Abstract

Intrachannel cross-phase modulation and four-wave mixing are investigated in a pseudolinear transmission system. The interaction range of the nonlinear effects is studied numerically, and approximate analytical methods are used to explain the results and predict the necessary word length for general systems. The method is shown to agree with experimentally found data. The generation rate, i.e., the growth of the nonlinear distortion in different parts of the system is calculated numerically, and the possibilities for counteracting the generation of nonlinear signal distortion are discussed.

© 2007 Optical Society of America

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  1. I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
    [CrossRef]
  2. R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
    [CrossRef]
  3. M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photon. Technol. Lett. 10, 373-375 (1998).
    [CrossRef]
  4. J. Mårtensson, 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]
  5. S. Kumar, "Intrachannel four-wave mixing in dispersion managed RZ systems," IEEE Photon. Technol. Lett. 13, 800-802 (2001).
    [CrossRef]
  6. 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]
  7. M. J. Ablowitz and T. Hirooka, "Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems," Opt. Lett. 25, 1750-1752 (2000).
    [CrossRef]
  8. P. Johannisson, D. Anderson, A. Berntson, and J. Mårtensson, "Generation and dynamics of ghost pulses in strongly dispersion-managed fiber-optic communication systems," Opt. Lett. 26, 1227-1229 (2001).
    [CrossRef]
  9. L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
    [CrossRef]
  10. P. Johannisson, D. Anderson, M. Marklund, A. Berntson, M. Forzati, and J. Mårtensson, "Suppression of nonlinear effects by phase alternation in strongly dispersion-managed optical transmission," Opt. Lett. 27, 1073-1075 (2002).
    [CrossRef]
  11. T. Inoue and A. Maruta, "Suppression of nonlinear intrachannel interactions between return-to-zero pulses in dispersion-managed optical transmission systems," J. Opt. Soc. Am. B 19, 440-447 (2002).
    [CrossRef]
  12. 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]
  13. R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
    [CrossRef]
  14. S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, "Intrachannel nonlinear penalties in dispersion-managed transmission systems," IEEE J. Sel. Top. Quantum Electron. 8, 626-631 (2002).
    [CrossRef]

2004

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

2002

2001

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]

J. Mårtensson, 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]

S. Kumar, "Intrachannel four-wave mixing in dispersion managed RZ systems," IEEE Photon. Technol. Lett. 13, 800-802 (2001).
[CrossRef]

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

2000

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]

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

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
[CrossRef]

1999

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
[CrossRef]

1998

M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photon. Technol. Lett. 10, 373-375 (1998).
[CrossRef]

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

Ablowitz, M. J.

Anderson, D.

Bayvel, P.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
[CrossRef]

Berntson, A.

Chowdhury, D. Q.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, "Intrachannel nonlinear penalties in dispersion-managed transmission systems," IEEE J. Sel. Top. Quantum Electron. 8, 626-631 (2002).
[CrossRef]

Chraplyvy, A. R.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Clausen, C. B.

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]

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]

Danielsson, A.

Essiambre, R.-J.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
[CrossRef]

Forzati, M.

Gnauck, A. H.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[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]

Hirooka, T.

Inoue, T.

Johannisson, P.

Kawanishi, S.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

Killey, R. I.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
[CrossRef]

Kumar, S.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, "Intrachannel nonlinear penalties in dispersion-managed transmission systems," IEEE J. Sel. Top. Quantum Electron. 8, 626-631 (2002).
[CrossRef]

S. Kumar, "Intrachannel four-wave mixing in dispersion managed RZ systems," IEEE Photon. Technol. Lett. 13, 800-802 (2001).
[CrossRef]

Lisak, M.

Marklund, M.

Mårtensson, J.

Maruta, A.

Matsumoto, M.

M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photon. Technol. Lett. 10, 373-375 (1998).
[CrossRef]

Mauro, J. C.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, "Intrachannel nonlinear penalties in dispersion-managed transmission systems," IEEE J. Sel. Top. Quantum Electron. 8, 626-631 (2002).
[CrossRef]

Mecozzi, A.

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]

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]

Mikhailov, V.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
[CrossRef]

Mikkelsen, B.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
[CrossRef]

Mori, K.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

Park, S.-G.

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]

Raghavan, S.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, "Intrachannel nonlinear penalties in dispersion-managed transmission systems," IEEE J. Sel. Top. Quantum Electron. 8, 626-631 (2002).
[CrossRef]

Raybon, G.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
[CrossRef]

Shake, I.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

Shtaif, M.

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]

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]

Takara, H.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

Thiele, H. J.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
[CrossRef]

Westlund, M.

Wickham, L. K.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Winzer, P. J.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Yamabayashi, Y.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

Electron. Lett.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, "Intrachannel nonlinear penalties in dispersion-managed transmission systems," IEEE J. Sel. Top. Quantum Electron. 8, 626-631 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
[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]

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
[CrossRef]

M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photon. Technol. Lett. 10, 373-375 (1998).
[CrossRef]

S. Kumar, "Intrachannel four-wave mixing in dispersion managed RZ systems," IEEE Photon. Technol. Lett. 13, 800-802 (2001).
[CrossRef]

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]

J. Opt. Soc. Am. B

Opt. Lett.

