Abstract

It is proposed and demonstrated that two fiber spans in a scaled translational symmetry could cancel out their intra-channel nonlinear effects to a large extent without using optical phase conjugation. Significant reduction of intra-channel nonlinear effects may be achieved in a long-distance transmission line consisting of multiple pairs of translationally symmetric spans. The results have been derived analytically from the nonlinear Schrödinger equation and verified by numerical simulations using commercial software.

© 2004 Optical Society of America

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References

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  1. A. H. Gnauck and R. M. Jopson, �??Dispersion compensation for optical fiber systems,�?? in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).
  2. F. Forghieri, R. W. Tkach and A. R. Chraplyvy, �??Fiber nonlinearities and their impact on transmission systems,�?? in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).
  3. V. Srikant, �??Broadband dispersion and dispersion slope compensation in high bit rate and ultra long haul systems,�?? OFC 2001, paper TuH1.
  4. M. J. Li, �??Recent progress in fiber dispersion compensators,�?? European Conference on Optical Communication 2001, paper Th.M.1.1.
  5. C. Pare, A. Villeneuve, and P.-A. Belanger, �??Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,�?? Opt. Lett. 21, 459-461 (1996).
    [CrossRef] [PubMed]
  6. D. M. Pepper and A. Yariv, �??Compensation for phase distortions in nonlinear media by phase conjugation,�?? Opt. Lett. 5, 59-60 (1980).
    [CrossRef] [PubMed]
  7. S. Watanabe and M. Shirasaki, �??Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,�?? J. Lightwave Technol. 14, 243-248 (1996).
    [CrossRef]
  8. I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and S. Kosinski, �??Cancellation of all Kerr nonlinearities in long fiber spans using a LiNbO3 phase conjugator and Raman amplification,�?? OFC 2000, paper PD33.
  9. H. Wei and D. V. Plant, �??Fundamental equations of nonlinear fiber optics,�?? in Optical Modeling and Performance Predictions, M. A. Kahan, ed., Proc. SPIE 5178, 255-266 (2003).
  10. M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, �??Cancellation of third-order nonlinear effects in amplified fiber links by dispersion compensation, phase conjugation, and alternating dispersion,�?? Opt. Lett. 20, no. 8, 863-865 (1995).
    [CrossRef] [PubMed]
  11. H. Wei and D. V. Plant, �??Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation,�?? Opt. Express 12, no. 9, 1938-1958 (2004), <a href ="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1938">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1938</a>
    [CrossRef] [PubMed]
  12. A. Chowdhury and R.-J. Essiambre, �??Optical phase conjugation and pseudolinear transmission,�?? Opt. Lett. 29, no. 10, 1105-1107 (2004).
    [CrossRef] [PubMed]
  13. R.-J. Essiambre, G. Raybon, and B. Mikkelson, �??Pseudo-linear transmission of high-speed TDM signals: 40 and 160 Gb/s,�?? in Optical Fiber Telecommunications IV B: Systems and Impairments, I. P. Kaminow and T. Li, eds. (Academic Press, San Diego, 2002).
  14. P. V. Mamyshev and N. A. Mamysheva, �??Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing,�?? Opt. Lett. 24, 1454-1456 (1999).
    [CrossRef]
  15. A. Mecozzi, C. B. Clausen, and M. Shtaif, �??Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,�?? IEEE Photon. Technol. Lett. 12, 392-394 (2000).
    [CrossRef]
  16. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, �??Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,�?? IEEE Photon. Technol. Lett. 13, 445-447 (2001).
    [CrossRef]
