the multimode connector and we numerically study the dependence of the matrix coefficients as a function of the butt-joint connection characteristics. The numerical results are then validated through an experiment with a five-mode setup. Finally, through numerical simulations, we assess the impact of the connector on the signal quality investigating different receiver digital signal processing (DSP) schemes.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  7. R. Ryf, M. Mestre, S. Randel, C. Schmidt, A. Gnauck, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. Peckham, A. McCurdy, and R. Lingle, “Mode-multiplexed transmission over a 184-km DGD-compensated few-mode fiber span,” in IEEE Photonics Society Summer Topical Meeting (IEEE, 2012), pp. 173–174.
    [Crossref]
  8. S. Warm, G. Rademacher, and K. Petermann, “DMD Management in Few-Mode Fiber MDM Transmission Systems with Mode Coupling”, in IEEE Photonics Society Summer Topical Meeting (IEEE, 2014), pp. 158–159.
    [Crossref]
  9. P. Sillard, M. Bigot-Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in 37th European Conference on Optical Communication (Optical Society of America, 2011), paper Tu5LeCervin7.
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  18. T. Duthel, C. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” in Optical Fiber Communication Conference (Optical Society of America, 2008), paper OThU5.
    [Crossref]
  19. D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).
  20. J. Damask, Polarization Optics In Telecommunications, (Springer, 2005).
  21. J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems”, in 37th European Conference and Exhibition on Optical Communication (ECOC2011), paper Tu5B2.
    [Crossref]
  22. J.-F. Cardoso and B. H. Laheld, “Equivariant adaptive source separation,” IEEE Trans. Signal Process. 44(12), 3017–3030 (1996).
    [Crossref]
  23. M. Chiani and A. Giorgetti, “Statistical analysis of asynchronous QPSK cochannel interference,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2002), pp. 1855–1859.
    [Crossref]
  24. D. Marcuse, Light transmission optics, (Van Nostrand Reinhold New York, 1982).

2014 (1)

2013 (1)

2012 (1)

2011 (1)

2002 (1)

C. Simos, P. Leproux, P. D. Bin, and P. Facq, “Influence of mode orientations on power transfer at misaligned fibre connections,” J. Opt. A, Pure Appl. Opt. 4(1), 8–15 (2002).
[Crossref]

1996 (1)

J.-F. Cardoso and B. H. Laheld, “Equivariant adaptive source separation,” IEEE Trans. Signal Process. 44(12), 3017–3030 (1996).
[Crossref]

1994 (1)

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

1973 (1)

J. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical,” Bell Syst. Tech. J. 52(8), 1439–1448 (1973).
[Crossref]

Bennett, K.

Bin, P. D.

C. Simos, P. Leproux, P. D. Bin, and P. Facq, “Influence of mode orientations on power transfer at misaligned fibre connections,” J. Opt. A, Pure Appl. Opt. 4(1), 8–15 (2002).
[Crossref]

Blondy, J.

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Cardoso, J.-F.

J.-F. Cardoso and B. H. Laheld, “Equivariant adaptive source separation,” IEEE Trans. Signal Process. 44(12), 3017–3030 (1996).
[Crossref]

Chiani, M.

M. Chiani and A. Giorgetti, “Statistical analysis of asynchronous QPSK cochannel interference,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2002), pp. 1855–1859.
[Crossref]

Cook, J.

J. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical,” Bell Syst. Tech. J. 52(8), 1439–1448 (1973).
[Crossref]

Di Bin, P.

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Facq, P.

C. Simos, P. Leproux, P. D. Bin, and P. Facq, “Influence of mode orientations on power transfer at misaligned fibre connections,” J. Opt. A, Pure Appl. Opt. 4(1), 8–15 (2002).
[Crossref]

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Faugeras, P.

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Foschini, G. J.

Giorgetti, A.

M. Chiani and A. Giorgetti, “Statistical analysis of asynchronous QPSK cochannel interference,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2002), pp. 1855–1859.
[Crossref]

Grow, R. J.

J. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical,” Bell Syst. Tech. J. 52(8), 1439–1448 (1973).
[Crossref]

Hu, J.

Huang, Y.-K.

Ip, E.

Katcharov, N.

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Kogelnik, H.

Koreshkov, K.

Korolev, A.

Laheld, B. H.

J.-F. Cardoso and B. H. Laheld, “Equivariant adaptive source separation,” IEEE Trans. Signal Process. 44(12), 3017–3030 (1996).
[Crossref]

Leproux, P.

C. Simos, P. Leproux, P. D. Bin, and P. Facq, “Influence of mode orientations on power transfer at misaligned fibre connections,” J. Opt. A, Pure Appl. Opt. 4(1), 8–15 (2002).
[Crossref]

Li, M.-J.

Mammel, W. L.

J. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical,” Bell Syst. Tech. J. 52(8), 1439–1448 (1973).
[Crossref]

Mateo, E.

Pagnoux, D.

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Petermann, K.

Simos, C.

C. Simos, P. Leproux, P. D. Bin, and P. Facq, “Influence of mode orientations on power transfer at misaligned fibre connections,” J. Opt. A, Pure Appl. Opt. 4(1), 8–15 (2002).
[Crossref]

Tanaka, A.

Warm, S.

Winzer, P. J.

Wood, W.

Yano, Y.

Ann. Telecommun. (1)

D. Pagnoux, J. Blondy, P. Di Bin, P. Faugeras, N. Katcharov, and P. Facq, “Modal effects in optical fibre connections: theory and experimentation,” Ann. Telecommun. 49, 619–628 (1994).

Bell Syst. Tech. J. (1)

J. Cook, W. L. Mammel, and R. J. Grow, “Effect of misalignments on coupling efficiency of single-mode optical,” Bell Syst. Tech. J. 52(8), 1439–1448 (1973).
[Crossref]

IEEE Trans. Signal Process. (1)

J.-F. Cardoso and B. H. Laheld, “Equivariant adaptive source separation,” IEEE Trans. Signal Process. 44(12), 3017–3030 (1996).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. A, Pure Appl. Opt. (1)

C. Simos, P. Leproux, P. D. Bin, and P. Facq, “Influence of mode orientations on power transfer at misaligned fibre connections,” J. Opt. A, Pure Appl. Opt. 4(1), 8–15 (2002).
[Crossref]

Opt. Express (2)

Other (16)

T. Duthel, C. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” in Optical Fiber Communication Conference (Optical Society of America, 2008), paper OThU5.
[Crossref]

J. Damask, Polarization Optics In Telecommunications, (Springer, 2005).

J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems”, in 37th European Conference and Exhibition on Optical Communication (ECOC2011), paper Tu5B2.
[Crossref]

M. Chiani and A. Giorgetti, “Statistical analysis of asynchronous QPSK cochannel interference,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2002), pp. 1855–1859.
[Crossref]

D. Marcuse, Light transmission optics, (Van Nostrand Reinhold New York, 1982).

A. Chraplyvy, “The coming capacity crunch,” in 35th European Conference on Optical Communications (Optical Society of America, 2009), plenary talk.

M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over two modes of 40km-long prototype fewmode fiber, using LCOS based mode multiplexer and demultiplexer,” in Optical Fiber Communication Conference, (Optical Society of America, 2011), paper PDPB9.

A. Snyder and J. Love, Optical waveguide theory. (Springer, 1983).

B. Saleh and M. Teich, Fundamentals of Photonics, (John Wiley & Sons Inc, 2007).

A. D. Yablon, Optical fiber fusion splicing, (Springer, 2005).

V. A. J. M. Sleiffer, Y. Jung, B. Inan, H. Chen, R. G. H. van Uden, M. Kuschnerov, D. van den Borne, S. L. Jansen, V. Veljanovski, A. M. J. Koonen, D. J. Richardson, S. Alam, F. Poletti, J. K. Sahu, A. Dhar, B. Corbett, R. Winfield, A. D. Ellis, and H. de Waardt, “Mode-division-multiplexed 3 x 112-Gb/s DP-QPSK transmission over 80-km few-mode fiber with inline MM-EDFA and blind DSP,” in 38th European Conference on Optical Communication (Optical Society of America, 2012), paper Tu1C2.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity”, in 37 European Conference on Optical Communication, (Optical Society of America, 2011), paper Th13C3.
[Crossref]

