Abstract

In optical fibers, stimulated Brillouin scattering are usually investigated in the regime of resonance. Whereas, in this paper, we discover for the first time that, without participation of Kerr effect, frequency detuning from resonance can give rise to rich dynamical behaviors for stimulated Brillouin scattering in optical fibers. Distinct from the dynamics presented in the conventional Brillouin lasers, this kind of phenomena does not need external feedback at all but also presents a variety of classifiable dynamical features for continuous-wave pumping, including steady state, periodic state and chaos. We analyze that the main mechanisms responsible for these dynamical behaviors include the transient response of acoustic wave, relaxation oscillation, frequency mixing effect induced by three-wave coherent coupling and Brillouin gain-induced group velocity change. Moreover, it should be pointed that it is the first time to discover in theory that there exists the frequency mixing effect induced by three-wave coherent coupling in the regime of non-resonance for the stimulated Brillouin scattering process, which as a consequence determines the periodic state.

© 2015 Optical Society of America

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    [Crossref]

2015 (1)

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Hybrid ytterbium/Brillouin gain assisted partial mode locking in Yb-doped fiber laser,” IEEE Photonics J. 7(3), 1501611 (2015).
[Crossref]

2014 (3)

2013 (1)

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

2012 (1)

2011 (1)

2009 (2)

G. Qin, T. Sakamoto, N. Yamamoto, T. Kawanishi, H. Sotobayashi, T. Suzuki, and Y. Ohishi, “Tunable all-optical pulse compression and stretching via doublet Brillouin gain lines in an optical fiber,” Opt. Lett. 34(8), 1192–1194 (2009).
[Crossref] [PubMed]

M. Djouher, K. Abdelamid, L. Hervé, and S. François, “Brillouin instabilities in continuously pumped high power fiber lasers,” J. Nonlinear Opt. Phys. Mater. 18(01), 111–120 (2009).
[Crossref]

2008 (2)

2007 (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

2005 (3)

2004 (2)

1999 (2)

1997 (2)

V. Lecoeuche, B. Ségard, and J. Zemmouri, “Modes of destabilization of Brillouin fiber ring lasers,” Opt. Commun. 134(1-6), 547–558 (1997).
[Crossref]

S. V. Chernikov, Y. Zhu, J. R. Taylor, and V. P. Gapontsev, “Supercontinuum self-Q-switched ytterbium fiber laser,” Opt. Lett. 22(5), 298–300 (1997).
[Crossref] [PubMed]

1996 (1)

1995 (1)

D. Yu, W. Lu, and R. G. Harrison, “Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback,” Phys. Rev. A 51(1), 669–674 (1995).
[Crossref] [PubMed]

1994 (1)

C. Montes, A. Mamhoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49(2), 1344–1349 (1994).
[Crossref] [PubMed]

1993 (2)

X. Bao, D. J. Webb, and D. A. Jackson, “32-km distributed temperature sensor based on Brillouin loss in an optical fiber,” Opt. Lett. 18(18), 1561–1563 (1993).
[Crossref] [PubMed]

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

1992 (1)

W. Lu, A. Johnstone, and R. G. Harrison, “Deterministic dynamics of stimulated scattering phenomena with external feedback,” Phys. Rev. A 46(7), 4114–4122 (1992).
[Crossref] [PubMed]

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(11), 1454–1457 (1991).
[Crossref] [PubMed]

1986 (2)

C. G. Atkins, D. Cotter, D. W. Smith, and R. Wyatt, “Application of Brillouin amplification in coherent optical transmission,” Electron. Lett. 22(10), 556–558 (1986).
[Crossref]

A. R. Chraplyvy and R. W. Tkach, “Narrowband tunable optical filter for channel selection in densely packed WDM systems,” Electron. Lett. 22(20), 1084–1085 (1986).
[Crossref]

1985 (1)

1978 (1)

S. Newhouse, D. Ruelle, and F. Takens, “Occurrence of strange Axiom A attractors near quasi periodic flows on Tm, m≥3,” Commun. Math. Phys. 64(1), 35–40 (1978).
[Crossref]

1971 (1)

R. V. Johnson and J. H. Marburger, “Relaxation oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4(3), 1175–1182 (1971).
[Crossref]

Abdelamid, K.

