Abstract

Applying the complete basis of chirped Gauss–Hermite functions, we present a theory of dispersion-managed (DM) solitons in communication systems with in-line filtering. In specific practical example we show that a DM soliton can be well described by a few modes in such an expansion (with the zero Gaussian mode), justifying the use of a Gaussian trial function in the previously developed variational approach. The method presented here is a regular way to estimate the accuracy of the approximate variational approach. An analytical formula to describe the dependence of excess gain on filter bandwidth and map parameters is derived. It is shown that use of the filters additionally increases the peak power of a DM soliton compared with that of a DM system without in-line filtering. The suggested expansion also presents a systematic method to account for the effect of practical perturbations. Theoretical results are verified by numerical simulations.

© 1999 Optical Society of America

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  1. L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, I. P. Kaminow and T. L. Koch eds. (Academic, San Diego, Calif., 1997), Vol. IIIA, Chap. 12, p. 373.
  2. L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, “Demonstration of soliton WDM transmission at up to 8 10 Gbit/s, error-free over transoceanic distances,” in Optical Fabrication and Testing, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper PD22.
  3. L. F. Mollenauer, S. G. Evangelides, Jr., and H. A. Haus, “Long-distance soliton propagation using lumped amplifiers and dispersion-shifted fiber,” J. Lightwave Technol. 9, 194–201 (1994).
    [CrossRef]
  4. A. Hasegawa and Y. Kodama, “Guiding-center soliton in optical fibers,” Opt. Lett. 15, 1443–1445 (1990); “Guiding-center soliton,” Phys. Rev. Lett. 66, 161–164 (1991).
    [CrossRef] [PubMed]
  5. K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photonics Technol. Lett. 3, 369–371 (1991).
    [CrossRef]
  6. C. Lin, H. Kogelnik, and L. G. Cohen, “Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3–1.7-μm spectral region,” Opt. Lett. 5, 476–479 (1980).
    [CrossRef] [PubMed]
  7. A. D. Ellis and D. M. Spirit, “Unrepeated transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
    [CrossRef]
  8. D. M. Rothnie and J. E. Midwinter, “Improved standard fibre performance by positioning the dispersion compensating fibre,” Electron. Lett. 32, 1907–1911 (1996).
    [CrossRef]
  9. C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
    [CrossRef]
  10. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
    [CrossRef]
  11. N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
    [CrossRef]
  12. I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–330 (1996); “Breathing solitons in optical fiber links,” JETP Lett. 63, 861–865 (1996).
    [CrossRef]
  13. M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
    [CrossRef]
  14. M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
    [CrossRef]
  15. N. S. Bergano, C. Davidson, M. Ma, A. Pilipetskii, S. Evangelides, H. Kidorf, J. Darcie, E. Golovchenko, K. Rottwitt, P. Corbett, R. Menges, M. Mils, B. Pedersen, D. Peckham, A. Abramov, and A. Vengsarkar, “320 Gb/s WDM transmission (64×5 Gb/s) over 7200 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), postdeadline paper PD12.
  16. N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, “4×SONET OC-192 field installed dispersion managed soliton system over 450 km of standard fiber in the 1550 nm erbium band,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD19.
  17. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
    [CrossRef]
  18. R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
    [CrossRef]
  19. M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
    [CrossRef]
  20. M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fibre and periodic dispersion compensation,” presented at the 1997 European Conference on Optical Communications, Edinburgh, September 19–23, 1997.
  21. D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, “320 Gbit/s soliton WDM transmission over 1100 km with 100 km dispersion-compensated spans of standard fibre,” presented at the 1997 European Conference on Optical Communications, Edinburgh, September 19–23, 1997.
  22. N. S. Bergano, C. R. Davidson, A. Mills, P. C. Corbett, S. G. Evangelides, B. Pedersen, R. Menges, J. L. Ztskind, J. W. Sulhoff, A. K. Srivastava, C. Wolf, and J. Judkins, “Long-haul WDM transmission using optimum channel modulation: a 160 Gb/s (32×5 Gb/s) 9, 3000 km demonstration,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD16.
  23. O. Leclerc and E. Desurvire, “Performance limits in 80–160 Gbit/s (N×20 Gbit/s) regenerated WDM soliton transmission,” presented at the 1997 European Conference on Optical Communications, Edinburgh, September 19–23, 1997.
  24. E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
    [CrossRef] [PubMed]
  25. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793–795 (1997).
    [CrossRef] [PubMed]
  26. M. Matsumoto, “Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,” Electron. Lett. 33, 1718–1719 (1997).
    [CrossRef]
  27. S. Wabnitz, “Stabilization of sliding-filtered soliton WDM transmissions by dispersion compensating fibers,” Opt. Lett. 21, 638–640 (1996).
    [CrossRef] [PubMed]
  28. A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
    [CrossRef]
  29. M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
    [CrossRef]
  30. D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
    [CrossRef]
  31. S. K. Turitsyn and V. K. Mezentsev, “Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions,” JETP Lett. 67, 640–645 (1998).
    [CrossRef]
  32. F. Matera and M. Settembre, “Comparison of the performance of optically amplified transmission systems,” J. Lightwave Technol. 14, 1–12 (1996).
    [CrossRef]
  33. A. Mattheus and S. K. Turitsyn, “Pulse interaction in nonlinear communication systems based on standard monomode fibres,” presented at the 1993 European Conference on Optical, Montreux, Switzerland, September 12–16, 1993.
