Abstract

We investigate the concept of principal modes and its application for mode division multiplexing in multimode fibers. We start by generalizing the formalism of the principal modes as to include mode dependent loss and show that principal modes overcome modal dispersion induced by modal coupling in mode division multiplexing operation, even for multi-mode-fibers guiding a large number of modes, if the product of modulation bandwidth, fiber length and differential group delay is equal or less than one in each transmission channel. If this condition is not sustained, modal dispersion and crosstalk at the receiver limit the transmission performance, setting very high constraints towards modal coupling.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [CrossRef]
  2. 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. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 x 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
    [CrossRef]
  3. S. Fan and J. M. Kahn, “Principal modes in multimode waveguides,” Opt. Lett. 30(2), 135–137 (2005).
    [CrossRef] [PubMed]
  4. M. B. Shemirani, W. Mao, R. A. Panicker, and J. M. Kahn, “Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling,” J. Lightwave Technol. 27(10), 1248–1261 (2009).
    [CrossRef]
  5. N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon. Technol. Lett. 12(10), 1337–1339 (2000).
    [CrossRef]
  6. P. Krummrich and K. Petermann, “Evaluation of potential optical amplifier concepts for coherent mode multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMH5.
  7. G. Stepniak, L. Maksymiuk, and J. Siuzdak, “Binary-Phase Spatial Light Filters for Mode-Selective Excitation of Multimode Fibers,” J. Lightwave Technol. 29(13), 1980–1987 (2011).
    [CrossRef]
  8. C. P. Tsekrekos and A. M. J. Koonen, “Mode-selective spatial filtering for increased robustness in a mode group diversity multiplexing link,” Opt. Lett. 32(9), 1041–1043 (2007).
    [CrossRef] [PubMed]
  9. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).
  10. K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron. 16(7), 761–770 (1980).
    [CrossRef]
  11. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWA4.
  12. N. K. Fontaine, C. R. Doerr, M. A. Mestre, R. R. Ryf, P. J. Winzer, L. L. Buhl, Y. Sun, X. Jiang, and R. Lingle, Jr., “Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), post-deadline paper PDP5B.
  13. E. Voges and K. Petermann, “Vielmodenfaser,” in Optische Kommunikationstechnik, (Springer Verlag 2002) 214–260.
  14. J. Carpenter and T. D. Wilkinson, “Precise modal excitation in multimode fiber for control of modal dispersion and mode-group division multiplexing,” in Proceedings of European Conf. Opt. Commun. (2011), paper We.10.P1.
  15. A. A. Juarez, S. Warm, C.-A. Bunge, P. Krummrich, and K. Petermann, “Perspectives of principal mode transmission in a multi-mode fiber,” in Proceedings of European Conf. Opt. Commun. (2010), paper P.4.10.
  16. R. K. Bocek, J. Hartpence, Y. Qian, and T. Lian OFS. “Ensuring low splice loss with high quality fibers”. [Online] http://stage.ofsinfo.com/resources/splice.pdf (2012).
  17. A. A. Juarez, S. Warm, C.-A. Bunge, and K. Petermann, “Number of usable principal modes in a mode division multiplexing transmission for different multi-mode fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTHA34.
  18. A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, and W. Shieh, “Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber,” J. Lightwave Technol. 30(4), 634–640 (2012).
    [CrossRef]
  19. A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
    [CrossRef]

2012

2011

2010

2009

2007

C. P. Tsekrekos and A. M. J. Koonen, “Mode-selective spatial filtering for increased robustness in a mode group diversity multiplexing link,” Opt. Lett. 32(9), 1041–1043 (2007).
[CrossRef] [PubMed]

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

2005

2000

N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon. Technol. Lett. 12(10), 1337–1339 (2000).
[CrossRef]

1980

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron. 16(7), 761–770 (1980).
[CrossRef]

Amin, A. A.

Bolle, C.

Burrows, E. C.

Chen, S.

Chen, X.

Esmaeelpour, M.

Essiambre, R.

Essiambre, R.-J.

Fan, S.

Foschini, G. J.

Gao, G.

Gnauck, A. H.

Goebel, B.

Hsu, R. C. J.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

Jalali, B.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

Kahn, J. M.

Koonen, A. M. J.

Kramer, G.

Li, A.

Lingle, R.

