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.

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References

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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)

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]

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).

2006 (2)

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]

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]

2005 (5)

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]

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]

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]

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)

2002 (3)

1999 (1)

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)

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.

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.

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.

Cambon, P.

Chen, L.

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.

Deparis, O.

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.

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.

Le Floch, S.

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.

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.

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.

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.

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.

Zou, L.

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)

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]

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]

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]

IEEE Trans. Evol. Comput. (2)

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]

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]

IEEE Trans. Magn. (1)

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]

IEEE Trans. Microw. Theory Tech. (1)

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]

Inf. Process. Lett. (1)

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]

J. Lightwave Technol. (3)

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]

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]

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]

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

Microw. Opt. Technol. Lett. (2)

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]

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]

Opt. Lett. (3)

Phys. Rev. A (1)

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

Other (2)

R. W. Boyd, Nonlinear Optics, 2nd ed., (Academic Press; 2 edition, 2002).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed., (Academic Press, New York, 2006).

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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

Tables Icon

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)

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

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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