  17. J. Martensson, A. Berntson, M. Westlund, A. Danielsson, P. Johannisson, D. Anderson, and M. Lisak, �??Timing jitter owing to intrachannel pulse interactions in dispersion-managed transmission systems,�?? Opt. Lett. 26, 55-57 (2001).
    [CrossRef]
  18. P. Johannisson, D. Anderson, A. Berntson, and J. Martensson, �??Generation and dynamics of ghost pulses in strongly dispersion-managed fiber-optic communication systems,�?? Opt. Lett. 26, 1227-1229 (2001).
    [CrossRef]
  19. M. J. Ablowitz and T. Hirooka, �??Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems,�?? Opt. Lett. 25, 1750-1752 (2000).
    [CrossRef]
  20. M. J. Ablowitz and T. Hirooka, �??Intrachannel pulse interactions in dispersion-managed transmission systems: timing shifts,�?? Opt. Lett. 26, 1846-1848 (2001).
    [CrossRef]
  21. M. J. Ablowitz and T. Hirooka, �??Intrachannel pulse interactions in dispersion-managed transmission systems: energy transfer,�?? Opt. Lett. 27, 203-205 (2002).
    [CrossRef]
  22. T. Hirooka and M. J. Ablowitz, �??Suppression of intrachannel dispersion-managed pulse interactions by distributed amplification,�?? IEEE Photon. Technol. Lett. 14, 316-318 (2002).
    [CrossRef]
  23. R. Hainberger, T. Hoshita, T. Terahara, and H. Onaka, �??Comparison of span configurations of Raman-amplified dispersion-managed fibers,�?? IEEE Photon. Technol. Lett. 14, 471-473 (2002).
    [CrossRef]
  24. J. A. Buck, Fundamentals of Optical Fibers (Wiley, New York, 1995), Chapter 4.
  25. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, San Diego, 1995), Chapter 2.
  26. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations (Springer-Verlag, New York, 2000).
  27. E. E. Narimanov and P. Mitra, �??The channel capacity of a fiber optics communication system: perturbation theory,�?? J. Lightwave Technol. 20, 530-537 (2002).
    [CrossRef]
  28. S. N. Knudsen and T. Veng, �??Large effective area dispersion compensating fiber for cabled compensation of standard single mode fiber,�?? OFC 2000, paper TuG5.
  29. K. Mukasa, H. Moridaira, T. Yagi, and K. Kokura, �??New type of dispersion management transmission line with MDFSD for long-haul 40 Gb/s transmission,�?? OFC 2002, paper ThGG2.
  30. K. Rottwitt and A. J. Stentz, �??Raman amplification in lightwave communication systems,�?? in Optical Fiber Telecommunications IV A: Components, I. P. Kaminow and T. Li, eds. (Academic Press, San Diego, 2002).
  31. M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, �??Reduction of Raman MPI and noise figure in dispersion-managed fiber,�?? Electron. Lett. 38, no. 6, 271-272 (2002)
    [CrossRef]
  32. J.-C. Bouteiller, K. Brar, and C. Headley, �??Quasi-constant signal power transmission,�?? European Conference on Optical Communication 2002, paper S3.04.
  33. M. Vasilyev, �??Raman-assisted transmission: toward ideal distributed amplification,�?? OFC 2003, paper WB1.
  34. C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, P. Reeves-Hall, �??DWDM 40G transmission over trans-Pacific distance (10,000 km) using CSRZ-DPSK, enhanced FEC and all-Raman amplified 100 km UltraWaveTM fiber spans,�?? OFC 2003, paper PD18.
  35. Gruner-Nielsen, Y. Qian, B. Palsdottir, P. B. Gaarde, S. Dyrbol, T. Veng, and Y. Qian, �??Module for simultaneous C + L-band dispersion compensation and Raman amplification,�?? OFC 2002, paper TuJ6.
  36. T. Miyamoto, T. Tsuzaki, T. Okuno, M. Kakui, M. Hirano, M. Onishi, and M. Shigematsu, �??Raman amplification over 100 nm-bandwidth with dispersion and dispersion slope compensation for conventional single mode fiber,�?? OFC 2002, paper TuJ7.
  37. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (John Wiley & Sons, New York, 1994).
  38. A. Striegler, A. Wietfeld, and B. Schmauss, �??Fiber based compensation of IXPM induced timing jitter,�?? OFC 2004, paper MF72.