Maksymiuk, L.

Mao, W.

McCurdy, A.

Mumtaz, S.

Panicker, R. A.

Peckham, D. W.

Petermann, K.

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron. 16(7), 761–770 (1980).
[CrossRef]

Randel, S.

Ryf, R.

Sayed, A. H.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

Shah, A.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

Shemirani, M. B.

Shieh, W.

Sierra, A.

Siuzdak, J.

Spellmeyer, N. W.

N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon. Technol. Lett. 12(10), 1337–1339 (2000).
[CrossRef]

Stepniak, G.

Tarighat, A.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

Tsekrekos, C. P.

Winzer, P. J.

IEEE Commun. Mag.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007).
[CrossRef]

IEEE Photon. Technol. Lett.

N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon. Technol. Lett. 12(10), 1337–1339 (2000).
[CrossRef]

J. Lightwave Technol.

J. Quantum Electron.

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron. 16(7), 761–770 (1980).
[CrossRef]

Opt. Lett.

Other

P. Krummrich and K. Petermann, “Evaluation of potential optical amplifier concepts for coherent mode multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMH5.

H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).

N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWA4.

N. K. Fontaine, C. R. Doerr, M. A. Mestre, R. R. Ryf, P. J. Winzer, L. L. Buhl, Y. Sun, X. Jiang, and R. Lingle, Jr., “Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), post-deadline paper PDP5B.

E. Voges and K. Petermann, “Vielmodenfaser,” in Optische Kommunikationstechnik, (Springer Verlag 2002) 214–260.

J. Carpenter and T. D. Wilkinson, “Precise modal excitation in multimode fiber for control of modal dispersion and mode-group division multiplexing,” in Proceedings of European Conf. Opt. Commun. (2011), paper We.10.P1.

A. A. Juarez, S. Warm, C.-A. Bunge, P. Krummrich, and K. Petermann, “Perspectives of principal mode transmission in a multi-mode fiber,” in Proceedings of European Conf. Opt. Commun. (2010), paper P.4.10.

R. K. Bocek, J. Hartpence, Y. Qian, and T. Lian OFS. “Ensuring low splice loss with high quality fibers”. [Online] http://stage.ofsinfo.com/resources/splice.pdf (2012).

A. A. Juarez, S. Warm, C.-A. Bunge, and K. Petermann, “Number of usable principal modes in a mode division multiplexing transmission for different multi-mode fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTHA34.

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 (10)

Fig. 1
Fig. 1

(a) Fiber mismatch in x and y direction, rotated by an angle, (b) Complete fiber is made out of 3 km long segments.

Fig. 2
Fig. 2

Main idea behind the PMs; (a) shows and input vector a p with only three components (Three mode fiber for example) corresponding to a PM at the input of the fiber. As we change the frequency interval from ω 1 ω 2 ... ω n the output vector b p stays unchanged; (b) shows the result if the input vector a is not a PM. As we change the frequency over a small frequency interval ω 1 ω 2 ... ω n the output vector b (ω) changes

Fig. 3
Fig. 3

Exemplary three mode transmission system. optical fields coming out of each modulator (MOD) are encoded and then matched to a desired spatial mode (M-MUX), which can either be a PM or EM. These are then multiplexed into the MMF. At the output of the MMF, the sum of all PMs or EMs is mode-de-multiplexed (M-DE-MUX) and detected at the receiver (Rx). The M-DE-MUX can be realized for instance by a diffractive element or a photodiode array together with a local oscillator to obtain space and phase information.

Fig. 4
Fig. 4

Eye diagram plotted for a PRBS OOK signal at 1 Gbits/s over 50 km MMF; a) using EM as carriers; b) using PMs as carriers.

Fig. 5
Fig. 5

EOP for a three mode fiber under MDM operation at 0.7 Gbit/s. a) EM as carriers and b) PM as carriers. MMF simulation parameters are given in Table 1.

Fig. 6
Fig. 6

EOP of MDM transmission for various bitrates in a three mode fiber; a) Using EM as carriers, b) using PM as carriers.