  34. F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fibre at 1.55 μm and the use of dispersion compensation,” IEEE J. Lightwave Technol. 13, 1955–1963 (1995).
    [CrossRef]
  35. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1984 (1997).
    [CrossRef]
  36. T. Georges and B. Charbonnier, “Reduction of the dispersive wave in periodically amplified links with initially chirped solitons,” IEEE Photon. Technol. Lett. 9, 127–128 (1997).
    [CrossRef]
  37. T. Georges and F. Favre, “Transmission systems based on dispersion-managed solitons: theory and experiment,” presented at the Second International Symposium on Physics and Applications of Optical Solitons in Fibers, Kyoto, Japan, November, 1997.
  38. T. Georges, “Soliton interaction in dispersion-managed links,” J. Opt. Soc. Am. B 15, 1553–1560 (1998).
    [CrossRef]
  39. T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).
    [CrossRef] [PubMed]
  40. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1996); “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
    [CrossRef]
  41. J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, “Experimental demonstration of soliton transmission over 28 Mm using mostly normal dispersion fiber,” IEEE Photon. Technol. Lett. 9, 130–132 (1997).
    [CrossRef]
  42. M. Matsumoto and H. A. Haus, “Stretched-pulse optical fiber communications,” IEEE Photon. Technol. Lett. 9, 785–788 (1997).
    [CrossRef]
  43. S. K. Turitsyn, “Theory of averaged pulse propagation in high-bit-rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–851 (1997).
    [CrossRef]
  44. T. S. Yang and W. L. Kath, “Analysis of enhanced-power solitons in dispersion-managed optical fibers,” Opt. Lett. 22, 985–987 (1997).
    [CrossRef] [PubMed]
  45. D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
    [CrossRef]
  46. M. Matsumoto, “Theory of stretched-pulse transmission in dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
    [CrossRef] [PubMed]
  47. A. Sahara, H. Kubota, and M. Nakazawa, “Optimum fiber dispersion for two-step dispersion-allocated optical soliton, RZ at zero GVD and NRZ systems,” IEEE Photon. Technol. Lett. 9, 1179–1181 (1997).
    [CrossRef]
  48. S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion managed optical fibers,” Opt. Lett. 22, 372–375 (1997).
    [CrossRef] [PubMed]
  49. A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197–213 (1997).
    [CrossRef]
  50. E. Shapiro and S. K. Turitsyn, “Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management,” Opt. Lett. 22, 1544–1547 (1997).
    [CrossRef]
  51. E. Shapiro and S. K. Turitsyn, “Enhanced power breathing soliton in communication systems with dispersion management,” Phys. Rev. E 56, R4951–R4954 (1997).
    [CrossRef]
  52. J. N. Kutz, P. Holmes, S. G. Evangelides, Jr., and J. P. Gordon, “Hamiltonian dynamics of dispersion managed breathers,” J. Opt. Soc. Am. B 15, 87–96 (1997).
    [CrossRef]
  53. J. N. Kutz and S. G. Evangelides, Jr., “Dispersion managed breathers with average normal dispersion,” Opt. Lett. 23, 685–688 (1998).
    [CrossRef]
  54. J. N. Kutz and A. Wai, “Noise-induced amplitude and chirp jitter in dispersion-managed soliton communications,” Opt. Lett. 23, 1022–1025 (1998).
    [CrossRef]
  55. T. S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett. 23, 597–599 (1998).
    [CrossRef]
  56. V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 22, 1609–1611 (1997).
    [CrossRef]
  57. V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed soliton at normal average dispersion,” Opt. Lett. 23, 609–611 (1998).
    [CrossRef]
  58. S. K. Turitsyn and E. G. Shapiro, “Variational approach to the design of optical communication systems with dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 151–168 (1998).
    [CrossRef]
  59. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
    [CrossRef]
  60. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
    [CrossRef]
  61. J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
    [CrossRef] [PubMed]
  62. M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
    [CrossRef]
  63. S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
    [CrossRef]
  64. S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998).
    [CrossRef]
  65. S. K. Turitsyn, N. F. Smyth, and E. G. Turitsyna, “Solitary waves in nonlinear dispersive systems with zero average dispersion,” Phys. Rev. E 58, R44–R48 (1998).
    [CrossRef]
  66. S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
    [CrossRef]
  67. T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
    [CrossRef]
  68. T. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
    [CrossRef]
  69. T. Lakoba and D. J. Kaup, “Hermite–Gaussian expansion for pulse propagation in strongly dispersion managed fibers,” Phys. Rev. E 58, 6728–6736 (1998).
    [CrossRef]
  70. S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
    [CrossRef]
  71. S. K. Turitsyn, “Self-similar dynamics and oscillatory tails of a breathing soliton in systems with varying dispersion,” Phys. Rev. E 58, R1256–R1260 (1998).
    [CrossRef]
  72. V. E. Zakharov and A. B. Shabat, “Exact theory of two dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971).
  73. P. Lazaridis, G. Debarge, and P. Gallion, “Exact solutions for linear propagation of chirped pulses using a chirped Gauss–Hermite orthogonal basis,” Opt. Lett. 22, 685–687 (1997).
    [CrossRef] [PubMed]
  74. M. Matsumoto, “Effect of guiding filters on stretched-pulse transmission in dispersion-managed fibers,” Electron. Lett. 33, 1718–1720 (1997).
    [CrossRef]
  75. 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]
  76. J. P. Gordon and L. F. Mollenauer, “Scheme for the characterization of dispersion-managed solitons,” Opt. Lett. 24, 223–225 (1999).
    [CrossRef]
  77. S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, “Dispersion-managed solitons and optimization of the dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 384–452 (1998).
    [CrossRef]
  78. A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, “Soliton transmission control,” Opt. Lett. 16, 1841–1843 (1991); “Modulation and filtering control of soliton transmission,” J. Opt. Soc. Am. B 9, 1350–1357 (1992).
    [CrossRef] [PubMed]

