Abstract

We propose a criterion to predict the relative value of the stimulated Brillouin scattering (SBS) threshold in single-mode optical fibers with different refractive index profiles. We confirm our results by several representative measurements. We show that with the proper profile design one can achieve more than 3 dB increase in the SBS threshold compared to the standard single-mode optical fiber.

© 2005 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics, 2nd edition, Academic Press, New York2003, Chapter 9.
  2. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, “Electrostriction mechanism of soliton interaction in optical fibers,” Opt. Lett. 15, 314–316 (1990).
    [Crossref] [PubMed]
  3. X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
    [Crossref]
  4. 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]
  5. F. W. Willems and W. Muys, “Suppression of interferometric noise in externally modulated lightwave AM-CATV systems by phase modulation,” Electron. Lett. 29, 2062–2063 (1993).
    [Crossref]
  6. N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” IEEE J. Lightwave Technol. 11, 1518–1522 (1993).
    [Crossref]
  7. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
    [Crossref]
  8. K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
    [Crossref]
  9. C. A. S. de Oliveira, C. K. Jen, A. Shang, and C. Saravanos, “Stimulated Brillouin scattering in cascaded fibers of different Brillouin frequency shift,” J. Opt. Soc. Am B 10, 969–972 (1993).
    [Crossref]
  10. A. Kobyakov, M. Sauer, and J. E. Hurley, “SBS threshold of segmented fibers,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington, DC, 2005), paper OME5.
    [PubMed]
  11. C. C. Lee and S. Chi, “Measurement of stimulated Brillouin scattering threshold for various types of fibers using Brillouin optical time-domain reflectometer,” IEEE Photon. Technol. Lett. 12, 672–674 (2000).
    [Crossref]
  12. A. Yeniay, J. -M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” IEEE J. Lightwave Technol. 20, 1425–1432 (2002).
    [Crossref]
  13. J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” IEEE J. Lightwave Technol. 21, 1779–1786 (2003).
    [Crossref]
  14. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
    [Crossref]
  15. E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1185–1195 (1999).
    [Crossref]
  16. C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guided fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. UFFC-33, 634–643 (1986).
  17. K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, New York2000.
  18. G. P. Agrawal, Nonlinear Fiber Optics, 3d editionAcademic Press, New York2001.
  19. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
    [Crossref]
  20. N. Lagakos, J. A. Bucaro, and R. Hughes, “Acoustic sensitivity predictions of single-mode optical fibers using Brillouin scattering,” Appl. Opt. 19, 3668–3670 (1980).
    [Crossref] [PubMed]
  21. S. T. Gulati and J. D. Helfinstine, “Fatigue behavior of GeO2-SiO2 glasses,” Mat. Res. Soc. Symp. Proc. 531, 133–138 (1998).
    [Crossref]
  22. http://www.corning.com/opticalfiber/products applications/products/nexcor.aspx
  23. D. Chowdhury, A. Kobyakov, S. Kumar, B. Ruffin, and S. Bickham, “Application of doped optical glass for optical communication,” in Proceedings of XX International Congress on Glass (The Ceramic Society of Japan, Kyoto, Japan, 2004) paper I-01-005.
  24. Patent application US Publication No. 2004/0218882.
  25. P. Bayvel and P. M. Radmore, “Solutions of the SBS equations in single mode optical fibers and implications for fiber transmission systems,” Electron. Lett. 26, 434–436 (1990).
    [Crossref]
  26. R. D. Esman and K. J. Williams, “Brillouin scattering: beyond threshold,” in Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 1996) 227–228, paper ThF5.
  27. A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
    [Crossref]
  28. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th edition, Academic Press, New York2001.

2004 (1)

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
[Crossref]

2003 (1)

J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” IEEE J. Lightwave Technol. 21, 1779–1786 (2003).
[Crossref]

2002 (2)

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

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
[Crossref]

2001 (1)

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
[Crossref]

2000 (1)

C. C. Lee and S. Chi, “Measurement of stimulated Brillouin scattering threshold for various types of fibers using Brillouin optical time-domain reflectometer,” IEEE Photon. Technol. Lett. 12, 672–674 (2000).
[Crossref]

1999 (1)

E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1185–1195 (1999).
[Crossref]

1998 (1)

S. T. Gulati and J. D. Helfinstine, “Fatigue behavior of GeO2-SiO2 glasses,” Mat. Res. Soc. Symp. Proc. 531, 133–138 (1998).
[Crossref]

1995 (1)

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

1994 (1)

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[Crossref]

