Abstract

Interactions between two femtosecond solitons or solitonlike pulses in single-mode optical fibers are studied. Because of Raman scattering, the total energy of the two input pulses is redistributed into two new solitons. The energy redistribution is controlled by various input parameters. The particular dependences on the initial values of relative phase, pulse separation, relative intensity, and wavelength separation are investigated. Numerical simulations are performed through a solution of the generalized nonlinear Schrödinger equation with the use of a modified version of the beam-propagation method. It is found that the interaction between the two pulses is determined by the interplay among the interpulse Raman scattering, the Raman self-frequency down-shift, the cross-phase modulation, and the walk-off effect. The energy redistribution between the two interacting pulses has potential applications to ultrafast switching devices and logic gates.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [Crossref]
  2. A. Hasegawa, “Numerical study of optical soliton transmission amplified periodically by the stimulated Raman process,” Appl. Opt. 23, 3302–3309 (1984).
    [Crossref] [PubMed]
  3. L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. QE-22, 157–173 (1986).
    [Crossref]
  4. L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 13, 675–677 (1988).
    [Crossref] [PubMed]
  5. N. J. Doran and D. Wood, “Soliton processing element for all-optical switching and logic,” J. Opt. Soc. Am. B 4, 1843–1846 (1987).
    [Crossref]
  6. N. J. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 56–58 (1988).
    [Crossref] [PubMed]
  7. M. N. Islam, “Ultrafast all-optical logic gates based on soliton trapping in fibers,” Opt. Lett. 14, 1257–1259 (1989).
    [Crossref] [PubMed]
  8. L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R. Simpson, and L. G. Cohen, “Experimental study of soliton transmission over more than 10,000 km in dispersion-shifted fiber,” Opt. Lett. 15, 1203–1205 (1990).
    [Crossref] [PubMed]
  9. J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
    [Crossref] [PubMed]
  10. D. Yevick and B. Hermansson, “Soliton analysis with the propagation beam method,” Opt. Commun. 47, 101–106 (1983).
    [Crossref]
  11. F. M. Mitschke and L. F. Mollenauer, “Experimental observation of interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
    [Crossref] [PubMed]
  12. K. Smith and L. F. Mollenauer, “Experimental observation of soliton interaction over long fiber paths: discovery of a long-range interaction,” Opt. Lett. 14, 1284–1286 (1989).
    [Crossref] [PubMed]
  13. L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, “Resistance of solitons to the effect of polarization dispersion in optical fibers,” Opt. Lett. 14, 1219–1221 (1989).
    [Crossref] [PubMed]
  14. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [Crossref]
  15. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
    [Crossref]
  16. R. H. Stolen, C. Lee, and R. K. Jain, “Development of the stimulated Raman spectrum in single-mode fibers,” J. Opt. Soc. Am. B 1, 652–657 (1984).
    [Crossref]
  17. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).
  18. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
    [Crossref] [PubMed]
  19. Y. Kodama and K. Nozaki, “Soliton interaction in optical fibers,” Opt. Lett. 12, 1038–1040 (1987).
    [Crossref] [PubMed]
  20. I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965)
    [Crossref]

1990 (1)

1989 (5)

1988 (2)

1987 (3)

1986 (2)

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
[Crossref] [PubMed]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[Crossref]

1985 (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

1984 (2)

1983 (2)

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

D. Yevick and B. Hermansson, “Soliton analysis with the propagation beam method,” Opt. Commun. 47, 101–106 (1983).
[Crossref]

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

1965 (1)

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

Cohen, L. G.

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Doran, N. J.

Evangelides, S. G.

Fomichev, A. A.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Gordon, J. P.

Hasegawa, A.

A. Hasegawa, “Numerical study of optical soliton transmission amplified periodically by the stimulated Raman process,” Appl. Opt. 23, 3302–3309 (1984).
[Crossref] [PubMed]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

Haus, H. A.

Hermansson, B.

D. Yevick and B. Hermansson, “Soliton analysis with the propagation beam method,” Opt. Commun. 47, 101–106 (1983).
[Crossref]

Islam, M. N.

M. N. Islam, “Ultrafast all-optical logic gates based on soliton trapping in fibers,” Opt. Lett. 14, 1257–1259 (1989).
[Crossref] [PubMed]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[Crossref]

Jain, R. K.

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Kodama, Y.

Lee, C.

Malitson, I.

Mamyshev, P. V.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

Neubelt, M. J.

Nozaki, K.

Prokhorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Simpson, J. R.

Smith, K.

Stel’makh, M. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Stolen, R. H.

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

Tomlinson, W. J.

Wood, D.

Yevick, D.

