Abstract

We show that in optical fiber the threshold exponential gain, Gth, for stimulated Brillouin scattering initiated by spontaneous Brillouin scattering is functionally and strongly dependent on the material, length and numerical aperture of the fiber and the pump wavelength. For silica fiber we show that the value of Gth at λ≅1 µm ranges from as low as ~5 in long fiber (≥ few kms) to ~10–12 in fibers of ~100 m length and ~20–23 for very short fibers (<10 cm).

© 2007 Optical Society of America

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  1. R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
    [CrossRef]
  2. R. G. Smith, "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering," Appl. Opt. 11, 2489-2494 (1972).
    [CrossRef] [PubMed]
  3. A. Liem, J. Limpert, H. Zellmer, and A. Tünnermann, "100-W single-frequency master-oscillator fiber power amplifier," Opt. Lett. 28, 1537-1539 (2003).
    [CrossRef] [PubMed]
  4. R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
    [CrossRef]
  5. 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 (2005).
    [CrossRef] [PubMed]
  6. R. W. Boyd, K. Rzazewski and P. Narum, "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514-5521 (1990).
    [CrossRef] [PubMed]
  7. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov. Principles of Phase Conjugation, (Springer-Verlag, Berlin, 1985).
  8. D. Cotter, "Stimulated Brillouin scattering in optical fibers," J. Opt. Commun. 4, 10-19 (1982).
  9. X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
    [CrossRef]
  10. 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]
  11. R. B. Jenkins, R. M. Sova, and R. I. Joseph, "Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers," J. Lightwave Technol. 25, 763-770 (2007).
    [CrossRef]
  12. K. S. Abedin, "Observation of strong stimulated Brillouin scattering in single-mode As2Se3 chalcogenide fiber," Opt. Express 13, 10266-10271 (2005).
    [CrossRef] [PubMed]
  13. C. L. Tang, "Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process," J. Appl. Phys. 37, 2945-2955 (1966).
    [CrossRef]
  14. I. L. Fabelinskii, Molecular Scattering of Light, (Plenum Press, NY, 1968).
  15. V. I. Kovalev, "Stimulated Brillouin scattering in the mid-infrared region of the spectrum," J. of Russian Laser Research,  23, 13-30 (2002).
    [CrossRef]
  16. J. A. Moon and D. T. Schaafsma, "Chalcogenide fibers: An overview of selected applications," Fiber Integr. Opt. 19, 201-210 (2000).
    [CrossRef]
  17. V. I. Kovalev, R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
    [CrossRef] [PubMed]
  18. S. Le Floch and P. Cambon, "Theoretical evaluation of the Brillouin threshold and the steady-state Brillouin equations in standard single-mode optical fibers," J. Opt. Soc. Am. A 20, 1132-1137 (2003).
    [CrossRef]
  19. A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, "Exact analytical treatment of noise initiation of SBS in the presence of loss," Opt. Commun. 260, 46-49 (2006).
    [CrossRef]
  20. V. I. Kovalev, R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber," Opt. Lett. 27, 2022-2024 (2002).
    [CrossRef]
  21. A. L. Gaeta, "Stochastic and deterministic fluctuations in stimulated Brillouin scattering," PhD Thesis, (Rochester, NY, 1990).

2007 (1)

2006 (1)

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, "Exact analytical treatment of noise initiation of SBS in the presence of loss," Opt. Commun. 260, 46-49 (2006).
[CrossRef]

2005 (2)

K. S. Abedin, "Observation of strong stimulated Brillouin scattering in single-mode As2Se3 chalcogenide fiber," Opt. Express 13, 10266-10271 (2005).
[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 (2005).
[CrossRef] [PubMed]

2003 (2)

2002 (3)

2000 (2)

J. A. Moon and D. T. Schaafsma, "Chalcogenide fibers: An overview of selected applications," Fiber Integr. Opt. 19, 201-210 (2000).
[CrossRef]

V. I. Kovalev, R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

1999 (1)

R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
[CrossRef]

1992 (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

1990 (1)

R. W. Boyd, K. Rzazewski and P. Narum, "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514-5521 (1990).
[CrossRef] [PubMed]

1982 (1)

D. Cotter, "Stimulated Brillouin scattering in optical fibers," J. Opt. Commun. 4, 10-19 (1982).

1972 (1)

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]

1964 (1)

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
[CrossRef]

Abedin, K. S.

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 (2005).
[CrossRef] [PubMed]

Boyd, R. W.

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 (2005).
[CrossRef] [PubMed]

R. W. Boyd, K. Rzazewski and P. Narum, "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514-5521 (1990).
[CrossRef] [PubMed]

Cambon, P.

Chiao, R. Y.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
[CrossRef]

Chowdhury, D. Q.

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, "Exact analytical treatment of noise initiation of SBS in the presence of loss," Opt. Commun. 260, 46-49 (2006).
[CrossRef]

Chraplyvy, A. R.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

Cotter, D.

D. Cotter, "Stimulated Brillouin scattering in optical fibers," J. Opt. Commun. 4, 10-19 (1982).

Darmanyan, S. A.

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, "Exact analytical treatment of noise initiation of SBS in the presence of loss," Opt. Commun. 260, 46-49 (2006).
[CrossRef]

Delavaux, J.-M.