1993 (3)

C. A. S. de Oliveira, C. K. Jen, A. Shang, and C. Saravanos, “Stimulated Brillouin scattering in cascaded fibers of different Brillouin frequency shift,” J. Opt. Soc. Am B 10, 969–972 (1993).
[Crossref]

F. W. Willems and W. Muys, “Suppression of interferometric noise in externally modulated lightwave AM-CATV systems by phase modulation,” Electron. Lett. 29, 2062–2063 (1993).
[Crossref]

N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” IEEE J. Lightwave Technol. 11, 1518–1522 (1993).
[Crossref]

1992 (1)

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

1990 (2)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, “Electrostriction mechanism of soliton interaction in optical fibers,” Opt. Lett. 15, 314–316 (1990).
[Crossref] [PubMed]

P. Bayvel and P. M. Radmore, “Solutions of the SBS equations in single mode optical fibers and implications for fiber transmission systems,” Electron. Lett. 26, 434–436 (1990).
[Crossref]

1986 (1)

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

1980 (1)

1972 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3d editionAcademic Press, New York2001.

Andrekson, P. A.

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
[Crossref]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th edition, Academic Press, New York2001.

Bayvel, P.

P. Bayvel and P. M. Radmore, “Solutions of the SBS equations in single mode optical fibers and implications for fiber transmission systems,” Electron. Lett. 26, 434–436 (1990).
[Crossref]

Bickham, S.

D. Chowdhury, A. Kobyakov, S. Kumar, B. Ruffin, and S. Bickham, “Application of doped optical glass for optical communication,” in Proceedings of XX International Congress on Glass (The Ceramic Society of Japan, Kyoto, Japan, 2004) paper I-01-005.

Bodeep, G. E.

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

Boot, A. J.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd edition, Academic Press, New York2003, Chapter 9.

Bucaro, J. A.

Chi, S.

C. C. Lee and S. Chi, “Measurement of stimulated Brillouin scattering threshold for various types of fibers using Brillouin optical time-domain reflectometer,” IEEE Photon. Technol. Lett. 12, 672–674 (2000).
[Crossref]

Chowdhury, D.

D. Chowdhury, A. Kobyakov, S. Kumar, B. Ruffin, and S. Bickham, “Application of doped optical glass for optical communication,” in Proceedings of XX International Congress on Glass (The Ceramic Society of Japan, Kyoto, Japan, 2004) paper I-01-005.

Chraplyvy, A. R.

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

Chujo, W.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
[Crossref]

Darcie, T. E.

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

de Oliveira, C. A. S.

C. A. S. de Oliveira, C. K. Jen, A. Shang, and C. Saravanos, “Stimulated Brillouin scattering in cascaded fibers of different Brillouin frequency shift,” J. Opt. Soc. Am B 10, 969–972 (1993).
[Crossref]

Delavaux, J. -M.

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

Derosier, R. M.

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

Dianov, E. M.

Dross, F.

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
[Crossref]

Esman, R. D.

R. D. Esman and K. J. Williams, “Brillouin scattering: beyond threshold,” in Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 1996) 227–228, paper ThF5.

Evans, A. F.

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
[Crossref]

Farnell, G. W.

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

Gulati, S. T.

S. T. Gulati and J. D. Helfinstine, “Fatigue behavior of GeO2-SiO2 glasses,” Mat. Res. Soc. Symp. Proc. 531, 133–138 (1998).
[Crossref]

Hansryd, J.

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
[Crossref]

Helfinstine, J. D.

S. T. Gulati and J. D. Helfinstine, “Fatigue behavior of GeO2-SiO2 glasses,” Mat. Res. Soc. Symp. Proc. 531, 133–138 (1998).
[Crossref]

Hughes, R.

Hurley, J. E.

A. Kobyakov, M. Sauer, and J. E. Hurley, “SBS threshold of segmented fibers,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington, DC, 2005), paper OME5.
[PubMed]

Imai, T.

N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” IEEE J. Lightwave Technol. 11, 1518–1522 (1993).
[Crossref]

Jen, C. K.

C. A. S. de Oliveira, C. K. Jen, A. Shang, and C. Saravanos, “Stimulated Brillouin scattering in cascaded fibers of different Brillouin frequency shift,” J. Opt. Soc. Am B 10, 969–972 (1993).
[Crossref]

Jen, C.-K.

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

Knudsen, S. N.

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
[Crossref]

Kobyakov, A.

