Abstract

We report the results of a detailed numerical analysis of stabilization provided by lumped notch filters against basic degradation factors in dense-wavelength-division-multiplexed (DWDM) soliton systems, which include the noise-induced timing jitter (Gordon–Haus effect), intrachannel interactions between solitons, and cross-talk effects due to interchannel soliton–soliton collisions, in the form of temporal shifts and loss of energy to the formation of shadows in the other channel. The filtering profile is a couple of rectangular notches that bound the transmission channel in the frequency domain. For typical values of parameters relevant to the DWDM systems, we show that the stabilization is quite efficient. The version of the model with distributed notch filtering also has a different realization in terms of spatial solitons in a planar waveguide equipped with a longitudinal grating.

© 2004 Optical Society of America

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  1. P. S. Kaler and T. S. Kamel, “Simulation results for DWDM systems with ultra-high capacity,” Fiber Integr. Opt. 21, 361–369 (2002).
    [CrossRef]
  2. G. P. Agrawal, Fiber-Optics Communication Systems (Wiley, New York, 1997).
  3. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).
  4. R. M. Mu and C. R. Menyuk, “Convergence of the chirped return-to-zero and dispersion managed soliton modulation formats in WDM systems,” J. Lightwave Technol. 20, 608–617 (2002).
    [CrossRef]
  5. I. Morita, T. Tsuritani, and N. Edagawa, “Experimental study on optically band-limited 40-Gb/s RZ signals with optically time-division demultiplexing receiver,” J. Lightwave Technol. 20, 2182–2188 (2002).
    [CrossRef]
  6. I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
    [CrossRef]
  7. R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
    [CrossRef]
  8. C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
    [CrossRef]
  9. K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
    [CrossRef]
  10. T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
    [CrossRef]
  11. J. McEntee, “Solitons go the distance in ultralong-haul DWDM,” FibreSyst. Eur., Jan. 19–21 (2003).
  12. P. V. Mamyshev and L. F. Mollenauer, “Soliton collisions in wavelength-division-multiplexed dispersion-managed systems,” Opt. Lett. 24, 448–450 (1999).
    [CrossRef]
  13. L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, “Effect of guiding filters on the behavior of dispersion-managed solitons,” Opt. Lett. 24, 220–222 (1999).
    [CrossRef]
  14. M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
    [CrossRef]
  15. L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
    [CrossRef]
  16. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
    [CrossRef]
  17. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dis-persion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
    [CrossRef]
  18. H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision induced frequency shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. 33, 1065–1066 (1997).
    [CrossRef]
  19. A. M. Niculae, W. Forysiak, and A. Gloag, “Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,” Opt. Lett. 23, 1354–1356 (1998).
    [CrossRef]
  20. D. J. Kaup, B. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1602 (1998).
    [CrossRef]
  21. Y. Chen and H. A. Haus, “Collisions in dispersion-managed soliton propagation,” Opt. Lett. 24, 217–219 (1999).
    [CrossRef]
  22. H. Sugahara and A. Maruta, “Collision-induced timing-jitter analysis in a wavelength-division-multiplexed optical soliton-transmission system with dispersion management,” J. Opt. Soc. Am. B 18, 419–431 (2001).
    [CrossRef]
  23. M. Wald, B. A. Malomed, and F. Lederer, “Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,” Opt. Lett. 26, 965–967 (2001).
    [CrossRef]
  24. D. J. Kaup, B. A. Malomed, and J. Yang, “Collision-induced pulse timing jitter in a wavelength-division-multiplexing system with strong dispersion management,” J. Opt. Soc. Am. B 16, 1628–1635 (1999).
    [CrossRef]
  25. M. J. Ablowitz, G. Biondini, and E. S. Olson, “Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons,” J. Opt. Soc. Am. B 18, 577–583 (2001).
    [CrossRef]
  26. S. Orlov, A. Yariv, and S. V. Essen, “Coupled-mode analysis of fiber-optic add–drop filters for dense wavelength-division multiplexing,” Opt. Lett. 22, 688–690 (1997).
    [CrossRef] [PubMed]
  27. X. J. Gu, “Wavelength-division multiplexing isolation fiber filter and light source using cascading long-period fiber gratings,” Opt. Lett. 23, 509–511 (1998).
    [CrossRef]
  28. G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
    [CrossRef]
  29. L. A. De Francisco, M. T. S. Silva, and M. A. Romero, “Analytical study of Bragg-grating fiber-optic filters for dense wavelength-division-multiplexing and temperature-sensing applications,” Opt. Eng. 41, 1491–1495 (2002).
    [CrossRef]
  30. R. Slavik and S. LaRochelle, “Large-band periodic filters for dense wavelength-division-multiplexing using multiple-superimposed fiber gratings,” IEEE Photon. Technol. Lett. 14, 1704–1706 (2002).
    [CrossRef]
  31. A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
    [CrossRef]
  32. B. A. Malomed, G. D. Peng, and P. L. Chu, “Soliton wavelength-division multiplexing system with channel-isolating notch filters,” Opt. Lett. 24, 1100–1102 (1999).
    [CrossRef]
  33. A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
    [CrossRef]
  34. P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
    [CrossRef]
  35. C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184, 375–384 (2000).
    [CrossRef]
  36. S. Shen and A. M. Weiner, “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photon. Technol. Lett. 13, 82–84 (2001).
    [CrossRef]
  37. A. Docherty, P. L. Chu, and B. A. Malomed, “Notch filters in soliton communication systems: comparison,” J. Opt. Soc. Am. B 19, 190–197 (2002).
    [CrossRef]
  38. B. A. Malomed, A. Docherty, P. L. Chu, and G. D. Peng, “Dense-WDM soliton systems using channel-isolating notch filters (‘soliton rail’),” in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).
  39. B. A. Malomed and S. Wabnitz, “Soliton annihilation and fusion from resonant inelastic collisions in birefringent optical fibers,” Opt. Lett. 16, 1388–1390 (1991).
    [CrossRef] [PubMed]
  40. Q. Wang, P. K. A. Wai, C. J. Chen, and C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265–1267 (1992).
    [CrossRef] [PubMed]
  41. See S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, Berlin, 2001).
  42. B. A. Malomed, Z. H. Wang, P. L. Chu, and G. D. Peng, “Multichannel switchable system for spatial solitons,” J. Opt. Soc. Am. B 16, 1197–1203 (1999).
    [CrossRef]
  43. A. Shipulin, G. Onishchukov, and B. A. Malomed, “Suppression of the soliton jitter by a copropagating support structure,” J. Opt. Soc. Am. B 14, 3393–3402 (1997).
    [CrossRef]
  44. M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
    [CrossRef]
  45. F. Forghieri, R. W. Tkach, and A. R. Chaplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897 (1995).
    [CrossRef]