Electron. Lett.

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, �??Reduction of Raman MPI and noise figure in dispersion-managed fiber,�?? Electron. Lett. 38, no. 6, 271-272 (2002)
[CrossRef]

European Conf. on Optical Comm. 2001

M. J. Li, �??Recent progress in fiber dispersion compensators,�?? European Conference on Optical Communication 2001, paper Th.M.1.1.

European Conf. on Optical Comm. 2002

J.-C. Bouteiller, K. Brar, and C. Headley, �??Quasi-constant signal power transmission,�?? European Conference on Optical Communication 2002, paper S3.04.

IEEE Photon. Technol. Lett.

A. Mecozzi, C. B. Clausen, and M. Shtaif, �??Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,�?? IEEE Photon. Technol. Lett. 12, 392-394 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, �??Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,�?? IEEE Photon. Technol. Lett. 13, 445-447 (2001).
[CrossRef]

T. Hirooka and M. J. Ablowitz, �??Suppression of intrachannel dispersion-managed pulse interactions by distributed amplification,�?? IEEE Photon. Technol. Lett. 14, 316-318 (2002).
[CrossRef]

R. Hainberger, T. Hoshita, T. Terahara, and H. Onaka, �??Comparison of span configurations of Raman-amplified dispersion-managed fibers,�?? IEEE Photon. Technol. Lett. 14, 471-473 (2002).
[CrossRef]

J. Lightwave Technol.

S. Watanabe and M. Shirasaki, �??Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,�?? J. Lightwave Technol. 14, 243-248 (1996).
[CrossRef]

E. E. Narimanov and P. Mitra, �??The channel capacity of a fiber optics communication system: perturbation theory,�?? J. Lightwave Technol. 20, 530-537 (2002).
[CrossRef]

OFC 2000

S. N. Knudsen and T. Veng, �??Large effective area dispersion compensating fiber for cabled compensation of standard single mode fiber,�?? OFC 2000, paper TuG5.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and S. Kosinski, �??Cancellation of all Kerr nonlinearities in long fiber spans using a LiNbO3 phase conjugator and Raman amplification,�?? OFC 2000, paper PD33.

OFC 2001

V. Srikant, �??Broadband dispersion and dispersion slope compensation in high bit rate and ultra long haul systems,�?? OFC 2001, paper TuH1.

OFC 2002

K. Mukasa, H. Moridaira, T. Yagi, and K. Kokura, �??New type of dispersion management transmission line with MDFSD for long-haul 40 Gb/s transmission,�?? OFC 2002, paper ThGG2.

Gruner-Nielsen, Y. Qian, B. Palsdottir, P. B. Gaarde, S. Dyrbol, T. Veng, and Y. Qian, �??Module for simultaneous C + L-band dispersion compensation and Raman amplification,�?? OFC 2002, paper TuJ6.

T. Miyamoto, T. Tsuzaki, T. Okuno, M. Kakui, M. Hirano, M. Onishi, and M. Shigematsu, �??Raman amplification over 100 nm-bandwidth with dispersion and dispersion slope compensation for conventional single mode fiber,�?? OFC 2002, paper TuJ7.

OFC 2003

M. Vasilyev, �??Raman-assisted transmission: toward ideal distributed amplification,�?? OFC 2003, paper WB1.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, P. Reeves-Hall, �??DWDM 40G transmission over trans-Pacific distance (10,000 km) using CSRZ-DPSK, enhanced FEC and all-Raman amplified 100 km UltraWaveTM fiber spans,�?? OFC 2003, paper PD18.

OFC 2004

A. Striegler, A. Wietfeld, and B. Schmauss, �??Fiber based compensation of IXPM induced timing jitter,�?? OFC 2004, paper MF72.

Opt. Express

Opt. Lett.

A. Chowdhury and R.-J. Essiambre, �??Optical phase conjugation and pseudolinear transmission,�?? Opt. Lett. 29, no. 10, 1105-1107 (2004).
[CrossRef] [PubMed]

P. V. Mamyshev and N. A. Mamysheva, �??Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing,�?? Opt. Lett. 24, 1454-1456 (1999).
[CrossRef]

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, �??Cancellation of third-order nonlinear effects in amplified fiber links by dispersion compensation, phase conjugation, and alternating dispersion,�?? Opt. Lett. 20, no. 8, 863-865 (1995).
[CrossRef] [PubMed]

C. Pare, A. Villeneuve, and P.-A. Belanger, �??Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,�?? Opt. Lett. 21, 459-461 (1996).
[CrossRef] [PubMed]

D. M. Pepper and A. Yariv, �??Compensation for phase distortions in nonlinear media by phase conjugation,�?? Opt. Lett. 5, 59-60 (1980).
[CrossRef] [PubMed]

J. Martensson, A. Berntson, M. Westlund, A. Danielsson, P. Johannisson, D. Anderson, and M. Lisak, �??Timing jitter owing to intrachannel pulse interactions in dispersion-managed transmission systems,�?? Opt. Lett. 26, 55-57 (2001).
[CrossRef]

