Abstract

The propagation of an optical soliton is studied in a fiber with randomly varying core diameter or random amplification along the fiber. The adiabatic dynamics of the soliton and radiative processes are investigated by a perturbation method based on the inverse scattering transform. The mean emitted power and the damping rate of the soliton are calculated. The interaction of solitons in random media is investigated by the Karpman–Solov'ev perturbation theory. Numerical simulations of the full nonlinear Schrödinger equation with multiplicative white- and colored-noise perturbations are performed for initial conditions corresponding to a single soliton and to two interacting solitons. The results obtained are in good agreement with the analytical estimates for white noise in the initial stage of the propagation. The numerical simulations reveal a new phenomenon in which single solitons disintegrate or split under white-noise perturbation but stabilize under colored-noise action. Finally, the existence of a bound state of two interacting solitons is observed in numerical simulations in media with colored-noise perturbation.

© 1998 Optical Society of America

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  24. V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).
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1997 (2)

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171 (1997).

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Propagation of chirped optical solitons in fibers with randomly varying parameters,” Opt. Commun. 138, 49 (1997).

1996 (3)

R. Grimshaw, J. He, and B. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385 (1996).

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

B. A. Malomed, “Resonant amplification of a chirped soliton in a long optical fiber with periodic amplification,” J. Opt. Soc. Am. B 13, 677 (1996).

1995 (2)

B. A. Malomed, “Bound states in a gas of solitons supported by a randomly fluctuating force,” Europhys. Lett. 30, 507 (1995).

R. G. Bauer and L. A. Mel’nikov, “Multisoliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Optics Commun. 115, 190 (1995).

1994 (2)

A. Mecozzi, “Long distance transmission at zero dispersion: combined effect of Kerr nonlinearity and the noise of the in-line amplifiers,” J. Opt. Soc. Am. B 11, 462 (1994).

F. Kh. Abdullaev, J. G. Caputo, and N. Flytzanis, “Envelope soliton propagation in media with temporally varying dispersion,” Phys. Rev. E 50, 1552 (1994).

1993 (1)

1992 (2)

J. P. Gordon, “Dispersive-perturbation of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 9 (1992).

S. A. Gredeskul and Yu. S. Kivshar, “Propagation and scattering of nonlinear waves in disordered systems,” Phys. Rep. 216, 1 (1992).

1991 (1)

1989 (1)

Yu. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763 (1989).

1987 (1)

Yu. S. Kivshar, V. V. Konotop, and Yu. A. Sinitsyn, “Emission of solitons in a fluctuating medium,” Radiofizika 30, 374 (1987).

1983 (1)

F. Kh. Abdullaev, “Propagation of a soliton in a fiber with fluctuating parameters,” Sov. Tech. Phys. Lett. 9, 305 (1983).

1981 (1)

V. I. Karpman and V. V. Solov’ev, “A perturbation theory for soliton systems,” Physica D 3, 142 (1981).

Abdullaev, F. Kh.

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Propagation of chirped optical solitons in fibers with randomly varying parameters,” Opt. Commun. 138, 49 (1997).

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171 (1997).

F. Kh. Abdullaev, J. G. Caputo, and N. Flytzanis, “Envelope soliton propagation in media with temporally varying dispersion,” Phys. Rev. E 50, 1552 (1994).

F. Kh. Abdullaev, “Propagation of a soliton in a fiber with fluctuating parameters,” Sov. Tech. Phys. Lett. 9, 305 (1983).

Abdumalikov, A. A.

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Propagation of chirped optical solitons in fibers with randomly varying parameters,” Opt. Commun. 138, 49 (1997).

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171 (1997).

Baizakov, B. B.

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171 (1997).

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Propagation of chirped optical solitons in fibers with randomly varying parameters,” Opt. Commun. 138, 49 (1997).

Bauer, R. G.

R. G. Bauer and L. A. Mel’nikov, “Multisoliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Optics Commun. 115, 190 (1995).

Caputo, J. G.

F. Kh. Abdullaev, J. G. Caputo, and N. Flytzanis, “Envelope soliton propagation in media with temporally varying dispersion,” Phys. Rev. E 50, 1552 (1994).

Elgin, J. N.

Flytzanis, N.

F. Kh. Abdullaev, J. G. Caputo, and N. Flytzanis, “Envelope soliton propagation in media with temporally varying dispersion,” Phys. Rev. E 50, 1552 (1994).

Gordon, J. P.

J. P. Gordon, “Dispersive-perturbation of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 9 (1992).

Gredeskul, S. A.

