Abstract

For the procedure of dispersion precompensation in fibers by prechirping, we found that there is a maximum distance over which a pulse initially compressed by prechirping can return to its original width. The distance constraint comes in the form of a mathematical relationship involving the distance, dispersion, initial pulse width, and peak power, implying that the restriction governs all the fiber parameters. Simple closed-form approximations for the constraint and for the corresponding required prechirp are derived on the basis of a variational approach. The validity of the analytical formulas is confirmed by split-step Fourier numerical simulation.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  4. T. Yang, W. Kath, S. Evangelides, “Optimal prechirping for dispersion-managed transmission of return-to-zero pulses,” in Optical Fiber Communication Conference, (OFC), Vol. 5 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 249–251.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).
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    [CrossRef]
  14. P. Belanger, C. Pare, “Second-order moment analysis of dispersion-managed solitons,” J. Lightwave Technol. 17, 445–451 (1999).
    [CrossRef]
  15. F. Cattani, D. Anderson, A. Berntson, M. Lisak, “Effect of self-phase modulation in chirped-pulse-amplification-like schemes,” J. Opt. Soc. Am. B 16, 1874–1879 (1999).
    [CrossRef]

2000 (3)

1999 (6)

1997 (1)

1988 (1)

1983 (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in fibers,” Phys. Rev. A 27, 3135–3145 (1983)
[CrossRef]

Abramov, A. A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Agrawal, G. P.

Anderson, D.

Belanger, P.

Bergano, N.

N. Bergano, “Undersea fiberoptic cable systems,” Opt. Photon. News 11, 20–25 (2000).
[CrossRef]

Bergano, N. S.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Bergman, K.

Berntson, A.

Boivin, L.

Brandt-Pearce, M.

Buck, J.

Cattani, F.

Collins, B.

Corbett, P. C.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Cundiff, S.

Darcie, J. M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Davidson, C. R.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Evangelides, S.

S. Cundiff, B. Collins, L. Boivin, M. Nuss, K. Bergman, W. Knox, S. Evangelides, “Propagation of highly chirped pulses in fiber-optic communication systems,” J. Lightwave Technol. 17, 811–816 (1999).
[CrossRef]

T. Yang, W. Kath, S. Evangelides, “Optimal prechirping for dispersion-managed transmission of return-to-zero pulses,” in Optical Fiber Communication Conference, (OFC), Vol. 5 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 249–251.

Evangelides, S. G.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Goluvchenko, E.

V. Grigorian, T. Yu, E. Goluvchenko, C. Menyuk, A. Pilipetski, “Dispersion-managed soliton dynamics,” Opt. Lett. 22, 1609–1611 (1997).
[CrossRef]

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Grigorian, V.

Jacobs, I.

Kath, W.

T. Yang, W. Kath, S. Evangelides, “Optimal prechirping for dispersion-managed transmission of return-to-zero pulses,” in Optical Fiber Communication Conference, (OFC), Vol. 5 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 249–251.

Kidorf, H. D.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Knox, W.

Lee, J.-H.

Liao, Z.

Lisak, M.

Ma, M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Matera, F.

McKinstrie, C.

Menges, R.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Menyuk, C.

Mills, M. A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Nuss, M.

Pare, C.

Peckham, D.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Pedersen, B.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Pilipetski, A.

Pilipetskii, A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Ralph, S.

Reichel, T.

Rottwitt, K.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Settembre, M.

Shaw, J. K.

Vengsarkar, A. M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

Washburn, B.

Wen, Y.

Y. Wen, X. Yang, “Quasi-transform-limited pulse transmission in dispersion managed soliton system,” Photon. Technol. Lett. 11, 433–435 (1999).
[CrossRef]

Yang, T.

T. Yang, W. Kath, S. Evangelides, “Optimal prechirping for dispersion-managed transmission of return-to-zero pulses,” in Optical Fiber Communication Conference, (OFC), Vol. 5 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 249–251.

Yang, X.

Y. Wen, X. Yang, “Quasi-transform-limited pulse transmission in dispersion managed soliton system,” Photon. Technol. Lett. 11, 433–435 (1999).
[CrossRef]

Yu, T.

Zitelli, M.

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (4)

Opt. Lett. (2)

Opt. Photon. News (1)

N. Bergano, “Undersea fiberoptic cable systems,” Opt. Photon. News 11, 20–25 (2000).
[CrossRef]

Photon. Technol. Lett. (1)

Y. Wen, X. Yang, “Quasi-transform-limited pulse transmission in dispersion managed soliton system,” Photon. Technol. Lett. 11, 433–435 (1999).
[CrossRef]

Phys. Rev. A (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in fibers,” Phys. Rev. A 27, 3135–3145 (1983)
[CrossRef]

Other (3)

N. S. Bergano, C. R. Davidson, M. Ma, A. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Goluvchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, A. M. Vengsarkar, “320 Gb/s WDM transmission (64 × 5 Gb/s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD12-1–PD12-4.

T. Yang, W. Kath, S. Evangelides, “Optimal prechirping for dispersion-managed transmission of return-to-zero pulses,” in Optical Fiber Communication Conference, (OFC), Vol. 5 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 249–251.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).

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Figures (3)

Fig. 1
Fig. 1

Comparison of the variational and split-step calculations of the value of C required to ensure equal input and output widths at the dimensionless propagation distance u. Parameters are (a) N = 0, u max = 1; (b) N = 0.2, u max = 0.98; (c) N = 0.5, u max = 0.92; (d) N = 1, u max = 0.77.

Fig. 2
Fig. 2

(a) Ratio of output to input pulse widths for u = 0.2, N = 0.4, u max = 0.98 for various C values near the perfect compensating chirp C = -0.215. (b) Ratio of output-to-input spectral widths for the same data as (a). (c) Ratio of output-to-input pulse widths near the minimum C = -1 for N = 0.2 and u = 1 > u max = 0.98. (d) Ratio of output-to-input spectral widths for the same data as (c). All data were obtained by split-step calculation.

Fig. 3
Fig. 3

(a) (b) Comparison of the variational and split-step calculations of the value of C required to assure equal input and output widths at the dimensionless propagation distance u for 0.2 ≤ u ≤ 1 in the anomalous dispersion case. Parameters are (a) N = 0.2, u max = 1.03, (b) N = 0.4, u max = 1.13. (c) (d) Evolution of twin identically chirped Gaussian pulses under normal dispersion. (c) The dashed curve is the pulse intensity at z = 0.25 L D and the solid curve is the input intensity. (d) The dashed curve is the pulse intensity at z = 0.5 L D and the solid curve is the output (final) intensity at z = L D . The nonlinearity parameter is N 2 = 0.25 in both (c) and (d).

Equations (13)

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

jψz=β2/2ψtt-γP0|ψ|2ψ ψ0, 0=1
ψz, t=Azexp-t212az2-jbz
az=-2β2azbz, abz=-2β2azbz2+β22az3+α0γP022az2,
azz=β22az3+β2a0γP02az2
az2a02+2β2Cz+β22a02+β2γP02+β22C2a02z2.
az2a021+u21+C2+u2C+F,
C2+2Cu+1+Fu=0.
C2+2Cu+1+N22=0,
C=-1+1-u21+N2/21/2u.
u21+N221.
Δωz2=1+C2a02+2γP0/β21-a0az.
C=1-1-u21-N2/21/2u, u2umax2=1-N22-1,
C=-1+1-4u21+N2/21/22u, uumax=1/21+N2/21/2.

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