This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: 93.180.53.211 This content was downloaded on 06/02/2014 at 09:13 Please note that terms and conditions apply. Design of application specific long period waveguide grating filters using adaptive particle swarm optimization algorithms View the table of contents for this issue, or go to the journal homepage for more 2014 J. Opt. 16 015504 (http://iopscience.iop.org/2040-8986/16/1/015504) Home Search Collections Journals About Contact us My IOPscience
Transcript
This content has been downloaded from IOPscience. Please scroll down to see the full text.
Download details:
IP Address: 93.180.53.211
This content was downloaded on 06/02/2014 at 09:13
Please note that terms and conditions apply.
Design of application specific long period waveguide grating filters using adaptive particle
swarm optimization algorithms
View the table of contents for this issue, or go to the journal homepage for more
2014 J. Opt. 16 015504
(http://iopscience.iop.org/2040-8986/16/1/015504)
Home Search Collections Journals About Contact us My IOPscience
J. Opt. 16 (2014) 015504 (8pp) doi:10.1088/2040-8978/16/1/015504
Design of application specific long periodwaveguide grating filters using adaptiveparticle swarm optimization algorithms
Girish Semwal1 and Vipul Rastogi2
1 Instrument Research and Development Establishment, Dehradun 248008, India2 Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, India
Received 22 July 2013, revised 8 November 2013Accepted for publication 18 November 2013Published 11 December 2013
AbstractWe present design optimization of wavelength filters based on long period waveguide gratings(LPWGs) using the adaptive particle swarm optimization (APSO) technique. We demonstrateoptimization of the LPWG parameters for single-band, wide-band and dual-band rejectionfilters for testing the convergence of APSO algorithms. After convergence tests on thealgorithms, the optimization technique has been implemented to design more complicatedapplication specific filters such as erbium doped fiber amplifier (EDFA) amplified spontaneousemission (ASE) flattening, erbium doped waveguide amplifier (EDWA) gain flattening andpre-defined broadband rejection filters. The technique is useful for designing and optimizingthe parameters of LPWGs to achieve complicated application specific spectra.
Keywords: particle swarm optimization, planar waveguide, long period grating, waveguidegrating
(Some figures may appear in colour only in the online journal)
1. Introduction
Long period fiber gratings (LPFGs) are widely used asband rejection filters, gain equalizers for optical amplifiers,dispersion controllers, and in various types of sensors [1–8].However, the constraints of geometry and materials usedin LPFGs limit the manipulation of their spectrum.To remove these constraints and achieve flexibility intailoring the spectrum of long period gratings (LPGs),long period waveguide gratings (LPWGs) in a four-layerplanar waveguide geometry have been proposed [9].Subsequently, applications of LPWGs in various devices,such as band rejection filters and band pass filters havebeen demonstrated [10, 11]. LPWGs formed by sinusoidalmodulation of the refractive index in the guiding film ofthe waveguide are known as phase gratings. Refractiveindex modulation to form an LPG can also be achievedby corrugation in a certain region of the guiding filmsuch an LPG is thus termed as a corrugated grating.
Writing a phase grating requires doping of the guidingfilm with photosensitive material such as germanium, and isachieved by recording the pattern with amplitude maskingfrom an ultra violet (UV) laser into the guiding filmof the waveguide [12]. The corrugated grating can bewritten by simply etching the pattern on the surface ofthe guiding film, followed by cladding layer deposition[13, 14]. The grating parameters namely, grating period, indexmodulation, length, corrugation height and cladding profilestrongly affect the output spectrum. Therefore, it is importantto optimize these parameters in order to obtain the desiredtransmission spectrum.
In the present work, we demonstrate the applicability of aglobal optimization technique known as APSO to optimize thedesign parameters of LPWG devices to achieve applicationspecific spectra. Simple PSO has been used for the design andoptimization of fiber Bragg gratings (FBGs) and long periodfiber grating (LPFG) devices [15–19] for limited numbersof parameters. Simple PSO exhibits poor convergence when
the number of parameters increases and has a tendencyto get trapped in local minima. On the other hand, theAPSO technique adopted in present work can converge toa global minimum with a large number of optimizationparameters. We test the convergence performance of thetechnique by optimizing the LPWG parameters for threespecific target spectra: single-band rejection, wide-bandrejection, and dual-band rejection. After the convergenceperformance had been tested for the applicability of APSO inLPWGs, the module was then utilized to design applicationspecific pre-defined complex rejection band filters. Theapplication has been demonstrated with examples of EDFAASE flattening, a rectangular rejection band filter and EDWAflattening.
