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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 1842–1853
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Particle swarm optimization on threshold exponential gain of stimulated Brillouin scattering in single mode fibers

H. A. Al-Asadi, M. H. Al-Mansoori, S. Hitam, M. I. Saripan, and M. A. Mahdi  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 1842-1853 (2011)
http://dx.doi.org/10.1364/OE.19.001842


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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

Among all optical non-linear effects observed in single-mode optical fiber, stimulated Brillouin scattering (SBS) particu1ar is of importance since it has numerous practical implications. When the intensity of the pump beam becomes important, the change in index of the environment induced by the wave and the scattering process becomes stimulated Brillouin [1

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

]. Basically, the environment will react to beating of optical waves through electrostriction [2

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

]. When an electromagnetic field is applied to an environment, material migrates through electrostriction to the regions where the electromagnetic field is most intense. Thus, the interaction between pump and scattered waves through hypersonic acoustic waves in the medium, leads to a beat frequency. The backscattered Stokes wave is down shifted in frequency with respect to the incident lightwave frequency. This effect is called as Brillouin frequency shift which depends on fiber parameters and wavelength of the incident light [3

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

]. The frequency shift is directly proportional to the acoustic velocity and ranges from 12 to 13 GHz for a silica fiber at wavelength of 1.5 µm [4

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

]. When the environmental quantities, such as temperature and strain changing the acoustic velocity, the Brillouin frequency shift is also changed [5

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).

]. For SBS, this feature is very useful for temperature and strain monitoring in optical fibers and it has been used widely in the design of fiber optic sensors [6

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]

].

In spontaneous scattering regime, where wave propagates through an optical fiber, only a very small part of its intensity is backscattered due to Brillouin effect. However, when the intensity of incident pump then the wave becomes very strong, this will result the regime of SBS is achieved and the conversion efficiency of pump wave into Stokes wave can reach several tens of percent, which is called SBS efficiency [7

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]

].

The aim of this paper is to implement the PSO algorithm in order to optimize and characterize the dependence of threshold exponential gain Gth, 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.

2. Implementation of PSO algorithm

In theory, let D be the particle swarm population, as in D-dimensional. Each the i-th particle can be represented as an object with several characteristics bounded by a D-dimensional vector, Xi=(xi1,xi2,...,xiD)T . The velocity of this particle can be bounded by another D-dimensional vector Vi=(vi1,vi2,...,viD)T, Pi=(pi1,pi2,...,piD)T is denoted as the best previously visited position of the i-th particle and also the best position explored so far known as gi=(gi1,gi2,...,giD)T. In all cases, T is the transpose operator. The g-th particle is the best as the index of the best particle in the swarm. Then the PSO algorithm can be described as below [17

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]

];
vijk=wvijk1+c1r1(pbijk1xijk1)+c2r2(gbjk1xijk1),
(1)
xijk=xijk1+vijk,
(2)
where c1 and c2 are positive constants, called acceleration constants (c1 is the self-confidence (cognitive) factor and c2 is the swarm confidence (social) factor), usually c1 and c2are in the range from 1.5 to 2.5, and r1 and r2 are two random functions uniformly distributed in the range [0, 1]. wis the inertia weight factor that takes linearly decreasing values downward from 1 to 0 [18

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]

]. The size of swarm population is ascertained by i = 1, 2, …, N and j = 1,2, …, D, where N is the size of swarm population and k=1, 2, ...,determines the iteration number.

Equations (1) and (2) describe the flight trajectory of a population of particles. The velocity is dynamically updated as described by Eq. (1) and the position update of the flying particles is determined by Eq. (2). The effect of the particle inertia, the particle memory influence, and the swarm (society) influence represent the 1st term, 2nd term, and 3rd term in Eq. (1), respectively. The flowchart of the procedure is shown in Fig. 1
Fig. 1 Particle swarm optimization algorithm flowchart used in this work.
.

3. Initiation of SBS source models and optimization

The scattering of light is functionally linked to the presence of inhomogeneities in the optical characteristic of the medium itself. Spontaneous Brillouin scattering follows from adiabatic density fluctuations, i.e. periodic perturbations of the refractive index generated by acoustic waves (acoustic phonons) of thermal origin. The amplitude of the Brillouin scattering is relatively low in the spontaneous regime, approximately 100 times less than intensity of the Rayleigh scattering [19

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]

]. It relates directly to the number of acoustic phonons in the fiber, which itself are simply determined by the thermal excitation. However, under stimulated environments, the population of phonons participating in the interaction lies in the strongly non-equilibrium conditions and therefore it grows very rapidly. As a result, the efficiency of the scattering process is thus significantly increased. So that at a certain level of intensity, optical fiber acts as a mirror and all the additional power that is injected automatically reflect. The phenomenon that is causing the stimulation of Brillouin scattering and leads to the creation of acoustics phonons in the presence of light in the fiber is electrostriction [1

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

].

