Abstract

Because the material time response of silica is very short (75 fs), it is neglected in most models of stimulated Raman scattering in optical fibers as soon as the characteristic pulse width involved in the interaction lies in the picosecond range. We discuss these models and the relevance of this approximation when both a pump and a Stokes wave are distinguishable. We show that the material excitation is resonantly coupled to the optical fields and thus can be responsible for chaotic dynamics, even in the picosecond regime, for strong pump power.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, “Stimulated Raman scattering,” in Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 8.
  2. 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 (1989).
    [CrossRef]
  3. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  4. R. J. Hawkins and C. R. Menyuk, “Effect of the detailed Raman cross section on soliton evolution,” Opt. Lett. 18, 1999 (1993).
    [CrossRef] [PubMed]
  5. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665 (1989).
    [CrossRef]
  6. V. V. Afanasyev, V. A. Vysloukh, and V. N. Serkin, “Decay and interaction of femtosecond optical solitons induced by the Raman self-scattering effect,” Opt. Lett. 15, 489 (1990).
    [CrossRef] [PubMed]
  7. J. Herrmann and A. Nazarkin, “Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations,” Opt. Lett. 19, 2065 (1994).
    [CrossRef] [PubMed]
  8. J. Herrmann and A. Nazarkin, “Coherent Raman response and spectral characteristics of ultrashort solitons in fibers,” Phys. Rev. E 53, 6492 (1996).
    [CrossRef]
  9. A. Höök, “Influence of stimulated Raman scattering on cross-phase modulation between waves in optical fibers,” Opt. Lett. 17, 115 (1992).
    [CrossRef] [PubMed]
  10. C. Headley III and G. P. Agrawal, “Noise characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058 (1995).
    [CrossRef]
  11. C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170 (1996).
    [CrossRef]
  12. Yinchieh Lai and Shinn-Sheng Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817 (1995).
    [CrossRef] [PubMed]
  13. C. Montes and R. Pellat, “Inertial response to nonstationary stimulated Brillouin backscattering: damage on optical and plasma fibers,” Phys. Rev. A 36, 2976 (1987); C. Montes, “Generation of solitonic pulses in cw-pumped Brillouin or Raman fiber-ring lasers,” in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), p. 145.
    [CrossRef] [PubMed]
  14. S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329 (1993).
    [CrossRef]
  15. L. F. Mollenauer, R. H. Stolen, and M. N. Islam, “Experimental demonstration of soliton propagation in long fibers: loss compensated by Raman gain,” Opt. Lett. 10, 229 (1985).
    [CrossRef] [PubMed]
  16. C. C. Chow, “Spatiotemporal chaos in nonintegrable three-wave interactions,” Physica D 81, 237 (1995).
    [CrossRef]
  17. G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Optical wave breaking and pulse compression due to cross-phase modulation in optical fibers,” Opt. Lett. 14, 137 (1989).
    [CrossRef] [PubMed]
  18. J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300 (1989).
    [CrossRef]
  19. C. Montes, A. Mamhoud, and E. Picholle, “Hopf bifurcation in a cw-pumped Brillouin fiber ring laser: coherent soliton morphogenesis,” Phys. Rev. A 49, 1344 (1994).
    [CrossRef] [PubMed]
  20. Dejin Yu, Weiping Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with external feedback,” Phys. Rev. A 51, 669 (1995).
    [CrossRef] [PubMed]

1996 (2)

J. Herrmann and A. Nazarkin, “Coherent Raman response and spectral characteristics of ultrashort solitons in fibers,” Phys. Rev. E 53, 6492 (1996).
[CrossRef]

C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170 (1996).
[CrossRef]

1995 (4)

Yinchieh Lai and Shinn-Sheng Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

C. C. Chow, “Spatiotemporal chaos in nonintegrable three-wave interactions,” Physica D 81, 237 (1995).
[CrossRef]

C. Headley III and G. P. Agrawal, “Noise characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058 (1995).
[CrossRef]

Dejin Yu, Weiping Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with external feedback,” Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

1994 (2)

C. Montes, A. Mamhoud, and E. Picholle, “Hopf bifurcation in a cw-pumped Brillouin fiber ring laser: coherent soliton morphogenesis,” Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

J. Herrmann and A. Nazarkin, “Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations,” Opt. Lett. 19, 2065 (1994).
[CrossRef] [PubMed]

1993 (2)

R. J. Hawkins and C. R. Menyuk, “Effect of the detailed Raman cross section on soliton evolution,” Opt. Lett. 18, 1999 (1993).
[CrossRef] [PubMed]

S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329 (1993).
[CrossRef]

1992 (1)

1990 (1)

1989 (4)

1986 (1)

1985 (1)

Afanasyev, V. V.