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
[Crossref]

D. Chowdhury, A. Kobyakov, S. Kumar, B. Ruffin, and S. Bickham, “Application of doped optical glass for optical communication,” in Proceedings of XX International Congress on Glass (The Ceramic Society of Japan, Kyoto, Japan, 2004) paper I-01-005.

A. Kobyakov, M. Sauer, and J. E. Hurley, “SBS threshold of segmented fibers,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington, DC, 2005), paper OME5.
[PubMed]

Koyamada, Y.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
[Crossref]

Kumar, S.

D. Chowdhury, A. Kobyakov, S. Kumar, B. Ruffin, and S. Bickham, “Application of doped optical glass for optical communication,” in Proceedings of XX International Congress on Glass (The Ceramic Society of Japan, Kyoto, Japan, 2004) paper I-01-005.

Kwon, I.-B.

J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” IEEE J. Lightwave Technol. 21, 1779–1786 (2003).
[Crossref]

Lagakos, N.

Lee, C. C.

C. C. Lee and S. Chi, “Measurement of stimulated Brillouin scattering threshold for various types of fibers using Brillouin optical time-domain reflectometer,” IEEE Photon. Technol. Lett. 12, 672–674 (2000).
[Crossref]

Luchnikov, A. V.

Mao, X. P.

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

Mehendale, M.

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
[Crossref]

Muys, W.

F. W. Willems and W. Muys, “Suppression of interferometric noise in externally modulated lightwave AM-CATV systems by phase modulation,” Electron. Lett. 29, 2062–2063 (1993).
[Crossref]

Nakamura, S.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
[Crossref]

Oh, K.

J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” IEEE J. Lightwave Technol. 21, 1779–1786 (2003).
[Crossref]

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, New York2000.

Peral, E.

E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1185–1195 (1999).
[Crossref]

Pilipetskii, A. N.

Radmore, P. M.

P. Bayvel and P. M. Radmore, “Solutions of the SBS equations in single mode optical fibers and implications for fiber transmission systems,” Electron. Lett. 26, 434–436 (1990).
[Crossref]

Ruffin, B.

D. Chowdhury, A. Kobyakov, S. Kumar, B. Ruffin, and S. Bickham, “Application of doped optical glass for optical communication,” in Proceedings of XX International Congress on Glass (The Ceramic Society of Japan, Kyoto, Japan, 2004) paper I-01-005.

Safaai-Jazi, A.

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

Saravanos, C.

C. A. S. de Oliveira, C. K. Jen, A. Shang, and C. Saravanos, “Stimulated Brillouin scattering in cascaded fibers of different Brillouin frequency shift,” J. Opt. Soc. Am B 10, 969–972 (1993).
[Crossref]

Sato, S.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
[Crossref]

Sauer, M.

A. Kobyakov, M. Sauer, and J. E. Hurley, “SBS threshold of segmented fibers,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington, DC, 2005), paper OME5.
[PubMed]

Shang, A.

C. A. S. de Oliveira, C. K. Jen, A. Shang, and C. Saravanos, “Stimulated Brillouin scattering in cascaded fibers of different Brillouin frequency shift,” J. Opt. Soc. Am B 10, 969–972 (1993).
[Crossref]

Shiraki, K.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

Smith, R. G.

Sotobayashi, H.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” IEEE J. Lightwave Technol. 22, 631–639 (2004).
[Crossref]

Starodumov, A. N.

Tateda, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

Tkach, R. W.

X. P. Mao, G. E. Bodeep, R. W. Tkach, A. R. Chraplyvy, T. E. Darcie, and R. M. Derosier, “Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems,” IEEE Photon. Technol. Lett. 4, 287–289 (1992).
[Crossref]

Toulouse, J.

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

Tsuda, S.

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
[Crossref]

van Deventer, M. O.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[Crossref]

Vasilyev, M.

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” IEEE J. Lightwave Technol. 20, 1635–1643 (2002).
[Crossref]

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th edition, Academic Press, New York2001.

Westlund, M.

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen “Increase in the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” IEEE J. Lightwave Technol. 19, 1691–1697 (2001).
[Crossref]

Willems, F. W.

F. W. Willems and W. Muys, “Suppression of interferometric noise in externally modulated lightwave AM-CATV systems by phase modulation,” Electron. Lett. 29, 2062–2063 (1993).
[Crossref]

Williams, K. J.

R. D. Esman and K. J. Williams, “Brillouin scattering: beyond threshold,” in Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 1996) 227–228, paper ThF5.

Yariv, A.

E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1185–1195 (1999).
[Crossref]

Yeniay, A.