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in 39th European Conference on Optical Communication, (Optical Society of America, 2013), paper We2D1.
[Crossref]

R. Ryf, M. Mestre, S. Randel, C. Schmidt, A. Gnauck, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. Peckham, A. McCurdy, and R. Lingle, “Mode-multiplexed transmission over a 184-km DGD-compensated few-mode fiber span,” in IEEE Photonics Society Summer Topical Meeting (IEEE, 2012), pp. 173–174.
[Crossref]

S. Warm, G. Rademacher, and K. Petermann, “DMD Management in Few-Mode Fiber MDM Transmission Systems with Mode Coupling”, in IEEE Photonics Society Summer Topical Meeting (IEEE, 2014), pp. 158–159.
[Crossref]

P. Sillard, M. Bigot-Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” in 37th European Conference on Optical Communication (Optical Society of America, 2011), paper Tu5LeCervin7.
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 a) Geometry and b) Refractive index profile in the cross section of a laterally misaligned butt-joint between identical SI-FMF. c) Geometry after rotation around the Z axis so that the lateral misalignment coincides with the X axis. In Figs. (a) and (c) the appearing LP11 mode illustrates our choice for the modal basis of the incoming and outgoing fiber (referred to as reference modal basis).
Fig. 2
Fig. 2 Schematic view of overlap integrals between incoming (solid contours) and outgoing modes (dashed contours), leading to a simplification of the coupling matrix coefficients. (a) example of even and odd modes that are not coupled (b)-(c): example of a pair of even modes and a pair of odd modes with a different positive coupling coefficient, (d)-(e) example of incoming and outgoing modes with overlap integrals changing signs when switching places for incoming and outgoing modes (f)-(g) example of incoming and outgoing modes with equal overlap integrals when switching places for incoming and outgoing modes.
Fig. 3
Fig. 3 (a) Primary (round markers) and secondary (triangle markers) ross-talk sources coupled upon the outgoing mode LPlp (filled round marker). Modes that are definitely guided are indicated by solid contours, while modes that are potentially not supported are indicated by dashed contours. (b) Application of (a) for the outgoing mode LP11. The numbers indicate the order of appearance for an increasing normalized frequency V.
Fig. 4
Fig. 4 Connector coupling or transmission matrix.
Fig. 5
Fig. 5 Power self-coupling (or transmission) coefficients [ c lp(s)lp(s) ] 2 .
Fig. 6
Fig. 6 Power cross-coupling coefficients [ c lp(s) l p ( s ) ] 2 as a function of the normalized offset D.
Fig. 7
Fig. 7 Experimental setup for the crosstalk ratios measurements.
Fig. 8
Fig. 8 Experimental versus numerical estimation of the matrix crosstalk coefficients.
Fig. 9
Fig. 9 Simplified system for the performance analysis of the connector.
Fig. 10
Fig. 10 Q2 for the five modes after a misaligned butt-joint connector as a function of the origin azimuthal offset φ11, for the partial MIMO receiver scheme.
Fig. 11
Fig. 11 Global MIMO performance vs. φ11.
Fig. 12
Fig. 12 Transmission coefficient or matching parameter T as a function of V for the modes LP11, LP21, LP02 and LP31.

