Abstract

We implement a particle swarm optimization (PSO) algorithm to characterize stimulated Brillouin scattering phenomena in optical fibers. The explicit and strong dependence of the threshold exponential gain on the numerical aperture, the pump laser wavelength and the optical loss coefficient are presented. The proposed PSO model is also evaluated with the localized, nonfluctuating source model and the distributed (non-localized) fluctuating source model. Using our model, for fiber lengths from 1 km to 29 km, the calculated threshold exponential gain of stimulated Brillouin scattering is gradually decreased from 17.4 to 14.6 respectively. The theoretical results of Brillouin threshold power predicted by the proposed PSO model show a good agreement with the experimental results for different fiber lengths from 1 km to 12 km.

© 2011 OSA

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  1. R. W. Boyd, Nonlinear Optics, 2nd ed., (Academic Press; 2 edition, 2002).
  2. E. L. Buckland, “Mode-profile dependence of the electrostrictive response in fibers,” Opt. Lett. 24(13), 872–874 (1999).
    [CrossRef]
  3. E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. 21(11), 539–541 (1972).
    [CrossRef]
  4. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed., (Academic Press, New York, 2006).
  5. Z. Weiwen, H. Zuyuan, K. Masato, and H. Kazuo, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 3, 600–602 (2007).
  6. L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
    [CrossRef] [PubMed]
  7. 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(1), 66–69 (1992).
    [CrossRef]
  8. A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20(8), 1425–1432 (2002).
    [CrossRef]
  9. S. Cui and D. S. Weile, “Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers,” IEEE Trans. Antenn. Propag. 53(11), 3616–3624 (2005).
    [CrossRef]
  10. J. Perez and J. Basterrechea, “Particle swarm optimization and its application to antenna far-field pattern prediction from planner scanning,” Microw. Opt. Technol. Lett. 44(5), 398–403 (2005).
    [CrossRef]
  11. W. Wang, Y. Lu, J. S. Fu, and Y. Z. Xiong, “Particle swarm optimization and finite-element based approach for microwave filter design,” IEEE Trans. Magn. 41(5), 1800–1803 (2005).
    [CrossRef]
  12. J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antenn. Propag. 52(2), 397–407 (2004).
    [CrossRef]
  13. D. Boeringer and D. Werner, “Particle swarm optimization versus genetic algorithms for phased array synthesis,” IEEE Trans. Antenn. Propag. 52(3), 771–779 (2004).
    [CrossRef]
  14. M. Jiang, Y. P. Luo, and S. Y. Yang, “Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm,” Inf. Process. Lett. 102(1), 8–16 (2007).
    [CrossRef]
  15. S. Mikki and A. A. Kishk, “Improved particle swarm optimization technique using Hard boundary conditions,” Microw. Opt. Technol. Lett. 46(5), 422–426 (2005).
    [CrossRef]
  16. X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. 55(3), 760–765 (2007).
    [CrossRef]
  17. M. Clerc and J. Kennedy, “The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
    [CrossRef]
  18. M. Donelli and A. Massa, “Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers,” IEEE Trans. Microw. Theory Tech. 53(5), 1761–1776 (2005).
    [CrossRef]
  19. A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
    [CrossRef]
  20. R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
    [CrossRef] [PubMed]
  21. 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(6), 1132–1137 (2003).
    [CrossRef]
  22. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
    [CrossRef] [PubMed]
  23. M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
    [CrossRef]
  24. V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Trans. Evol. Comput. 10(3), 245–255 (2006).
    [CrossRef]
  25. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
    [CrossRef]

2007 (3)

Z. Weiwen, H. Zuyuan, K. Masato, and H. Kazuo, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 3, 600–602 (2007).

M. Jiang, Y. P. Luo, and S. Y. Yang, “Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm,” Inf. Process. Lett. 102(1), 8–16 (2007).
[CrossRef]

X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. 55(3), 760–765 (2007).
[CrossRef]

2006 (2)

L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
[CrossRef] [PubMed]