2003

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
[CrossRef]

R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
[CrossRef]

C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
[CrossRef]

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

2002

P. S. Kaler and T. S. Kamel, “Simulation results for DWDM systems with ultra-high capacity,” Fiber Integr. Opt. 21, 361–369 (2002).
[CrossRef]

R. M. Mu and C. R. Menyuk, “Convergence of the chirped return-to-zero and dispersion managed soliton modulation formats in WDM systems,” J. Lightwave Technol. 20, 608–617 (2002).
[CrossRef]

I. Morita, T. Tsuritani, and N. Edagawa, “Experimental study on optically band-limited 40-Gb/s RZ signals with optically time-division demultiplexing receiver,” J. Lightwave Technol. 20, 2182–2188 (2002).
[CrossRef]

L. A. De Francisco, M. T. S. Silva, and M. A. Romero, “Analytical study of Bragg-grating fiber-optic filters for dense wavelength-division-multiplexing and temperature-sensing applications,” Opt. Eng. 41, 1491–1495 (2002).
[CrossRef]

R. Slavik and S. LaRochelle, “Large-band periodic filters for dense wavelength-division-multiplexing using multiple-superimposed fiber gratings,” IEEE Photon. Technol. Lett. 14, 1704–1706 (2002).
[CrossRef]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

A. Docherty, P. L. Chu, and B. A. Malomed, “Notch filters in soliton communication systems: comparison,” J. Opt. Soc. Am. B 19, 190–197 (2002).
[CrossRef]

2001

2000

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184, 375–384 (2000).
[CrossRef]

1999

Y. Chen and H. A. Haus, “Collisions in dispersion-managed soliton propagation,” Opt. Lett. 24, 217–219 (1999).
[CrossRef]

B. A. Malomed, Z. H. Wang, P. L. Chu, and G. D. Peng, “Multichannel switchable system for spatial solitons,” J. Opt. Soc. Am. B 16, 1197–1203 (1999).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, “Soliton wavelength-division multiplexing system with channel-isolating notch filters,” Opt. Lett. 24, 1100–1102 (1999).
[CrossRef]

