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, 2d edition Academic Press, New York 2003, 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 Tech. 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 Tech. 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 York 2000.
  18. G. P. Agrawal, Nonlinear Fiber Optics, 3d edition Academic Press, New York 2001.
  19. M. O. van Deventer and A. J. Boot, �??Polarization properties of stimulated Brillouin scattering in single-mode fibers,�?? IEEE J. Lightwave Tech. 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 GeO_2-SiO_2 glasses,�?? Mat. Res. Soc. Symp. Proc. 531, 133-138 (1998).
    [CrossRef]
  22. <a href="http://www.corning.com/opticalfiber/products__applications/products/nexcor.aspx">http://www.corning.com/opticalfiber/products__applications/products/nexcor.aspx</a>
  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 Tech. 20, 1635-1643 (2002).
    [CrossRef]
  28. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th edition, Academic Press, New York 2001.

Applied Optics

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]

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]

Electron. Lett.

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]

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]

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]

IEEE J. Lightwave Tech.

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

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, �??Simulating and designing Brillouin gain spectrum in single-mode fibers,�?? IEEE J. Lightwave Tech. 22, 631-639 (2004).
[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 Tech. 20, 1635-1643 (2002).
[CrossRef]

M. O. van Deventer and A. J. Boot, �??Polarization properties of stimulated Brillouin scattering in single-mode fibers,�?? IEEE J. Lightwave Tech. 12, 585-590 (1994).
[CrossRef]

IEEE J. Lightwave Technol.

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]

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]

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]

IEEE J. Quantum Electron.

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]

IEEE Photon. Technol. Lett.

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]

IEEE Photon. Techonol. Lett.

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]

IEEE Trans. Ultrason. Ferroelectr. Freq.

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).

J. Opt. Soc. Am B

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]

Mat. Res. Soc. Symp. Proc.

S. T. Gulati and J. D. Helfinstine, �??Fatigue behavior of GeO_2-SiO_2 glasses,�?? Mat. Res. Soc. Symp. Proc. 531, 133-138 (1998).
[CrossRef]

Opt. Lett.

Optical Fiber Communication Conference

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]

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.

Other

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th edition, Academic Press, New York 2001.

<a href="http://www.corning.com/opticalfiber/products__applications/products/nexcor.aspx">http://www.corning.com/opticalfiber/products__applications/products/nexcor.aspx</a>

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.

Patent application US Publication No. 2004/0218882.

R. W. Boyd, Nonlinear Optics, 2d edition Academic Press, New York 2003, Chapter 9.

K. Okamoto, Fundamentals of Optical Waveguides Academic Press, New York 2000.

G. P. Agrawal, Nonlinear Fiber Optics, 3d edition Academic Press, New York 2001.

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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)

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

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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