Abstract

We investigate both experimentally and numerically the evolution of slow light in the limit of high stimulated-Brillouin-scattering gain, as in a Brillouin fiber laser. The Stokes pulse transit time is measured to decrease and the resonant modes to shift to higher frequencies with increasing pump power. Numerical simulations reveal that pump depletion introduces a nonuniform group index across the Stokes pulse as it interacts with the pump, the index being greater for the leading edge and decreasing progressively towards the trailing edge in proportion to the remaining pump power. This results in a progressive acceleration of the Stokes pulse from slow to fast as it propagates through the cavity.

© 2008 Optical Society of America

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  1. N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34-43 (1965).
    [CrossRef]
  2. C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945-2955 (1966).
    [CrossRef]
  3. V. S. Starunov and I. L. Fabelinskiĭ, “Stimulated Mandel'shtam-Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463-488 (1970).
    [CrossRef]
  4. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  5. E. Picholle, in Guided Wave Nonlinear Optics, D.B.Ostrowsky and R.Reinisch, eds. (Kluwer, 1992), pp. 627-647.
  6. G. P. Agrawal, Nonlinear Fiber Optics, 2nd. ed. (Academic, 1995).
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    [CrossRef]
  8. N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6, 1167-1174 (1989).
    [CrossRef]
  9. A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425-1432 (2002).
    [CrossRef]
  10. A. I. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of feedback,” Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
    [CrossRef]
  11. C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhound, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16, 932-951 (1999).
    [CrossRef]
  12. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
    [CrossRef] [PubMed]
  13. K. Y. Song, M. González-Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
    [CrossRef] [PubMed]
  14. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
    [CrossRef]
  15. M. González-Herráez, K.-Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
    [CrossRef]
  16. R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, pp. 497-530.
    [CrossRef]
  17. J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a stimulated Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300-312 (1989).
    [CrossRef]
  18. I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, “Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers,” J. Opt. Soc. Am. B 2, 1606-1611 (1985).
    [CrossRef]
  19. A. Yariv, Optical Electronics (Holt, Rinehart and Winston, 1976), Chap. 6.
  20. M. Dämmig and F. Mitschke, “Velocity of pulse propagation in media with amplitude nonlinearity,” Appl. Phys. B , 59, 345-349 (1994).
    [CrossRef]
  21. J. E. McElhenny, R. K. Pattnaik, J. Toulouse, K. Saitoh, and M. Koshiba, “Unique characteristic features of stimulated Brillouin scattering in small-core photonic crystal fibers,” J. Opt. Soc. Am. B 25, 582-593 (2008).
    [CrossRef]
  22. M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
    [CrossRef] [PubMed]
  23. E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
    [CrossRef] [PubMed]
  24. D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51, 669-674 (1995).
    [CrossRef] [PubMed]
  25. V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
    [CrossRef]
  26. C. Montes, A. Mamhmoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49, 1344-1349 (1994).
    [CrossRef] [PubMed]
  27. J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
    [CrossRef]
  28. Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering without external feedback in large nonlinear refractive index regime,” Opt. Rev. 4, 636-638 (1997).
    [CrossRef]
  29. Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering dependent on pump power, nonlinear refractive index, feedback power, and fiber length,” Opt. Rev. 4, 476-480 (1997).
    [CrossRef]
  30. C. C. Chow and A. Bers, “Chaotic stimulated Brillouin scattering in a finite-length medium,” Phys. Rev. A 47, 5144-5150 (1993).
    [CrossRef] [PubMed]
  31. R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49, R24-R27 (1994).
    [CrossRef] [PubMed]
  32. L. Chen and X. Bao, “Analytical and numerical solutions for steady-state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65-70 (1998).
    [CrossRef]
  33. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

2008 (1)

2005 (4)

K. Y. Song, M. González-Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

M. González-Herráez, K.-Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

2002 (2)

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, pp. 497-530.
[CrossRef]

A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425-1432 (2002).
[CrossRef]

1999 (1)

1998 (1)