Derosier, R. M.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (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 (2005).
[CrossRef] [PubMed]

Gauthier, D. J.

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 (2005).
[CrossRef] [PubMed]

Harrison, R. G.

V. I. Kovalev, R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber," Opt. Lett. 27, 2022-2024 (2002).
[CrossRef]

V. I. Kovalev, R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
[CrossRef]

Jenkins, R. B.

Jopson, R. M.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

Joseph, R. I.

Kobyakov, A.

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, "Exact analytical treatment of noise initiation of SBS in the presence of loss," Opt. Commun. 260, 46-49 (2006).
[CrossRef]

Kovalev, V. I.

V. I. Kovalev, "Stimulated Brillouin scattering in the mid-infrared region of the spectrum," J. of Russian Laser Research,  23, 13-30 (2002).
[CrossRef]

V. I. Kovalev, R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber," Opt. Lett. 27, 2022-2024 (2002).
[CrossRef]

V. I. Kovalev, R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
[CrossRef]

Le Floch, S.

Liem, A.

Limpert, J.

Lu, W.

R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
[CrossRef]

Mao, X. P.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

Moon, J. A.

J. A. Moon and D. T. Schaafsma, "Chalcogenide fibers: An overview of selected applications," Fiber Integr. Opt. 19, 201-210 (2000).
[CrossRef]

Narum, P.

R. W. Boyd, K. Rzazewski and P. Narum, "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514-5521 (1990).
[CrossRef] [PubMed]

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 (2005).
[CrossRef] [PubMed]

Rzazewski, K.

R. W. Boyd, K. Rzazewski and P. Narum, "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514-5521 (1990).
[CrossRef] [PubMed]

Schaafsma, D. T.

J. A. Moon and D. T. Schaafsma, "Chalcogenide fibers: An overview of selected applications," Fiber Integr. Opt. 19, 201-210 (2000).
[CrossRef]

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 (2005).
[CrossRef] [PubMed]

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 (2005).
[CrossRef] [PubMed]

Smith, R. G.

Sova, R. M.

Stoicheff, B. P.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
[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]

Tkach, R. W.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

Toulouse, J.

Townes, C. H.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
[CrossRef]

Tünnermann, A.

Yeniay, A.

Yu, D.

R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
[CrossRef]

Zellmer, H.

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 (2005).
[CrossRef] [PubMed]

Appl. Opt. (1)

Fiber Integr. Opt. (1)

J. A. Moon and D. T. Schaafsma, "Chalcogenide fibers: An overview of selected applications," Fiber Integr. Opt. 19, 201-210 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

J. Appl. Phys. (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]

J. Lightwave Technol. (2)

J. of Russian Laser Research (1)

V. I. Kovalev, "Stimulated Brillouin scattering in the mid-infrared region of the spectrum," J. of Russian Laser Research,  23, 13-30 (2002).
[CrossRef]

J. Opt. Commun. (1)

D. Cotter, "Stimulated Brillouin scattering in optical fibers," J. Opt. Commun. 4, 10-19 (1982).

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

Opt. Commun. (2)

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, "Exact analytical treatment of noise initiation of SBS in the presence of loss," Opt. Commun. 260, 46-49 (2006).
[CrossRef]

R. G. Harrison, V. I. Kovalev, W. Lu, and D. Yu, "SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre," Opt. Commun. 163, 208-211 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

R. W. Boyd, K. Rzazewski and P. Narum, "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514-5521 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
[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 (2005).
[CrossRef] [PubMed]

V. I. Kovalev, R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

Other (3)

I. L. Fabelinskii, Molecular Scattering of Light, (Plenum Press, NY, 1968).

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov. Principles of Phase Conjugation, (Springer-Verlag, Berlin, 1985).

A. L. Gaeta, "Stochastic and deterministic fluctuations in stimulated Brillouin scattering," PhD Thesis, (Rochester, NY, 1990).

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Figures (3)

Fig. 1.
Fig. 1.

Dependence of Gth on ΘKL.

Fig. 2.
Fig. 2.

Dependence of Gth on λ in bulk silica.

Fig. 3.
Fig. 3.

Dependencies of Gth in silica fibers on (a) L for NA=0.2 and λ=1.06 µm, (b) NA for L=100 m and λ=1.06 µm, and (c) λ for L=100 m and NA=0.2.

Tables (2)

Tables Icon

Table 1. Calculated bulk Gth for some materials

Tables Icon

Table 2. Comparison of measured and calculated Gth in silica fibers

Equations (7)

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

I S ( 0 ) = I S ( 0 , ω ) d ω ,
d I S ( z , ω ) d z = g ( ω ) I S ( z , ω ) I p ( 0 ) + I S s p ( 0 , ω ) ,
I S s p ( 0 , ω ) = I S s p ( z , ω ) = I p ( z ) 2 K Θ Γ π [ 4 ( ω ω B ) 2 + Γ 2 ] ,
K = π 2 k B T γ 2 ρ ν 2 λ 4 ,
I S ( 0 , ω ) = I S s p ( 0 , ω ) g ( ω ) I p ( 0 ) { exp [ g ( ω ) I p ( 0 ) L ] 1 } .
I S ( 0 ) Θ K L G 3 2 I p ( 0 ) exp G ,
G t h 3 2 e G t h = 100 Θ K L .

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