1999 (2)

1998 (18)

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, “Dispersion-managed solitons and optimization of the dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 384–452 (1998).
[CrossRef]

V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed soliton at normal average dispersion,” Opt. Lett. 23, 609–611 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Variational approach to the design of optical communication systems with dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 151–168 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998).
[CrossRef]

S. K. Turitsyn, N. F. Smyth, and E. G. Turitsyna, “Solitary waves in nonlinear dispersive systems with zero average dispersion,” Phys. Rev. E 58, R44–R48 (1998).
[CrossRef]

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Hermite–Gaussian expansion for pulse propagation in strongly dispersion managed fibers,” Phys. Rev. E 58, 6728–6736 (1998).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
[CrossRef]

S. K. Turitsyn, “Self-similar dynamics and oscillatory tails of a breathing soliton in systems with varying dispersion,” Phys. Rev. E 58, R1256–R1260 (1998).
[CrossRef]

T. Georges, “Soliton interaction in dispersion-managed links,” J. Opt. Soc. Am. B 15, 1553–1560 (1998).
[CrossRef]

S. K. Turitsyn and V. K. Mezentsev, “Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions,” JETP Lett. 67, 640–645 (1998).
[CrossRef]

J. N. Kutz and S. G. Evangelides, Jr., “Dispersion managed breathers with average normal dispersion,” Opt. Lett. 23, 685–688 (1998).
[CrossRef]

J. N. Kutz and A. Wai, “Noise-induced amplitude and chirp jitter in dispersion-managed soliton communications,” Opt. Lett. 23, 1022–1025 (1998).
[CrossRef]

T. S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett. 23, 597–599 (1998).
[CrossRef]

1997 (26)

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 22, 1609–1611 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1984 (1997).
[CrossRef]

T. Georges and B. Charbonnier, “Reduction of the dispersive wave in periodically amplified links with initially chirped solitons,” IEEE Photon. Technol. Lett. 9, 127–128 (1997).
[CrossRef]

T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).
[CrossRef] [PubMed]

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, “Experimental demonstration of soliton transmission over 28 Mm using mostly normal dispersion fiber,” IEEE Photon. Technol. Lett. 9, 130–132 (1997).
[CrossRef]

M. Matsumoto and H. A. Haus, “Stretched-pulse optical fiber communications,” IEEE Photon. Technol. Lett. 9, 785–788 (1997).
[CrossRef]

S. K. Turitsyn, “Theory of averaged pulse propagation in high-bit-rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–851 (1997).
[CrossRef]

T. S. Yang and W. L. Kath, “Analysis of enhanced-power solitons in dispersion-managed optical fibers,” Opt. Lett. 22, 985–987 (1997).
[CrossRef] [PubMed]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

M. Matsumoto, “Theory of stretched-pulse transmission in dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
[CrossRef] [PubMed]

A. Sahara, H. Kubota, and M. Nakazawa, “Optimum fiber dispersion for two-step dispersion-allocated optical soliton, RZ at zero GVD and NRZ systems,” IEEE Photon. Technol. Lett. 9, 1179–1181 (1997).
[CrossRef]

S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion managed optical fibers,” Opt. Lett. 22, 372–375 (1997).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197–213 (1997).
[CrossRef]

E. Shapiro and S. K. Turitsyn, “Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management,” Opt. Lett. 22, 1544–1547 (1997).
[CrossRef]

E. Shapiro and S. K. Turitsyn, “Enhanced power breathing soliton in communication systems with dispersion management,” Phys. Rev. E 56, R4951–R4954 (1997).
[CrossRef]

J. N. Kutz, P. Holmes, S. G. Evangelides, Jr., and J. P. Gordon, “Hamiltonian dynamics of dispersion managed breathers,” J. Opt. Soc. Am. B 15, 87–96 (1997).
[CrossRef]

E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
[CrossRef] [PubMed]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793–795 (1997).
[CrossRef] [PubMed]

M. Matsumoto, “Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,” Electron. Lett. 33, 1718–1719 (1997).
[CrossRef]

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

P. Lazaridis, G. Debarge, and P. Gallion, “Exact solutions for linear propagation of chirped pulses using a chirped Gauss–Hermite orthogonal basis,” Opt. Lett. 22, 685–687 (1997).
[CrossRef] [PubMed]

M. Matsumoto, “Effect of guiding filters on stretched-pulse transmission in dispersion-managed fibers,” Electron. Lett. 33, 1718–1720 (1997).
[CrossRef]

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
[CrossRef]

1996 (6)

M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
[CrossRef]

S. Wabnitz, “Stabilization of sliding-filtered soliton WDM transmissions by dispersion compensating fibers,” Opt. Lett. 21, 638–640 (1996).
[CrossRef] [PubMed]

D. M. Rothnie and J. E. Midwinter, “Improved standard fibre performance by positioning the dispersion compensating fibre,” Electron. Lett. 32, 1907–1911 (1996).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
[CrossRef]

F. Matera and M. Settembre, “Comparison of the performance of optically amplified transmission systems,” J. Lightwave Technol. 14, 1–12 (1996).
[CrossRef]

1995 (5)

F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fibre at 1.55 μm and the use of dispersion compensation,” IEEE J. Lightwave Technol. 13, 1955–1963 (1995).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
[CrossRef]

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

1994 (3)

L. F. Mollenauer, S. G. Evangelides, Jr., and H. A. Haus, “Long-distance soliton propagation using lumped amplifiers and dispersion-shifted fiber,” J. Lightwave Technol. 9, 194–201 (1994).
[CrossRef]

R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
[CrossRef]

A. D. Ellis and D. M. Spirit, “Unrepeated transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

1991 (1)

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photonics Technol. Lett. 3, 369–371 (1991).
[CrossRef]

1983 (1)

1980 (1)

1971 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971).