2. LPWG structure
Figure 1 shows the LPWG structure used in the presentstudy. The structure consists of a four-layer planar waveguidewith a thick substrate layer of refractive index ns, a guidingfilm of refractive index nf and thickness df, a cladding layerof refractive index ncl and thickness dcl and an infinitelyextended external layer of refractive index nex. The refractiveindex of each layer is taken in such a way that it satisfies thecondition nf > ncl > ns ≥ nex. The thickness of the guidingfilm is selected such that it supports only the fundamentalmode, while higher order modes are supported by thecladding layer. A corrugated grating of corrugation height his embedded in the guiding film region of the waveguide. Thegrating behaves as a perturbation for coupling of the guidedmode with co-propagating cladding modes.
3. LPWG analysis
The LPG in a four-layer waveguide structure as describedabove has been considered for the analysis. To calculate thecoupling coefficient between the modes coupled through theLPWG, we have solved the scalar wave equation for TEmodes numerically by using suitable boundary conditions.The solutions give the propagation constants and the modalfields of the modes. If E0 is the modal field of the TE0 modeand Em, m = 1, 2, 3, . . . are the modal fields of the coupledTEm modes then the coupling coefficient can be given by
K =k01n2
2πcµ0
∫ df
df−hE0Emdx (1)
where c is the velocity of light, 1n2 is the index modulation,µ0 is the free space permeability, and k0 is the free spacewavenumber, defined by 2π/λ0, with λ0 being the free spacewavelength.
The corresponding coupled mode equations are given by
dA0
dz= jKAmejδz (2)
dAm
dz= −jKA0e−jδz (3)
δ = β0 − βm −2π3
(4)
where δ is the phase mismatch, A0(z),Am(z) are theamplitudes of the core mode and mth cladding mode; β0,βm are the propagation constants of the core mode andmth cladding modes, and 3 is the grating period. Thecoupled mode equations have been solved by the transfermatrix method to calculate the transmitted power at agiven wavelength; thereby, the transmission spectrum hasbeen computed for an optimized set of grating length (L),grating period (3), cladding thickness (dcl) and corrugationheight (h).
LPWGs designed on the basis of above discussion canproduce only simple rejection band spectra. However, thepractical application of LPWGs requires more complicatedand asymmetric rejection band characteristics. Differentmethods have been proposed to obtain complicated applica-tion specific spectra in long period fiber gratings (LPFGs).Two proposed methods are step-changed long period fibergratings and apodized phase shift long period gratings[20, 21]. The waveguide grating has greater flexibility inchanging the waveguide parameters and materials due toits structure. Cladding layer parameters were found moreeffective and easy to change in LPWGs. Designs of phaseshift gratings, chirped gratings and broad band filters havebeen proposed by changing the cladding layer profile of anLPWG [22]. The refractive index profile and thickness profilehave been utilized to change the profile of the cladding layerof an LPWG in [22]. We adopted a similar procedure forthe design of an application specific rejection band. We haveconsidered the simplest case by segmenting the cladding layerinto two parts, each having different refractive indices. In thepresent study, two parameters α and γ have been introduced
2
J. Opt. 16 (2014) 015504 G Semwal and V Rastogi
to design an LPWG with a segmented cladding structure.Factor α divides the total grating length into two parts, onehaving length L1 = αL and the other length L2 = (1 − αL).Similarly γ is the difference between the refractive indices ofthe two cladding sections. Hence the LPWG has a total lengthL, which consists of the refractive index ncl(1) = ncl in thecladding section of length L1 and refractive index ncl(2) =ncl − γ in the cladding section of length L2. In the proposedLPWG structure the transmission spectrum and rejection bandcharacteristics are governed by the cladding layer parameters(α, γ ) and grating parameters (L,3, dcl, h).
The output rejection band spectrum of a simple gratingis a function of a few optimized parameters (L,3, dcl, h);however, complicated application specific grating spectrarequire more parameters (L,3, dcl, h, α, γ ), which can beobtained by the implementation of suitable optimizationalgorithms.