V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Trans. Evol. Comput. 10(3), 245–255 (2006).
[CrossRef]

2005 (5)

S. Cui and D. S. Weile, “Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers,” IEEE Trans. Antenn. Propag. 53(11), 3616–3624 (2005).
[CrossRef]

J. Perez and J. Basterrechea, “Particle swarm optimization and its application to antenna far-field pattern prediction from planner scanning,” Microw. Opt. Technol. Lett. 44(5), 398–403 (2005).
[CrossRef]

W. Wang, Y. Lu, J. S. Fu, and Y. Z. Xiong, “Particle swarm optimization and finite-element based approach for microwave filter design,” IEEE Trans. Magn. 41(5), 1800–1803 (2005).
[CrossRef]

S. Mikki and A. A. Kishk, “Improved particle swarm optimization technique using Hard boundary conditions,” Microw. Opt. Technol. Lett. 46(5), 422–426 (2005).
[CrossRef]

M. Donelli and A. Massa, “Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers,” IEEE Trans. Microw. Theory Tech. 53(5), 1761–1776 (2005).
[CrossRef]

2004 (2)

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antenn. Propag. 52(2), 397–407 (2004).
[CrossRef]

D. Boeringer and D. Werner, “Particle swarm optimization versus genetic algorithms for phased array synthesis,” IEEE Trans. Antenn. Propag. 52(3), 771–779 (2004).
[CrossRef]

2003 (1)

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(6), 1132–1137 (2003).
[CrossRef]

2002 (3)

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[CrossRef]

M. Clerc and J. Kennedy, “The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[CrossRef]

A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20(8), 1425–1432 (2002).
[CrossRef]

1999 (1)

E. L. Buckland, “Mode-profile dependence of the electrostrictive response in fibers,” Opt. Lett. 24(13), 872–874 (1999).
[CrossRef]

1994 (1)

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[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(1), 66–69 (1992).
[CrossRef]

1990 (1)

R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

1989 (1)

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[CrossRef]

1972 (2)

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
[CrossRef] [PubMed]

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[CrossRef]

Artiglia, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[CrossRef]

Bao, X.

L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
[CrossRef] [PubMed]

Basterrechea, J.

J. Perez and J. Basterrechea, “Particle swarm optimization and its application to antenna far-field pattern prediction from planner scanning,” Microw. Opt. Technol. Lett. 44(5), 398–403 (2005).
[CrossRef]

Blondel, M.

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[CrossRef]

Boeringer, D.

D. Boeringer and D. Werner, “Particle swarm optimization versus genetic algorithms for phased array synthesis,” IEEE Trans. Antenn. Propag. 52(3), 771–779 (2004).
[CrossRef]

Boot, A. J.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

Boyd, R.

R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

Buckland, E. L.

E. L. Buckland, “Mode-profile dependence of the electrostrictive response in fibers,” Opt. Lett. 24(13), 872–874 (1999).
[CrossRef]

Cambon, P.

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(6), 1132–1137 (2003).
[CrossRef]

Chen, L.

L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
[CrossRef] [PubMed]

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(1), 66–69 (1992).
[CrossRef]

Clerc, M.

M. Clerc and J. Kennedy, “The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[CrossRef]

Coppa, G.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[CrossRef]

Cui, S.

S. Cui and D. S. Weile, “Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers,” IEEE Trans. Antenn. Propag. 53(11), 3616–3624 (2005).
[CrossRef]

Delavaux, J.

A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20(8), 1425–1432 (2002).
[CrossRef]

Deparis, O.

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[CrossRef]

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(1), 66–69 (1992).
[CrossRef]

Di Vita, P.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[CrossRef]

Donelli, M.

M. Donelli and A. Massa, “Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers,” IEEE Trans. Microw. Theory Tech. 53(5), 1761–1776 (2005).
[CrossRef]

Fleming, P. J.

V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Trans. Evol. Comput. 10(3), 245–255 (2006).
[CrossRef]

Fotiadi, A. A.

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[CrossRef]

Fu, J. S.