P. Johannisson, D. Anderson, A. Berntson, and J. Martensson, �??Generation and dynamics of ghost pulses in strongly dispersion-managed fiber-optic communication systems,�?? Opt. Lett. 26, 1227-1229 (2001).
[CrossRef]

M. J. Ablowitz and T. Hirooka, �??Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems,�?? Opt. Lett. 25, 1750-1752 (2000).
[CrossRef]

M. J. Ablowitz and T. Hirooka, �??Intrachannel pulse interactions in dispersion-managed transmission systems: timing shifts,�?? Opt. Lett. 26, 1846-1848 (2001).
[CrossRef]

M. J. Ablowitz and T. Hirooka, �??Intrachannel pulse interactions in dispersion-managed transmission systems: energy transfer,�?? Opt. Lett. 27, 203-205 (2002).
[CrossRef]

Proc SPIE

H. Wei and D. V. Plant, �??Fundamental equations of nonlinear fiber optics,�?? in Optical Modeling and Performance Predictions, M. A. Kahan, ed., Proc. SPIE 5178, 255-266 (2003).

Other

A. H. Gnauck and R. M. Jopson, �??Dispersion compensation for optical fiber systems,�?? in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).

F. Forghieri, R. W. Tkach and A. R. Chraplyvy, �??Fiber nonlinearities and their impact on transmission systems,�?? in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).

J. A. Buck, Fundamentals of Optical Fibers (Wiley, New York, 1995), Chapter 4.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, San Diego, 1995), Chapter 2.

K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations (Springer-Verlag, New York, 2000).

R.-J. Essiambre, G. Raybon, and B. Mikkelson, �??Pseudo-linear transmission of high-speed TDM signals: 40 and 160 Gb/s,�?? in Optical Fiber Telecommunications IV B: Systems and Impairments, I. P. Kaminow and T. Li, eds. (Academic Press, San Diego, 2002).

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (John Wiley & Sons, New York, 1994).

K. Rottwitt and A. J. Stentz, �??Raman amplification in lightwave communication systems,�?? in Optical Fiber Telecommunications IV A: Components, I. P. Kaminow and T. Li, eds. (Academic Press, San Diego, 2002).

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Figures (8)

Fig. 1.
Fig. 1.

The signal power and dispersion maps for a cascade of two fiber spans in scaled translational symmetry with scaling ratio R = 1. Top: the variation of signal power along the propagation distance. Bottom: the dispersion map, namely, the variation of accumulated dispersion along the propagation distance.

Fig. 2.
Fig. 2.

The signal power and dispersion maps for a cascade of two fiber spans in scaled translational symmetry with lumped dispersion compensators. Top: the variation of signal power along the propagation distance. Bottom: the dispersion map, namely, the variation of accumulated dispersion along the propagation distance.

Fig. 3.
Fig. 3.

A transmission line consists of 6 pairs of fiber spans, with the first span in each pair having 50 km SMF followed by 50 km RDF then 15.74 dB EDFA gain, and the second span having 39.35 km RDF followed by 39.35 km SMF then 20 dB EDFA gain.

Fig. 4.
Fig. 4.

A transmission line consists of 6 pairs of fiber spans, with the first span in each pair having 50 km SMF followed by 50 km RDF then 15.74 dB EDFA gain, and the second span having 39.35 km SMF followed by 39.35 km RDF then 20 dB EDFA gain.

Fig. 5.
Fig. 5.

The transmission results with δD = 0 and amplifier noise turned off to signify the nonlinear effects. Left: received optical eye diagram of the scaled translationally symmetric setup in Fig. 3. Right: received optical eye diagram of the setup in Fig. 4 without scaled translational symmetry.

Fig. 6.
Fig. 6.

The transmission results with δD = 0 and amplifier noise turned on. Left: received optical eye diagram of the scaled translationally symmetric setup in Fig. 3. Right: received optical eye diagram of the setup in Fig. 4 without scaled translational symmetry.

Fig. 7.
Fig. 7.

The transmission results with δD = 0.2 ps/nm/km and amplifier noise turned on. Left: received optical eye diagram of the scaled translationally symmetric setup in Fig. 3. Right: received optical eye diagram of the setup in Fig. 4 without scaled translational symmetry.

Fig. 8.
Fig. 8.