4. Optimization algorithms
We have used PSO to optimize the LPWG parameters.PSO is a class of population based heuristic algorithms.These algorithms evolved from the laws of nature andare extensively used in solving problems in science andengineering. PSO originated from an understanding of thesocio-cognitive behavior of the graceful motion of swarms ofbirds or schools of fish in their social environment. The PSOalgorithm consists of three basic steps: random generationof the velocity (v) and position (x) of particles, velocityupdate, and position update. Velocity update is governed bythree basic socio-cognitive factors, inertia weight (w), selfconfidence (c1) and swarm confidence (c2). The convergenceof PSO algorithms is governed completely by the appropriateselection of these three factors. The mathematical relationsgoverning the basic steps of these algorithms are given as [23]
xi0 = xmin + rand(xmax − xmin) (5)
vi0 =[xmin + rand(xmax − xmin)]
1t(6)
vik+1 = wvi
k + c1rand
(pi − xi
k
1t
)+ c2rand
(pg
k − xik
1t
)(7)
xik+1 = xi
k + vik+11t (8)
where xi, i= 1, 2, . . . ,N signify the variables to be optimizedand k is the time step (iteration number) for forward motionof particles. xmin and xmax are the minimum and maximumvalues assigned to xi. pi and pg
k are the local and globalminimum of xi. Local minimum is the minimum positionin the total population for the current iteration while globalminimum is the minimum of all previous iterations, includingthe current iteration. 1t is the time interval for the motion ofswarms in the defined domain and has been taken as 1 forthe computation. Equations (5) and (6) generate the randominitial position and random initial velocity of swarms in thepre-defined domain of variables. Equation (7) implements thevelocity update for the next iteration and is related to theposition and velocity of the previous generation as well as
the socio-cognitive factors. w controls the momentum of theparticle and preserves the past memory of motion. Thus, whas a tendency to retain the particle’s past history of motionin the next time step (kth time history for the (k + 1)th timestep) as shown in equation (7). Hence it generates inertia toretain its previous state of motion for forward movement andis therefore also known as the inertia factor. c1 and c2 arethe acceleration coefficients and determine the motion of aparticle toward its local and global minimum respectively. c1has a tendency to move the particle toward its local minimumand c2 has a tendency to move the particle to its globalminimum. Equation (8) describes the position update in the(k + 1)th time step.
Considerable research has been carried out to assignsuitable values to the socio-cognitive factors. Special careshould be taken in assigning values to these parametersotherwise the optimization will become trapped in a localminimum instead of a global minimum. For example, if wis taken very large (w > 1), then it generates high inertia toretain the particle in its original position. On the other hand,if w is very small (w� 1 or w = 0), then the motion loses itsreference control and the particle moves without knowledgeof its previous velocity. Fixed values from defined ranges ofinertia weight [0.9, 0.4] and acceleration coefficients [0, 4]were suggested; however, these values change with differentoptimization problems [24]. Recently, adaptive particle swarmoptimization (APSO) based on clustering methods [25] andfuzzy logic methods [26] have been suggested. In APSO,the inertia weight and acceleration coefficients (w, c1 andc2) change adaptively in the above defined ranges of inertiaweight and acceleration coefficients. Fuzzy logic based APSOhas been carried out by calculating the mean distance ofeach variable from the other variables with the help of aEuclidean metric. The mean distance of the ith variable(xi) with respect to all other variables has been defined asdi. If, for each variable, the population size is M, then atotal of M mean distances are computed in the optimizationprocess. Minimum and maximum values of the distances areidentified as dmin and dmax. The distance corresponding toglobal optimum values is denoted as dg. An evolutionaryfunction f = (dg − dmin)/(dmax − dmin), is generated with thehelp of these distances. The function f is used to compute w aswell as the membership functions given in [26]. f is classifiedas one of four states named as exploration, exploitation,convergence and jumping based on membership functions,called fuzzy classifiers. A small increment or decrement in c1and c2 is carried out on the basis of the above four classifiedstates to make them adaptive. The increment or decrementvalue in each case is suggested in [26]. The membershipfunctions are not completely isolated and there are certainregions of overlap in the states with respect to f . In suchcases, defuzzification has been carried out with the help ofthe centroid method. f changes in each iteration, hence w, c1and c2 also change adaptively as per the above classifications.APSO based on fuzzy logic ensures rapid convergence of thevariables to a global minimum. During the velocity updateprocess, the new velocity may be out of bounds and suitableboundary conditions are required to keep the value within a
3
J. Opt. 16 (2014) 015504 G Semwal and V Rastogi
pre-defined domain. Damping boundary conditions are mostpopularly used to prevent the escape of particles from thespecified domain of variables [27].
