Abstract

Taking into account the delayed Raman response, an expression for the collision-induced frequency shift is derived. In a wavelength-division multiplexed soliton system, solitons undergo cross-frequency shifts owing to collisions, which leads to timing jitter for transmission systems with bit rates of more than 40 Gbits/s per channel.

© 1998 Optical Society of America

Full Article  |  PDF Article

Corrections

Shiva Kumar, "Influence of Raman effects in wavelength-division multiplexed soliton systems:?errata," Opt. Lett. 24, 357-357 (1999)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-24-5-357

References

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  1. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  2. F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  3. S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
    [CrossRef]
  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), p. 293.
  5. C. Headley and G. P. Agrawal, J. Opt. Soc. Am. B 13, 2170 (1996).
    [CrossRef]
  6. C. S. Aparna, S. Kumar, and A. Selvarajan, Opt. Commun. 131, 267 (1996).
    [CrossRef]
  7. S. Chi and S. Wen, Opt. Lett. 14, 1216 (1989).
    [CrossRef] [PubMed]
  8. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, J. Opt. Soc. Am. B 6, 1149 (1989).
    [CrossRef]
  9. R. H. Stolen and W. J. Tomlinson, J. Opt. Soc. Am. B 9, 565 (1992).
    [CrossRef]
  10. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 181.
  11. Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [CrossRef]
  12. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]

1996 (2)

C. Headley and G. P. Agrawal, J. Opt. Soc. Am. B 13, 2170 (1996).
[CrossRef]

C. S. Aparna, S. Kumar, and A. Selvarajan, Opt. Commun. 131, 267 (1996).
[CrossRef]

1993 (1)

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

1992 (1)

1991 (1)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

1989 (2)

1987 (1)

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

1986 (2)

Agrawal, G. P.

C. Headley and G. P. Agrawal, J. Opt. Soc. Am. B 13, 2170 (1996).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), p. 293.

Anand, G. V.

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Aparna, C. S.

C. S. Aparna, S. Kumar, and A. Selvarajan, Opt. Commun. 131, 267 (1996).
[CrossRef]

Chi, S.

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 181.

Haus, H. A.

Headley, C.

Kodama, Y.

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 181.

Kumar, S.

C. S. Aparna, S. Kumar, and A. Selvarajan, Opt. Commun. 131, 267 (1996).
[CrossRef]

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
[CrossRef] [PubMed]

Selvarajan, A.

C. S. Aparna, S. Kumar, and A. Selvarajan, Opt. Commun. 131, 267 (1996).
[CrossRef]

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Stolen, R. H.

Tomlinson, W. J.

Wen, S.

IEEE J. Quantum Electron. (1)

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

J. Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

C. S. Aparna, S. Kumar, and A. Selvarajan, Opt. Commun. 131, 267 (1996).
[CrossRef]

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Opt. Lett. (3)

Other (2)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), p. 181.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), p. 293.

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Figures (1)

Fig. 1
Fig. 1

Frequency shift of channel 1 as a function of distance. Solid curve, result obtained by solution of Eqs. (11) and (12); +, direct numerical simulation of Eq. (5). The channel separation is 2.24 THz, pulse width τ=1 ps, dispersion k=1 ps2/km, ΔT=10 5.67 ps, α Re KiαC=0.0052, ImH1CΔB, n2=3.2×10-16 cm2/W, and λ=1.55 µm.

Equations (23)

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iuiZ+ViuiZ+di22uiT2+1-αui2+2uj2ui=-αdSfSuiT-S2+ujT-S2uiT+uiT-SujT-SujTexpiΩi-ΩjS,
uii=12uiT2-Cui2T+ujHiuiuj-KiuiujT,
C=Imdf˜ΩdΩΩ=0,    Hi=f˜Ω=Ωi-Ωj,
Ki=-idf˜ΩdΩΩ=Ωi-Ωj,
iuiZ+ViuiT+di22uiT2+ui2+δiuj2ui=αCuiui2+uj2T+αKiujuiujT-iα ImHiuj2ui,
u1=IpZexpiθ1Z,u2=IsZexpiΩT+θ2Z
dIpdZ=-2αImH1+ReK1ΩIpIs.
gRΩ1-Ω2+Ω=gRΩ1-Ω2+ΩdgR/dΩΩ1-Ω2,
ui=ηi sechτiexp-iκiT+ϕiZ,    i=1,2,
τi=ηidiT-Ti+diκi-ViZ.
dη1dZ=-αη1η22ReK1κ1-κ2+ImH1I0T0,
dκ1dZ=-815αCη2η12+α4η2η222C+ReK1ddT0×I1T0+α3ReK1η2η22ddT0I2T0+δ1η222ΔVddZI0T0,
I1T0=dI0dT0,
I0T0=4T0coshT0-sinhT0sinh3T0,
I2T0=dx tanh3x-T0/2sech2x+T0/2=21-ddT0T0coshT0+eT0 sinh2 T0-sinhT0 sinh3 T0,
ΔηZ=2αCη022-T0-exp-T0sinhT0sinh2T0.
κ1Z=-8/15αCη03η0-40ZΔηxdx-η03αC12ΔV9I1T0+4I2T0+2+η0ΔV×η0+2ΔηI0T0-2η02αC-ZI02xdx.
κCFS=-8.63αCη03ΔV.
κCFSZ=-8.63αCη03ZTs.
κCFSZ=-4.25Zη0252.8πtcTs.
fCFSGHz=-22.33kztsτ3,
ΔκSFSZ=8αCTs15ΔVm=0N-14η03mΔη=64αC2η05Z2ΔV15Ts.
ΔfSFSGHz=6.39×10-4k2z2fcτ5ts,

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