Agrawal, G. P.

Alfano, R. R.

Anand, G. V.

S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329 (1993).
[CrossRef]

Baldeck, P. L.

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 (1989).
[CrossRef]

Botineau, J.

Chow, C. C.

C. C. Chow, “Spatiotemporal chaos in nonintegrable three-wave interactions,” Physica D 81, 237 (1995).
[CrossRef]

Gordon, J. P.

Harrison, R. G.

Dejin Yu, Weiping Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with external feedback,” Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

Haus, H. A.

Hawkins, R. J.

Headley III, C.

C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170 (1996).
[CrossRef]

C. Headley III and G. P. Agrawal, “Noise characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058 (1995).
[CrossRef]

Herrmann, J.

J. Herrmann and A. Nazarkin, “Coherent Raman response and spectral characteristics of ultrashort solitons in fibers,” Phys. Rev. E 53, 6492 (1996).
[CrossRef]

J. Herrmann and A. Nazarkin, “Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations,” Opt. Lett. 19, 2065 (1994).
[CrossRef] [PubMed]

Höök, A.

Islam, M. N.

Kumar, S.

S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329 (1993).
[CrossRef]

Lai, Yinchieh

Yinchieh Lai and Shinn-Sheng Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Leycuras, C.

Lu, Weiping

Dejin Yu, Weiping Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with external feedback,” Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

Mamhoud, A.

C. Montes, A. Mamhoud, and E. Picholle, “Hopf bifurcation in a cw-pumped Brillouin fiber ring laser: coherent soliton morphogenesis,” Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

Menyuk, C. R.

Mollenauer, L. F.

Montes, C.

C. Montes, A. Mamhoud, and E. Picholle, “Hopf bifurcation in a cw-pumped Brillouin fiber ring laser: coherent soliton morphogenesis,” Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300 (1989).
[CrossRef]

Nazarkin, A.

J. Herrmann and A. Nazarkin, “Coherent Raman response and spectral characteristics of ultrashort solitons in fibers,” Phys. Rev. E 53, 6492 (1996).
[CrossRef]

J. Herrmann and A. Nazarkin, “Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations,” Opt. Lett. 19, 2065 (1994).
[CrossRef] [PubMed]

Picholle, E.

C. Montes, A. Mamhoud, and E. Picholle, “Hopf bifurcation in a cw-pumped Brillouin fiber ring laser: coherent soliton morphogenesis,” Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300 (1989).
[CrossRef]

Selvarajan, A.

S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329 (1993).
[CrossRef]

Serkin, V. N.

Stolen, R. H.

Tomlinson, W. J.

Vysloukh, V. A.

Wood, D.

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

Yu, Dejin

Dejin Yu, Weiping Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with external feedback,” Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

Yu, Shinn-Sheng

Yinchieh Lai and Shinn-Sheng Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

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

C. Headley III and G. P. Agrawal, “Noise characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058 (1995).
[CrossRef]

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

Opt. Commun. (1)

S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329 (1993).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (3)

C. Montes, A. Mamhoud, and E. Picholle, “Hopf bifurcation in a cw-pumped Brillouin fiber ring laser: coherent soliton morphogenesis,” Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

Dejin Yu, Weiping Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with external feedback,” Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

Yinchieh Lai and Shinn-Sheng Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J. Herrmann and A. Nazarkin, “Coherent Raman response and spectral characteristics of ultrashort solitons in fibers,” Phys. Rev. E 53, 6492 (1996).
[CrossRef]

Physica D (1)

C. C. Chow, “Spatiotemporal chaos in nonintegrable three-wave interactions,” Physica D 81, 237 (1995).
[CrossRef]

Other (2)

C. Montes and R. Pellat, “Inertial response to nonstationary stimulated Brillouin backscattering: damage on optical and plasma fibers,” Phys. Rev. A 36, 2976 (1987); C. Montes, “Generation of solitonic pulses in cw-pumped Brillouin or Raman fiber-ring lasers,” in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), p. 145.
[CrossRef] [PubMed]

G. P. Agrawal, “Stimulated Raman scattering,” in Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 8.

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 (6)

Fig. 1
Fig. 1

Validity domains of a, the standard and b, the inertial models. The curve defines ZD=Zin.

