Abstract

Stimulated Brillouin scattering in optical fibers is carefully reassessed for the case of distributed optical gain (achievable in optical fibers lightly doped with rare-earth ions) instead of the usual loss. The effects of gain and amplified spontaneous emission on the threshold power are discussed, together with treatments of the effects of amplification on the line-narrowing process normally associated with stimulated Brillouin scattering in a lossy medium and the appearance of strong higher-order Stokes waves. The implications for erbium-doped fiber amplifier systems are explored.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. G. Smith, “Optical power handling capacity of low loss optical fibres as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 248–2494 (1972).
    [CrossRef]
  2. S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
    [CrossRef]
  3. S. T. Davey, “Doped fibres for optical systems,” Opt. Comput. Process. 11, 61–80 (1991).
  4. J. Digonnet, ed., Fiber Laser Sources and Amplifiers, Proc. Soc. Photo-Opt. Instrum. Eng.11711990.
  5. J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
    [CrossRef]
  6. K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
    [CrossRef]
  7. P. Urquhart and T. J. Whitley, “Long span fiber amplifiers,” Appl. Opt. 29, 3503–3509 (1990).
    [CrossRef] [PubMed]
  8. P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
    [CrossRef]
  9. A. Safaai-Jazi, C. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguide,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59–68 (1986).
    [CrossRef]
  10. C. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634–643 (1986).
  11. C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
    [CrossRef]
  12. X. P. Mao, R. W. Tkach, Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Tech. Lett. 4, 66–69 (1992).
    [CrossRef]
  13. 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]
  14. C. K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018–2023 (1989).
    [CrossRef]
  15. I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
    [CrossRef]
  16. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  18. R. V. Johnson and J. H. Marburger, “Relaxation oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4, 1175–1182 (1971).
    [CrossRef]
  19. I. Bar-Joseph, A. A. Friesem, E. Lichfman, 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]
  20. P. St. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibres,” IEEE J. Quantum Electron. 27, 836–842 (1991).
    [CrossRef]
  21. C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
    [CrossRef]
  22. R. W. Boyd, K. Rzazewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
    [CrossRef] [PubMed]
  23. M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
    [CrossRef]
  24. K. O. Hill, D. C. Johnson, and B. S. Kawasaki, “CW generation of multiple Stokes and anti-Stokes Brillouin shifted frequencies,” Appl. Phys. Lett. 29, 185–187 (1976).
    [CrossRef]
  25. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-fiber stimulated Brillouin ring laser with submilliwatt pump threshold,” Opt. Lett. 7, 509–511 (1982).
    [CrossRef] [PubMed]

1992 (2)

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

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

1991 (4)

P. St. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibres,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[CrossRef]

S. T. Davey, “Doped fibres for optical systems,” Opt. Comput. Process. 11, 61–80 (1991).

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
[CrossRef]

1990 (2)

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

P. Urquhart and T. J. Whitley, “Long span fiber amplifiers,” Appl. Opt. 29, 3503–3509 (1990).
[CrossRef] [PubMed]

1989 (3)

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]

C. K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018–2023 (1989).
[CrossRef]

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

1988 (1)

C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

1986 (3)

A. Safaai-Jazi, C. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguide,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59–68 (1986).
[CrossRef]

C. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634–643 (1986).

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

1985 (1)

1982 (1)

1979 (1)

P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
[CrossRef]

1976 (1)

K. O. Hill, D. C. Johnson, and B. S. Kawasaki, “CW generation of multiple Stokes and anti-Stokes Brillouin shifted frequencies,” Appl. Phys. Lett. 29, 185–187 (1976).
[CrossRef]

1972 (1)

R. G. Smith, “Optical power handling capacity of low loss optical fibres as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 248–2494 (1972).
[CrossRef]

1971 (1)

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

Abe, K.

C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Anikeev, I. Y.

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

Azuma, Y.

Bar-Joseph, I.

Becker, P. C.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Bjarklev, A.

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

Boyd, R. W.

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

Chodorow, M.

Chraplyvy,

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

Culverhouse, D.

P. St. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibres,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[CrossRef]

Davey, S. T.

S. T. Davey, “Doped fibres for optical systems,” Opt. Comput. Process. 11, 61–80 (1991).

Derosier, R. M.

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

Farahi, F.

P. St. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibres,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[CrossRef]

Farnell, G. W.

A. Safaai-Jazi, C. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguide,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59–68 (1986).
[CrossRef]

C. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634–643 (1986).

Fermann, M. E.

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

Friesem, A. A.

Glazkov, D. A.

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

Gordeev, A. A.

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

Goto, N.

C. K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018–2023 (1989).
[CrossRef]

C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Hill, K. O.

K. O. Hill, D. C. Johnson, and B. S. Kawasaki, “CW generation of multiple Stokes and anti-Stokes Brillouin shifted frequencies,” Appl. Phys. Lett. 29, 185–187 (1976).
[CrossRef]

Jen, C.