L. Chen and X. Bao, “Analytical and numerical solutions for steady-state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65-70 (1998).
[CrossRef]

1997 (2)

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering without external feedback in large nonlinear refractive index regime,” Opt. Rev. 4, 636-638 (1997).
[CrossRef]

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering dependent on pump power, nonlinear refractive index, feedback power, and fiber length,” Opt. Rev. 4, 476-480 (1997).
[CrossRef]

1996 (1)

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
[CrossRef]

1995 (2)

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

D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51, 669-674 (1995).
[CrossRef] [PubMed]

1994 (4)

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49, R24-R27 (1994).
[CrossRef] [PubMed]

C. Montes, A. Mamhmoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49, 1344-1349 (1994).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
[CrossRef]

M. Dämmig and F. Mitschke, “Velocity of pulse propagation in media with amplitude nonlinearity,” Appl. Phys. B , 59, 345-349 (1994).
[CrossRef]

1993 (2)

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

C. C. Chow and A. Bers, “Chaotic stimulated Brillouin scattering in a finite-length medium,” Phys. Rev. A 47, 5144-5150 (1993).
[CrossRef] [PubMed]

1992 (3)

A. I. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of feedback,” Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 1992).

E. Picholle, in Guided Wave Nonlinear Optics, D.B.Ostrowsky and R.Reinisch, eds. (Kluwer, 1992), pp. 627-647.

1991 (1)

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

1989 (2)

1985 (1)

1982 (1)

D. Cotter, “Observation of stimulated Brillouin scattering in low-loss silica fiber at 1.3 μm,” Electron. Lett. 18, 495-496 (1982).
[CrossRef]

1976 (1)

A. Yariv, Optical Electronics (Holt, Rinehart and Winston, 1976), Chap. 6.

1970 (1)

V. S. Starunov and I. L. Fabelinskiĭ, “Stimulated Mandel'shtam-Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463-488 (1970).
[CrossRef]

1966 (1)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945-2955 (1966).
[CrossRef]

1965 (1)

N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34-43 (1965).
[CrossRef]

1960 (1)

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Agrawal, G. P.

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

Aso, H.

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering dependent on pump power, nonlinear refractive index, feedback power, and fiber length,” Opt. Rev. 4, 476-480 (1997).
[CrossRef]

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering without external feedback in large nonlinear refractive index regime,” Opt. Rev. 4, 636-638 (1997).
[CrossRef]

Azuma, Y.

Bahloul, D.

Bao, X.

L. Chen and X. Bao, “Analytical and numerical solutions for steady-state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65-70 (1998).
[CrossRef]

Bar-Joseph, I.

Bers, A.

C. C. Chow and A. Bers, “Chaotic stimulated Brillouin scattering in a finite-length medium,” Phys. Rev. A 47, 5144-5150 (1993).
[CrossRef] [PubMed]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Bongrand, I.

Botineau, J.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhound, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16, 932-951 (1999).
[CrossRef]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
[CrossRef]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a stimulated Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300-312 (1989).
[CrossRef]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, pp. 497-530.
[CrossRef]

A. I. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of feedback,” Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Chen, L.

L. Chen and X. Bao, “Analytical and numerical solutions for steady-state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65-70 (1998).
[CrossRef]

Cheval, G.

Chow, C. C.

C. C. Chow and A. Bers, “Chaotic stimulated Brillouin scattering in a finite-length medium,” Phys. Rev. A 47, 5144-5150 (1993).
[CrossRef] [PubMed]

Cotter, D.

D. Cotter, “Observation of stimulated Brillouin scattering in low-loss silica fiber at 1.3 μm,” Electron. Lett. 18, 495-496 (1982).
[CrossRef]

Dämmig, M.

M. Dämmig and F. Mitschke, “Velocity of pulse propagation in media with amplitude nonlinearity,” Appl. Phys. B , 59, 345-349 (1994).
[CrossRef]

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Delavaux, J.-M.

Fabelinskii, I. L.

V. S. Starunov and I. L. Fabelinskiĭ, “Stimulated Mandel'shtam-Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463-488 (1970).
[CrossRef]

Friesem, A. A.