The transmission results with δD = 0.6 ps/nm/km and amplifier noise turned on. Left: received optical eye diagram of the scaled translationally symmetric setup in Fig. 3. Right: received optical eye diagram of the setup in Fig. 4 without scaled translational symmetry.

Equations (28)

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

E z t = A z t exp [ i z β 0 ( ς ) i ω 0 t ] ,
A z t z + k = 2 + i k 1 β k ( z ) k ! ( t ) 2 A z t + α ( z ) 2 A z t =
i γ ( z ) A z t 2 A z t + i [ g z t A z t 2 ] A z t ,
β k ( z ) = def 1 2 β 0 ( z ) k [ β 2 ω z ] ω k ω = ω 0 , k 2 ,
A z t z + k = 2 + i k 1 β k ( z ) k ! ( t ) k A z t + α ( z ) 2 A z t = 0 ,
H ( z 1 , z 2 , ω ) = def exp [ i k = 2 + ω k k ! z 1 z 2 β k ( z ) dz 1 2 z 1 z 2 α ( z ) dz ] .
P z 1 z 2 = def F 1 H ( z 1 , z 2 , ω ) F .
h ( z 1 , z 2 , t ) = def F 1 [ H ( z 1 , z 2 , ω ) ] ,
P ( z 1 , z 2 ) = h ( z 1 , z 2 , t ) .
A 0 ( z 2 , t ) = P ( z 1 , z 2 ) A ( z 1 , t ) ,
A 1 ( z 2 , t ) = z 1 z 2 P ( z 1 , z 2 ) { i γ ( z ) A 0 ( z , t ) 2 A 0 ( z , t )
+ i [ g ( z , t ) A 0 ( z , t ) 2 ] A 0 ( z , t ) } dz ,
α ( z ) α ( z ) = β 2 ( z ) β 2 ( z ) = β 3 ( z ) β 3 ( z ) = γ ( z ) A ( z , t ) 2 γ ( z ) A ( z , t ) 2 = z z = 1 R ,
α ( z ) α ( z + L ) = β 2 ( z ) β 2 ( z + L ) = β 3 ( z ) β 3 ( z + L ) = γ ( z ) A ( z , t ) 2 γ ( z + L ) A ( z + L , t ) 2 = 1 ,
u k z + i β 2 ( z ) 2 2 u k t 2 + α ( z ) 2 u k = ( z ) m n u m u n u m + n k * , k Z ,
H ( z 1 , z 2 , ω ) = exp [ i 2 b 2 ( z 1 , z 2 ) ω 2 1 2 z 1 z 2 α ( z ) dz ] ,
b 2 ( z 1 , z 2 ) = def z 1 z 2 β 2 ( z ) dz ,
h ( z 1 , z 2 , t ) = 1 b 2 ( z 1 , z 2 ) exp [ i t 2 2 b 2 ( z 1 , z 2 ) 1 2 z 1 z 2 α ( z ) dz ] ,
v k ( z , t ) = P ( 0 , z ) u k ( 0 , t ) ,
v k ( z , t ) = i m 0 z n P ( s , z ) [ γ ( s ) v m ( s , t ) v n ( s , t ) v m + n k * ( s , t ) ] ds ,
P ( 0 , z + L ) = P * ( 0 , z ) = def h * ( 0 , z , t ) ,
P ( z + L , 2 L ) = P * ( z , 2 L ) = def h * ( z , 2 L , t ) ,
0 2 L P ( z , 2 L ) [ γ ( z ) v m ( z , t ) v n ( z , t ) v m + n k * ( z , t ) ] dz
= 0 L P ( z , 2 L ) [ γ ( z ) v m ( z , t ) v n ( z , t ) v m + n k * ( z , t ) ] dz +
0 L P ( z + L , 2 L ) [ γ ( z ) v m ( z + L , t ) v n ( z + L , t ) v m + n k * ( z + L , t ) ] dz
= 0 L P ( z , 2 L ) [ γ ( z ) v m ( z , t ) v n ( z , t ) v m + n k * ( z , t ) ] dz +
0 L P * ( z , 2 L ) [ γ ( z ) v m * ( z , t ) v n * ( z , t ) v m + n k ( z , t ) ] dz ,
t k = t u k 2 dt u k 2 dt t v k 2 dt v k 2 dt = kT ,

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