## Particle swarm optimization on threshold exponential gain of stimulated Brillouin scattering in single mode fibers |

Optics Express, Vol. 19, Issue 3, pp. 1842-1853 (2011)

http://dx.doi.org/10.1364/OE.19.001842

Acrobat PDF (1314 KB)

### 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

## 1. Introduction

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]

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]

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]

*G*, on the numerical aperture, pump laser wavelength and the optical loss coefficient in single mode optical fibers. These parameters are usually chosen to describe the fiber sensitivity to SBS which is initiated by spontaneous Brillouin scattering interaction along optical fibers.

_{th}## 2. Implementation of PSO algorithm

_{best}. On the other hand, the position vector of the best solution (fitness) this particle can be achieved (called l

_{best}) when each particle (solution) moves towards its previous best position and towards the best particle in its restricted local neighborhood. The detailed process for implementing PSO was described in [9

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]

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]

## 3. Initiation of SBS source models and optimization

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]

*r*), the SBS threshold occurrence and noise properties such as the Brillouin amplification gain factor

*G*and linewidth variations. Here,

*r*is defined as the ratio between the average Stokes intensity and the intensity of the laser pump power at the near end of optical fiber. The transition between the spontaneous and stimulated processes is not really steep, in the sense that when the Stokes and laser pump waves are simultaneously present in the fiber, there may be a stimulation of the acoustic wave. Two different models can be distinguished, corresponding to the origin of SBS: 1. Localized, nonfluctuating source model. 2. Distributed (nonlocalized), fluctuating source model.

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

*c*is the velocity of light,

*α*is the optical loss coefficient in the fiber,

*ρ*is the acoustic density disturbance with a velocity

*f*, which is responsible for the thermal excitation of acoustic waves (spontaneous Brillouin scattering) and which lead to the initiation of the SBS process,

*Floch et. al.*solved Eqs. (3)–(5) in a low-loss medium, using Fourier Transform technique, to give the backward Stokes wave intensity

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]

*K*is the Boltzman constant,

*T*is the temperature, the effective mode cross-sectional area is

*L*is the fiber length. The Brillouin amplification gain factor

*G*is defined as

*g*and the threshold exponential gain

_{B}*G*and it can be defined as [22

_{th}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]

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]

*α*and the normalized frequency parameter

*V*, is [23

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]

*NA*that can be calculated from the refractive indices of the core (

*n*) and cladding (

_{1}*n*) as;

_{2}## 4. Experimental and simulation results

*P*) is launched into a single mode fiber (SMF) through an erbium doped fiber amplifier (EDFA) and circulator (Cir). The pump power (

_{p}*P*) and its backward scattering Stokes peak power (

_{p}*P*) are measured by an optical spectrum analyzer (OSA) at port 1 and 3 respectively.

_{s}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]

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]

*NA*and

*G*of 21 is commonly used in the localized, nonfluctuating source model, independent of the optical fiber lengths, which was originally calculated at (

_{th}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]

**20**(6), 1132–1137 (2003). [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]

## 5. Conclusions

## Acknowledgments

## References and links

1. | R. W. Boyd, |

2. | E. L. Buckland, “Mode-profile dependence of the electrostrictive response in fibers,” Opt. Lett. |

3. | E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. |

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. |

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. |

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. |

8. | A. Yeniay, J. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. |

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. |

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. |

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. |

12. | J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antenn. Propag. |

13. | D. Boeringer and D. Werner, “Particle swarm optimization versus genetic algorithms for phased array synthesis,” IEEE Trans. Antenn. Propag. |

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. |

15. | S. Mikki and A. A. Kishk, “Improved particle swarm optimization technique using Hard boundary conditions,” Microw. Opt. Technol. Lett. |

16. | X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. |

17. | M. Clerc and J. Kennedy, “The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space,” IEEE Trans. Evol. Comput. |

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. |

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. |

20. | R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A |

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 |

22. | R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. |

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. |

24. | V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Trans. Evol. Comput. |

25. | M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.5890) Nonlinear optics : Scattering, stimulated

(290.5900) Scattering : Scattering, stimulated Brillouin

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 7, 2010

Revised Manuscript: October 15, 2010

Manuscript Accepted: October 15, 2010

Published: January 18, 2011

**Citation**

H. A. Al-Asadi, M. H. Al-Mansoori, S. Hitam, M. I. Saripan, and M. A. Mahdi, "Particle swarm optimization on threshold exponential gain of stimulated Brillouin scattering in single mode fibers," Opt. Express **19**, 1842-1853 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-1842

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### References

- R. W. Boyd, Nonlinear Optics, 2nd ed., (Academic Press; 2 edition, 2002).
- E. L. Buckland, “Mode-profile dependence of the electrostrictive response in fibers,” Opt. Lett. 24(13), 872–874 (1999). [CrossRef]
- E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fiber,” Appl. Phys. Lett. 21(11), 539–541 (1972). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 4th ed., (Academic Press, New York, 2006).
- 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).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- X. Shenheng and Y. Rahmat-Samii, “Boundary conditions in particle swarm optimization revisited,” IEEE Trans. Antenn. Propag. 55(3), 760–765 (2007). [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]
- 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]
- 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]
- R. Boyd, K. Rza̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]

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