Aceves, A. B.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
[CrossRef]

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

Bennion, I.

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Berntson, A.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

Blow, K. J.

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photonics Technol. Lett. 3, 369–371 (1991).
[CrossRef]

Breuer, D.

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

Carter, G. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, “Experimental demonstration of soliton transmission over 28 Mm using mostly normal dispersion fiber,” IEEE Photon. Technol. Lett. 9, 130–132 (1997).
[CrossRef]

E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
[CrossRef] [PubMed]

Charbonnier, B.

T. Georges and B. Charbonnier, “Reduction of the dispersive wave in periodically amplified links with initially chirped solitons,” IEEE Photon. Technol. Lett. 9, 127–128 (1997).
[CrossRef]

Chernikov, S. V.

R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
[CrossRef]

Cohen, L. G.

Cole, M. J.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Das, C.

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

Debarge, G.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1984 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fibre at 1.55 μm and the use of dispersion compensation,” IEEE J. Lightwave Technol. 13, 1955–1963 (1995).
[CrossRef]

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photonics Technol. Lett. 3, 369–371 (1991).
[CrossRef]

Durkin, M.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

Ellis, A. D.

A. D. Ellis and D. M. Spirit, “Unrepeated transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

Evangelides Jr., S. G.

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1984 (1997).
[CrossRef]

F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fibre at 1.55 μm and the use of dispersion compensation,” IEEE J. Lightwave Technol. 13, 1955–1963 (1995).
[CrossRef]

Franco, P.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Gabitov, I.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

Gallion, P.

Gaubatz, U.

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

Geiger, H.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Georges, T.

T. Georges, “Soliton interaction in dispersion-managed links,” J. Opt. Soc. Am. B 15, 1553–1560 (1998).
[CrossRef]

T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).
[CrossRef] [PubMed]

T. Georges and B. Charbonnier, “Reduction of the dispersive wave in periodically amplified links with initially chirped solitons,” IEEE Photon. Technol. Lett. 9, 127–128 (1997).
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

Gottwald, E.

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

Grandi, E.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Grigoryan, V. S.

Grudinin, A. B.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Gusmeroli, V.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Hasegawa, A.

S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion managed optical fibers,” Opt. Lett. 22, 372–375 (1997).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197–213 (1997).
[CrossRef]

Haus, H. A.

M. Matsumoto and H. A. Haus, “Stretched-pulse optical fiber communications,” IEEE Photon. Technol. Lett. 9, 785–788 (1997).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
[CrossRef]

L. F. Mollenauer, S. G. Evangelides, Jr., and H. A. Haus, “Long-distance soliton propagation using lumped amplifiers and dispersion-shifted fiber,” J. Lightwave Technol. 9, 194–201 (1994).
[CrossRef]

Holmes, P.

Ibsen, M.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Ippen, E. P.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
[CrossRef]

Jacob, J. M.

E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
[CrossRef] [PubMed]

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, “Experimental demonstration of soliton transmission over 28 Mm using mostly normal dispersion fiber,” IEEE Photon. Technol. Lett. 9, 130–132 (1997).
[CrossRef]

Jones, C. K. R. T.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
[CrossRef]

Juergensen, K.

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

Kashyap, R.

R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
[CrossRef]

Kath, W. L.

Kaup, D. J.

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Hermite–Gaussian expansion for pulse propagation in strongly dispersion managed fibers,” Phys. Rev. E 58, 6728–6736 (1998).
[CrossRef]

Knox, F. M.

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1984 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fibre at 1.55 μm and the use of dispersion compensation,” IEEE J. Lightwave Technol. 13, 1955–1963 (1995).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197–213 (1997).
[CrossRef]

Kogelnik, H.

Kotten, K.

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

Kubota, H.

A. Sahara, H. Kubota, and M. Nakazawa, “Optimum fiber dispersion for two-step dispersion-allocated optical soliton, RZ at zero GVD and NRZ systems,” IEEE Photon. Technol. Lett. 9, 1179–1181 (1997).
[CrossRef]

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
[CrossRef]

M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
[CrossRef]

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

Kueppers, F.

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

Kumar, S.

Küppers, F.

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

Kutz, J. N.

Laedke, E. W.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

Lakoba, T.

T. Lakoba and D. J. Kaup, “Hermite–Gaussian expansion for pulse propagation in strongly dispersion managed fibers,” Phys. Rev. E 58, 6728–6736 (1998).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

Laming, R. I.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Lazaridis, P.

Lederer, F.

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
[CrossRef]

Lin, C.

Loh, W. H.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Malomed, B. A.

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
[CrossRef]

Mamyshev, P. V.

Maruta, A.

A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197–213 (1997).
[CrossRef]

Matera, F.

F. Matera and M. Settembre, “Comparison of the performance of optically amplified transmission systems,” J. Lightwave Technol. 14, 1–12 (1996).
[CrossRef]

Matsumoto, M.