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

Yoshizawa, N.

N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” IEEE J. Lightwave Technol. 11, 1518–1522 (1993).
[Crossref]

Yu, J.

J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” IEEE J. Lightwave Technol. 21, 1779–1786 (2003).
[Crossref]

Appl. Opt. (2)

Electron. Lett. (3)

F. W. Willems and W. Muys, “Suppression of interferometric noise in externally modulated lightwave AM-CATV systems by phase modulation,” Electron. Lett. 29, 2062–2063 (1993).
[Crossref]

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Figures (1)

Fig. 1.
Fig. 1.

Normalized index profile, fundamental optical mode f(r), and calculated from (5), (13) acoustic modes ξm (r) with the three smallest Amao for fiber 1 (a) and fiber 2 (b).

Tables (1)

Tables Icon

Table 1. Three smallest Amao in µm2, optical effective area A eff [µm2] calculated from (12) and calculated and measured SBS threshold powers P th in dBm for various GeO2-doped fibers

Equations (25)

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2 ρ t 2 Γ 2 ρ t v l 2 ( r ) 2 ρ = γ 2 2 E 2 ,
E ( r , z , t ) = 1 2 f ( r ) [ A 1 ( z , t ) e i ( ω 1 t β 1 z ) u 1 + A 2 ( z , t ) e i ( ω 2 t + β 2 z ) u 2 ] + c . c . ,
2 E 2 1 2 f 2 ( r ) A 1 ( z , t ) A 2 * ( z , t ) q 2 e i ( Ω t qz ) + c . c . ,
ρ ( z , t , r , θ ) = 1 2 m = 1 M ρ ¯ m ( z , t ) ξ m ( r , θ ) e i ( Ω t qz ) + c . c . ,
2 ξ m ( r , θ ) + [ Ω m 2 v l 2 ( r ) q 2 ] ξ m ( r , θ ) = 0 ,
ρ ¯ m ( z , t ) = γ q 2 A 1 ( z , t ) A 2 * ( z , t ) 2 ( Ω m 2 Ω 2 + i Ω Γ q 2 ) ξ m ( r ) f 2 ( r ) ξ m 2 ( r ) ,
ρ ( z , t , r ) = 1 4 m = 1 M [ ξ m ( r ) ξ m ( r ) f 2 ( r ) ξ m 2 ( r ) γ q 2 A 1 ( z , t ) A 2 * ( z , t ) Ω m 2 Ω 2 + i Ω Γ q 2 e i ( Ω t qz ) ] + c . c .
d P 2 d z α P 2 + g B A m ao 𝓛 ( ν ) P 1 P 2 = 0 .
g B = 4 π n 8 p 12 2 λ 3 ρ 0 c w ν B
𝓛 ( ν ) = ( w 2 ) 2 ( ν ν 1 + ν B ) 2 + ( w 2 ) 2 ,
A m ao = [ f 2 ( r ) ξ m ( r ) f 2 ( r ) ] 2 ξ m 2 ( r ) ,
A eff = f 2 ( r ) 2 f 4 ( r )
v l ( r ) = 5944 [ 1 0.078 Δ % ( r ) ]
P S ( 0 ) = m = 1 M 2 κ T ν B + ν G m ( ν ) d ν = η P 1 ( 0 )
G m ( ν ) = exp [ g B P 1 ( 0 ) A m ao α 𝓛 ( ν ) ( 1 e α L ) α L ] .
e α L 1 e α L m = 1 M exp [ r mk x ( 1 e α L ) ] r mk = x 3 2 B .
B = η A 11 ao α ν B λ π κ T g B cw
P th calc = x A 11 ao α g B .
Δ P th [ dB ] 10 log 10 ( A 1 k ao A 11 ao ) .
2 E ε L c 2 2 E t 2 μ 0 2 𝓟 NL t 2 = 0
2 E = ε tot c 2 2 E t 2 ,
ε NL = ξ m [ U A 1 A 2 * e i ( ω 1 ω 2 ) t i ( β 1 + β 2 ) z + c . c . ]
U = γ 2 q 2 4 ρ 0 ε 0 ( Ω m 2 Ω 2 + i Ω Γ q 2 ) ξ m f 2 ξ m 2 .
A j 2 f ( r ) f ( r ) ( 2 i β i A j z ± β j 2 A j )
= [ n 2 ( r ) i n α c ω ] f ( r ) c 2 A j ω 2 U ˜ ξ m ( r ) f ( r ) c 2 ω 2 A j A 3 j 2 ,

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