Abstract

We present a comprehensive study of the effects of third-order dispersion (TOD) on dispersion-managed (DM) solitons. The two main effects of TOD are creation of asymmetry of the DM soliton’s profile and generation of continuum radiation. Considering these two effects, we derive a conservative bound on the magnitude of TOD below which it will not have a significant detrimental effect on DM solitons over transoceanic distances. We also calculate the shifts in the DM soliton’s position and central frequency that are due to TOD. Finally, we discuss a novel possibility of observing a nonradiating soliton in DM systems with TOD.

© 1999 Optical Society of America

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  1. A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197 (1997); J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, “Soliton collisions in dispersion-managed wavelength-division-multiplexed systems,” Opt. Lett. 22, 1695 (1997); R.-M. Mu, V. S. Grigoryan, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, “Timing-jitter reduction in a dispersion managed soliton system,” Opt. Lett. OPLEDP 23, 930 (1998); I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and M. Suzuki, “40 Gbit/s single-channel soliton transmission over 8600 km using periodic dispersion compensation,” Electron. Lett. ELLEAK 34, 1863 (1998).
    [CrossRef]
  2. 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 (1996).
    [CrossRef] [PubMed]
  3. 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 (1997).
    [CrossRef]
  4. A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900 (1998).
    [CrossRef]
  5. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, “20 Gbit/s-based soliton WDM transmission over transoceanic distances using periodic compensation of dispersion and its slope,” Electron. Lett. 33, 691 (1997); M. Suzuki, I. Morita, N. Takeda, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and dispersion compensation,” Electron. Lett. 34, 475 (1998).
    [CrossRef]
  6. K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
    [CrossRef]
  7. K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Variational approach to transmission in DM long optical links,” in New Trends in Optical Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1998).
  8. X. Wang, Y. Takushima, and K. Kikuchi, “Performance restriction from third-order dispersion in long-distance high-speed dispersion-managed IM/DD systems,” presented at the Optoelectronics and Communications Conference, Japan (1998); M. Suzuki, N. Edagawa, N. Takeda, K. Imai, S. Yamamoto, and S. Akiba, “20 WDM, 10.66 Gbit/s transmission experiment over 9000 km using periodic dispersion slope compensation,” Electron. Lett. 34, 479 (1998).
  9. T. I. Lakoba and D. J. Kaup, “Shape of stationary soliton in strong dispersion management regime,” Electron. Lett. 34, 1124 (1998).
    [CrossRef]
  10. S. K. Turitsyn and V. K. Mezentsev, “Dynamics of a self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions,” JETP Lett. 67, 640 (1998).
    [CrossRef]
  11. 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 (1998).
    [CrossRef]
  12. T. I. Lakoba and D. J. Kaup, “A Hermite–Gaussian expansion for pule propagation in strongly dispersion-managed fibers,” Phys. Rev. E 58, 6728 (1998).
    [CrossRef]
  13. T. I. 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 (1998).
    [CrossRef]
  14. Y. Kodama, “Nonlinear chirped RZ and NRZ pulses in optical transmission lines,” preprint (Osaka University, Osaka, Japan); V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed solitons at normal average dispersion,” Opt. Lett. 23, 609 (1998).
    [CrossRef]
  15. P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiation by solitons at the zero group-velocity-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
    [CrossRef] [PubMed]
  16. V. I. Karpman, “Radiation by solitons due to higher-order dispersion,” Phys. Rev. E 47, 2073 (1993).
    [CrossRef]
  17. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fiber,” Phys. Rev. A 51, 2602 (1995).
    [CrossRef] [PubMed]
  18. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), p. 47.
  19. Y. Kodama, A. V. Mikhailov, and S. Wabnitz, “Input pulse optimization in wavelength-division-multiplexed soliton transmission,” Opt. Commun. 143, 53 (1997).
    [CrossRef]
  20. J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third-order dispersion,” Opt. Commun. 114, 321 (1995).
    [CrossRef]
  21. I. M. Uzunov, M. Gölles, and F. Lederer, “Soliton interaction near the zero-dispersion wavelength,” Phys. Rev. E 52, 1059 (1995).
    [CrossRef]
  22. P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
    [CrossRef]
  23. J. D. Moores, W. S. Wong, and H. A. Haus, “Stability and timing maintainance in soliton transmission and storage rings,” Opt. Commun. 113, 152 (1994); R.-J. Essiambre and G. P. Agrawal, “Timing jitter of ultrashort solitons in high-speed communication systems. I. General formulation and application to dispersion-decreasing fibers,” J. Opt. Soc. Am. B 14, 314 (1997).
    [CrossRef]
  24. Y. Takushima, X. Wang, and K. Kikuchi, “Transmission of 3-ps dispersion-managed soliton pulses under influence of third-order dispersion,” Electron. Lett. 35, 739 (1999).
    [CrossRef]
  25. M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
    [CrossRef]