D. Yevick and B. Hermansson, “Soliton analysis with the propagation beam method,” Opt. Commun. 47, 101–106 (1983).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[Crossref]

IEEE J. Quantum Electron. (2)

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. QE-22, 157–173 (1986).
[Crossref]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

JETP Lett. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Opt. Commun. (1)

D. Yevick and B. Hermansson, “Soliton analysis with the propagation beam method,” Opt. Commun. 47, 101–106 (1983).
[Crossref]

Opt. Lett. (10)

F. M. Mitschke and L. F. Mollenauer, “Experimental observation of interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
[Crossref] [PubMed]

K. Smith and L. F. Mollenauer, “Experimental observation of soliton interaction over long fiber paths: discovery of a long-range interaction,” Opt. Lett. 14, 1284–1286 (1989).
[Crossref] [PubMed]

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, “Resistance of solitons to the effect of polarization dispersion in optical fibers,” Opt. Lett. 14, 1219–1221 (1989).
[Crossref] [PubMed]

N. J. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 56–58 (1988).
[Crossref] [PubMed]

M. N. Islam, “Ultrafast all-optical logic gates based on soliton trapping in fibers,” Opt. Lett. 14, 1257–1259 (1989).
[Crossref] [PubMed]

L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R. Simpson, and L. G. Cohen, “Experimental study of soliton transmission over more than 10,000 km in dispersion-shifted fiber,” Opt. Lett. 15, 1203–1205 (1990).
[Crossref] [PubMed]

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

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
[Crossref] [PubMed]

Y. Kodama and K. Nozaki, “Soliton interaction in optical fibers,” Opt. Lett. 12, 1038–1040 (1987).
[Crossref] [PubMed]

L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 13, 675–677 (1988).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Interactions between two 40-fs identical solitons at 1.51 μm. The dotted, dotted–dashed, and solid curves describe the two solitons at the input end, at a 28.9-cm distance, and at a 57.8-cm distance, respectively. The initial relative phase is π and the initial separation is 140 fs.

Fig. 2
Fig. 2

Same as Fig. 1, except that the initial relative phase is zero.

Fig. 3
Fig. 3

Interactions between two solitons at 1.51 and 1.47 μm, respectively. The dotted, dotted–dashed, and solid curves describe the two solitons at the input end, at a 14.5-cm distance, and at a 57.8-cm distance, respectively. The initial relative phase is zero.

Fig. 4
Fig. 4

Same as Fig. 3, except that the initial relative phase is π.

Fig. 5
Fig. 5

Dependences of the normalized total energy carried by the two output solitons at a 57.8-cm distance on the relative phase of the two input solitons. The solid curves depict the dependences in the case when both solitons are at 1.51 μm, and the dotted curves are for the case when two solitons are at 1.51 and 1.47 μm, respectively. The curves labeled L, T, and S represent the results of the leading soliton, the trailing soliton, and their sum, respectively.

Fig. 6
Fig. 6

Same as Fig. 2, except that the initial separation is 117 fs.

Fig. 7
Fig. 7

Same as Fig. 2, except that the initial separation is 187 fs.

Fig. 8
Fig. 8

Dependences of the total energy carried by the two output solitons at a 57.8-cm distance on the temporal separation between the two input solitons. The curves labeled L, T, and S have the same meanings as those in Fig. 5.

Fig. 9
Fig. 9

Same as Fig. 2, except that the relative intensity of the input trailing soliton is 0.64.

Fig. 10
Fig. 10

Same as Fig. 2, except that the relative intensity of the input trailing soliton is 1.44.

Fig. 11
Fig. 11

Same as Fig. 9, except that the wavelength of the input trailing soliton is 1.47 μm.

Fig. 12
Fig. 12

Same as Fig. 10, except that the wavelength of the input trailing soliton is 1.47 μm.

Fig. 13
Fig. 13

Dependences of the total energy carried by the two output solitons at a 57.8-cm distance on the relative intensity of the two input pulses. The curves labeled L, T, and S have the same meanings as those in Fig. 5.

Fig. 14
Fig. 14

Same as Fig. 2, except that the wavelength of the input trailing soliton is 1.46 μm.

Fig. 15
Fig. 15

Same as Fig. 2, except that the wavelength of the input trailing soliton is 1.41 μm.

Fig. 16
Fig. 16

Dependences of the total energy carried by the two output solitons at a 57.8-cm distance on the wavelength separation between the two input solitons. The curves labeled L, T, and S have the same meanings as those in Fig. 5.

Equations (2)

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

j q ζ + 1 2 2 q τ 2 + q 2 q = 0 ,
j q ζ + 1 2 2 q τ 2 - j β 3 q τ 3 + ( 1 + j ω 0 T τ ) [ α q 2 q + ( 1 - α ) q - τ f R ( τ - τ ) q ( τ ) 2 d τ ] = 0 ,

Metrics