Equations (24)

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

F lp (s) ( r,θ )= Q lp ( r ) f l (s) ( θ ), Q lp (r)= c lp { J l ( u lp .r ) J l ( u lp . r core ) ,r r core K l ( w lp .r ) K l ( w lp . r core ) ,r> r core
0 2π dθ 0 F lp (s) ( r,θ ) F lp (s) ( r,θ )rdr=1
f l (s) ( θ )={ cos(lθ),s="a" sin(lθ),s="b" 1,for circ. symmetric modes
0 2π 0 F lp (s) (r,θ)  F l'p' (s') (r,θ)rdr dθ={ 1, l=l',p=p',s=s' 0, otherwise  
E in (z,r,θ,ω)= a 01 (ω) e j ψ 01 F 01 (r,θ) e j β 01 (ω)z + + a 11 a (ω) e j ψ 11 a F 11 a (r,θ) e j β 11 (ω)z + + a 11 b (ω) e j ψ 11 b F 11 b (r,θ) e j β 11 (ω)z + + a 21 a (ω) e j ψ 21 a F 21 a (r,θ) e j β 21 (ω)z + + a 21 b (ω) e j ψ 21 b F 21 b (r,θ) e j β 21 (ω)z +
0 2π 0 F lp (s) (r,θϕ) F l p ( s ) ( r,θ ϕ )rdrdθ=0
A in con = [ A 01 (ω) A 11 a (ω) A 11 b (ω) A 21 a (ω) A 21 b (ω) ] T
A out con = C con A in con
C con =[ c 0101 c 11a01 c 11b01 c 21a01 c 21b01 c 0111a c 11a11a c 11b11a c 21a11a c 21a11a c 0111b c 11a11b c 11b11b c 21a11b c 21b11b c 0121a c 11a21a c 11b21a c 21a21a c 21b21a c 0121b c 11a21b c 11b21b c 21a21b c 21b21b ]
c lp(s)l'p'(s') =  0 2π dθ 0 F lp (s) ( r,θ )  F l'p' (s') * ( r',θ' )rdr  
C con =[ c 0101 c 11a01 0 c 21a01 0 c 11a01 c 11a11a 0 c 21a11a 0 0 0 c 11b11b 0 c 21b11b c 21a01 c 21a11a 0 c 21a21a 0 0 0 c 21b11b 0 c 21b21b ]
R lp ={ 1, l=0 R( l φ lp ), l0
R( α )=[ cosα sinα sinα cosα ]
M dec ( φ )=[ 1 0 0 0 0 0 0 R 11 0 0 0 0 0 0 0 0 0 0 R 21 ]
Γ( φ )= M dec ( φ ) C con M dec ( φ )
A out =Γ( φ ) A in
P C lp(s) l ' p ' ( φ lp )={ | c 0p0p' | 2 , | c 0pl'p'a | 2 , l= l ' =0 l=0,l'0 [ f l (s) ( φ lp ) ] 2 | c lpa0p' | 2 , [ f l (s) ( φ lp ) ] 2 | c lpal'p'a | 2 + [ f l ( s ¯ ) ( φ lp ) ] 2 | c lpbl'p'b | 2 , l0,l'=0 l0,l'0
T r lp(s) gl ( ϕ lp )= ( l , p ) P C lp(s) l p ( ϕ lp )
Γ( φ )=[ Γ 0101 Γ 1101 Γ 2101 Γ 0111 Γ 1111 Γ 2111 Γ 0121 Γ 1121 Γ 2121 ]
T r lp(s) sub ( ϕ lp )=P C lp(s)lp ( ϕ lp )
C con =[ a c 0 0 0 c b 0 c 0 0 0 a 0 c 0 c 0 b 0 0 0 c 0 b ]
Γ( φ )=[ a ccos φ 11 csin φ 11 0 0 ccos φ 11 csin φ 11 b+(ab) sin 2 φ 11 0.5(ab)sin2 φ 11 0.5(ab)sin2 φ 11 b+(ab) cos 2 φ 11 cR( φ 11 2 φ 21 ) 0 0 c R T ( φ 11 2 φ 21 ) bI ]
F lp (s) (r,θ)exp( V ρ 2 /2 ) ( V ρ 2 ) l 2 L p1 l (V ρ 2 ) f l (s) (θ)
| l=m p=n+1 V= 2 W 0 2

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