Gaeta, A. I.

A. I. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of feedback,” Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, pp. 497-530.
[CrossRef]

González-Herráez, M.

M. González-Herráez, K.-Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

K. Y. Song, M. González-Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
[CrossRef] [PubMed]

Harrison, R. G.

D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51, 669-674 (1995).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49, R24-R27 (1994).
[CrossRef] [PubMed]

Imai, Y.

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering dependent on pump power, nonlinear refractive index, feedback power, and fiber length,” Opt. Rev. 4, 476-480 (1997).
[CrossRef]

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering without external feedback in large nonlinear refractive index regime,” Opt. Rev. 4, 636-638 (1997).
[CrossRef]

Koshiba, M.

Kroll, N. M.

N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34-43 (1965).
[CrossRef]

Lecoeuche, V.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
[CrossRef]

Legrand, O.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

Leycuras, C.

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
[CrossRef]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a stimulated Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300-312 (1989).
[CrossRef]

Lichtman, E.

Lu, W.

D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51, 669-674 (1995).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49, R24-R27 (1994).
[CrossRef] [PubMed]

Mamhmoud, A.

C. Montes, A. Mamhmoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49, 1344-1349 (1994).
[CrossRef] [PubMed]

Mamhound, A.

McElhenny, J. E.

Mitschke, F.

M. Dämmig and F. Mitschke, “Velocity of pulse propagation in media with amplitude nonlinearity,” Appl. Phys. B , 59, 345-349 (1994).
[CrossRef]

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Montes, C.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhound, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16, 932-951 (1999).
[CrossRef]

C. Montes, A. Mamhmoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49, 1344-1349 (1994).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
[CrossRef]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a stimulated Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300-312 (1989).
[CrossRef]

Okamoto, K.

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Pattnaik, R. K.

Picholle, E.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhound, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16, 932-951 (1999).
[CrossRef]

C. Montes, A. Mamhmoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49, 1344-1349 (1994).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
[CrossRef]

E. Picholle, in Guided Wave Nonlinear Optics, D.B.Ostrowsky and R.Reinisch, eds. (Kluwer, 1992), pp. 627-647.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Stabilization of a stimulated Brillouin fiber ring laser by strong pump modulation,” J. Opt. Soc. Am. B 6, 300-312 (1989).
[CrossRef]

Picozzi, A.

Randoux, S.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
[CrossRef]

Ripley, P. M.

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49, R24-R27 (1994).
[CrossRef] [PubMed]

Saitoh, K.

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Segard, B.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
[CrossRef]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Shibata, N.

Song, K. Y.

Song, K.-Y.

M. González-Herráez, K.-Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Starunov, V. S.

V. S. Starunov and I. L. Fabelinskiĭ, “Stimulated Mandel'shtam-Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463-488 (1970).
[CrossRef]

Tang, C. L.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945-2955 (1966).
[CrossRef]

Thévenaz, L.

M. González-Herráez, K.-Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

K. Y. Song, M. González-Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
[CrossRef] [PubMed]

Toulouse, J.

Waarts, R. G.

Welling, H.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Willner, A. E.

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rinehart and Winston, 1976), Chap. 6.

Yeniay, A.

Yu, D.

D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51, 669-674 (1995).
[CrossRef] [PubMed]

Zemmouri, J.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
[CrossRef]

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Zinner, G.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Appl. Phys. B (1)

M. Dämmig and F. Mitschke, “Velocity of pulse propagation in media with amplitude nonlinearity,” Appl. Phys. B , 59, 345-349 (1994).
[CrossRef]

Appl. Phys. Lett. (1)

M. González-Herráez, K.-Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Electron. Lett. (1)

D. Cotter, “Observation of stimulated Brillouin scattering in low-loss silica fiber at 1.3 μm,” Electron. Lett. 18, 495-496 (1982).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

A. I. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of feedback,” Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

J. Appl. Phys. (2)

N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34-43 (1965).
[CrossRef]

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945-2955 (1966).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (6)