M. Matsumoto and H. A. Haus, “Stretched-pulse optical fiber communications,” IEEE Photon. Technol. Lett. 9, 785–788 (1997).
[CrossRef]

M. Matsumoto, “Theory of stretched-pulse transmission in dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
[CrossRef] [PubMed]

M. Matsumoto, “Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,” Electron. Lett. 33, 1718–1719 (1997).
[CrossRef]

M. Matsumoto, “Effect of guiding filters on stretched-pulse transmission in dispersion-managed fibers,” Electron. Lett. 33, 1718–1720 (1997).
[CrossRef]

Mattheus, A.

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

McKee, P. F.

R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
[CrossRef]

Menyuk, C. R.

Mezentsev, V. K.

S. K. Turitsyn and V. K. Mezentsev, “Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions,” JETP Lett. 67, 640–645 (1998).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
[CrossRef]

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, “Dispersion-managed solitons and optimization of the dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 384–452 (1998).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

Midwinter, J. E.

D. M. Rothnie and J. E. Midwinter, “Improved standard fibre performance by positioning the dispersion compensating fibre,” Electron. Lett. 32, 1907–1911 (1996).
[CrossRef]

Mollenauer, L. F.

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

Musher, S. L.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

Nakazawa, M.

A. Sahara, H. Kubota, and M. Nakazawa, “Optimum fiber dispersion for two-step dispersion-allocated optical soliton, RZ at zero GVD and NRZ systems,” IEEE Photon. Technol. Lett. 9, 1179–1181 (1997).
[CrossRef]

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
[CrossRef]

M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
[CrossRef]

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
[CrossRef]

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

Pilipetskii, A. N.

Romagnoli, M.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Rothnie, D. M.

D. M. Rothnie and J. E. Midwinter, “Improved standard fibre performance by positioning the dispersion compensating fibre,” Electron. Lett. 32, 1907–1911 (1996).
[CrossRef]

Sahara, A.

A. Sahara, H. Kubota, and M. Nakazawa, “Optimum fiber dispersion for two-step dispersion-allocated optical soliton, RZ at zero GVD and NRZ systems,” IEEE Photon. Technol. Lett. 9, 1179–1181 (1997).
[CrossRef]

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
[CrossRef]

Schäfer, T.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
[CrossRef]

Schiffini, A.

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

Set, S. Y.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Settembre, M.

F. Matera and M. Settembre, “Comparison of the performance of optically amplified transmission systems,” J. Lightwave Technol. 14, 1–12 (1996).
[CrossRef]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971).

Shapiro, E.

E. Shapiro and S. K. Turitsyn, “Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management,” Opt. Lett. 22, 1544–1547 (1997).
[CrossRef]

E. Shapiro and S. K. Turitsyn, “Enhanced power breathing soliton in communication systems with dispersion management,” Phys. Rev. E 56, R4951–R4954 (1997).
[CrossRef]

Shapiro, E. G.

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, “Dispersion-managed solitons and optimization of the dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 384–452 (1998).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Variational approach to the design of optical communication systems with dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 151–168 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998).
[CrossRef]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

Smith, N.

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Smith, N. J.

Smyth, N. F.

S. K. Turitsyn, N. F. Smyth, and E. G. Turitsyna, “Solitary waves in nonlinear dispersive systems with zero average dispersion,” Phys. Rev. E 58, R44–R48 (1998).
[CrossRef]

Spatschek, K. H.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

Spirit, D. M.

A. D. Ellis and D. M. Spirit, “Unrepeated transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

Suzuki, K.

M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
[CrossRef]

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

Taga, H.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

Tamura, K.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
[CrossRef]

Taylor, J. R.

R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn and V. K. Mezentsev, “Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions,” JETP Lett. 67, 640–645 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Variational approach to the design of optical communication systems with dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 151–168 (1998).
[CrossRef]

T. S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett. 23, 597–599 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998).
[CrossRef]

S. K. Turitsyn, N. F. Smyth, and E. G. Turitsyna, “Solitary waves in nonlinear dispersive systems with zero average dispersion,” Phys. Rev. E 58, R44–R48 (1998).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
[CrossRef]

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, “Dispersion-managed solitons and optimization of the dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 384–452 (1998).
[CrossRef]

S. K. Turitsyn, “Self-similar dynamics and oscillatory tails of a breathing soliton in systems with varying dispersion,” Phys. Rev. E 58, R1256–R1260 (1998).
[CrossRef]

E. Shapiro and S. K. Turitsyn, “Enhanced power breathing soliton in communication systems with dispersion management,” Phys. Rev. E 56, R4951–R4954 (1997).
[CrossRef]

E. Shapiro and S. K. Turitsyn, “Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management,” Opt. Lett. 22, 1544–1547 (1997).
[CrossRef]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

S. K. Turitsyn, “Theory of averaged pulse propagation in high-bit-rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–851 (1997).
[CrossRef]

Turitsyna, E. G.

S. K. Turitsyn, N. F. Smyth, and E. G. Turitsyna, “Solitary waves in nonlinear dispersive systems with zero average dispersion,” Phys. Rev. E 58, R44–R48 (1998).
[CrossRef]

Uzunov, I. M.

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
[CrossRef]

Wabnitz, S.

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
[CrossRef]

S. Wabnitz, “Stabilization of sliding-filtered soliton WDM transmissions by dispersion compensating fibers,” Opt. Lett. 21, 638–640 (1996).
[CrossRef] [PubMed]

Wai, A.

Wald, M.

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
[CrossRef]

Weiske, C. J.

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

Yamada, E.

M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
[CrossRef]

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

Yang, J.

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
[CrossRef]

Yang, T. S.

Yu, T.

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971).