M. Djouher, K. Abdelamid, L. Hervé, and S. François, “Brillouin instabilities in continuously pumped high power fiber lasers,” J. Nonlinear Opt. Phys. Mater. 18(01), 111–120 (2009).
[Crossref]

Adikan, F. R.

Atkins, C. G.

C. G. Atkins, D. Cotter, D. W. Smith, and R. Wyatt, “Application of Brillouin amplification in coherent optical transmission,” Electron. Lett. 22(10), 556–558 (1986).
[Crossref]

Bahloul, D.

Bao, X.

Bar-Joseph, I.

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(15), 153902 (2005).
[Crossref] [PubMed]

Blondel, M.

Bongrand, I.

Botineau, J.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16(6), 932 (1999).
[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(11), 1454–1457 (1991).
[Crossref] [PubMed]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[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(15), 153902 (2005).
[Crossref] [PubMed]

Byer, M. W.

Cahill, J. P.

Chen, Z.

J. Gao, Y. Ding, Z. Chen, and C. Lin, “Extended chaotic domain in the long optical fibers based on SBS process,” Physica B 442, 1–5 (2014).
[Crossref]

Chernikov, S. V.

Cheval, G.

Chraplyvy, A. R.

A. R. Chraplyvy and R. W. Tkach, “Narrowband tunable optical filter for channel selection in densely packed WDM systems,” Electron. Lett. 22(20), 1084–1085 (1986).
[Crossref]

Collins, J. J.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

Cotter, D.

C. G. Atkins, D. Cotter, D. W. Smith, and R. Wyatt, “Application of Brillouin amplification in coherent optical transmission,” Electron. Lett. 22(10), 556–558 (1986).
[Crossref]

De Luca, C. J.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

Ding, Y.

J. Gao, Y. Ding, Z. Chen, and C. Lin, “Extended chaotic domain in the long optical fibers based on SBS process,” Physica B 442, 1–5 (2014).
[Crossref]

Djouher, M.

M. Djouher, K. Abdelamid, L. Hervé, and S. François, “Brillouin instabilities in continuously pumped high power fiber lasers,” J. Nonlinear Opt. Phys. Mater. 18(01), 111–120 (2009).
[Crossref]

Dong, X. Y.

Fan, Y. X.

Fotiadi, A. A.

François, S.

M. Djouher, K. Abdelamid, L. Hervé, and S. François, “Brillouin instabilities in continuously pumped high power fiber lasers,” J. Nonlinear Opt. Phys. Mater. 18(01), 111–120 (2009).
[Crossref]

Friesem, A. A.

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(15), 153902 (2005).
[Crossref] [PubMed]

Gan, G. K. W.

Gao, J.

J. Gao, Y. Ding, Z. Chen, and C. Lin, “Extended chaotic domain in the long optical fibers based on SBS process,” Physica B 442, 1–5 (2014).
[Crossref]

Gapontsev, V. P.

Garus, D.

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[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(15), 153902 (2005).
[Crossref] [PubMed]

Gilles, H.

Girard, S.

Gogolla, T.

González Herráez, M.

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(1), 669–674 (1995).
[Crossref] [PubMed]

W. Lu, A. Johnstone, and R. G. Harrison, “Deterministic dynamics of stimulated scattering phenomena with external feedback,” Phys. Rev. A 46(7), 4114–4122 (1992).
[Crossref] [PubMed]

He, J. L.

Henker, R.

Herráez, M.

Hervé, L.

M. Djouher, K. Abdelamid, L. Hervé, and S. François, “Brillouin instabilities in continuously pumped high power fiber lasers,” J. Nonlinear Opt. Phys. Mater. 18(01), 111–120 (2009).
[Crossref]

Hu, S. L.

Jackson, D. A.

Jiang, Z.