1999 (1)

Y. Takushima, X. Wang, and K. Kikuchi, “Transmission of 3-ps dispersion-managed soliton pulses under influence of third-order dispersion,” Electron. Lett. 35, 739 (1999).
[CrossRef]

1998 (7)

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900 (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 (1998).
[CrossRef]

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
[CrossRef]

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

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

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

T. I. 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 (1998).
[CrossRef]

1997 (2)

Y. Kodama, A. V. Mikhailov, and S. Wabnitz, “Input pulse optimization in wavelength-division-multiplexed soliton transmission,” Opt. Commun. 143, 53 (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 (1997).
[CrossRef]

1996 (1)

1995 (3)

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third-order dispersion,” Opt. Commun. 114, 321 (1995).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, “Soliton interaction near the zero-dispersion wavelength,” Phys. Rev. E 52, 1059 (1995).
[CrossRef]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fiber,” Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

1993 (2)

V. I. Karpman, “Radiation by solitons due to higher-order dispersion,” Phys. Rev. E 47, 2073 (1993).
[CrossRef]

M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
[CrossRef]

1990 (1)

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiation by solitons at the zero group-velocity-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

1988 (1)

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fiber,” Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Berntson, A.

Brabec, T.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third-order dispersion,” Opt. Commun. 114, 321 (1995).
[CrossRef]

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiation by solitons at the zero group-velocity-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Doran, N. J.

Elgin, J. N.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third-order dispersion,” Opt. Commun. 114, 321 (1995).
[CrossRef]

Forysiak, W.

Frantzeskakis, D.

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
[CrossRef]

Gölles, M.

I. M. Uzunov, M. Gölles, and F. Lederer, “Soliton interaction near the zero-dispersion wavelength,” Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Hizanidis, K.

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fiber,” Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Karpman, V. I.

V. I. Karpman, “Radiation by solitons due to higher-order dispersion,” Phys. Rev. E 47, 2073 (1993).
[CrossRef]

Kaup, D. J.

T. I. 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 (1998).
[CrossRef]

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

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

Kelly, S. M. J.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third-order dispersion,” Opt. Commun. 114, 321 (1995).
[CrossRef]

Kikuchi, K.

Y. Takushima, X. Wang, and K. Kikuchi, “Transmission of 3-ps dispersion-managed soliton pulses under influence of third-order dispersion,” Electron. Lett. 35, 739 (1999).
[CrossRef]

Klauder, M.

M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
[CrossRef]

Knox, F. M.

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 (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 (1996).
[CrossRef] [PubMed]

Kodama, Y.

Y. Kodama, A. V. Mikhailov, and S. Wabnitz, “Input pulse optimization in wavelength-division-multiplexed soliton transmission,” Opt. Commun. 143, 53 (1997).
[CrossRef]

Laedke, E. W.

M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
[CrossRef]

Lakoba, T. I.

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

T. I. 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 (1998).
[CrossRef]

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

Lederer, F.

I. M. Uzunov, M. Gölles, and F. Lederer, “Soliton interaction near the zero-dispersion wavelength,” Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiation by solitons at the zero group-velocity-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Malomed, B. A.

T. I. 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 (1998).
[CrossRef]

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
[CrossRef]

Menyuk, C. R.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Mezentsev, V. K.