S. A. Gredeskul and Yu. S. Kivshar, “Propagation and scattering of nonlinear waves in disordered systems,” Phys. Rep. 216, 1 (1992).

Grimshaw, R.

R. Grimshaw, J. He, and B. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385 (1996).

Haus, H. A.

He, J.

R. Grimshaw, J. He, and B. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385 (1996).

Hopkins, V. A.

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

Karpman, V. I.

V. I. Karpman and V. V. Solov’ev, “A perturbation theory for soliton systems,” Physica D 3, 142 (1981).

Keat, J.

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

Kivshar, Yu. S.

S. A. Gredeskul and Yu. S. Kivshar, “Propagation and scattering of nonlinear waves in disordered systems,” Phys. Rep. 216, 1 (1992).

Yu. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763 (1989).

Yu. S. Kivshar, V. V. Konotop, and Yu. A. Sinitsyn, “Emission of solitons in a fluctuating medium,” Radiofizika 30, 374 (1987).

Konotop, V. V.

Yu. S. Kivshar, V. V. Konotop, and Yu. A. Sinitsyn, “Emission of solitons in a fluctuating medium,” Radiofizika 30, 374 (1987).

Malomed, B.

R. Grimshaw, J. He, and B. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385 (1996).

Malomed, B. A.

B. A. Malomed, “Resonant amplification of a chirped soliton in a long optical fiber with periodic amplification,” J. Opt. Soc. Am. B 13, 677 (1996).

B. A. Malomed, “Bound states in a gas of solitons supported by a randomly fluctuating force,” Europhys. Lett. 30, 507 (1995).

Yu. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763 (1989).

Maynard, J. D.

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

Mecozzi, A.

Meegan, G. D.

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

Mel’nikov, L. A.

R. G. Bauer and L. A. Mel’nikov, “Multisoliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Optics Commun. 115, 190 (1995).

Sinitsyn, Yu. A.

Yu. S. Kivshar, V. V. Konotop, and Yu. A. Sinitsyn, “Emission of solitons in a fluctuating medium,” Radiofizika 30, 374 (1987).

Solov’ev, V. V.

V. I. Karpman and V. V. Solov’ev, “A perturbation theory for soliton systems,” Physica D 3, 142 (1981).

Zhang, T.

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

Europhys. Lett. (1)

B. A. Malomed, “Bound states in a gas of solitons supported by a randomly fluctuating force,” Europhys. Lett. 30, 507 (1995).

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Propagation of chirped optical solitons in fibers with randomly varying parameters,” Opt. Commun. 138, 49 (1997).

Opt. Lett. (1)

Optics Commun. (1)

R. G. Bauer and L. A. Mel’nikov, “Multisoliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Optics Commun. 115, 190 (1995).

Phys. Rep. (1)

S. A. Gredeskul and Yu. S. Kivshar, “Propagation and scattering of nonlinear waves in disordered systems,” Phys. Rep. 216, 1 (1992).

Phys. Rev. E (1)

F. Kh. Abdullaev, J. G. Caputo, and N. Flytzanis, “Envelope soliton propagation in media with temporally varying dispersion,” Phys. Rev. E 50, 1552 (1994).

Phys. Rev. Lett. (1)

V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996).

Phys. Scr. (1)

R. Grimshaw, J. He, and B. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385 (1996).

Physica D (1)

V. I. Karpman and V. V. Solov’ev, “A perturbation theory for soliton systems,” Physica D 3, 142 (1981).

Quantum Electron. (1)

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171 (1997).

Radiofizika (1)

Yu. S. Kivshar, V. V. Konotop, and Yu. A. Sinitsyn, “Emission of solitons in a fluctuating medium,” Radiofizika 30, 374 (1987).

Rev. Mod. Phys. (1)

Yu. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763 (1989).

Sov. Tech. Phys. Lett. (1)

F. Kh. Abdullaev, “Propagation of a soliton in a fiber with fluctuating parameters,” Sov. Tech. Phys. Lett. 9, 305 (1983).

Other (8)

V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevsky, Theory of Solitons. Inverse Scattering Method (Consultants Bureau, New York, 1984).

V. V. Konotop and L. Vasquez, Nonlinear Random Waves (World Scientific, Singapore, 1994).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1990).

F. Kh. Abdullaev, S. A. Darmanyan, and P. K. Khabibullaev, Optical Solitons (Springer-Verlag, Heidelberg, 1993).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

A. Hasegawa and Yu. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).

H. Risken, The Fokker-Planck Equation (Springer-Verlag, Heidelberg, 1984).

S. Molchanov, Lectures on Random Media, Vol. 1581 of Springer Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1994), Lecture 7.

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