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Hybrid ytterbium/Brillouin gain assisted partial mode locking in Yb-doped fiber laser,” IEEE Photonics J. 7(3), 1501611 (2015).
[Crossref]

Johnson, R. V.

R. V. Johnson and J. H. Marburger, “Relaxation oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4(3), 1175–1182 (1971).
[Crossref]

Johnstone, A.

W. Lu, A. Johnstone, and R. G. Harrison, “Deterministic dynamics of stimulated scattering phenomena with external feedback,” Phys. Rev. A 46(7), 4114–4122 (1992).
[Crossref] [PubMed]

Kawanishi, T.

Keaton, G. L.

Krebber, K.

Laroche, M.

Lecœuche, V.

V. Lecœuche, B. Ségard, and J. Zemmouri, “On route to chaos in stimulated Brillouin scattering with feedback,” Opt. Commun. 172(1-6), 335–345 (1999).
[Crossref]

Lecoeuche, V.

V. Lecoeuche, B. Ségard, and J. Zemmouri, “Modes of destabilization of Brillouin fiber ring lasers,” Opt. Commun. 134(1-6), 547–558 (1997).
[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(11), 1454–1457 (1991).
[Crossref] [PubMed]

Leonardo, M. J.

Leycuras, C.

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(11), 1454–1457 (1991).
[Crossref] [PubMed]

Lichtman, E.

Lin, C.

J. Gao, Y. Ding, Z. Chen, and C. Lin, “Extended chaotic domain in the long optical fibers based on SBS process,” Physica B 442, 1–5 (2014).
[Crossref]

Lu, F. Y.

Lu, K. C.

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(1), 669–674 (1995).
[Crossref] [PubMed]

W. Lu, A. Johnstone, and R. G. Harrison, “Deterministic dynamics of stimulated scattering phenomena with external feedback,” Phys. Rev. A 46(7), 4114–4122 (1992).
[Crossref] [PubMed]

Lü, H.

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Hybrid ytterbium/Brillouin gain assisted partial mode locking in Yb-doped fiber laser,” IEEE Photonics J. 7(3), 1501611 (2015).
[Crossref]

Madhiraji, G. A.

Mahdi, M. A.

Mamhoud, A.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16(6), 932 (1999).
[Crossref]

C. Montes, A. Mamhoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49(2), 1344–1349 (1994).
[Crossref] [PubMed]

Marburger, J. H.

R. V. Johnson and J. H. Marburger, “Relaxation oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4(3), 1175–1182 (1971).
[Crossref]

Mégret, P.

Montes, C.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16(6), 932 (1999).
[Crossref]

C. Montes, A. Mamhoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49(2), 1344–1349 (1994).
[Crossref] [PubMed]

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(11), 1454–1457 (1991).
[Crossref] [PubMed]

Mungan, C. E.

Newhouse, S.

S. Newhouse, D. Ruelle, and F. Takens, “Occurrence of strange Axiom A attractors near quasi periodic flows on Tm, m≥3,” Commun. Math. Phys. 64(1), 35–40 (1978).
[Crossref]

Ohishi, Y.

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(15), 153902 (2005).
[Crossref] [PubMed]

Okusaga, O.

Petersen, E.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

Picholle, E.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16(6), 932 (1999).
[Crossref]

C. Montes, A. Mamhoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49(2), 1344–1349 (1994).
[Crossref] [PubMed]

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(11), 1454–1457 (1991).
[Crossref] [PubMed]

Picozzi, A.

Qin, G.

Rakuljic, G.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Richard, D. J.

Rosenstein, M. T.

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

Ruelle, D.

S. Newhouse, D. Ruelle, and F. Takens, “Occurrence of strange Axiom A attractors near quasi periodic flows on Tm, m≥3,” Commun. Math. Phys. 64(1), 35–40 (1978).
[Crossref]

Sakamoto, T.

Satyan, N.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Schliep, F.

Schneider, T.

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(15), 153902 (2005).
[Crossref] [PubMed]

Ségard, B.