Zervas, M. N.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Zharnitsky, V.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
[CrossRef]

Electron. Lett. (15)

A. D. Ellis and D. M. Spirit, “Unrepeated transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

D. M. Rothnie and J. E. Midwinter, “Improved standard fibre performance by positioning the dispersion compensating fibre,” Electron. Lett. 32, 1907–1911 (1996).
[CrossRef]

C. Das, U. Gaubatz, E. Gottwald, K. Kotten, F. Küppers, A. Mattheus, and C. J. Weiske, “Straightforward upgrading of transmission systems to 4×10 Gbit/s through 617 km and 8×10 Gbit/s through 412 km of SMF,” Electron. Lett. 31, 305–307 (1995).
[CrossRef]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2028 (1995).
[CrossRef]

N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fiber transmission line,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

R. Kashyap, S. V. Chernikov, P. F. McKee, and J. R. Taylor, “30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbit/s in optical fibers using an all photoinduced chirped reflection grating,” Electron. Lett. 30, 1078–1080 (1994).
[CrossRef]

M. Nakazawa, K. Suzuki, H. Kubota, and E. Yamada, “60 G/bits WDM (20 G/bits × 3 unequally spaced channels) soliton transmission over 10000 km using in-line synchronous modulation and optical filtering,” Electron. Lett. 32, 1686–1688 (1996).
[CrossRef]

M. Matsumoto, “Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,” Electron. Lett. 33, 1718–1719 (1997).
[CrossRef]

A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
[CrossRef]

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, and V. Gusmeroli, “Broadband dispersion-compensating chirped fibre gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 μm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Shape of stationary pulse in strong dispersion management regime,” Electron. Lett. 34, 1124–1126 (1998).
[CrossRef]

M. Matsumoto, “Effect of guiding filters on stretched-pulse transmission in dispersion-managed fibers,” Electron. Lett. 33, 1718–1720 (1997).
[CrossRef]

IEEE J. Lightwave Technol. (1)

F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fibre at 1.55 μm and the use of dispersion compensation,” IEEE J. Lightwave Technol. 13, 1955–1963 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31, 591–603 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (6)

T. Georges and B. Charbonnier, “Reduction of the dispersive wave in periodically amplified links with initially chirped solitons,” IEEE Photon. Technol. Lett. 9, 127–128 (1997).
[CrossRef]

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, “Marked increase in the power margin through the use of a dispersion-allocated soliton,” IEEE Photon. Technol. Lett. 8, 452–454 (1996).
[CrossRef]

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of periodically dispersion compensated breathing soliton transmissions,” IEEE Photon. Technol. Lett. 9, 1670–1672 (1997).
[CrossRef]

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, “Experimental demonstration of soliton transmission over 28 Mm using mostly normal dispersion fiber,” IEEE Photon. Technol. Lett. 9, 130–132 (1997).
[CrossRef]

M. Matsumoto and H. A. Haus, “Stretched-pulse optical fiber communications,” IEEE Photon. Technol. Lett. 9, 785–788 (1997).
[CrossRef]

A. Sahara, H. Kubota, and M. Nakazawa, “Optimum fiber dispersion for two-step dispersion-allocated optical soliton, RZ at zero GVD and NRZ systems,” IEEE Photon. Technol. Lett. 9, 1179–1181 (1997).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photonics Technol. Lett. 3, 369–371 (1991).
[CrossRef]

J. Lightwave Technol. (2)

F. Matera and M. Settembre, “Comparison of the performance of optically amplified transmission systems,” J. Lightwave Technol. 14, 1–12 (1996).
[CrossRef]

L. F. Mollenauer, S. G. Evangelides, Jr., and H. A. Haus, “Long-distance soliton propagation using lumped amplifiers and dispersion-shifted fiber,” J. Lightwave Technol. 9, 194–201 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

JETP Lett. (2)

S. K. Turitsyn, “Theory of averaged pulse propagation in high-bit-rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–851 (1997).
[CrossRef]

S. K. Turitsyn and V. K. Mezentsev, “Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions,” JETP Lett. 67, 640–645 (1998).
[CrossRef]

Opt. Commun. (3)

D. Breuer, K. Juergensen, F. Kueppers, A. Mattheus, I. Gabitov, and S. K. Turitsyn, “Optimal schemes for dispersion compensation of standard monomode fiber based links,” Opt. Commun. 140, 15–18 (1997).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–142 (1998).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366–374 (1998).
[CrossRef]

Opt. Fiber Technol.: Mater., Devices Syst. (3)

S. K. Turitsyn and E. G. Shapiro, “Variational approach to the design of optical communication systems with dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 151–168 (1998).
[CrossRef]

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, “Dispersion-managed solitons and optimization of the dispersion management,” Opt. Fiber Technol.: Mater., Devices Syst. 4, 384–452 (1998).
[CrossRef]

A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197–213 (1997).
[CrossRef]

Opt. Lett. (22)

E. Shapiro and S. K. Turitsyn, “Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management,” Opt. Lett. 22, 1544–1547 (1997).
[CrossRef]

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
[CrossRef] [PubMed]

J. N. Kutz and S. G. Evangelides, Jr., “Dispersion managed breathers with average normal dispersion,” Opt. Lett. 23, 685–688 (1998).
[CrossRef]

J. N. Kutz and A. Wai, “Noise-induced amplitude and chirp jitter in dispersion-managed soliton communications,” Opt. Lett. 23, 1022–1025 (1998).
[CrossRef]

T. S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett. 23, 597–599 (1998).
[CrossRef]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 22, 1609–1611 (1997).
[CrossRef]