A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, “Collision-induced pulse timing jitter in a wavelength-division-multiplexing system with strong dispersion management,” J. Opt. Soc. Am. B 16, 1628–1635 (1999).
[CrossRef]

P. V. Mamyshev and L. F. Mollenauer, “Soliton collisions in wavelength-division-multiplexed dispersion-managed systems,” Opt. Lett. 24, 448–450 (1999).
[CrossRef]

L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, “Effect of guiding filters on the behavior of dispersion-managed solitons,” Opt. Lett. 24, 220–222 (1999).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
[CrossRef]

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
[CrossRef]

1998

1997

S. Orlov, A. Yariv, and S. V. Essen, “Coupled-mode analysis of fiber-optic add–drop filters for dense wavelength-division multiplexing,” Opt. Lett. 22, 688–690 (1997).
[CrossRef] [PubMed]

A. Shipulin, G. Onishchukov, and B. A. Malomed, “Suppression of the soliton jitter by a copropagating support structure,” J. Opt. Soc. Am. B 14, 3393–3402 (1997).
[CrossRef]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dis-persion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision induced frequency shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. 33, 1065–1066 (1997).
[CrossRef]

1995

F. Forghieri, R. W. Tkach, and A. R. Chaplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897 (1995).
[CrossRef]

1993

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
[CrossRef]

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

1992

1991

Ablowitz, M. J.

Absil, P. P.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

Biondini, G.

Chaplyvy, A. R.

F. Forghieri, R. W. Tkach, and A. R. Chaplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897 (1995).
[CrossRef]

Chen, C. J.

Chen, Y.

Chryssou, C. E.

C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184, 375–384 (2000).
[CrossRef]

Chu, P. L.

De Francisco, L. A.

L. A. De Francisco, M. T. S. Silva, and M. A. Romero, “Analytical study of Bragg-grating fiber-optic filters for dense wavelength-division-multiplexing and temperature-sensing applications,” Opt. Eng. 41, 1491–1495 (2002).
[CrossRef]

Docherty, A.

Driben, R.

R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
[CrossRef]

Edagawa, N.

Eggleton, B. J.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Essen, S. V.

Forghieri, F.

F. Forghieri, R. W. Tkach, and A. R. Chaplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897 (1995).
[CrossRef]

Forysiak, W.

Fukuchi, K.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

Giles, C. R.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Gloag, A.

Goedgebuer, J.-P.

Golovchenko, E. A.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dis-persion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

Gordon, J. P.

Gu, X. J.

Gutin, M.

R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
[CrossRef]

Hanna, M.

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
[CrossRef]

Haus, H. A.

Hirano, A.

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

Ho, P. T.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

Hryniewicz, J. V.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

Ito, T.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

Joneckis, L. G.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

Kaler, P. S.

P. S. Kaler and T. S. Kamel, “Simulation results for DWDM systems with ultra-high capacity,” Fiber Integr. Opt. 21, 361–369 (2002).
[CrossRef]

Kamel, T. S.

P. S. Kaler and T. S. Kamel, “Simulation results for DWDM systems with ultra-high capacity,” Fiber Integr. Opt. 21, 361–369 (2002).
[CrossRef]

Kato, H.

H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision induced frequency shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. 33, 1065–1066 (1997).
[CrossRef]

Kaup, D. J.

Kawanishi, S.

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

Kimura, Y.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Kodama, Y.

H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision induced frequency shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. 33, 1065–1066 (1997).
[CrossRef]

Kubota, H.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

LaRochelle, S.

R. Slavik and S. LaRochelle, “Large-band periodic filters for dense wavelength-division-multiplexing using multiple-superimposed fiber gratings,” IEEE Photon. Technol. Lett. 14, 1704–1706 (2002).
[CrossRef]

Lederer, F.

Lenz, G.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Lichtman, E.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
[CrossRef]

Lima, A. O.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
[CrossRef]

Lima, I. T.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
[CrossRef]

Little, B. E.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

Liu, X.

C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
[CrossRef]

Madsen, C. K.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Mahlab, U.

R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
[CrossRef]

Malomed, B.

Malomed, B. A.