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Figures (12)

Fig. 1
Fig. 1

Function i E 1 ( i x ) in the complex plane. The value of the positive real argument x has been indicated at chosen points on the curve.

Fig. 2
Fig. 2

Ghost pulse amplitude using different asymmetric pulse trains with SMF of length (from below) L SMF = 50 , 100, 150, and 200 km .

Fig. 3
Fig. 3

Ghost pulse amplitude using different symmetric pulse trains with SMF of length (from below) L SMF = 50 , 100, 150, and 200 km .

Fig. 4
Fig. 4

Amplitude shift using different asymmetric pulse trains with SMF of length (from below) L SMF = 50 , 100, 150, and 200 km .

Fig. 5
Fig. 5

Amplitude shift using different symmetric pulse trains with SMF of length (from above at the global minima) L SMF = 50 , 100, 150, and 200 km .

Fig. 6
Fig. 6

Timing shift using different asymmetric pulse trains with SMF of length (from above) L SMF = 50 , 100, 150, and 200 km .

Fig. 7
Fig. 7

Ghost pulse amplitude as a function of propagation distance. The bit trains used to generate the different curves are described in the text.

Fig. 8
Fig. 8

Ghost pulse amplitude as a function of propagation distance using (from below) a group-velocity dispersion parameter β 2 4 , β 2 2 , β 2 , 2 β 2 , and 4 β 2 .

Fig. 9
Fig. 9

Ghost pulse amplitude as a function of propagation distance using different amounts of precompensation. Counting the horizontal parts of the curves from below the initial DCF compensates for 0 , 1 4 , 1 2 , 3 4 , and 1 times the length of the SMF.

Fig. 10
Fig. 10

Amplitude shift as a function of propagation distance using symmetric bit trains with (from above at the global maxima) N = 6 , 5, 4,3, 2, 1, 0.

Fig. 11
Fig. 11

Amplitude shift as a function of propagation distance using (from below at L = 200 km ) an initial DCF that compensates for 0 , 1 4 , 1 2 , 3 4 , and 1 times the length of the SMF.

Fig. 12
Fig. 12

Timing shift as a function of propagation distance using (from below at L = 200 km ) an initial DCF that compensates for 0 , 1 4 , 1 2 , 3 4 , and 1 times the length of the SMF.

Tables (1)

Tables Icon

Table 1 Analytically Calculated Values for N at the First Maximum Using Different Fiber Lengths

Equations (21)

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i ψ z = β 2 2 2 ψ t 2 i α 2 ψ γ ψ 2 ψ ,
i ψ s z β 2 2 2 ψ s t 2 + i α 2 ψ s = 0 ,
i ψ p z β 2 2 2 ψ p t 2 + i α 2 ψ p = γ ψ s 2 ψ s ,
B ( z ) 1 t 0 2 0 z β 2 ( z ) d z .
ψ p , k , l ( L ) = i A 0 3 0 L γ p 1 + 2 i B + 3 B 2 exp { ν 2 2 ( 1 i B ) [ ( k + l ) 2 1 3 i B 1 + 3 i B + k 2 + l 2 ] } d z ,
ψ p , k , l ( L ) i A 0 3 0 L γ p 3 B e i [ ( 3 ν 2 k l 1 ) ( 3 B ) ] H ( B 2 B th 2 ) d z ,
B th 2 ν 2 3 ( k 2 + l 2 k l ) 1 .
ψ p , k , l ( L SMF ) = i γ A 0 3 t 0 2 3 β 2 [ E 1 ( i 3 ν 2 k l 1 3 B min ) E 1 ( i 3 ν 2 k l 1 3 ν 2 ( k 2 + l 2 k l ) 9 ) ] ,
E 1 ( z ) z e t t d t , arg z < π ,
i E 1 ( i x ) π 2 i γ E i log x ,
t = 0 T B t ψ 2 d t 0 T B ψ 2 d t ,
i 3 ν 2 k l 1 3 B min i ν 2 ( N 1 ) B min 3.38 i .
i 3 ν 2 k l 1 3 B min i ν 2 k 2 B min 1.93 i .
N 1.93 B min ν 2 ,
i 3 ν 2 k l 1 3 B i ν 2 B 2 i ,
z th T B 2 2 β 2 15 km .
exp { ν 2 2 1 1 + B 2 [ ( k + l ) 2 1 3 B 2 1 + 9 B 2 + k 2 + l 2 ] } × exp { i ν 2 2 B 1 + B 2 [ ( k + l ) 2 5 + 9 B 2 1 + 9 B 2 ( k 2 + l 2 ) ] } .
exp { ν 2 2 1 1 + B 2 [ ( k + l ) 2 1 3 B 2 1 + 9 B 2 + k 2 + l 2 ] } = e 1 .
1 3 B 2 1 + 9 B 2 1 3 .
1 1 + 2 i B + 3 B 2 1 3 B 2 ( 1 i 3 B ) 1 3 B 2 e [ i ( 3 B ) ] ,
e exp { i ν 2 2 B [ ( k + l ) 2 ( k 2 + l 2 ) ] } = e i ν 2 k l B .

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