Opt. Commun. (2)

L. Chen and X. Bao, “Analytical and numerical solutions for steady-state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65-70 (1998).
[CrossRef]

J. Botineau, C. Leycuras, C. Montes, and E. Picholle, “Coherent modal analysis of a Brillouin fiber ring laser,” Opt. Commun. 109, 126-132 (1994).
[CrossRef]

Opt. Express (1)

Opt. Rev. (2)

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering without external feedback in large nonlinear refractive index regime,” Opt. Rev. 4, 636-638 (1997).
[CrossRef]

Y. Imai and H. Aso, “Chaos in fiber-optic stimulated Brillouin scattering dependent on pump power, nonlinear refractive index, feedback power, and fiber length,” Opt. Rev. 4, 476-480 (1997).
[CrossRef]

Phys. Rev. A (5)

C. C. Chow and A. Bers, “Chaotic stimulated Brillouin scattering in a finite-length medium,” Phys. Rev. A 47, 5144-5150 (1993).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49, R24-R27 (1994).
[CrossRef] [PubMed]

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51, 669-674 (1995).
[CrossRef] [PubMed]

C. Montes, A. Mamhmoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49, 1344-1349 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454-1457 (1991).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902-153905 (2005).
[CrossRef] [PubMed]

Quantum Semiclassic. Opt. (1)

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassic. Opt. 8, 1109-1145 (1996).
[CrossRef]

Sov. Phys. Usp. (1)

V. S. Starunov and I. L. Fabelinskiĭ, “Stimulated Mandel'shtam-Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463-488 (1970).
[CrossRef]

Other (6)

R. W. Boyd, Nonlinear Optics (Academic, 1992).

E. Picholle, in Guided Wave Nonlinear Optics, D.B.Ostrowsky and R.Reinisch, eds. (Kluwer, 1992), pp. 627-647.

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

R. W. Boyd and D. J. Gauthier, “'Slow' and 'fast' light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43, Chap. 6, pp. 497-530.
[CrossRef]

A. Yariv, Optical Electronics (Holt, Rinehart and Winston, 1976), Chap. 6.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the experimental setup. The test fiber was 500 m long and was butt-coupled to the output of the circulator. The AOM was used to shift the frequencies of the modes by 55 MHz .

Fig. 2
Fig. 2

Oscilloscope traces of Stokes pulses at the output end as a function of time. (a) is the result of 23.2 dBm and (b) of 24 dBm of input power. The period in (a) is 4.74 μ s while in (b) it is 4.6 μ s . The period decreases by about 0.1 μ s as the input power is increased.

Fig. 3
Fig. 3

(a) Spectrum of the lasing modes (to the third harmonic) in a 500 m long fiber Brillouin laser. The fundamental or the first harmonic (labeled by the integer m 0 ) is at 55 MHz . Note that the harmonics shift to higher frequencies as the pump power is increased. (b) Expanded view of the second and third harmonics for two pump powers. As the pump power is increased, the frequency shift increases with the order of the harmonic mode. Inset: increase of frequency (in percent) of the three harmonics with pump power.

Fig. 4
Fig. 4

Pump power dependence of the resonant modes in PCF. As the pump power is increased, the gain increases and modes shift to higher frequencies. Expanded view is provided in the inset.

Fig. 5
Fig. 5

Schematics of the Fabry–Pérot Brillouin fiber laser. The pump is injected from the right. R 1 and R 2 are the amplitude reflectivities of the end faces. The initial CW Stokes emission (dotted arrows) evolving from the noise near the left end face develops into resonant modes upon Fresnel reflection from the end faces.

Fig. 6
Fig. 6

(a) Simulation results for the average reflected power (solid circles) and the transmitted power (open circles) for a 500 m long SMF fiber. The SBS threshold is near 30 mW of pump power. (b) Stokes amplitude at z = L as a function of time when the input power is near threshold. When the gain is low ( 29.7 mW ) , the output is constant in time. As the gain is increased, the output exhibits oscillations with a period equal to the round-trip transit time.