Fig. 7
Fig. 7

Left: Crosstalk of: (a) LP11 (b) PM 2 and (c) PM 2 at the output of the MMF for three different splice losses. Right: Crosstalk for each guided (a) EM (b) PM and (c) PM using the detection vectors for constant total splice loss of 0.5 dB; Fig. (b) and (c) differ only at the demultiplexing stage at the receiver; (b) uses the conjugate complex of the PMs as mode filter whereas (c) uses the detection vector defined in Eq. (28). Each EM or PM exited at the input of the MMF contains unit power.

Fig. 8
Fig. 8

Number of usable principal modes in a 36 mode fiber for various bitrates. The maximal differential group delay has the value of Δ τ m =134ps/km and limits the maximal transmission rate down to 0.1Gbit/s .

Fig. 9
Fig. 9

Usable principal modes in a 50 km transmission link, at 10Gbit/s . This implies 16 splicing points. Results represent an enhanced version of the results presented in [17].

Fig. 10
Fig. 10

Crosstalk of two PMs. Figure shows very clearly that crosstalk varies between principal modes and in this case a difference of 25 dB can be observed at 0.5 GHz between the dashed red and blue lines.

Tables (2)

Tables Icon

Table 1 Fiber Simulation Parameters Used for MDM Simulation in Three Mode Fiber

Tables Icon

Table 2 Maximal Group Delays for Different MMF

Equations (28)

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

E in (x,y)= i=1 I a i E i (x,y) .
1 ξ 2 E i (x,y)· E j * (x,y)·dxdy= δ i,j ,
E out (x,y)= i=1 I b i E i (x,y) .
b = e j ϕ 0 (ω) T(ω)· a .
M m (ω)=( 1 0 0 0 e j(Δ ϕ 1 + ζ 1,m ) 0 0 0 0 0 e j(Δ ϕ I + ζ I,m ) ),
K ij,m = 1 ξ 2 E i,m (x,y)· E j,m+1 * (x´,y´)dxdy.
T(ω)= m=1 M M m (ω)· K m ,
ω b =[ jT(ω) ω ϕ 0 (ω)+ ω T(ω) ] e j ϕ 0 (ω) a ,
ω b =[ jT(ω) ω ϕ 0 (ω)+ ω T(ω) ]T (ω) 1 b .
ω b =[ j τ 0 LI+G(ω) ] b ,
G(ω)· b p = γ p b p .
G(ω) γ p I=0,
ω b p =[ j( τ 0 + τ p )L α p L ] b p ,
ω a =[ j ω ϕ 0 (ω)IF(ω) ] a =0,
[ F(ω) τ p I ] a p =0
n( r )= n 1 ( 12Δ ( r/ r 0 ) 2 ) ,
E l,q (r,φ)= C l,q ( r ξ ) l L q l ( r 2 ξ 2 ) e r 2 2 ξ 2 { sinlφ coslφ .
ξ= r 0 /( k 0 n 1 2Δ ) .
β q,l = n 1 k 0 ( 1 2 2Δ n 1 k 0 r 0 (2q+2l+1) )
τ q,l = N 1 c ( 1+Δ ( 2q+l+1 n 1 k 0 r 0    ) 2 ),
E 01 ( r,φ )= 1 π e r 2  2 ξ 2  
E 11 ( r,φ )= 2/π r e r 2  2 ξ 2 { sinφ cosφ
K m =( e b 2 2 ξ 2 b e b 2 2 ξ 2 ( cos φ 0 +sin φ 0 ) 2 ξ b e b 2 2 ξ 2 ( sin φ 0 cos φ 0 ) 2 ξ b e b 2 2 ξ 2 2 ξ e b 2 2 ξ 2 ( sin φ 0 b 2 +( b 2 2 ξ 2 )cos φ 0 ) 2 ξ 2 e b 2 2 ξ 2 ( ( b 2 2 ξ 2 )sin φ 0 b 2 cos φ 0 ) 2 ξ 2 b e b 2 2 ξ 2 2 ξ e b 2 2 ξ 2 ( cos φ 0 b 2 +( b 2 2 ξ 2 )sin φ 0 ) 2 ξ 2 e b 2 2 ξ 2 ( b 2 sin φ 0 ( b 2 2 ξ 2 )cos φ 0 ) 2 ξ 2 )
B 1 Δ τ m L 0.7GHz.
a T (ω)= i=1 I S i (ω) a i .
EOP=10log( E O BTB EO ),
P j C (ω)= i=1,ij I ( b i · d j )( b i · d j ) * .
P·D=I.

Metrics