Abstract

Optical-soliton propagation in a dispersion-flattened fiber is investigated, of which third-order dispersion is nil and fourth-order dispersion exists with linear and quadratic intensity-dependent refractive-index changes. For four possible sign combinations of the second-order dispersion and the Kerr-effect terms, we found that there are two types of bright-soliton solutions and two types of dark-soliton solutions. The magnitude of the fourth-order dispersion parameter is related to the quadratic intensity-dependent nonlinearity coefficient, and their signs are opposite. The peak power and the period of the soliton are determined by the magnitude of the fourth-order dispersion parameter. We numerically show that the bright-soliton solution in anomalous second-order dispersion and the positive Kerr coefficient regime is stable and becomes quasi stable when the Raman effect is considered.

© 1998 Optical Society of America

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References

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  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  3. A. Hasegawa, Optical Solitons in Fibers, Vol. 116 of Springer Tracts in Modern Physics (Springer-Verlag, New York, 1989).
    [CrossRef]
  4. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
  5. P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, “Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers,” Opt. Lett. 11, 464 (1986).
    [CrossRef] [PubMed]
  6. P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by solitons at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426 (1990).
    [CrossRef] [PubMed]
  7. M. Karisson and A. Hook, “Soliton-like pulses governed by fourth-order dispersion in optical fibers,” Opt. Commun. 104, 303 (1994).
    [CrossRef]
  8. M. Piché, J. F. Cormier, and X. Zhu, “Bright optical soliton in the presence of fourth-order dispersion,” Opt. Lett. 21, 845 (1996).
    [CrossRef] [PubMed]
  9. N. N. Akhmediev, A. V. Buryak, and A. Hook, “Radiationless optical soliton with oscillating tails,” Opt. Commun. 110, 540 (1994).
    [CrossRef]
  10. N. N. Akhmediev and A. V. Buryak, “Interaction of solitons with oscillating tails,” Opt. Commun. 121, 109 (1995).
    [CrossRef]
  11. A. Höök and M. Karlsson, “Ultrashort solitons at the minimum-dispersion wavelength: effects of fourth-order dispersion,” Opt. Lett. 18, 1388 (1993).
    [CrossRef] [PubMed]
  12. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  13. R. H. Stolen and W. J. Tomlinson, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  14. E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).
  15. N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
    [CrossRef]
  16. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510 (1984).
    [CrossRef] [PubMed]
  17. S. Gatz and J. Herrmann, “Soliton propagation materials with saturable nonlinearity,” J. Opt. Soc. Am. B 8, 2296 (1991).
    [CrossRef]
  18. S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive index change,” Opt. Lett. 17, 484 (1992).
    [CrossRef] [PubMed]
  19. S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refractive index change,” IEEE J. Quantum Electron. 28, 1732 (1992).
    [CrossRef]
  20. A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291 (1985).
    [CrossRef] [PubMed]
  21. J. M. Hickmann, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Lett. 18, 182 (1993).
    [CrossRef] [PubMed]

1996 (1)

1995 (1)

N. N. Akhmediev and A. V. Buryak, “Interaction of solitons with oscillating tails,” Opt. Commun. 121, 109 (1995).
[CrossRef]

1994 (2)

M. Karisson and A. Hook, “Soliton-like pulses governed by fourth-order dispersion in optical fibers,” Opt. Commun. 104, 303 (1994).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and A. Hook, “Radiationless optical soliton with oscillating tails,” Opt. Commun. 110, 540 (1994).
[CrossRef]

1993 (2)

1992 (2)

S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive index change,” Opt. Lett. 17, 484 (1992).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refractive index change,” IEEE J. Quantum Electron. 28, 1732 (1992).
[CrossRef]

1991 (1)

1990 (1)

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

1989 (1)

1986 (2)

1985 (2)

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).

1984 (1)

1981 (1)

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[CrossRef]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev and A. V. Buryak, “Interaction of solitons with oscillating tails,” Opt. Commun. 121, 109 (1995).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and A. Hook, “Radiationless optical soliton with oscillating tails,” Opt. Commun. 110, 540 (1994).
[CrossRef]

Borges, N. M.

Buryak, A. V.

N. N. Akhmediev and A. V. Buryak, “Interaction of solitons with oscillating tails,” Opt. Commun. 121, 109 (1995).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and A. Hook, “Radiationless optical soliton with oscillating tails,” Opt. Commun. 110, 540 (1994).
[CrossRef]

Cavalcanti, S. B.

Chen, H. H.

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

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, “Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers,” Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Cormier, J. F.

Gatz, S.

Golovchenko, E. A.

E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).

Gordon, J. P.

J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Gouveia, E. A.

Gouveia-Neto, A. S.

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Herrmann, J.

Hickmann, J. M.

Hook, A.

N. N. Akhmediev, A. V. Buryak, and A. Hook, “Radiationless optical soliton with oscillating tails,” Opt. Commun. 110, 540 (1994).
[CrossRef]

M. Karisson and A. Hook, “Soliton-like pulses governed by fourth-order dispersion in optical fibers,” Opt. Commun. 104, 303 (1994).
[CrossRef]

Höök, A.

Jain, M.

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

Karisson, M.

M. Karisson and A. Hook, “Soliton-like pulses governed by fourth-order dispersion in optical fibers,” Opt. Commun. 104, 303 (1994).
[CrossRef]

Karlsson, M.