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 (1998).
[CrossRef]

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

Mikhailov, A. V.

Y. Kodama, A. V. Mikhailov, and S. Wabnitz, “Input pulse optimization in wavelength-division-multiplexed soliton transmission,” Opt. Commun. 143, 53 (1997).
[CrossRef]

Nijhof, J. H. B.

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900 (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 (1997).
[CrossRef]

Nistazakis, H. E.

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
[CrossRef]

Schäfer, T.

Smith, N. J.

Spatschek, K. H.

M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
[CrossRef]

Takushima, Y.

Y. Takushima, X. Wang, and K. Kikuchi, “Transmission of 3-ps dispersion-managed soliton pulses under influence of third-order dispersion,” Electron. Lett. 35, 739 (1999).
[CrossRef]

Turitsyn, S. K.

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 (1998).
[CrossRef]

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

M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
[CrossRef]

Uzunov, I. M.

I. M. Uzunov, M. Gölles, and F. Lederer, “Soliton interaction near the zero-dispersion wavelength,” Phys. Rev. E 52, 1059 (1995).
[CrossRef]

Wabnitz, S.

Y. Kodama, A. V. Mikhailov, and S. Wabnitz, “Input pulse optimization in wavelength-division-multiplexed soliton transmission,” Opt. Commun. 143, 53 (1997).
[CrossRef]

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiation by solitons at the zero group-velocity-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Wang, X.

Y. Takushima, X. Wang, and K. Kikuchi, “Transmission of 3-ps dispersion-managed soliton pulses under influence of third-order dispersion,” Electron. Lett. 35, 739 (1999).
[CrossRef]

Yang, J.

T. I. 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 (1998).
[CrossRef]

Electron. Lett. (3)

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 (1997).
[CrossRef]

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

Y. Takushima, X. Wang, and K. Kikuchi, “Transmission of 3-ps dispersion-managed soliton pulses under influence of third-order dispersion,” Electron. Lett. 35, 739 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, “Effect of axial inhomogeneity on solitons near the zero dispersion point,” IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

JETP Lett. (1)

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

Opt. Commun. (3)

T. I. 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 (1998).
[CrossRef]

Y. Kodama, A. V. Mikhailov, and S. Wabnitz, “Input pulse optimization in wavelength-division-multiplexed soliton transmission,” Opt. Commun. 143, 53 (1997).
[CrossRef]

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third-order dispersion,” Opt. Commun. 114, 321 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiation by solitons at the zero group-velocity-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fiber,” Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (4)

V. I. Karpman, “Radiation by solitons due to higher-order dispersion,” Phys. Rev. E 47, 2073 (1993).
[CrossRef]

I. M. Uzunov, M. Gölles, and F. Lederer, “Soliton interaction near the zero-dispersion wavelength,” Phys. Rev. E 52, 1059 (1995).
[CrossRef]

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

M. Klauder, E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, “Pulse propagation in optical fibers near the zero-dispersion point,” Phys. Rev. E 47, R3844 (1993).
[CrossRef]

Pure Appl. Opt. (1)

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fiber links,” Pure Appl. Opt. 7, L57 (1998).
[CrossRef]

Other (7)

K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. Frantzeskakis, “Variational approach to transmission in DM long optical links,” in New Trends in Optical Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1998).

X. Wang, Y. Takushima, and K. Kikuchi, “Performance restriction from third-order dispersion in long-distance high-speed dispersion-managed IM/DD systems,” presented at the Optoelectronics and Communications Conference, Japan (1998); M. Suzuki, N. Edagawa, N. Takeda, K. Imai, S. Yamamoto, and S. Akiba, “20 WDM, 10.66 Gbit/s transmission experiment over 9000 km using periodic dispersion slope compensation,” Electron. Lett. 34, 479 (1998).