In reality, the configurations can be categorized depending on whether the Stokes wave is derived from the Brillouin spontaneous circulation or whether the wave has been artificially introduced into the environment. We can classify it as the Brillouin generator, if the Stokes wave grows from the spontaneous scattering or Brillouin amplifier when an external signal is injected into the medium. The external signal must have an adequate frequency, i.e. close to that of Stokes waves released spontaneously by the community, to undergo amplification by SBS effect.

The operation of a Brillouin generator is generally characterized by SBS efficiency (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.

The origin of SBS is ascribed to spontaneous Brillouin scattering in the first model, but the actual source of the SBS phenomena by a spatially distributed fluctuation noise source in the second model. In both cases of SBS generator or amplifier the optical laser and Stokes fields describe the SBS including the initiation of noise are given by [20

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

];
ELz+n1cELt+αEL=iγeωs4ρon1cρEs,
(3)
Eszn1cEstαEs=iγeωL4ρon1cρ*EL,
(4)
vAρz+ρt+12τBρ=iγeεoq24ΩEsEL*+f,
(5)
where EL, Esare the forward laser and backward Stokes wave amplitudes in Brillouin medium, ωL, ωsare the laser and backward Stokes wave frequencies, n1 is the core refractive index, c is the velocity of light, α is the optical loss coefficient in the fiber, ρ is the acoustic density disturbance with a velocity vA caused by the Langevin noise source f, which is responsible for the thermal excitation of acoustic waves (spontaneous Brillouin scattering) and which lead to the initiation of the SBS process, λe=ρερ is the electrostrictive coupling coefficient of the medium, εo is the medium dielectric constant, ρo is the material density, τB is the acoustic phonon lifetime (inverse of the phonon decay rate ΓB=2πΔvB, ΔvB is the Brillouin linewidth), the acoustic frequency is defined by Ω=ωLωs, and the acoustic wave number is determined by q=kLks .

Floch et. al. solved Eqs. (3)(5) in a low-loss medium, using Fourier Transform technique, to give the backward Stokes wave intensity Is(z), at the fiber input as [21

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]

];
Is(0)=KTΓB4AeffvLvBexp(αL).G.exp(G2)[Io(G2)I1(G2)]
(6)
where K is the Boltzman constant, T is the temperature, the effective mode cross-sectional area is Aeff, vB the Brillouin frequency shift, and L is the fiber length. The Brillouin amplification gain factor G is defined as G=gBIL(0)Leff. The interaction (effective) length is Leff=1α[1exp(αL)] and gB is a Brillouin gain coefficient. Io, I1 are the modified Bessel functions of zeroth and first orders, respectively. The optical intensities of the fields can be defined as IL,s=12n1εo|EL,s|2.

The steady state behavior of the forward laser pump power intensity IL(z) and backward Stokes wave intensity Is(z) are usually reduce to two equations depending on Eqs. (3)(5). These can be rewritten in simple form of;

ILz+αIL=gBILIS,
(7)
IszαIs=gBILIS.
(8)

This model is called as the localized, nonfluctuating source model. Depending on this model, the backward Stokes wave intensity at near end of optical fiber is given by Is(0)=Is(L)exp(IL(0)gBLeffαL), where IL(0)is the forward laser pump power intensity at z=0. In the case of an SBS amplifier Is(L) (backward Stokes wave intensity at the far end of optical fiber) is generated externally and so its magnitude is known, but for the generator this arises from spontaneous scattering and is therefore generated internally and so its size is unknown. However, it is possible to estimate the size of spontaneous scattering from the threshold condition for SBS. Threshold parameters that are commonly used to characterize the SBS phenomenon are the threshold power and threshold exponential gain.

In low-loss optical fibers, the localized, nonfluctuating source model has typically used to find the SBS threshold power, when SBS is seed with noise. The fit parameters in this model are the Brillouin gain coefficient gB and the threshold exponential gain Gth and it can be defined as [22

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]

];
Pth=GthAeffgBLeff.
(9)
Gth can be defined physically as the amplification factor of the seeded Stokes wave to the output Stokes wave power level of rPth at the input of optical fiber. The term SBS efficiency that is used to describe the ratio between the backward Stokes wave intensity Is(z) and the laser pump wave intensity IL(z) at z=0as r=Is(0)/IL(0) .

The localized, nonfluctuating source model was apparently the first to use the term SBS efficiency equal to one (r=1) to find the threshold exponential gain as a constant value (Gth=21), independent of the laser pump characteristic and the optical fiber. As a result of Eqs. (6) and (9), we define threshold exponential gain with the mean value of Brillouin amplification gain factor [21

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]

];

Gth=ln[4AeffvBcG3/2π1/2gBKTΓBλLLeff].
(10)

Equation (10) shows that the threshold exponential gain is directly and inversely proportional to the effective mode cross-sectional area and the effective length of optical fiber, respectively.

For cylindrical waveguide fibers, the properties of fiber and the pump laser wavelength lead to estimate the maximum effective area. For single mode fiber the light mode can be approximated by a Gaussian and the area is simply (πwo2), where w0 is the 1/e field radius. w0 can be calculated from the fiber core radius 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]

];
w0=α[0.632+1.478V3/2+4.76V6],
(11)
where V=2πaλLn12n22, and n2 is the cladding refraction index.