Lee, Y. C.

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

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, “Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers,” Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Menyuk, C. R.

Menyuk, E. M.

E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Piché, M.

Prokhorov, A. M.

E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).

Serkin, V. N.

E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).

Shen, Y. R.

Stolen, R. H.

R. H. Stolen and W. J. Tomlinson, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159 (1989).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Tomlinson, W. J.

Tzoar, N.

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[CrossRef]

Wai, P. K. A.

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

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, “Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers,” Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Yang, G.

Zhu, X.

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refractive index change,” IEEE J. Quantum Electron. 28, 1732 (1992).
[CrossRef]

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

JETP Lett. (1)

E. A. Golovchenko, E. M. Menyuk, A. M. Prokhorov, and V. N. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87 (1985).

Opt. Commun. (3)

M. Karisson and A. Hook, “Soliton-like pulses governed by fourth-order dispersion in optical fibers,” Opt. Commun. 104, 303 (1994).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and A. Hook, “Radiationless optical soliton with oscillating tails,” Opt. Commun. 110, 540 (1994).
[CrossRef]

N. N. Akhmediev and A. V. Buryak, “Interaction of solitons with oscillating tails,” Opt. Commun. 121, 109 (1995).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (2)

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[CrossRef]

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

Phys. Rev. Lett. (2)

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Other (2)

A. Hasegawa, Optical Solitons in Fibers, Vol. 116 of Springer Tracts in Modern Physics (Springer-Verlag, New York, 1989).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

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Figures (6)

Fig. 1
Fig. 1

β as a function of (a) α<0 and (b) α>0 for case A with r=0.8 (thick solid curve), r=1 (solid curve), and r=1.2 (dashed curve).

Fig. 2
Fig. 2

Amplitude as a function of (a) α<0 and (b) α>0 for case A with r=0.8 (thick solid curve), r=1 (solid curve), and r=1.2 (dashed curve).

Fig. 3
Fig. 3

δ0 as a function of (a) α<0 and (b) α>0 for case A with r=0.8 (thick solid curve), r=1 (solid curve), and r=1.2 (dashed curve).

Fig. 4
Fig. 4

Pulse shapes of the modified soliton (solid curve), Ai=0.934, and the conventional soliton (thick solid curve), Ai=1, at ξ=30LD. The dashed curve shows the initial conventional soliton.

Fig. 5
Fig. 5

Power evolution of pulse shapes of the modified soliton, including the Raman effect.

Fig. 6
Fig. 6

(a) Peak power and (b) pulse width versus distance for the conventional soliton (dashed-dotted curve) and the modified soliton without (dashed curve) and with (solid curve) the Raman effect.

Equations (37)

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z A=-i β22 2AT2+i β424 4AT4+i ω0c Δn(|A|2)A,
Δn(|A|2)=n2|A|2+n4|A|4.
ξ=zLD,τ=TT0,u=NP0 A,β=β424|β2|T02,
ξ u=-i2 Sβ2 2uτ2+iβ 4uτ4+iSn2|u|2u+iα|u|4u,
ξ u=i2 2uτ2+iβ 4uτ4+i|u|2u+iα|u|4u.
u(ξ, τ)=A0r sech(rτ)exp(iδ0r2ξ/2).
δ0=1+2βr2,
A0=(1+20βr2)1/2,
α=-24βA04.
β=-(12/α+20r2)+(12/α)(12/α+40r2)400r4.
β=-(12/α+20r2)±(12/α)(12/α+40r2)400r4;
-ξ u=i2 2uτ2-iβ 4uτ4+i|u|2u-iα|u|4u.
u(ξ, τ)=A0r sech(rτ)exp(-iδ0r2ξ/2).
δ0=1-2βr2,
A0=(1-20βr2)1/2,
α=-24βA04.
β=-(12/α-20r2)±(12/α)(12/α-40r2)400r4;
β=-(12/α-20r2)-(12/α)(12/α-40r2)400r4.
ξ u=-i2 2uτ2+iβ 4uτ4+i|u|2u+iα|u|4u.
u(ξ, τ)=A0r tanh(rτ)exp(iδ0r2ξ).
δ0=1+16βr2,
A0=(1+40βr2)1/2,
α=-24βA04.
β=-(12/α+40r2)+(12/α)(12/α+80r2)1600r4.
β=-(12/α+40r2)±(12/α)(12/α+80r2)1600r4;
-ξ u=-i2 2uτ2-iβ 4uτ4+i|u|2u-iα|u|4u.
u(ξ, τ)=A0r tanh(rτ)exp(-iδ0r2ξ).
δ0=1-16βr2,
A0=(1-40βr2)1/2,
α=-24βA04.
β=-(12/α-40r2)±(12/α)(12/α-80r2)1600r4;
β=-(12/α-40r2)-(12/α)(12/α-80r2)1600r4.
Δn(|A|2)=n2(a)|A|2-|n2(b)| |A|21+|A|2/Isat(b)
Δn(|A|2)=n2(a) |A|21+|A|2/Isat(a)-|n2(b)||A|2,
α=|n2(b)|P0|n2(a)-|n2(b)||Isat(b)
α=-n2(a)P0|n2(a)-|n2(b)||Isat(a).
|u|2u|u|2u-TRT0 u |u|2τ,

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