Abstract

The authors develop a second-order perturbation technique for the study of self-phase modulation (SPM) and cross-phase modulation (XPM) effects in optical fibers. When the dispersion distance is much shorter than the nonlinear length, it is found that the difference between the first-and second-order solution is negligible. However, as the dispersion distance increases,nonlinearity becomes a stronger perturbation, and the first-order theory is not adequate to describe the SPM effects. However, the results obtained using the second-order perturbation technique is in good agreement with numerical simulations even when the dispersion distance is longer than the nonlinear length. When pulses of different channels are copropagating in a fiber, they undergo amplitude distortion and timing shift due to XPM. The perturbation technique presented in this paper accounts for both amplitude distortion and timing shift of a pulse due to XPM.

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  1. F. Forghieri, R. W. Tkach and A. R. Chraplyvy, Optical Fiber Telecommunications, I. P. Kaminov, and T. L. Koch, Eds. New York: Academic, 1997, vol. IIIA, ch. 8.
  2. D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Dependence of cross-phase modulation in channel number in fiber WDM systems", J. Lightw. Technol., vol. 12, no. 5, pp. 885-890, May 1994.
  3. G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA: Academic, 1995, ch. 3 and 7.
  4. L. F. Mollenauer, S. G. Evangelides and J. P. Gordon, "Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers", J. Lightw. Technol., vol. 9, no. 3, pp. 362-367, Mar. 1991.
  5. A. Hasegawa, S. Kumar and Y. Kodama, "Reduction of collision-induced time jitters in dispersion-managed transmission systems", Opt. Lett., vol. 21, pp. 39-41, Jan. 1996.
  6. M. Shtaif, "Analytical description of cross-phase modulation in dispersive optical fibers", Opt. Lett., vol. 23, no. 15, pp. 1191-1193, 1998.
  7. M. Shtaif and M. Eiselt, "Analysis of intensity interference caused by cross-phase modulation in dispersive optical fibers", IEEE Photon. Technol. Lett., vol. 10, no. 7, pp. 979-981, Jul. 1998.
  8. L. E. Nelson, R. M. Jopson, A. H. Gnauck and A. R. Chraplyvy, "Resonances in cross-phase modulation impairment in wavelength division multiplexed lightwave transmission", IEEE Photon. Technol. Lett., vol. 11, no. 7, pp. 907-909, Jul. 1999.
  9. R. Hui, K. R. Demarest and C. T. Allen, "Cross-phase modulation in multispan WDM optical fiber systems", J. Lightw. Technol., vol. 17, no. 6, pp. 1018-1026, Jun. 1999.
  10. S. Betti and M. Giaconi, "Effect of the cross-phase modulation on WDM optical systems: Analysis of fiber propagation", IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 305-307, Apr. 2001.
  11. S. Betti and M. Giaconi, "Analysis of the cross-phase modulation in dispersion compensated WDM optical fiber systems", IEEE Photon. Technol. Lett., vol. 13, no. 12, pp. 1304-1306, Dec. 2001.
  12. R. Hui, Y. Wang, K. R. Demarest and C. Allen, "Frequency response of cross-phase modulation in multispan WDM optical fiber systems", IEEE Photon. Technol. Lett., vol. 10, no. 9, pp. 1271-1273, Sep. 1998.
  13. B. Xu and M. Brandt-Pearce, "Comparison of FWM-and XPM-induced crosstalk using the Volterra series transfer function method", J. Lightw. Technol. , vol. 21, no. 1, pp. 40-53, Jan. 2003.
  14. M. Eiselt, L. D. Garrett and R. W. Tkach, "Experimental comparison of WDM system capacity in conventional and nonzero dispersion shifted fiber", IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 281-283, Feb. 1999.
  15. M. Eiselt, M. Shtaif and L. D. Garrett, "Contribution of timing jitter and amplitude distortion to XPM system penalty in WDM systems", IEEE Photon. Technol. Lett., vol. 11, no. 6, pp. 748-750, Jun. 1999.
  16. R. A. Saunders, B. L. Patel, H. J. Harvey and A. Robinson, "Impact of cross-phase modulation for WDM systems over positive and negative dispersion NZ-DSF and methods for its suppression", Electron. Lett., vol. 32, pp. 2206-2207, Nov. 1996.
  17. N. Kikuchi, K. Sekine and S. Sasaki, "Analysis of cross-phase modulation effect on WDM transmission performance", Electron. Lett., vol. 33, pp. 653-654, Apr. 1997.
  18. H. J. Thiele, R. I. Killey and P. Bayvel, "Influence of fiber dispersion and bit rate on cross-phase modulation-induced distortion in amplified optical fiber links", Electron. Lett., vol. 34, pp. 2050-2051, Oct. 1998 .
  19. H. J. Thiele, R. I. Killey and P. Bayvel, "Influence of fiber dispersion and bit rate on cross-phase modulation-induced distortion in amplified optical fiber links", Electron. Lett., vol. 34, pp. 2050-2051, Oct. 1998 .
  20. R. I. Killey, H. J. Thiele, V. Mikhailov and P. Bayvel, "Prediction of Transmission penalties due to cross-phase modulation in WDM systems using a simplified technique", IEEE Photon. Technol. Lett., vol. 12, no. 7, pp. 804-806, Jul. 2000.
  21. J. Tang, "The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver", J. Lightw. Technol., vol. 20, no. 7, pp. 1095-1101, Jul. 2002.
  22. A. Hasegawa and Y. Kodama, Solitons in Optical Communication, Oxford: U.K.: Oxford Univ. Press, 1995, ch. 5.