V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed soliton at normal average dispersion,” Opt. Lett. 23, 609–611 (1998).
[CrossRef]

T. S. Yang and W. L. Kath, “Analysis of enhanced-power solitons in dispersion-managed optical fibers,” Opt. Lett. 22, 985–987 (1997).
[CrossRef] [PubMed]

D. Breuer, F. Kueppers, A. Mattheus, E. G. Shapiro, I. Gabitov, and S. K. Turitsyn, “Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifying spacing,” Opt. Lett. 22, 546–549 (1997).
[CrossRef]

M. Matsumoto, “Theory of stretched-pulse transmission in dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
[CrossRef] [PubMed]

T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).
[CrossRef] [PubMed]

S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion managed optical fibers,” Opt. Lett. 22, 372–375 (1997).
[CrossRef] [PubMed]

P. Lazaridis, G. Debarge, and P. Gallion, “Exact solutions for linear propagation of chirped pulses using a chirped Gauss–Hermite orthogonal basis,” Opt. Lett. 22, 685–687 (1997).
[CrossRef] [PubMed]

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]

J. P. Gordon and L. F. Mollenauer, “Scheme for the characterization of dispersion-managed solitons,” Opt. Lett. 24, 223–225 (1999).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse,” Opt. Lett. 23, 1351–1353 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998).
[CrossRef]

S. Wabnitz, “Stabilization of sliding-filtered soliton WDM transmissions by dispersion compensating fibers,” Opt. Lett. 21, 638–640 (1996).
[CrossRef] [PubMed]

C. Lin, H. Kogelnik, and L. G. Cohen, “Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3–1.7-μm spectral region,” Opt. Lett. 5, 476–479 (1980).
[CrossRef] [PubMed]

E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
[CrossRef] [PubMed]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793–795 (1997).
[CrossRef] [PubMed]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1984 (1997).
[CrossRef]

Phys. Rev. E (5)

S. K. Turitsyn, N. F. Smyth, and E. G. Turitsyna, “Solitary waves in nonlinear dispersive systems with zero average dispersion,” Phys. Rev. E 58, R44–R48 (1998).
[CrossRef]

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R52 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, “Hermite–Gaussian expansion for pulse propagation in strongly dispersion managed fibers,” Phys. Rev. E 58, 6728–6736 (1998).
[CrossRef]

S. K. Turitsyn, “Self-similar dynamics and oscillatory tails of a breathing soliton in systems with varying dispersion,” Phys. Rev. E 58, R1256–R1260 (1998).
[CrossRef]

E. Shapiro and S. K. Turitsyn, “Enhanced power breathing soliton in communication systems with dispersion management,” Phys. Rev. E 56, R4951–R4954 (1997).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971).

Other (14)

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, “Soliton transmission control,” Opt. Lett. 16, 1841–1843 (1991); “Modulation and filtering control of soliton transmission,” J. Opt. Soc. Am. B 9, 1350–1357 (1992).
[CrossRef] [PubMed]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1996); “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
[CrossRef]

T. Georges and F. Favre, “Transmission systems based on dispersion-managed solitons: theory and experiment,” presented at the Second International Symposium on Physics and Applications of Optical Solitons in Fibers, Kyoto, Japan, November, 1997.

A. Mattheus and S. K. Turitsyn, “Pulse interaction in nonlinear communication systems based on standard monomode fibres,” presented at the 1993 European Conference on Optical, Montreux, Switzerland, September 12–16, 1993.

A. Hasegawa and Y. Kodama, “Guiding-center soliton in optical fibers,” Opt. Lett. 15, 1443–1445 (1990); “Guiding-center soliton,” Phys. Rev. Lett. 66, 161–164 (1991).
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, I. P. Kaminow and T. L. Koch eds. (Academic, San Diego, Calif., 1997), Vol. IIIA, Chap. 12, p. 373.

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, “Demonstration of soliton WDM transmission at up to 8 10 Gbit/s, error-free over transoceanic distances,” in Optical Fabrication and Testing, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper PD22.

I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–330 (1996); “Breathing solitons in optical fiber links,” JETP Lett. 63, 861–865 (1996).
[CrossRef]

N. S. Bergano, C. Davidson, M. Ma, A. Pilipetskii, S. Evangelides, H. Kidorf, J. Darcie, E. Golovchenko, K. Rottwitt, P. Corbett, R. Menges, M. Mils, B. Pedersen, D. Peckham, A. Abramov, and A. Vengsarkar, “320 Gb/s WDM transmission (64×5 Gb/s) over 7200 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), postdeadline paper PD12.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, “4×SONET OC-192 field installed dispersion managed soliton system over 450 km of standard fiber in the 1550 nm erbium band,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD19.

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fibre and periodic dispersion compensation,” presented at the 1997 European Conference on Optical Communications, Edinburgh, September 19–23, 1997.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, “320 Gbit/s soliton WDM transmission over 1100 km with 100 km dispersion-compensated spans of standard fibre,” presented at the 1997 European Conference on Optical Communications, Edinburgh, September 19–23, 1997.

N. S. Bergano, C. R. Davidson, A. Mills, P. C. Corbett, S. G. Evangelides, B. Pedersen, R. Menges, J. L. Ztskind, J. W. Sulhoff, A. K. Srivastava, C. Wolf, and J. Judkins, “Long-haul WDM transmission using optimum channel modulation: a 160 Gb/s (32×5 Gb/s) 9, 3000 km demonstration,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD16.