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, “20 Gbit/s-based soliton WDM transmission over transoceanic distances using periodic compensation of dispersion and its slope,” Electron. Lett. 33, 691 (1997); M. Suzuki, I. Morita, N. Takeda, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and dispersion compensation,” Electron. Lett. 34, 475 (1998).
[CrossRef]

Y. Kodama, “Nonlinear chirped RZ and NRZ pulses in optical transmission lines,” preprint (Osaka University, Osaka, Japan); V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed solitons at normal average dispersion,” Opt. Lett. 23, 609 (1998).
[CrossRef]

J. D. Moores, W. S. Wong, and H. A. Haus, “Stability and timing maintainance in soliton transmission and storage rings,” Opt. Commun. 113, 152 (1994); R.-J. Essiambre and G. P. Agrawal, “Timing jitter of ultrashort solitons in high-speed communication systems. I. General formulation and application to dispersion-decreasing fibers,” J. Opt. Soc. Am. B 14, 314 (1997).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), p. 47.

A. Hasegawa, Y. Kodama, and A. Maruta, “Recent progress in dispersion-managed soliton transmission technologies,” Opt. Fiber Technol.: Mater., Devices Syst. 3, 197 (1997); J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, “Soliton collisions in dispersion-managed wavelength-division-multiplexed systems,” Opt. Lett. 22, 1695 (1997); R.-M. Mu, V. S. Grigoryan, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, “Timing-jitter reduction in a dispersion managed soliton system,” Opt. Lett. OPLEDP 23, 930 (1998); I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and M. Suzuki, “40 Gbit/s single-channel soliton transmission over 8600 km using periodic dispersion compensation,” Electron. Lett. ELLEAK 34, 1863 (1998).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Normalized value of the TOD coefficient for which the energy in the third HG component equals 1% of the total DM soliton energy, plotted as a function of map strength S. (a) Lossless case; (b), (c), (d), periodically amplified case with α=0.22 dB/km, Lmap=Lamp=40 km, and L1/Lmap=0.9, 0.1, 7/18, respectively.

Fig. 2
Fig. 2

Rate of the normalized frequency shift ω˙0τ0/I0 that occurs as the result (a) of spectral recoil in a lossless fiber and (b)–(d) of generation of a third HG component of a DM soliton in a periodically amplified DM fiber. Parameters for (b)–(d) are the same as in Fig. 1.

Fig. 3
Fig. 3

Evolution of the ratio of the energies of the third and zeroth HG components for S=1 and S=3. In both cases, μ=μ1%(S). Other parameters are specified in the text.

Fig. 4
Fig. 4

Evolution over 300Lmap (a) of the pulse amplitude and (b) of the ratio of the radiation energy to the total DM soliton energy for S=1 and μ=μ1%. Other parameters are specified in Subsection 4.C.

Fig. 5
Fig. 5

Normalized radiation frequency |ωr|τ0 as a function of the TOD parameter for five values of the DM strength S.

Fig. 6
Fig. 6

Numerically calculated ratio of the radiation energy to the total DM soliton energy as a function of S at Z=300Lmap for β3=β31% and β3=β31%/2. The additional factor of (1/4) is included in the data for β3=β31% to demonstrate that for large values of S the radiation energy scales as β32, as predicted in Subsection 4.D. Dashed and solid curves provide a cubic spline to the discrete data. The dotted–dashed curve shows the analytical estimate for the radiation energy in the lossless case as obtained from relation (29).

Equations (59)