Opt. Lett. (1)

Other (21)

M. Shtaif, "Analytical description of cross-phase modulation in dispersive optical fibers", Opt. Lett., vol. 23, no. 15, pp. 1191-1193, 1998.

M. Shtaif and M. Eiselt, "Analysis of intensity interference caused by cross-phase modulation in dispersive optical fibers", IEEE Photon. Technol. Lett., vol. 10, no. 7, pp. 979-981, Jul. 1998.

L. E. Nelson, R. M. Jopson, A. H. Gnauck and A. R. Chraplyvy, "Resonances in cross-phase modulation impairment in wavelength division multiplexed lightwave transmission", IEEE Photon. Technol. Lett., vol. 11, no. 7, pp. 907-909, Jul. 1999.

R. Hui, K. R. Demarest and C. T. Allen, "Cross-phase modulation in multispan WDM optical fiber systems", J. Lightw. Technol., vol. 17, no. 6, pp. 1018-1026, Jun. 1999.

S. Betti and M. Giaconi, "Effect of the cross-phase modulation on WDM optical systems: Analysis of fiber propagation", IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 305-307, Apr. 2001.

S. Betti and M. Giaconi, "Analysis of the cross-phase modulation in dispersion compensated WDM optical fiber systems", IEEE Photon. Technol. Lett., vol. 13, no. 12, pp. 1304-1306, Dec. 2001.

R. Hui, Y. Wang, K. R. Demarest and C. Allen, "Frequency response of cross-phase modulation in multispan WDM optical fiber systems", IEEE Photon. Technol. Lett., vol. 10, no. 9, pp. 1271-1273, Sep. 1998.

B. Xu and M. Brandt-Pearce, "Comparison of FWM-and XPM-induced crosstalk using the Volterra series transfer function method", J. Lightw. Technol. , vol. 21, no. 1, pp. 40-53, Jan. 2003.

M. Eiselt, L. D. Garrett and R. W. Tkach, "Experimental comparison of WDM system capacity in conventional and nonzero dispersion shifted fiber", IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 281-283, Feb. 1999.

M. Eiselt, M. Shtaif and L. D. Garrett, "Contribution of timing jitter and amplitude distortion to XPM system penalty in WDM systems", IEEE Photon. Technol. Lett., vol. 11, no. 6, pp. 748-750, Jun. 1999.

R. A. Saunders, B. L. Patel, H. J. Harvey and A. Robinson, "Impact of cross-phase modulation for WDM systems over positive and negative dispersion NZ-DSF and methods for its suppression", Electron. Lett., vol. 32, pp. 2206-2207, Nov. 1996.

N. Kikuchi, K. Sekine and S. Sasaki, "Analysis of cross-phase modulation effect on WDM transmission performance", Electron. Lett., vol. 33, pp. 653-654, Apr. 1997.

H. J. Thiele, R. I. Killey and P. Bayvel, "Influence of fiber dispersion and bit rate on cross-phase modulation-induced distortion in amplified optical fiber links", Electron. Lett., vol. 34, pp. 2050-2051, Oct. 1998 .

H. J. Thiele, R. I. Killey and P. Bayvel, "Influence of fiber dispersion and bit rate on cross-phase modulation-induced distortion in amplified optical fiber links", Electron. Lett., vol. 34, pp. 2050-2051, Oct. 1998 .

R. I. Killey, H. J. Thiele, V. Mikhailov and P. Bayvel, "Prediction of Transmission penalties due to cross-phase modulation in WDM systems using a simplified technique", IEEE Photon. Technol. Lett., vol. 12, no. 7, pp. 804-806, Jul. 2000.

J. Tang, "The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver", J. Lightw. Technol., vol. 20, no. 7, pp. 1095-1101, Jul. 2002.

A. Hasegawa and Y. Kodama, Solitons in Optical Communication, Oxford: U.K.: Oxford Univ. Press, 1995, ch. 5.

F. Forghieri, R. W. Tkach and A. R. Chraplyvy, Optical Fiber Telecommunications, I. P. Kaminov, and T. L. Koch, Eds. New York: Academic, 1997, vol. IIIA, ch. 8.

D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Dependence of cross-phase modulation in channel number in fiber WDM systems", J. Lightw. Technol., vol. 12, no. 5, pp. 885-890, May 1994.

G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA: Academic, 1995, ch. 3 and 7.

L. F. Mollenauer, S. G. Evangelides and J. P. Gordon, "Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers", J. Lightw. Technol., vol. 9, no. 3, pp. 362-367, Mar. 1991.

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