The optical fiber is also characterized by another coefficient which is the maximum half-angle accepted by the fiber. This coefficient is also known as the numerical aperture, NA that can be calculated from the refractive indices of the core (n1) and cladding (n2) as;

sin θ12=NA=n12n22.
(12)

4. Experimental and simulation results

The experimental setup for the SBS threshold is shown in Fig. 2
Fig. 2 Experimental setup to measure SBS threshold using single mode optical fiber.
. The pump wave (Pp) is launched into a single mode fiber (SMF) through an erbium doped fiber amplifier (EDFA) and circulator (Cir). The pump power (Pp) and its backward scattering Stokes peak power (Ps) are measured by an optical spectrum analyzer (OSA) at port 1 and 3 respectively.

The PSO algorithm, implemented in MATLAB, is capable of minimizing threshold exponential gain. Parameter values required in numerical calculations are listed in Table 2

Table 2. Simulation parameters used for PSO algorithm

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.

The goal of the optimization algorithm is to locate all the global best values of the optical fiber parameters that used to characterize SBS, numerical aperture, pump laser wavelength and optical loss coefficient. The PSO algorithm can actually achieve that goal for fiber length from 1 to 29 km with 2 km step. In this case, the fiber length is not optimized and is just used for the purpose of comparison. The optimum values of three parameters with different optical fiber lengths are then calculated as shown in Table 4

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

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.

The optimum threshold exponential gain Gth, depends on the optimal value of these three parameters as presented in Table 4. In addition, the effective length of optical fiber is also influenced by these optimal parameters. Figure 3
Fig. 3 Characteristics of threshold exponential gain with respect to (a) optimal numerical aperture, and (b) optimal pump laser wavelength.
reports the threshold exponential gain as a function of optimal NA and λLwith different lengths of optical fiber from 1 km to 29 km with step of 2 km. When NA increases to the value over 1.4 and decreases λL to the value less than 1555 nm, they reduce the efficiency of the SBS interaction and the optimal Gth decreases dramatically and it is closer ≈14.6.

The dependence of the exponential gain on the optical fiber lengths using PSO model is shown in Fig. 4(a)
Fig. 4 Characteristics of (a) threshold exponential gain and (b) threshold power of SBS with respect to fiber length.
. The constant value of Gth of 21 is commonly used in the localized, nonfluctuating source model, independent of the optical fiber lengths, which was originally calculated at (r=1) [21

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]

]. On the other hand, based on Eqs. (9) and (10), the numerical results of power and exponential gain at threshold by using the distributed (nonlocalized), fluctuating source model are plotted as in [21

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]

]. For short fibers (L < 5 km with low optical attenuation), the threshold exponential gain is increased from 17.0 to 18.3. The similar pattern is also observed for the PSO model, the threshold exponential gain increases from 15.9 to 17.4 in the range of 1-5 km fiber lengths. For long fibers (L > 5 km with high optical attenuation), the threshold exponential gain is gradually decreased to about 16.6 and 14.6 for the distributed (nonlocalized), fluctuating source model and PSO model respectively.

For the experimental configuration shown in Fig. 2, the measured SBS threshold power is in the range of 37.7 mW to 8.5 mW from 1 km to 12 km of fiber lengths, respectively as depicted in Fig. 4(b). For the purpose of verification, the calculated SBS threshold powers for all models are also depicted in Fig. 4(b). For long fibers, all the theoretical values converge to 13.7 mW, 9.7 mW and 7.2 mW for the localized, nonfluctuating source model, the distributed (nonlocalized), fluctuating source model and PSO model respectively. Based on the findings, our proposed PSO model and the distributed (nonlocalized), fluctuating source model predict the SBS threshold power close to the experimental value with error of less than 20%. In addition, for short fibers, the theoretical values of SBS threshold power calculated from the PSO model show good agreement with the ones obtained experimentally. In this case, the error between these two values is less than 20%. The other two models cannot predict the threshold power characteristics close enough to the experimental values with error of larger than 20%. Overall, in comparison with all the models, the theoretical values calculated from the PSO model are in good agreement with the experimental values for the whole range of fiber lengths. The discrepancies between these two values are in the range of 9-20% which are contributed by some uncertainties of measurement errors. This might be due to the omission of polarization effect in our proposed PSO model which has been reported to be affecting Brillouin gain efficiency [25

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]

]. The exponential gain and SBS power at threshold using the PSO algorithm is interdependent; which depends primarily on the optical fiber length (the optimal optical loss coefficient), the optimal numerical aperture and the optimal pump laser wavelength.

5. Conclusions

Acknowledgments

This work was partly supported by the Ministry of Science, Technology and Innovation, Malaysia and the Brain Gain Malaysia Program, R&D Collaboration under research grant # MOSTI/BGM/R&D/19(3).

References and links

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]

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

  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]
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