R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
[CrossRef]

A. Docherty, P. L. Chu, and B. A. Malomed, “Notch filters in soliton communication systems: comparison,” J. Opt. Soc. Am. B 19, 190–197 (2002).
[CrossRef]

M. Wald, B. A. Malomed, and F. Lederer, “Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,” Opt. Lett. 26, 965–967 (2001).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, “Collision-induced pulse timing jitter in a wavelength-division-multiplexing system with strong dispersion management,” J. Opt. Soc. Am. B 16, 1628–1635 (1999).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, “Soliton wavelength-division multiplexing system with channel-isolating notch filters,” Opt. Lett. 24, 1100–1102 (1999).
[CrossRef]

B. A. Malomed, Z. H. Wang, P. L. Chu, and G. D. Peng, “Multichannel switchable system for spatial solitons,” J. Opt. Soc. Am. B 16, 1197–1203 (1999).
[CrossRef]

A. Shipulin, G. Onishchukov, and B. A. Malomed, “Suppression of the soliton jitter by a copropagating support structure,” J. Opt. Soc. Am. B 14, 3393–3402 (1997).
[CrossRef]

B. A. Malomed and S. Wabnitz, “Soliton annihilation and fusion from resonant inelastic collisions in birefringent optical fibers,” Opt. Lett. 16, 1388–1390 (1991).
[CrossRef] [PubMed]

Mamyshev, P. V.

Martinelli, M.

Maruta, A.

McKay, T.

A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
[CrossRef]

Melloni, A.

Menyuk, C. R.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
[CrossRef]

R. M. Mu and C. R. Menyuk, “Convergence of the chirped return-to-zero and dispersion managed soliton modulation formats in WDM systems,” J. Lightwave Technol. 20, 608–617 (2002).
[CrossRef]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dis-persion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

Q. Wang, P. K. A. Wai, C. J. Chen, and C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265–1267 (1992).
[CrossRef] [PubMed]

Mollenauer, L. F.

C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
[CrossRef]

P. V. Mamyshev and L. F. Mollenauer, “Soliton collisions in wavelength-division-multiplexed dispersion-managed systems,” Opt. Lett. 24, 448–450 (1999).
[CrossRef]

L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, “Effect of guiding filters on the behavior of dispersion-managed solitons,” Opt. Lett. 24, 220–222 (1999).
[CrossRef]

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
[CrossRef]

Mori, K.

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

Morita, I.

Mu, R. M.

Munch, J.

A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
[CrossRef]

Niculae, A. M.

Ohara, T.

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

Ohira, R.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

Olson, E. S.

Onishchukov, G.

Ono, T.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

Orlov, S.

Peng, G. D.

Pilipetskii, A. N.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dis-persion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

Porte, H.

Rhodes, W. T.

Romero, M. A.

L. A. De Francisco, M. T. S. Silva, and M. A. Romero, “Analytical study of Bragg-grating fiber-optic filters for dense wavelength-division-multiplexing and temperature-sensing applications,” Opt. Eng. 41, 1491–1495 (2002).
[CrossRef]

Sekiya, K.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

Shen, S.

S. Shen and A. M. Weiner, “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photon. Technol. Lett. 13, 82–84 (2001).
[CrossRef]

Shipulin, A.

Silva, M. T. S.

L. A. De Francisco, M. T. S. Silva, and M. A. Romero, “Analytical study of Bragg-grating fiber-optic filters for dense wavelength-division-multiplexing and temperature-sensing applications,” Opt. Eng. 41, 1491–1495 (2002).
[CrossRef]

Slavik, R.

R. Slavik and S. LaRochelle, “Large-band periodic filters for dense wavelength-division-multiplexing using multiple-superimposed fiber gratings,” IEEE Photon. Technol. Lett. 14, 1704–1706 (2002).
[CrossRef]

Slusher, R. E.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Staromlyska, J.

A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
[CrossRef]

Sugahara, H.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

H. Sugahara and A. Maruta, “Collision-induced timing-jitter analysis in a wavelength-division-multiplexed optical soliton-transmission system with dispersion management,” J. Opt. Soc. Am. B 18, 419–431 (2001).
[CrossRef]

H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision induced frequency shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. 33, 1065–1066 (1997).
[CrossRef]

Suzuki, K.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Takara, H.

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

Takaya, M.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Tikhomirov, A. Y.

A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
[CrossRef]

Tkach, R. W.

F. Forghieri, R. W. Tkach, and A. R. Chaplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897 (1995).
[CrossRef]

Tsuritani, T.

Wabnitz, S.

Wai, P. K. A.

Wald, M.

Wang, Q.

Wang, Z. H.

Wei, X.

C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
[CrossRef]

Weiner, A. M.

