Abstract

We report the experimental observation of the fission of picosecond solitons in a fiber with sine-wave variation of the core diameter along the longitudinal direction of propagation. The experimental pulse dynamics is reproduced by numerical simulations. The fission of high-intensity solitons caused by both the variation of the fiber dispersion and stimulated Raman scattering is demonstrated. The number of output pulses and their frequencies can be managed by periodical modulation of the fiber dispersion even under the strong effect of the Raman scattering.

© 2007 Optical Society of America

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  1. E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).
  2. K. Tai, A. Hasegawa, N. Bekki "Fission of optical solitons induced by stimulated Raman effect," Opt. Lett. 13, 392-394 (1988).
    [CrossRef] [PubMed]
  3. P. K. 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, 464-466 (1986).
    [CrossRef] [PubMed]
  4. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
    [CrossRef]
  5. R. Driben and B. A. Malomed, "Split-step solitons in long fiber links", Opt. Commun. 185, 439-456 (2000).
    [CrossRef]
  6. T. Inoue, H. Tobioka, S. Namiki, "Stationary rescaled pulse in alternately concatenated fibers with O(1)-accumulated nonlinear perturbations" Phys. Rev. E 72, 025601(R) (2005).
    [CrossRef]
  7. M. Böhm, F. Mitschke, "Soliton propagation in a dispersion map with deviation from periodicity" Appl. Phys. B 81, 983-987 (2005).
    [CrossRef]
  8. K. Lee, J. Buck, "Wavelength conversion through higher-order soliton splitting initiated by localized channel perturbations", J. Opt. Soc. Am. B 20, 514-519 (2003).
    [CrossRef]
  9. S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
    [CrossRef] [PubMed]
  10. B.A. Malomed, D.F. Parker, N.F. Smyth "Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber," Phys. Rev. E 48, 1418-1425 (1993).
    [CrossRef]
  11. R.G. Bauer, L.A. Melnikov "Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter," Opt. Commun. 115, 190-195 (1995).
    [CrossRef]
  12. A. Hasegawa, Y. Kodama, "Guiding center solitons," Phys. Rev. Lett. 66, 161-164 (1991).
    [CrossRef] [PubMed]
  13. H. Sakaguchi, B.A. Malomed "Resonant nonlinearity management for nonlinear Schr¨odinger solitons," Phys. Rev. E 70, 066613 (2004).
    [CrossRef]
  14. B.A. Malomed, N.F. Smyth "Resonant splitting of a vector soliton in a periodically inhomogeneous birefringent optical fiber," Phys. Rev. E 50, 1535-1542 (1994).
    [CrossRef]
  15. G. Agrawal, Nonlinear Fiber Optics, (Academic Press, 1989).
  16. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva "Nonautonomous solitons in external potentials" Phys. Rev. Lett. 98, 074102 (2007).
    [CrossRef] [PubMed]
  17. V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
    [CrossRef]

2007 (1)

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva "Nonautonomous solitons in external potentials" Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef] [PubMed]

2005 (2)

T. Inoue, H. Tobioka, S. Namiki, "Stationary rescaled pulse in alternately concatenated fibers with O(1)-accumulated nonlinear perturbations" Phys. Rev. E 72, 025601(R) (2005).
[CrossRef]

M. Böhm, F. Mitschke, "Soliton propagation in a dispersion map with deviation from periodicity" Appl. Phys. B 81, 983-987 (2005).
[CrossRef]

2004 (1)

H. Sakaguchi, B.A. Malomed "Resonant nonlinearity management for nonlinear Schr¨odinger solitons," Phys. Rev. E 70, 066613 (2004).
[CrossRef]

2003 (1)

2002 (1)

V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
[CrossRef]

2000 (2)

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

R. Driben and B. A. Malomed, "Split-step solitons in long fiber links", Opt. Commun. 185, 439-456 (2000).
[CrossRef]

1996 (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

1995 (1)

R.G. Bauer, L.A. Melnikov "Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter," Opt. Commun. 115, 190-195 (1995).
[CrossRef]

1994 (1)

B.A. Malomed, N.F. Smyth "Resonant splitting of a vector soliton in a periodically inhomogeneous birefringent optical fiber," Phys. Rev. E 50, 1535-1542 (1994).
[CrossRef]

1993 (1)

B.A. Malomed, D.F. Parker, N.F. Smyth "Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber," Phys. Rev. E 48, 1418-1425 (1993).
[CrossRef]

1991 (1)

A. Hasegawa, Y. Kodama, "Guiding center solitons," Phys. Rev. Lett. 66, 161-164 (1991).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

1985 (1)

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).

Bauer, R.G.

R.G. Bauer, L.A. Melnikov "Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter," Opt. Commun. 115, 190-195 (1995).
[CrossRef]

Bekki, N.