Fig. 7
Fig. 7

Simulation results for the Stokes amplitude at the output end as a function of time. (a) When the pump power is just above the threshold the pulse repetition rate is nearly equal to the round-trip transit time of the passive cavity. (b) At higher pump powers, the transit time decreases suggesting faster light.

Fig. 8
Fig. 8

Amplitudes of the pump and Stokes light at z = 0.8 L as a function of time. (a) Just above the threshold, the pump depletion is a mere 6% of the incident pump power. (b) At higher pump powers the depletion exceeds 80%.

Fig. 9
Fig. 9

Variation of group index across the Stokes pulse. (a) Evolution with time at a fixed z = 0.8 L , it decreases from 0.05 to 0.02 from the leading edge to the trailing edge. (b) Evolution along the depth of the fiber cavity at a given instant of time, τ = 0.8 .

Fig. 10
Fig. 10

Envelope of the Stokes amplitude as a function of the retarded time for various positions along the fiber cavity. (a) Near the threshold, the pulse propagates without any change in group velocity. (b) Above the threshold the pulse propagates with an accelerated group velocity as it approaches the exit or output end.

Fig. 11
Fig. 11

Numerically computed frequency spectrum of the Stokes signal. Note that, for 50 mW of input power, the modes appear at higher frequencies than for 40 mW . The inset shows that the first mode shifts by about 6 kHz .

Tables (1)

Tables Icon

Table 1 Fiber Parameters for Simulation

Equations (19)

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n eff = n ( ω ) + g c ω Δ Ω Γ B I L ,
g = g B ( Γ B 2 ) 2 ( Γ B 2 ) 2 + ( Δ Ω ) 2 ,
n g = n g 0 ( ω ) + g B c I L Γ B 4 ( Γ B 2 ) 2 ( Δ Ω ) 2 ( ( Γ B 2 ) 2 + ( Δ Ω ) 2 ) 2 n g 0 ( ω ) + g B c I L Γ B ,
Δ ν = c 2 n g L = v g 2 L ,
E L z + n g 0 c E L t + α 2 E L = i ω L γ e 4 c n ρ 0 ρ E S ,
E S z + n g 0 c E S t + α 2 E S = i ω L γ e 4 c n ρ 0 ρ * E L ,
ρ t + ( Γ B 2 + i Δ Ω ) ρ = i ϵ 0 Ω B γ e 4 V a 2 E L E S * ,
A L z + n g 0 c A L t + α 2 A L = Γ B 4 g B Γ B 2 ( Γ B 2 ) 2 + Δ Ω 2 1 2 g B I A L ,
A z + n g 0 c A t + α 2 A = Γ B 4 g B Γ B 2 ( Γ B 2 ) 2 + Δ Ω 2 1 2 g B I L A ,
ϕ L z + n g 0 c ϕ L t = Γ B 4 g B Δ Ω ( Γ B 2 ) 2 + Δ Ω 2 I g B Δ Ω Γ B I ,
ϕ z + n g 0 c ϕ t = Γ B 4 g B Δ Ω ( Γ B 2 ) 2 + Δ Ω 2 I L g B Δ Ω Γ B I L ,
T d = d ϕ d ω = L v g L v g 0 = L c Δ n g ,
T d z + n g 0 c T d t = g B Γ B 4 ( Γ B 2 ) 2 Δ Ω 2 [ ( Γ B 2 ) 2 + Δ Ω 2 ] 2 I L g B Γ B I L ,
T d = g B L Γ B I L = G Γ B ,
a L ξ + a L τ + α L 2 a L = 1 2 G a 2 a L ,
a ξ + a τ + α L 2 a = 1 2 G a L 2 a ,
Δ n g ξ + Δ n g τ = G c L Γ B a L 2 ,
a ( 0 , τ ) = f ( 0 , τ ) + ( R 1 R 2 e α L 2 ) a ( L , τ 1 ) ,
a L ( L , τ ) = 1 + ( R 1 R 2 e α L 2 ) a L ( 0 , τ 1 ) ,

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