S. Shen and A. M. Weiner, “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photon. Technol. Lett. 13, 82–84 (2001).
[CrossRef]

Wilson, R. A.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

Xu, C.

C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
[CrossRef]

Yamada, E.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Yang, J.

Yariv, A.

Zweck, J.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
[CrossRef]

Electron. Lett.

K. Sekiya, T. Ito, H. Sugahara, K. Fukuchi, R. Ohira, and T. Ono, “Flexible 40 Gbit/s WDM transmission beyond 1000 km enabled by 195μm2 Aeff PSCF and AC-RZ signal format,” Electron. Lett. 39, 386–388 (2003).
[CrossRef]

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey, “Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit/s, single channel, and more than 13 Mm at 20 Gbit/s in a two-channel WDM,” Electron. Lett. 29, 910–911 (1993).
[CrossRef]

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dis-persion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision induced frequency shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. 33, 1065–1066 (1997).
[CrossRef]

Fiber Integr. Opt.

P. S. Kaler and T. S. Kamel, “Simulation results for DWDM systems with ultra-high capacity,” Fiber Integr. Opt. 21, 361–369 (2002).
[CrossRef]

IEEE J. Quantum Electron.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for wavelength-division-multiplexed systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Compact microring notch filters,” IEEE Photon. Technol. Lett. 12, 398–400 (2000).
[CrossRef]

S. Shen and A. M. Weiner, “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photon. Technol. Lett. 13, 82–84 (2001).
[CrossRef]

R. Slavik and S. LaRochelle, “Large-band periodic filters for dense wavelength-division-multiplexing using multiple-superimposed fiber gratings,” IEEE Photon. Technol. Lett. 14, 1704–1706 (2002).
[CrossRef]

T. Ohara, H. Takara, A. Hirano, K. Mori, and S. Kawanishi, “S40-Gb/s×4-channel all-optical multichannel limiter utilizing spectrally filtered optical solitons,” IEEE Photon. Technol. Lett. 15, 763–765 (2003).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Performance-characterization of chirped return-to-zero modulation format using an accurate receiver model,” IEEE Photon. Technol. Lett. 15, 608–610 (2003).
[CrossRef]

C. Xu, X. Liu, L. F. Mollenauer, and X. Wei, “Comparison of return-to-zero differential phase-shift keying and on-off keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15, 617–619 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
[CrossRef]

R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
[CrossRef]

C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184, 375–384 (2000).
[CrossRef]

Opt. Eng.

L. A. De Francisco, M. T. S. Silva, and M. A. Romero, “Analytical study of Bragg-grating fiber-optic filters for dense wavelength-division-multiplexing and temperature-sensing applications,” Opt. Eng. 41, 1491–1495 (2002).
[CrossRef]

Opt. Lett.

B. A. Malomed and S. Wabnitz, “Soliton annihilation and fusion from resonant inelastic collisions in birefringent optical fibers,” Opt. Lett. 16, 1388–1390 (1991).
[CrossRef] [PubMed]

Q. Wang, P. K. A. Wai, C. J. Chen, and C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265–1267 (1992).
[CrossRef] [PubMed]

S. Orlov, A. Yariv, and S. V. Essen, “Coupled-mode analysis of fiber-optic add–drop filters for dense wavelength-division multiplexing,” Opt. Lett. 22, 688–690 (1997).
[CrossRef] [PubMed]

X. J. Gu, “Wavelength-division multiplexing isolation fiber filter and light source using cascading long-period fiber gratings,” Opt. Lett. 23, 509–511 (1998).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, “Soliton wavelength-division multiplexing system with channel-isolating notch filters,” Opt. Lett. 24, 1100–1102 (1999).
[CrossRef]

M. Wald, B. A. Malomed, and F. Lederer, “Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,” Opt. Lett. 26, 965–967 (2001).
[CrossRef]

P. V. Mamyshev and L. F. Mollenauer, “Soliton collisions in wavelength-division-multiplexed dispersion-managed systems,” Opt. Lett. 24, 448–450 (1999).
[CrossRef]

L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, “Effect of guiding filters on the behavior of dispersion-managed solitons,” Opt. Lett. 24, 220–222 (1999).
[CrossRef]

M. Hanna, H. Porte, J.-P. Goedgebuer, and W. T. Rhodes, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–734 (1999).
[CrossRef]

A. M. Niculae, W. Forysiak, and A. Gloag, “Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,” Opt. Lett. 23, 1354–1356 (1998).
[CrossRef]

D. J. Kaup, B. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1602 (1998).
[CrossRef]

Y. Chen and H. A. Haus, “Collisions in dispersion-managed soliton propagation,” Opt. Lett. 24, 217–219 (1999).
[CrossRef]

Opt. Quantum Electron.