V. Lecœuche, B. Ségard, and J. Zemmouri, “On route to chaos in stimulated Brillouin scattering with feedback,” Opt. Commun. 172(1-6), 335–345 (1999).
[Crossref]

V. Lecoeuche, B. Ségard, and J. Zemmouri, “Modes of destabilization of Brillouin fiber ring lasers,” Opt. Commun. 134(1-6), 547–558 (1997).
[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(15), 153902 (2005).
[Crossref] [PubMed]

Shee, Y. G.

Smith, D. W.

C. G. Atkins, D. Cotter, D. W. Smith, and R. Wyatt, “Application of Brillouin amplification in coherent optical transmission,” Electron. Lett. 22(10), 556–558 (1986).
[Crossref]

Song, K. Y.

Sotobayashi, H.

Suzuki, T.

Takens, F.

S. Newhouse, D. Ruelle, and F. Takens, “Occurrence of strange Axiom A attractors near quasi periodic flows on Tm, m≥3,” Commun. Math. Phys. 64(1), 35–40 (1978).
[Crossref]

Taylor, J. R.

Thévenaz, L.

Tkach, R. W.

A. R. Chraplyvy and R. W. Tkach, “Narrowband tunable optical filter for channel selection in densely packed WDM systems,” Electron. Lett. 22(20), 1084–1085 (1986).
[Crossref]

Vasilyev, A.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Waarts, R. G.

Wang, H. J.

Wang, H. T.

Wang, X.

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Hybrid ytterbium/Brillouin gain assisted partial mode locking in Yb-doped fiber laser,” IEEE Photonics J. 7(3), 1501611 (2015).
[Crossref]

Webb, D. J.

White, J. O.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Wiatrek, A.

Wyatt, R.

C. G. Atkins, D. Cotter, D. W. Smith, and R. Wyatt, “Application of Brillouin amplification in coherent optical transmission,” Electron. Lett. 22(10), 556–558 (1986).
[Crossref]

Yamamoto, N.

Yang, Z.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

Yariv, A.

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Yeo, K. S.

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(1), 669–674 (1995).
[Crossref] [PubMed]

Zemmouri, J.

V. Lecœuche, B. Ségard, and J. Zemmouri, “On route to chaos in stimulated Brillouin scattering with feedback,” Opt. Commun. 172(1-6), 335–345 (1999).
[Crossref]

V. Lecoeuche, B. Ségard, and J. Zemmouri, “Modes of destabilization of Brillouin fiber ring lasers,” Opt. Commun. 134(1-6), 547–558 (1997).
[Crossref]

Zhou, P.

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Hybrid ytterbium/Brillouin gain assisted partial mode locking in Yb-doped fiber laser,” IEEE Photonics J. 7(3), 1501611 (2015).
[Crossref]

Zhu, Y.

Zhu, Z.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[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(15), 153902 (2005).
[Crossref] [PubMed]

Commun. Math. Phys. (1)

S. Newhouse, D. Ruelle, and F. Takens, “Occurrence of strange Axiom A attractors near quasi periodic flows on Tm, m≥3,” Commun. Math. Phys. 64(1), 35–40 (1978).
[Crossref]

Electron. Lett. (2)

C. G. Atkins, D. Cotter, D. W. Smith, and R. Wyatt, “Application of Brillouin amplification in coherent optical transmission,” Electron. Lett. 22(10), 556–558 (1986).
[Crossref]

A. R. Chraplyvy and R. W. Tkach, “Narrowband tunable optical filter for channel selection in densely packed WDM systems,” Electron. Lett. 22(20), 1084–1085 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

E. Petersen, Z. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

IEEE Photonics J. (1)

H. Lü, P. Zhou, X. Wang, and Z. Jiang, “Hybrid ytterbium/Brillouin gain assisted partial mode locking in Yb-doped fiber laser,” IEEE Photonics J. 7(3), 1501611 (2015).
[Crossref]

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

M. Djouher, K. Abdelamid, L. Hervé, and S. François, “Brillouin instabilities in continuously pumped high power fiber lasers,” J. Nonlinear Opt. Phys. Mater. 18(01), 111–120 (2009).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

Opt. Commun. (2)