W. Wang, Y. Lu, J. S. Fu, and Y. Z. Xiong, “Particle swarm optimization and finite-element based approach for microwave filter design,” IEEE Trans. Magn. 41(5), 1800–1803 (2005).
[CrossRef]

Ippen, E. P.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[CrossRef]

Jiang, M.

M. Jiang, Y. P. Luo, and S. Y. Yang, “Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm,” Inf. Process. Lett. 102(1), 8–16 (2007).
[CrossRef]

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(1), 66–69 (1992).
[CrossRef]

Kadirkamanathan, V.

V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Trans. Evol. Comput. 10(3), 245–255 (2006).
[CrossRef]

Kazuo, H.

Z. Weiwen, H. Zuyuan, K. Masato, and H. Kazuo, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 3, 600–602 (2007).

Kennedy, J.

M. Clerc and J. Kennedy, “The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[CrossRef]

Kishk, A. A.

S. Mikki and A. A. Kishk, “Improved particle swarm optimization technique using Hard boundary conditions,” Microw. Opt. Technol. Lett. 46(5), 422–426 (2005).
[CrossRef]

Kiyan, R.

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[CrossRef]

Le Floch, S.

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(6), 1132–1137 (2003).
[CrossRef]

Lu, Y.

W. Wang, Y. Lu, J. S. Fu, and Y. Z. Xiong, “Particle swarm optimization and finite-element based approach for microwave filter design,” IEEE Trans. Magn. 41(5), 1800–1803 (2005).
[CrossRef]

Luo, Y. P.

M. Jiang, Y. P. Luo, and S. Y. Yang, “Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm,” Inf. Process. Lett. 102(1), 8–16 (2007).
[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(1), 66–69 (1992).
[CrossRef]

Masato, K.

Z. Weiwen, H. Zuyuan, K. Masato, and H. Kazuo, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 3, 600–602 (2007).

Massa, A.

M. Donelli and A. Massa, “Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers,” IEEE Trans. Microw. Theory Tech. 53(5), 1761–1776 (2005).
[CrossRef]

Mégret, P.

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[CrossRef]

Mikki, S.

S. Mikki and A. A. Kishk, “Improved particle swarm optimization technique using Hard boundary conditions,” Microw. Opt. Technol. Lett. 46(5), 422–426 (2005).
[CrossRef]

Narum, P.

R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

Perez, J.

J. Perez and J. Basterrechea, “Particle swarm optimization and its application to antenna far-field pattern prediction from planner scanning,” Microw. Opt. Technol. Lett. 44(5), 398–403 (2005).
[CrossRef]

Potenza, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[CrossRef]

Rahmat-Samii, Y.

X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. 55(3), 760–765 (2007).
[CrossRef]

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antenn. Propag. 52(2), 397–407 (2004).
[CrossRef]

Ravet, F.

L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
[CrossRef] [PubMed]

Robinson, J.

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antenn. Propag. 52(2), 397–407 (2004).
[CrossRef]

Rza¸ewski, K.

R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

Selvarajah, K.

V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Trans. Evol. Comput. 10(3), 245–255 (2006).
[CrossRef]

Sharma, A.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[CrossRef]

Shenheng, X.

X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. 55(3), 760–765 (2007).
[CrossRef]

Smith, R. G.

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
[CrossRef] [PubMed]

Stolen, R. H.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[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(1), 66–69 (1992).
[CrossRef]

Toulouse, J.

A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20(8), 1425–1432 (2002).
[CrossRef]

van Deventer, M. O.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

Wang, W.

W. Wang, Y. Lu, J. S. Fu, and Y. Z. Xiong, “Particle swarm optimization and finite-element based approach for microwave filter design,” IEEE Trans. Magn. 41(5), 1800–1803 (2005).
[CrossRef]

Weile, D. S.

S. Cui and D. S. Weile, “Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers,” IEEE Trans. Antenn. Propag. 53(11), 3616–3624 (2005).
[CrossRef]

Weiwen, Z.