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iAZ+β1 AT-12β2(Z) 2AT2+γ|A|2A-i6β3 3AT3
=i2[g(Z)-α]A,
β2=-λ22πcD,β3=λ22πc22Dλ+dDdλ,
β3λ22πc2 dDdλ.
z=Z/Lmap,τ=(T-β1Z)/TDM,
u=A exp1/20Zg(Z)dZ-1/2αZP0,
TDM=(|β21-β22|L1L2/Lmap)1/2.
i uz+12D(z) 2uτ2+12D0 2uτ2+G(z)|u|2u
=iμ 3uτ3,
G(z)=exp{Lmap[0zg(z)dz-αz]}
=γP0Lmap,μ=β3/(6γP0TDM3).
D0=-(β21L1+β22L2)Lmap|β21-β22|L1L2,
D(z)=sgn(β22-β21)Lmap/L10<z<L1/Lmap-sgn(β22-β21)Lmap/L2L1/Lmap<z<1.
u0=n=0 an1+iδ1-iδ1+iδn/2Hn(ξ)×exp-ξ22(1-iδ)-iω0τ01+δ2ξ+iϕ(z)+O(),
δδ(z)=δ0+1τ020zD(z)dz,
ξ=τ-τc(z)τ01+δ2,
dτcdz=-ω0[D(z)+D0],
dϕdz=ω022[D(z)+D0]+ |a0|22I0-I24+O(2),
In=01 dzG(z)1+δ21+iδ1-iδn/2,n=0, 1, 2,.
zz¯=z,
ττ¯=τ+[(δτ02+D0z)ω0-3μω02z],
uu¯=u exp{i[ω0τ-μzω03+ω02(δτ02+D0z)/2]},
D0D¯0=D0-6µω0.
|a0|2=D02/(τ02 Re I2),Im I2=0.
ia˙n+[asinRef.12]
=iμτ03[(n+1)(n+2)(n+3)an+3-32(n+1)2an+1+34nan-1-18an-3],
|a3|τ˙cω˙0μ.
3a3D0τ02-a02I-22-a3*3a02I422
-a03iμ4τ03-ω˙0τ02-iτ˜˙c2τ0=0,
D0τ02=a02I22,
-a33D02τ02+3a02I082+a3*5a02I6162+a0iμ8τ03
=0,
τ˜˙c=τ˙c+ω˙0[sgn(β22-β21)/2+δ0τ02].
a3Ra0=5µI6I2τ03a02[(3I0+12I2)2-(5/2|I6|)2],
a3Ia0=2μ(3I0+12I2-5/2I6R)τ03a02[(3I0+12I2)2-(5/2|I6|)2].
ω˙0=3a022τ0a3Ra0I4R+a3Ia0I4I,
τ˜˙c=3µ2τ02+3a02τ02a3Ra0I4I-a3Ia0I4R
S=12τ02=2 ln 2|β21-β22|L1L2LmapTFWHM2=ln 2 |(β21-β2av)L1-(β22-β2av)L2|TFWHM2,
a3a0=2(2 ln 2)3/2|β3|3γ(P0a02)TFWHM313I0+12I2+5/2I6.
-Hn2(x)exp(-x2)dx=2nn!π,
β3γPavTFWHM3LNLLTOD92(2 ln 2)3/20.1481+4 I2I0+56I6I0,
LTOD=TFWHM3|β3|,LNL=1γPav.
Tc(Z)=(ln 2)β3ZTFWHM21-2I43I0+12I2+5/2I6.
u0=a0+a41-iδ01+iδ02H4(τ/τi)×exp-τ22τi2(1-iδ0),
Eradzμ2ωr5|uˆ0(ωr)|2(3µωr+D0).
μωr3+D02ωr2=-a022I0-I24,
β31/2β31%(S),
β3<number.
β3<functionofS.
ωf/2<ωr<ωch-ωf/2,
iuˆr,z-ω22[D(z)+D0]+μω3uˆr=μω3uˆ0,
uˆ0(ω)=τ02πexp-12(ωτ0)2(1+iδ)×n=0(-1)3n/2anHn(ωτ0).
ur(τ, z)=-μ exp(izksol)2π-ω3uˆ0(ω)exp(iωτ)-exp[iωτ-iz(μω3+D0ω2/2+ksol)]ksol+μω3+D0ω2/2dω,
ksol= |a0|22I0-I24
- f(ω)exp(iωτ)ω-ω0dω=πif(ω0)exp(iω0τ)sgn(τ)+O[exp(-|τ|)],
ur(τ, z)=-iμωr3uˆ0(ωr)exp(izksol+iωrτ)2(3µωr2+D0ωr)×{sgn(τ)-sgn[τ-z(3µωr2+D0ωr)]}+O(z-1/2).
P=-u* uτ-u u*τdτ.
ωsol-|u0|2dτ-ωr|ur|2dτ.
dωsoldz-μ2ωr6|uˆ0(ωr)|2a02T0π(3µωr+D0).

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