V. Lecoeuche, B. Ségard, and J. Zemmouri, “Modes of destabilization of Brillouin fiber ring lasers,” Opt. Commun. 134(1-6), 547–558 (1997).
[Crossref]

V. Lecœuche, B. Ségard, and J. Zemmouri, “On route to chaos in stimulated Brillouin scattering with feedback,” Opt. Commun. 172(1-6), 335–345 (1999).
[Crossref]

Opt. Express (5)

Opt. Lett. (8)

G. K. W. Gan, Y. G. Shee, K. S. Yeo, G. A. Madhiraji, F. R. Adikan, and M. A. Mahdi, “Brillouin slow light: substantial optical delay in the second-order Brillouin gain spectrum,” Opt. Lett. 39(17), 5118–5121 (2014).
[Crossref] [PubMed]

X. Bao, D. J. Webb, and D. A. Jackson, “32-km distributed temperature sensor based on Brillouin loss in an optical fiber,” Opt. Lett. 18(18), 1561–1563 (1993).
[Crossref] [PubMed]

G. Qin, T. Sakamoto, N. Yamamoto, T. Kawanishi, H. Sotobayashi, T. Suzuki, and Y. Ohishi, “Tunable all-optical pulse compression and stretching via doublet Brillouin gain lines in an optical fiber,” Opt. Lett. 34(8), 1192–1194 (2009).
[Crossref] [PubMed]

M. Laroche, H. Gilles, and S. Girard, “High-peak-power nanosecond pulse generation by stimulated Brillouin scattering pulse compression in a seeded Yb-doped fiber amplifier,” Opt. Lett. 36(2), 241–243 (2011).
[Crossref] [PubMed]

S. V. Chernikov, Y. Zhu, J. R. Taylor, and V. P. Gapontsev, “Supercontinuum self-Q-switched ytterbium fiber laser,” Opt. Lett. 22(5), 298–300 (1997).
[Crossref] [PubMed]

D. Garus, K. Krebber, F. Schliep, and T. Gogolla, “Distributed sensing technique based on Brillouin optical-fiber frequency-domain analysis,” Opt. Lett. 21(17), 1402–1404 (1996).
[Crossref] [PubMed]

Y. X. Fan, F. Y. Lu, S. L. Hu, K. C. Lu, H. J. Wang, X. Y. Dong, J. L. He, and H. T. Wang, “Tunable high-peak-power, high-energy hybrid Q-switched double-clad fiber laser,” Opt. Lett. 29(7), 724–726 (2004).
[Crossref] [PubMed]

A. A. Fotiadi, P. Mégret, and M. Blondel, “Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror,” Opt. Lett. 29(10), 1078 (2004).
[Crossref] [PubMed]

Phys. Rev. A (4)

C. Montes, A. Mamhoud, and E. Picholle, “Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis,” Phys. Rev. A 49(2), 1344–1349 (1994).
[Crossref] [PubMed]

W. Lu, A. Johnstone, and R. G. Harrison, “Deterministic dynamics of stimulated scattering phenomena with external feedback,” Phys. Rev. A 46(7), 4114–4122 (1992).
[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(1), 669–674 (1995).
[Crossref] [PubMed]

R. V. Johnson and J. H. Marburger, “Relaxation oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4(3), 1175–1182 (1971).
[Crossref]

Phys. Rev. Lett. (2)

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(15), 153902 (2005).
[Crossref] [PubMed]

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(11), 1454–1457 (1991).
[Crossref] [PubMed]

Physica B (1)

J. Gao, Y. Ding, Z. Chen, and C. Lin, “Extended chaotic domain in the long optical fibers based on SBS process,” Physica B 442, 1–5 (2014).
[Crossref]

Physica D (1)

M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

Science (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Other (1)

G. P. Agawal, Nonlinear Fiber Optics (Academic, 2001), Chap. 9.

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Figures (13)