Z. Weiwen, H. Zuyuan, K. Masato, and H. Kazuo, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 3, 600–602 (2007).

Werner, D.

D. Boeringer and D. Werner, “Particle swarm optimization versus genetic algorithms for phased array synthesis,” IEEE Trans. Antenn. Propag. 52(3), 771–779 (2004).
[CrossRef]

Xiong, Y. Z.

W. Wang, Y. Lu, J. S. Fu, and Y. Z. Xiong, “Particle swarm optimization and finite-element based approach for microwave filter design,” IEEE Trans. Magn. 41(5), 1800–1803 (2005).
[CrossRef]

Yang, S. Y.

M. Jiang, Y. P. Luo, and S. Y. Yang, “Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm,” Inf. Process. Lett. 102(1), 8–16 (2007).
[CrossRef]

Yeniay, A.

A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20(8), 1425–1432 (2002).
[CrossRef]

Zou, L.

L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
[CrossRef] [PubMed]

Zuyuan, H.

Z. Weiwen, H. Zuyuan, K. Masato, and H. Kazuo, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 3, 600–602 (2007).

Appl. Opt. (2)

L. Zou, X. Bao, F. Ravet, and L. Chen, “Distributed Brillouin fiber sensor for detecting pipeline buckling in an energy pipe under internal pressure,” Appl. Opt. 45(14), 3372–3377 (2006).
[CrossRef] [PubMed]

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[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(1), 66–69 (1992).
[CrossRef]

IEEE Trans. Antenn. Propag. (4)

S. Cui and D. S. Weile, “Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers,” IEEE Trans. Antenn. Propag. 53(11), 3616–3624 (2005).
[CrossRef]

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antenn. Propag. 52(2), 397–407 (2004).
[CrossRef]

D. Boeringer and D. Werner, “Particle swarm optimization versus genetic algorithms for phased array synthesis,” IEEE Trans. Antenn. Propag. 52(3), 771–779 (2004).
[CrossRef]

X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. 55(3), 760–765 (2007).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Particle swarm optimization algorithm flowchart used in this work.

Fig. 2
Fig. 2

Experimental setup to measure SBS threshold using single mode optical fiber.

Fig. 3
Fig. 3

Characteristics of threshold exponential gain with respect to (a) optimal numerical aperture, and (b) optimal pump laser wavelength.

Fig. 4
Fig. 4

Characteristics of (a) threshold exponential gain and (b) threshold power of SBS with respect to fiber length.

Tables (4)

Tables Icon

Table 1 Ranges of parameter values used in PSO algorithm to determine SMF sensitivity on SBS effect

Tables Icon

Table 2 Simulation parameters used for PSO algorithm

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Table 3 Parameters of PSO used for the purpose of optimizations

Tables Icon

Table 4 PSO results of SMF parameters sensitivity to SBS for different fiber lengths

Equations (12)

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v i j k = w v i j k 1 + c 1 r 1 ( p b i j k 1 x i j k 1 ) + c 2 r 2 ( g b j k 1 x i j k 1 ) ,
x i j k = x i j k 1 + v i j k ,
E L z + n 1 c E L t + α E L = i γ e ω s 4 ρ o n 1 c ρ E s ,
E s z n 1 c E s t α E s = i γ e ω L 4 ρ o n 1 c ρ * E L ,
v A ρ z + ρ t + 1 2 τ B ρ = i γ e ε o q 2 4 Ω E s E L * + f ,
I s ( 0 ) = K T Γ B 4 A e f f v L v B exp ( α L ) . G . exp ( G 2 ) [ I o ( G 2 ) I 1 ( G 2 ) ]
I L z + α I L = g B I L I S ,
I s z α I s = g B I L I S .
P t h = G t h A e f f g B L e f f .
G t h = ln [ 4 A e f f v B c G 3 / 2 π 1 / 2 g B K T Γ B λ L L e f f ] .
w 0 = α [ 0.632 + 1.478 V 3 / 2 + 4.76 V 6 ] ,
sin   θ 1 2 = N A = n 1 2 n 2 2 .

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