O. Leclerc and E. Desurvire, “Performance limits in 80–160 Gbit/s (N×20 Gbit/s) regenerated WDM soliton transmission,” presented at the 1997 European Conference on Optical Communications, Edinburgh, September 19–23, 1997.

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Figures (6)

Fig. 1
Fig. 1

Top, evolution of T (solid curve), M (longer-dashed curve), and R (shorter-dashed curve) over one compensation period for a typical DM soliton forming in a fiber system that uses in-line filtering with the dispersion map shown in the bottom figure.

Fig. 2
Fig. 2

Top, power profile of the typical stable DM soliton–forming system with in-line fixed frequency filters at the beginning of the compensation cell. Bottom, the soliton chirp (a first derivative of the pulse phase over time) at z=0. Dispersion-allocation parameter, D˜=2.82 ps/(nm×km); average dispersion, D=0; Gaussian filter bandwidth [Bf=1.665 Ωf/(2π)], Bf=375 GHz.

Fig. 3
Fig. 3

Same soliton as in Fig. 2 but shown in a three-dimensional plot. Evolution of the soliton power over one period is shown on (a) the usual scale and (b) a logarithmic scale (dBm). Although in the leading order the dynamics is self-similar (a), there are some non-self-similar dips in the solution, as shown in (b). Inset, evolution of the function J(z) (definition in the text) that characterizes self-similarity of the solution.

Fig. 4
Fig. 4

Comparison of the zero-mode approximation (n=0; open circles) and the two-mode approximation (n=0, 4; crosses) with the profile of the true DM soliton (solid curve) in the system with in-line fixed frequency filters. The power profile is shown at the beginning of the compensation cell. Same parameters as in Fig. 2.

Fig. 5
Fig. 5

Dependence of the optimal excess gain on the filter bandwidth. Open squares, direct numerical simulations; solid curve, the analytical formula. δ=-0.25 ln(1-W02/Ωf2); dispersion-allocation parameter, D˜=2.82 ps/(nm×km); average dispersion, D=0.

Fig. 6
Fig. 6

Dependence of power enhancement on filter bandwidth. The soliton peak power is shown at the beginning of the compensation section (solid curve) and at the first chirp-free point (dashed curve). The limit Ωf corresponds to the DM soliton in the same map but without filtering.

Equations (32)

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i EZ-12β2(z) 2ET2+σ(z)|E|2E
=i-γ(z)+rkk=1Nδ(Z-Zk)E,
iA˜z+d(z)A¯tt+c0(z)|A˜|2A¯
=iL-γk+[exp(γkZa)-1]k=1Nδ(z-zk)
×A˜iG(z)A˜,
iAz+d(z)Att+c(z)|A|2A=0,
c(z)=c0 exp20zG(z)dz.
Aout(t)=A(zk+, t)=12π-+A(zk-, ω)×exp[γ+δ-ω2/(2Ωf2)]exp(-iωt)dω,
A(z, t)=Nτ(z)n=0 an2nn!πexp-x22+iC(z)x2-i(1+2n)Φ(z)Hn(x),x=tτ(z),
A(z, t)=N exp(iMt2/T)T×n=0n=Bn(z)fntT(z)exp[iλnR(z)],
dTdz=4d(z)M,dMdz=d(z)T3-c(z)N2T2,
fn(x)=12nn!πexp-x22Hn(x).
i dBndz+dT2λnBn+β(z)m=0 exp[2i(n-m)R(z)]
×Sn,mBm+β(z)m,l,k exp[2i(n+k-m-l)
×R(z)]BmBlBk*Vm,l,k,n=0.
Sn,m=-+fm(x)x2fn(x)dx,
Vn,m,l,k=-+fn(x)fm(x)fl(x)fk(x)dx.
A(z, ω)=12π-A(z, t)exp(-iωt)dt=NT exp(iYω2)1-2iMTn=0Bn(z)fn(ω/W)exp(iϕn),
A(L+, ω)=N exp(δ)T1(1-2iM1T1)1/2n=0 Bn(L-)(2nn!π)1/2×exp-ω22W12-ω22Ωf2+iY1ω2×HnωW1exp[iϕn(L-)],
Y1=Y0,1W12+1Ωf2=1W02.
Tin2=T2(0)=Tout2=(T12+Ωf-2)2+4M12T12Ωf-4T12+Ωf-2[1+4M12T12],
MinTin=M(0)T(0)=MoutTout=M1T1T14(T12+Ωf-2)2+4M12T12Ωf-4.
T12=(T02-2Ωf-2)2+16M02T02Ωf-4T02-2Ωf-2(1+4M02T02),
M1T1=M0T0T04(T02-2Ωf-2)2+16M02T02Ωf-4.
A(L+, ω)=NT0(1-2iM0T0)1/2n=0 Bn(L+)(2nn!π)1/2×exp-ω22W02+iY0ω2HnωW0×exp[iϕn(L+)].
Bn(0)exp[iΦn(0)]
=exp(δ)k=0 Bn+2k(L)2kk!exp[iΦn+2k(L)]×(n+2k)!n!1/2W0W1n+0.5W02W12-1k,
A(z, t)=NB0π1/4T(z)exp-x22+iMTx2-iR(z)+ikz,x=tT(z).
A(z, t)=NB0π1/4T(z)×1+B4(4x4-12x2+3)exp[-8iR(z)]B026×exp-x22+iMTx2-iR(z)+ikz.
J(z)=Δ(z)Δ(0),
Δ(z)=TrmsPrms=t2|A|2dt|A|2dt1/2 |A|4dt|A|2dt.
δ=-0.25 ln[1-(W02/Ωf2)].

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