A. Y. Tikhomirov, J. Munch, T. McKay, and J. Staromlyska, “Construction of high-quality narrow-band holographic filters,” Opt. Quantum Electron. 31, 535–543 (1999).
[CrossRef]

Other

See S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, Berlin, 2001).

B. A. Malomed, A. Docherty, P. L. Chu, and G. D. Peng, “Dense-WDM soliton systems using channel-isolating notch filters (‘soliton rail’),” in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

J. McEntee, “Solitons go the distance in ultralong-haul DWDM,” FibreSyst. Eur., Jan. 19–21 (2003).

G. P. Agrawal, Fiber-Optics Communication Systems (Wiley, New York, 1997).

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

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Figures (8)

Fig. 1
Fig. 1

Temporal position of the soliton’s center versus the propagation distance in the single-channel model with and without the lumped NFs in the case in which the soliton is originally given a large inverse-velocity shift c=0.1, ten times that generating the actual Gordon–Haus jitter (in physical units, it corresponds to the instantaneous shift of the soliton’s central frequency by ≃6 GHz).

Fig. 2
Fig. 2

Transmission of the soliton perturbed by the periodically injected noise: (a) without filters, (b) with the lumped NFs inserted.

Fig. 3
Fig. 3

Comparison of the rms temporal shift of the soliton’s center as a function of the propagation distance averaged over many realizations of the random noise, with and without the lumped NFs. The total propagation distance corresponds to 12,000 km.

Fig. 4
Fig. 4

Eye diagram (superposition of the soliton profiles corresponding to different realizations of the random perturbations) at point z=140, which corresponds to 8400 km in physical units (at this point, the BER in the notched-filtered model attains the value 10-9; see Fig. 5): (a) without filters, (b) with the lumped NFs.

Fig. 5
Fig. 5

Standard BER characteristic corresponding to the transmission of a soliton without and with the notch filters versus the propagation distance z=140 corresponding to 8400 km.

Fig. 6
Fig. 6

Interaction of two solitons in the single-channel model with the initial separation between the solitons Δτ=10.8 (tantamount to 182 ps in physical units) and zero initial phase difference: (a) without filters, (b) with the lumped NFs, (c) the initial and final shapes of the wave field in the latter case.

Fig. 7
Fig. 7

Collision of two solitons belonging to different channels with the inverse-group-velocity difference of 2.4 in normalized units (5.4 ps/km in physical units) between them, which corresponds to the frequency separation of 180 GHz between adjacent channels in the DWDM system and with the transmission distance z=100 corresponding to 6000 km. The u component of the field is shown: (a) collision without filters, (b) collision between solitons belonging to channels supported by the NFs, (c) comparison between initial (no collision) and final configurations of the wave fields.

Fig. 8
Fig. 8

Factors demonstrating the reduction by the NFs of the eventual temporal shift of solitons after the interchannel collision (squares) and of the energy lost to the shadow generation (triangles) as functions of the separation between the channels (which is shown as the inverse group-velocity difference between them). The continuous curves are interpolations based on data points. The range of the inverse-group-velocity difference from 1.0 to 1.8, comprised by this figure, corresponds to the frequency separation between the channels ranging from 75 to 135 GHz.

Tables (1)

Tables Icon

Table 1 Effects of Collisions between Solitons Belonging to Different Channels and Their Suppression by the NFa

Equations (6)

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

iuz+12uττ+(|u|2+2|v|2)u=i-γ+Γnδ(z-nza)u-iF+, - exp(iΩτ)-+exp(±iΩτ)u(τ)dτ,
i(vz+cvτ)+12vττ+(|v|2+2|u|2)v=i-γ+Γnδ(z-nza)v-iF+, - exp(iΩτ)-+exp(±iΩτ)v(τ)dτ,
-2πiF+, -δ(ω±Ω){uˆ(z, ω=Ω),vˆ(z, ω=Ω)},
-iεnδ(z-nza)+, -NΔΩ(ω±Ω){uˆ(z, ω),vˆ(z, ω)};
NΔΩ(ω)0if|ω|>ΔΩ,NΔΩ(ω)1if|ω|<ΔΩ,
BER=12 erfcS2N,

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