The APSO technique proposed in [26] has beenimplemented for the design and optimization of applicationspecific LPWG device parameters.
5. LPWG design optimization
Calculation of the coupling coefficient described by equa-tion (1) requires knowledge of the modal fields of thecoupled modes. These modal fields have been computednumerically, as suggested in [9]. The refractive indexmodulation with corrugation height h acts as a perturbationfield and is responsible for coupling of the modes. Theoverlap integral of the coupled modal field has been computedby integrating the product of the guided mode field andthe cladding mode field (E0Em) in the corrugated region(h). The transmission spectrum of the grating has beencomputed by solving equations (2) and (3) using the transfermatrix method, as given in [22]. The output spectrum ofthe grating is a function of a suitable combination ofparameters (L,3, dcl, h, α, γ ). The desired output spectrumis an application specific spectrum; named henceforth as thetarget spectrum and denoted as St in our computation. Theoptimized set of parameters (L,3, dcl, h, α, γ ) is achievedby using the optimization techniques for a specific targetspectrum (St). The steps of optimization for PSO are describedas follows.
5.1. Steps for APSO optimization
APSO is based on the simulation of the swarm’s intelligencedynamics and used to optimize the LPWG parameters indesigning application specific devices. The steps are broadlydescribed as follows:
(a) Randomly generate an initial position of the swarmcorresponding to the parameters (L,3, dcl, h, α, γ ) andthe initial velocity of the swarm in a pre-defined domainof variables using equations (5) and (6). The domainboundary of the swarm depends on the range in whichthe values of parameters to be optimized are confined.For example, 3 is the grating period and the typicalrange in which it lies is 50–800 µm. Thus, the lowerboundary of the swarm corresponding to the gratingperiod is set as 50 µm and the upper boundary as 800 µm.During the search process the period will be within thesepre-defined boundaries of the domain. Domain boundariesfor the other parameters are fixed in a similar manner.The number of swarms (population) corresponding toeach variable is taken as 20, as suggested by the originalinventor of PSO [28, 29] and the same value has been usedby most researchers in different optimization problems.
(b) Each set of parameters (L,3, dcl, h, α, γ ) in the popu-lation, generated using equations (5)–(8), is called themember of a swarm and its value is representative of themember’s position with respect to the global minimum
(desired spectrum). The spectrum corresponding to thevalue of each member is denoted as the computedspectrum (Sc).
(c) Compute the fitness between the target spectrum (St)and the computed spectrum (Sc) corresponding to eachmember using the relation given as
Fitness =√(St − Sc)2. (9)
Fitness has been used to verify the convergence of theoptimization process.
(d) The velocity of the swarm for the next time stepis computed according to equation (7). The updatevelocity depends on the inertia factor (w) and accelerationcoefficients (c1, c2). The inertia factor changes adaptivelywith respect to the global minimum and local minimumbetween the limits (0.9–0.4). Similarly the accelerationcoefficients also change adaptively in each iteration.
(e) The velocity of an individual swarm member may driftoutside of the pre-defined domain of parameters during theupdate. Using suitable boundary conditions the velocity iskept within the domain. We have used damping boundaryconditions here to keep the particle within the domain. Indamping boundary conditions, if the particle’s velocity isoutside the pre-defined domain, then a random value ofvelocity within the domain is assigned to the member.
(f) Update the position with respect to the new velocity as perequation (8).
(g) Continue from step (b) until the best desired solution isobtained.
A preset maximum number of iterations is used toterminate the optimization process. This maximum numbervaries from problem to problem; hence it has to be determinedby a certain number of numerical experiments for any givenproblem.
6. Numerical simulation
To demonstrate the application of the optimization methods inthe design of LPWG devices, we have considered an LPG inthe four-layer waveguide structure as discussed in [10]. Thewaveguide structure is shown in figure 1 and is defined by thefollowing parameters.
ns = 1.5, nf = 1.52,
ncl = 1.51, nc = 1, df = 2 µm.(10)
The first step in the implementation of the APSOalgorithms is to verify their convergence in applications forintegrated optics. We have considered three specific targetspectra, as shown in figure 2, to carry out the convergencetest. These spectra are in fact the transmission spectra ofsinusoidal gratings corresponding to the parameters definedin table 1. The parameters of the corrugated LPG havebeen optimized by APSO in order to achieve these targetspectra. This is the simplest case and only the three gratingparameters (L,3, h) corresponding to a corrugated grating
Table 1. Grating parameters of the sinusoidal grating.