Fig. 1
Fig. 1 Illustration of a Brillouin fiber amplifier.
Fig. 2
Fig. 2 Dynamical behaviors of the Stokes wave when the frequency detuning from the Brillouin resonance is nonzero at the injected pump power (a) Pp0 = |Ap(z = 0)|2 = 0.25W, (b) Pp0 = 0.6W, and (c) Pp0 = 3W. The left column presents the temporal intensity evolution of the Stokes wave and the right one gives the corresponding optical spectrum when it has evolved to the final state after a long enough time.
Fig. 3
Fig. 3 Temporal characteristics and corresponding optical spectrum of the output Stokes wave during the evolution process to the CW state when the injected pump power Pp0 = 0.4W. (a) Temporal traces of the output pump and Stokes waves; (b) the optical spectrum of the output Stokes wave. All the other parameters except the pump power are kept the same with those employed in Fig. 2.
Fig. 4
Fig. 4 Relative changes of relaxation-oscillation frequency as a function of the pump power. fr is the actual relaxation-oscillation frequency while fr0 = 1/2Tr = vg/2L.
Fig. 5
Fig. 5 Change of relaxation-oscillation frequency as a function of the fiber length. fr is the actual relaxation-oscillation frequency while fr0 = 1/2Tr = vg/2L.
Fig. 6
Fig. 6 Temporal characteristics (a) and corresponding optical spectrum (b) of the output Stokes wave when the transient response of acoustic wave is neglected. All the simulation parameters are kept the same with those employed in Fig. 3.
Fig. 7
Fig. 7 Instability threshold pump power as a function of the input Stokes power for the CW state. The other simulation parameters are as follows: the fiber attention α = 0.2dB/km, the frequency detuning ΔΩ/2π = 30MHz, the fiber length L = 50m, the effective mode area Aeff = 46.6μm2, the phonon lifetime TB = 1/ΓB = 5ns, gB = 4κ1κ2AeffB = 5.0 × 10−11m/W, vg = 2.1 × 108m/s.
Fig. 8
Fig. 8 Optical spectrum corresponding to the evolution process to the periodic state presented in Fig. 2(b). The relaxation-oscillation frequency is about 1.8MHz.
Fig. 9
Fig. 9 Respective spectrum for the output pump and Stokes wave in the periodic state. All the simulation parameters are kept the same with those employed in Fig. 2(b).
Fig. 10
Fig. 10 The Stokes resonant frequency components in the periodic state (or the frequency spacing between the harmonic components) at different pump powers, frequency detuning, and fiber lengths; (a) The fiber length L = 50m for all the three frequency detuning ΔΩ/2π = 25, 30, and 35MHz; (b) the frequency detuning ΔΩ/2π = 30MHz for all the three fiber length L = 25, 50, and 100m.
Fig. 11
Fig. 11 The largest Lyapunov exponent of the output Stokes wave for different injected pump powers.
Fig. 12
Fig. 12 Phase portraits for the output Stokes wave shown in Fig. 2(b) and (c); (a) Pp0 = 0.6W; (b) Pp0 = 3W. I(t) is the temporal output Stokes intensity, and τ is the time delay.
Fig. 13
Fig. 13 Fine structure of the whole optical spectrum given in Fig. 2(c).

Equations (8)

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A p z + 1 v g A p t = α 2 A p +i κ 1 A s Q
A s z + 1 v g A s t = α 2 A s +i κ 1 A p Q
Q t =( 1 2 Γ B +iΔΩ )Q+i κ 2 A p A s
Δ f r = Δ v g 2L = c 2 n g0 2 g B P p 2L Γ B A eff 1 (δ) 2 ( 1+ (δ) 2 ) 2
A ˜ s ( z,ω )= A ˜ s ( L,ω ) e α/2 (Lz) e iω (Lz) / v g e g ˜ s ( ΔΩ,ω )(Lz)
g ˜ s ( ΔΩ,ω )= κ 1 κ 2 | A p | 2 1 2 Γ B i(ω+ΔΩ)
A p z + 1 v g A p t = α 2 A p κ 1 κ 2 1 2 Γ B +iΔΩ | A s | 2 A p
A s z + 1 v g A s t = α 2 A s + κ 1 κ 2 1 2 Γ B iΔΩ | A p | 2 A s

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