Belyaeva, T. L.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva "Nonautonomous solitons in external potentials" Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef] [PubMed]

Benion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

Bergman, K.

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

Bespalov, V. G.

V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
[CrossRef]

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

Böhm, M.

M. Böhm, F. Mitschke, "Soliton propagation in a dispersion map with deviation from periodicity" Appl. Phys. B 81, 983-987 (2005).
[CrossRef]

Buck, J.

Chen, H. H.

Dianov, E. M.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).

Doran, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

Driben, R.

R. Driben and B. A. Malomed, "Split-step solitons in long fiber links", Opt. Commun. 185, 439-456 (2000).
[CrossRef]

Golovchenko, E. A.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).

Hasegawa, A.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva "Nonautonomous solitons in external potentials" Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, "Guiding center solitons," Phys. Rev. Lett. 66, 161-164 (1991).
[CrossRef] [PubMed]

K. Tai, A. Hasegawa, N. Bekki "Fission of optical solitons induced by stimulated Raman effect," Opt. Lett. 13, 392-394 (1988).
[CrossRef] [PubMed]

Inoue, T.

T. Inoue, H. Tobioka, S. Namiki, "Stationary rescaled pulse in alternately concatenated fibers with O(1)-accumulated nonlinear perturbations" Phys. Rev. E 72, 025601(R) (2005).
[CrossRef]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, "Guiding center solitons," Phys. Rev. Lett. 66, 161-164 (1991).
[CrossRef] [PubMed]

Kozlov, S. A.

V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
[CrossRef]

Krylov, D.

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

Lee, K.

Lee, Y. C.

Malomed, B. A.

R. Driben and B. A. Malomed, "Split-step solitons in long fiber links", Opt. Commun. 185, 439-456 (2000).
[CrossRef]

Malomed, B.A.

H. Sakaguchi, B.A. Malomed "Resonant nonlinearity management for nonlinear Schr¨odinger solitons," Phys. Rev. E 70, 066613 (2004).
[CrossRef]

B.A. Malomed, N.F. Smyth "Resonant splitting of a vector soliton in a periodically inhomogeneous birefringent optical fiber," Phys. Rev. E 50, 1535-1542 (1994).
[CrossRef]

B.A. Malomed, D.F. Parker, N.F. Smyth "Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber," Phys. Rev. E 48, 1418-1425 (1993).
[CrossRef]

Melnikov, L.A.

R.G. Bauer, L.A. Melnikov "Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter," Opt. Commun. 115, 190-195 (1995).
[CrossRef]

Menyuk, C. R.

Mitschke, F.

M. Böhm, F. Mitschke, "Soliton propagation in a dispersion map with deviation from periodicity" Appl. Phys. B 81, 983-987 (2005).
[CrossRef]

Namiki, S.

T. Inoue, H. Tobioka, S. Namiki, "Stationary rescaled pulse in alternately concatenated fibers with O(1)-accumulated nonlinear perturbations" Phys. Rev. E 72, 025601(R) (2005).
[CrossRef]

Parker, D.F.

B.A. Malomed, D.F. Parker, N.F. Smyth "Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber," Phys. Rev. E 48, 1418-1425 (1993).
[CrossRef]

Prokhorov, A. M.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).

Sakaguchi, H.

H. Sakaguchi, B.A. Malomed "Resonant nonlinearity management for nonlinear Schr¨odinger solitons," Phys. Rev. E 70, 066613 (2004).
[CrossRef]

Sears, S.

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

Segev, M.

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

Serkin, V. N.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva "Nonautonomous solitons in external potentials" Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef] [PubMed]

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).

Shpolyanskiy, Yu. A.

V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
[CrossRef]

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

Smyth, N.F.

B.A. Malomed, N.F. Smyth "Resonant splitting of a vector soliton in a periodically inhomogeneous birefringent optical fiber," Phys. Rev. E 50, 1535-1542 (1994).
[CrossRef]

B.A. Malomed, D.F. Parker, N.F. Smyth "Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber," Phys. Rev. E 48, 1418-1425 (1993).
[CrossRef]

Soljacic, M.

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

Tai, K.

Tobioka, H.

T. Inoue, H. Tobioka, S. Namiki, "Stationary rescaled pulse in alternately concatenated fibers with O(1)-accumulated nonlinear perturbations" Phys. Rev. E 72, 025601(R) (2005).
[CrossRef]

Wai, P. K.

Walmsley, I. A.

V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
[CrossRef]

Appl. Phys. B (1)

M. Böhm, F. Mitschke, "Soliton propagation in a dispersion map with deviation from periodicity" Appl. Phys. B 81, 983-987 (2005).
[CrossRef]

Electron. Lett. (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Benion, "Enhanced power solitons in optical fibers with periodic dispersion management," Electron. Lett.,  32, 54-55 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, "Decay of optical solitons," JETP Lett. 42, 87-91 (1985).