Fig. 2
Fig. 2

Evolution of a 1-ps sech Stokes pulse in the normal-dispersion regime at three propagation lengths in the comoving reference frame (Ecw=30 MV/m).

Fig. 3
Fig. 3

Same as Fig. 1 but for the anomalous-dispersion regime.

Fig. 4
Fig. 4

Evolution of the normalized difference between a perturbed solution and the unperturbed one in the comoving Stokes reference frame. The exponential divergence saturates when the difference becomes comparable with the erratic oscillations.

Fig. 5
Fig. 5

Time profile of the same initial 1-ps Stokes pulse without chromatic dispersion at the propagation length L=96 m.

Fig. 6
Fig. 6

Temporal profiles of a picosecond initial Stokes pulse after a total propagation gain G=9.6 in the normal-dispersion regime: The relative weight between Zin and ZD governs the dynamics.

Equations (47)

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

1vgp t-x+i2 βptt+αpAp
=-gp2 |AS|2Ap+iγp(|Ap|2+2|AS|2)Ap,
1vgS t+σx+i2 βStt+αSAS
=gS2 |Ap|2AS+iγS(|AS|2+2|Ap|2)AS,
ZR=1gp|Ap|2,Zκ=1γp|Ap|2,
ZD=t02/βp,
(tt+2Γt+ωR2)q˜=12m χq˜0E˜2,
q˜(x, t)=q0+q1(x, t)exp[i(kRx-ωRt)],
t-cn x+i2 ρtt+γeEp
=-KESEa+iKEqEp+iKr(|Ep|2+2|ES|2)Ep,
t+σ cn x+i2 ρtt+γeES
=KEpEa*+iKEqES+iKr(|ES|2+2|Ep|2)ES,
i2ωR tt+1+i ΓωRt+ΓEa=KEpES*,
(tt+2Γt+ωR2)Eq=κ(|ES|2+|Ep|2),
Ea=KΓ EpES*-KΓ2 (1+iΓ/ωR)t(EpES*).
t-cn x+i2 ρtt+γeEp
=-K2Γ |ES|2Ep+iKr(2|ES|2+|Ep|2)Ep
-K2Γ2 (1+iΓ/ωR)ESt(EpES*),
(t+x+i2 ρtt+γe)ES
=K2Γ |Ep|2ES+iKr[2|Ep|2+|ES|2]ES
-K2Γ2 (1-iΓ/ωR)Ept(Ep*ES).
Zin=2ωRt0gp|Ap|2.
Ea(x, t)=-2iωRK-tG(t-t)Ep(x, t)ES*(x, t)dt,
Eq(x, t)=κ-tF(t-t)[|Ep(x, t)|2+|ES(x, t)|2]dt,
F(t)=exp(-Γt)(ωR2-Γ2)1/2 sin[(ωR2-Γ2)1/2t];
G(t)=F(t)exp(iωRt).
t-cn x+i2 ρtt+γeEp
=-KES[G(-2iωRKEpES*)]+iKEp×[Fκ(|Ep|2+|ES|2)]+iKr[|Ep|2+2|ES|2]Ep,
t-cn x+γeap=-K2Γ aS2ap+Kaqap sin Φq,
t+σ cn x+γeaS=K2Γ ap2aS+KaqaS sin Φq,
ttaq-aq(tΦq)2+2Γtaq+ωR2aq
=κ(ap2+aS2)cos Φq,
t-cn xΦp=Kr(ap2+2aS2)-Kaqap cos Φq,
t+σ cn xΦS=Kr(aS2+2ap2)-KaqaS cos Φq,
2taqtΦq+aqttΦq+2ΓaqtΦq
=-κ(ap2+aS2)sin Φq.
t-cn x+γeap=-KaSaa cos Φ,
t+σ cn x+γeaS=Kapaa cos Φ,
-12ωR [2tΦa(Γ+t)+ttΦa]aa+taa+Γaa
=KapaS cos Φ,
t-cn xΦp=Kr(ap2+2aS2)+K aSaaap sin Φ,
t+σ cn xΦS=Kr(aS2+2ap2)+K apaaaS sin Φ,
12ωR [tt-(tΦa)2+2Γt]aa+aatΦa=KapaS sin Φ,
-tG(t-t)Ep(x, t)ES*(x, t)dt
=n=0 1n! fn t[Ep(x, t)ES*(x, t)]tn,
fn=(-1)n0tnG(t)dt=in dndωn G(ω)|ω=0,
G(ω)=1-2iωRΓ-ω2-2iω(Γ-iωR).

Metrics