A. Safaai-Jazi, C. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguide,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59–68 (1986).
[CrossRef]

C. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634–643 (1986).

Jen, C. K.

C. K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018–2023 (1989).
[CrossRef]

C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Johnson, D. C.

K. O. Hill, D. C. Johnson, and B. S. Kawasaki, “CW generation of multiple Stokes and anti-Stokes Brillouin shifted frequencies,” Appl. Phys. Lett. 29, 185–187 (1976).
[CrossRef]

Johnson, R. V.

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

Jopson, R. M.

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

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, and B. S. Kawasaki, “CW generation of multiple Stokes and anti-Stokes Brillouin shifted frequencies,” Appl. Phys. Lett. 29, 185–187 (1976).
[CrossRef]

Kranz, K. S.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Laming, R. I.

M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
[CrossRef]

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

Lemaire, P. J.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Lichfman, E.

Lumholt, O.

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

Mao, X. P.

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

Marburger, J. H.

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

Mears, R. J.

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

Mikhailor, S. I.

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

Mironov, A. B.

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

Mollenauer, L. F.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Morkel, P. R.

M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
[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]

Neubelt, M. J.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Okamoto, K.

Oliveira, J. B. B.

C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Olsson, N. A.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Payne, D. N.

M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
[CrossRef]

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

Poole, S. B.

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

Povlsen, J. H.

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

Rasmussen, T. P.

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

Rottwitt, K.

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

Rowell, N. L.

P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibres,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[CrossRef]

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]

Safaai-Jazi, A.

A. Safaai-Jazi, C. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguide,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59–68 (1986).
[CrossRef]

C. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634–643 (1986).

Shang, H. T.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Shaw, H. J.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Shibata, N.

Simpson, J. R.

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

Smith, R. G.

R. G. Smith, “Optical power handling capacity of low loss optical fibres as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 248–2494 (1972).
[CrossRef]

Stegeman, G. I.

P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
[CrossRef]

Stokes, L. F.

Tachibana, M.

M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
[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]

Thomas, P. J.

P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
[CrossRef]

Tkach, R. W.

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

Urquhart, P.

VanDriel, H. M.

P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
[CrossRef]

Waarts, R. G.

Whitley, T. J.

Zubarev, I. G.

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

Appl. Opt. (2)

R. G. Smith, “Optical power handling capacity of low loss optical fibres as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 248–2494 (1972).
[CrossRef]

P. Urquhart and T. J. Whitley, “Long span fiber amplifiers,” Appl. Opt. 29, 3503–3509 (1990).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

K. O. Hill, D. C. Johnson, and B. S. Kawasaki, “CW generation of multiple Stokes and anti-Stokes Brillouin shifted frequencies,” Appl. Phys. Lett. 29, 185–187 (1976).
[CrossRef]

Electron. Lett. (2)

K. Rottwitt, A. Bjarklev, O. Lumholt, J. H. Povlsen, and T. P. Rasmussen, “Design of long distance distributed erbium doped fibre amplifier,” Electron. Lett. 28, 287–289 (1992).
[CrossRef]

C. K. Jen, J. B. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

I. Y. Anikeev, D. A. Glazkov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailor, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414–420 (1989).
[CrossRef]

P. St. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibres,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[CrossRef]

IEEE Photon. Tech. Lett. (2)

M. Tachibana, R. I. Laming, P. R. Morkel, and D. N. Payne, “Erbium doped fibre amplifier with flattened gain spectrum,” IEEE Photon. Tech. Lett. 3, 118–120 (1991).
[CrossRef]

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

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

A. Safaai-Jazi, C. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguide,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59–68 (1986).
[CrossRef]

C. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634–643 (1986).

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. (3)

C. K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018–2023 (1989).
[CrossRef]

J. R. Simpson, H. T. Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, and M. J. Neubelt, “Performance of a distributed erbium doped dispersion-shifted fibre amplifier,” J. Lightwave Technol. 9, 228–233 (1991).
[CrossRef]

S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and characterisation of low loss optical fibres containing rare-earth ions,” J. Lightwave Technol. 2, 870–876 (1986).
[CrossRef]

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

Opt. Comput. Process. (1)

S. T. Davey, “Doped fibres for optical systems,” Opt. Comput. Process. 11, 61–80 (1991).

Opt. Lett. (1)

Phys. Rev. A (2)

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

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

Phys. Rev. B (1)

P. J. Thomas, N. L. Rowell, H. M. VanDriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibres,” Phys. Rev. B 19, 4986–4998 (1979).
[CrossRef]

Other (3)

J. Digonnet, ed., Fiber Laser Sources and Amplifiers, Proc. Soc. Photo-Opt. Instrum. Eng.11711990.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

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 (4)

Fig. 1
Fig. 1

Variation of threshold power with gain for a selection of fiber lengths in the range 250 m to 10 km. The fiber parameters are given in Subsection 4.A.

Fig. 2
Fig. 2

Normalized Stokes intensity as a function of deviation from Brillouin center frequency for a range of fiber gains.