Opt. Commun. (2)

R. Driben and B. A. Malomed, "Split-step solitons in long fiber links", Opt. Commun. 185, 439-456 (2000).
[CrossRef]

R.G. Bauer, L.A. Melnikov "Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter," Opt. Commun. 115, 190-195 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

V. G. Bespalov, S. A. Kozlov, Yu. A. Shpolyanskiy, and I. A. Walmsley "Simplified field wave equations for the nonlinear propagation of extremely short light pulses" Phys. Rev. A 66, 013811 (2002).
[CrossRef]

Phys. Rev. E (4)

H. Sakaguchi, B.A. Malomed "Resonant nonlinearity management for nonlinear Schr¨odinger solitons," Phys. Rev. E 70, 066613 (2004).
[CrossRef]

B.A. Malomed, N.F. Smyth "Resonant splitting of a vector soliton in a periodically inhomogeneous birefringent optical fiber," Phys. Rev. E 50, 1535-1542 (1994).
[CrossRef]

B.A. Malomed, D.F. Parker, N.F. Smyth "Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber," Phys. Rev. E 48, 1418-1425 (1993).
[CrossRef]

T. Inoue, H. Tobioka, S. Namiki, "Stationary rescaled pulse in alternately concatenated fibers with O(1)-accumulated nonlinear perturbations" Phys. Rev. E 72, 025601(R) (2005).
[CrossRef]

Phys. Rev. Lett. (3)

S. Sears, M. Soljacic, M. Segev, D. Krylov, K. Bergman, "Cantor set fractals from solitons", Phys. Rev. Lett. 84, 1902-1905 (2000).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, "Guiding center solitons," Phys. Rev. Lett. 66, 161-164 (1991).
[CrossRef] [PubMed]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva "Nonautonomous solitons in external potentials" Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef] [PubMed]

Other (1)

G. Agrawal, Nonlinear Fiber Optics, (Academic Press, 1989).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Distribution of the refractive index in cross-section of the fiber preform, Δn is the difference between refractive index of the glass and refractive index of the silica. (b) The dispersion (D) measured for three fibers with the fixed outer diameter: 128µm, 133µm and 138µm.

Fig. 2.
Fig. 2.

Experimental setup: Pritel UOC, picosecond pulse source; EDFA, Er-doped fiber amplifier; DOF, dispersion oscillating fiber; AC, autocorrelator; OSA, optical spectrum analyzer, OSCI, wide-bandwidth oscilloscope.

Fig. 3.
Fig. 3.

Soliton splitting into the pulse pair. (a) Temporal distance ΔT between peaks of the pulses at z=0.8km. Simulations were performed for φm =π (red curve) and φm =0 (blue curve). (b) Contour plot of pulse trajectory (bottom) and intensity pulse shape at z=0.8km (top). (c) Autocorrelation traces for output pulses; (d) Output spectrum, dashed curve on the top shows the spectrum of input pulse; In simulations the soliton order N=1.72 was used. T FWHM=2.05 ps. For Fig. (b),(c) and (d) φm =π, zm =0.16km. Plots are normalized.

Fig. 4.
Fig. 4.

Splitting of high-intensity pulse. (a) Contour plot of pulse trajectory (bottom) and intensity pulse shape at z=0.8km (top); (b) output spectrum; (c) oscilloscope record. N=3.02, φm =π, zm =0.16km Other parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Effect of the modulation of the fiber diameter on the soliton fission in presence of the stimulated Raman scattering. (a) Fiber diameter is constant (zm =∞); (b) zm =0.16km; (c) zm =0.08km; Top inserts (red curves) show output pulses (z=0.8km). N=2.33, φm =π. Other parameters are the same as in Fig. 3.

Fig. 6.
Fig. 6.

Fission of third-order soliton under the strong effect of the stimulated Raman scattering. Red curves show output pulse shapes. Blue curves show output spectra. Propagation distance is z=0.8km. (a) Soliton fission due to the Raman scattering. Fiber diameter is constant (zm =∞); (b) Simultaneous effect of dispersion oscillation (zm =0.08km) and Raman scattering on the soliton fission. N=3.02, φm =π. Pulses and spectra are normalized to the peak power of input radiation. Other parameters are the same as in Fig. 3.

Equations (3)

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

A z + α 2 A ( z , t ) = i β 2 ( z ) 2 2 A t 2 + β 3 ( z ) 6 3 A t 3 + i ( P NL + i 1 π v 0 P NL t ) ,
β 2 , 3 ( z ) = β 2 , 3 [ 1 + β 2 , 3 ( m ) sin ( 2 π z z m + φ m ) ] ,
γ K , R ( z ) = γ K , R [ 1 γ m sin ( 2 π z z m + φ m ) ] ,

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