L(mm)
3(µm)
dcl(µm) 1n2
Outputspectrum
16 154 4.5 6.08× 10−4 Single-bandrejection
16 191.6 5.5 6.08× 10−4 Wide-bandrejection
18 278 7.5 6.08× 10−4 Dual-bandrejection
to achieve the target spectra have been optimized. APSO isa population based heuristic optimization method. We testedall approaches of PSO and found that the adaptive approach
Figure 3. Adaptive variation of parameters for PSO: (a) weightfactor (w) and (b) acceleration coefficients (c1, c2).
Figure 4. Fitness function variation with the number of generationsfor PSO.
Table 2. Optimized parameters of the corrugated grating.
L (mm) 3(µm) h (nm) Output spectrum
15.00 154.03 312.0 Single-bandrejection
15.35 191.65 112.0 Wide-bandrejection
15.40 278.02 73.0 Dual-bandrejection
5
J. Opt. 16 (2014) 015504 G Semwal and V Rastogi
Figure 5. Target and corresponding optimized spectra with PSO:(a) single-band rejection filter, (b) wide-band rejection filter and(c) dual-band rejection filter.
based on fuzzy logic is most suitable for our numericalsimulation. The population size has been taken as 20 in thecase of APSO optimization. The values of w, c1, c2 have beencomputed adaptively using the fuzzy adaptation method assuggested in [26]. The values of w, c1, c2 as a function of thenumber of generations are plotted in figure 3 for the targetspectrum corresponding to figure 2(a). The value of the inertiafactor depends on the randomness of the swarm. Initially theswarms (parameters) are randomly distributed in the domainso the value of the inertia factor is close to the upper bound(0.9). As the number of iterations increases the inertia factor
Figure 6. Broadband rejection filter: (a) pre-defined target and(b) target (St) and computed (Sc) spectrum using the designedgrating parameters. Optimized parameters are listed in table 3 (BB).
approaches its lower bound (0.4), as shown in figure 3(a),and settles down there. The acceleration coefficients initiallychange adaptively and settle to the optimum value, around 2,in about 250 generations, as shown in figure 3(b). Almost 90%of the swarms converge to the optimum parameter values,when the inertia factors and acceleration coefficients attainthe convergence as described above. The APSO is mostsensitive to socio-cognitive parameters; however, using thefuzzy based adaptive approach, the weight factor adaptivelychanges according to pre-defined constraints. This approachmakes the convergence extremely fast and forces the processto converge to its global optimum. The value of the fitnessfunction has also been computed and is shown in figure 4. TheAPSO based optimized parameters of the corrugated gratingare shown in table 2. The optimized spectra and correspondingtarget spectra are shown in figure 5.
Once the convergence test for the algorithms had beencompleted, the APSO algorithms were implemented to designLPWGs for real problems, such as a pre-defined broadbandfilter and ASE spectrum flattening. The following waveguideparameters have been used for the design of the LPWG.
ns = 1.444, nf = 1.53,
ncl = 1.50, nex = 1, df = 2 µm.(11)
The grating parameters (L,3, dcl, h, α, γ ) have beenoptimized to achieve the desired output spectrum using
6
J. Opt. 16 (2014) 015504 G Semwal and V Rastogi
Figure 7. Target spectrum (St), computed spectrum (Sc) and ASEflattening with Sc: (a) target spectrum (St) and computed spectrum(Sc) and (b) ASE spectrum and flattened spectrum with Sc.Optimized parameters are listed in table 3 (ASE).