Fig. 3
Fig. 3

Steady-state power distributions for the pump and first two Stokes orders in a transparent 10-km fiber.

Fig. 4
Fig. 4

Steady-state power distributions for the pump and first two Stokes orders for a 10-km fiber having a distributed gain of 2.8 dB/km.

Equations (49)

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

τ d = 1 π Δ ν s ;
I p z = - g B I p I s - α I p ,
I s z = - g B I s I p + α I s ,
I s z = - g B I p ( I s + I N ) + α I s ,
I N ( ν ) = D q ( ν ) h ν v g ,
D = 1 V 2 n L c = 2 n c A eff ,
q p h ( ν ) = { exp [ h ( ν p - ν ) / k T ] - 1 } - 1
p ( ν ) = 2 π Δ ν s L ( ν ) ,
L ( ν ) = { 1 + [ 2 ( ν - ν s ) / Δ ν s ] 2 } - 1 .
I N ( ν ) = 4 h ν A eff L ( ν ) { exp [ h ( ν p - ν ) / k T ] - 1 } - 1 .
I p z = ( g - α ) I p ,
I ase - z = - ( g - α ) I ase - + ( g - α ) h ν / A eff ,
I p ( z , ν ) = I p ( 0 , ν ) exp [ ( g - α ) z ] ,
I ase - ( z , ν ) = h ν { exp [ ( g - α ) ( L - z ) ] - 1 } / A eff .
I p z = - g B I p I s + ( g - α ) I p ,
I s z = - g B I p ( I s + I N + I ase - ) - ( g - α ) I s ,
I p , s = I p , s ( z , ν ) .
g B ( ν ) = g B O L ( ν ) .
I s z = - μ ( ν ) ( I s + I N + I ase - ) exp [ ( g - α ) z ] - ( g - α ) I s ,
μ ( ν ) = I p ( 0 ) g B ( ν ) .
exp [ u ( z ) + ( g - α ) z ] ,
I s ( 0 , ν ) = 0 L μ I N exp [ 2 ( g - α ) z + u ( z ) ] d z + ( 1 / A eff ) 0 L μ h ν { exp [ ( g - α ) L ] - exp [ ( g - a ) z ] } × u ( z ) d z ,
I 0 ( 0 , ν ) = G ( ν ) I N ( ν ) + J ( ν ) .
μ ( ν ) = I p ( 0 ) S p ( ν ) g B ( ν ) ,
G ( ν ) = exp ( μ L eff ) [ 1 + ( g - α ) ( L eff - 1 / μ ) ] + ( g - α ) / μ - 1 ,
L eff = { exp [ ( g - α ) L ] - 1 } / ( g - α ) .
G ( ν ) [ exp ( μ / α ) - 1 ] / ( μ / α )
I s ( 0 ) = 0 D q ( ν ) h ν v g G ( ν ) d ν ,
= 0 4 L ( ν ) h ν G ( ν ) d ν A eff { exp [ h ( ν p - ν ) / k T ] - 1 } .
h ( ν p - ν ) / k T 1
exp [ h ( ν p - ν s ) / k T ] - 1 h ν A / k T ,
ν A = ν p - ν s .
I s ( 0 ) 4 k T A eff ( ν s ν A ) 0 G ( ν ) L ( ν ) d ν ,
{ exp ( μ / α ) - 1 } d ν { exp ( μ / α ) - 1 } B eff ,
f ( ν ) = exp [ σ L ( ν ) ] - 1
B eff = Δ ν s ( log e 2 / σ ) 1 / 2 ,
P s ( 0 ) = 4 k T ( ν s ν A ) 0 + H ( ζ ) 1 + ζ 2 d ζ ,
H ( ζ ) = exp ( Λ L eff ) { 1 + ( g - α ) [ L eff - 1 / Λ ] } + ( g - α ) / Λ - 1 ,
Λ ( ζ ) = g B O P p ( 0 ) A eff 1 1 + ζ 2 .
P s ( 0 ) = F [ P p ( 0 ) ] .
P th f - F ( P th ) = 0.
H ( ζ ) Λ ( ζ ) L eff ( 1 + ( g - α ) L eff ) ,
P s ( 0 ) = g B O P p ( 0 ) P N TOT L eff { 1 + ( g - α ) L eff } / A eff ,
P N TOT = ω s Δ ω s ω A k T ,
G ( ν ) = α I p ( 0 ) g B O L ( ν ) { exp [ I p ( 0 ) g B O L ( ν ) ] - 1 } .
i p η = - g N i p ( i s 1 + i n ) + γ i P ,
i s 1 η = - g N i p ( i s 1 + i n ) + g B i s 1 ( i s 2 + i n ) - γ i s 1 ,
i s 2 η = + g N i s 1 ( i s 2 + i n ) + γ i s 2 ,
i s 1 , 2 = L g B O I s 1 , 2 , i N = L g B O I n , i p = L g B O I p , η = z / L , γ = L ( g - α ) .

Metrics