APSO. A segmented cladding grating, with two segments inthe cladding layer, generates two rejection bands. A suitablecombination of grating parameters forces the merging oftwo rejection bands and generates a broadband rejectionfilter. A pre-defined rectangular rejection band of 30 nm hasbeen obtained by implementing the present approach. Thetarget spectrum and the corresponding computed spectrumfor the rectangular broadband filter are shown in figure 6.The same approach has been implemented to obtain anasymmetric target spectrum. A suitable combination ofparameters merges two rejection bands of different widthsand different resonance depths to generate the asymmetricrejection band. Application of an asymmetric rejectionband has been demonstrated for ASE gain of EDFA andEDWA gain equalization. The target spectrum, corresponding
Figure 8. Target spectrum (St), computed spectrum (Sc) and EDWAflattening with Sc: (a) target spectrum (St) and computed spectrum(Sc) and (b) EDWA spectrum and flattened spectrum with Sc.Optimized parameters are listed in table 3 (EDWA).
computed spectrum and gain flattened curves are shown infigure 7. The ASE flattened curve has a ripple of ±1.0 dB ina 30 nm band with the rejection band obtained from LPWGoptimally designed with APSO. The target spectrum andcorresponding computed spectrum for gain flattened curvesof EDWA are shown in figure 8(a). The gain curve andflattened curve for EDWA are shown in figure 8(b). TheEDWA flattened curve has a ripple of ±0.20 dB in a 30 nmband with the rejection band obtained from LPWG optimallydesigned with APSO. The optimized parameters of the gratingfor the broadband filter, EDWA spectrum and ASE spectrumare shown in table 3.
Table 3. Different applications: broadband rejection filter (BB), flattening of the ASE spectrum (ASE) and flattening of the EDWA gainspectrum (EDWA).
We demonstrated methods using APSO for the optimizationof corrugated LPG parameters to obtain a desired targetspectrum as a convergence test for APSO algorithms. Theresults of the convergence study show that the APSOefficiently converges to achieve optimum values of theinertia factor and acceleration coefficients; and, consequently,optimum values of the grating design parameters. Thealgorithms have subsequently been used to determine theparameters of a complex grating to achieve desired applicationspecific target spectra, such as ASE flattening, EDWA gainflattening and a pre-defined broadband rejection filter. Weoptimized three parameters for the convergence test and thensuccessfully increased the number of parameters up to sixto design gratings for the more complicated output spectra.APSO proved to be a suitable choice to solve issues oflocal trapping during convergence and always converged toa global minimum even with a large number of parameters.APSO is simple to implement, as the velocity update andposition update are the only two simple procedures usedin conjunction with boundary conditions for optimizationand fuzzy logic algorithms for adaptive updating of thecontrol parameters of PSO. The APSO optimization techniquecould be implemented to design complex LPWG structuresconsisting of a large number of parameters for the design ofapplication specific target spectra.
References
[1] Vengsarkar A M, Lemaire P J, Judkins J B, Bhatia V,Erdogan T and Sipe J 1996 Long period fiber grating asband rejection filter J. Lightwave Technol. 14 58–65
[2] Stegall D B and Erdogan T 2000 Dispersion control with useof long period fiber gratings J. Opt. Soc. Am. A 17 304–12
[3] Das M and Thyagarajan K 2001 Dispersion compensation intransmission using uniform long period fiber grating Opt.Commun. 190 159–63
[4] Das M and Thyagarajan K 2001 Wavelength divisionmultiplexing isolation filter using concatenated chirpedlong period gratings Opt. Commun. 197 67–71
[5] Kersey A D, Davis M A, Patrick H J, LeBlanc M, Koo P K,Askins C G, Putnam M A and Friebele E J 1997 Fibergrating sensors J. Lightwave Technol. 15 1442–63
[6] Bhatia V 1999 Application of long period gratings to singleand multi-parameters sensing Opt. Express 4 457–66
[7] Lee B 2003 Review of present status of optical fiber sensorsOpt. Fiber Technol. 9 57–79
[8] Hochreiner H, Cada M and Wentzell P D 2008 Modeling theresponses of a long-period fiber grating to ambientrefractive index change in chemical sensing applicationJ. Lightwave Technol. 26 1986–92
[9] Rastogi V and Chiang K S 2002 Long period grating in planaroptical waveguide Appl. Opt. 14 6351–5
[10] Chiang K S, Chow C K, Liu Q, Chan H P and Lor K P 2006Band-rejection filter with widely tunable centre wavelengthand contrast using metal long-period grating on polymerwaveguide IEEE Photon. Technol. Lett. 18 1109–11
[11] Chu Y M, Chiang K S and Liu Q 2006 Widely tunable opticalband pass filter by use of polymer long-period waveguidegratings Appl. Opt. 45 2755–60
[12] Vasiliev S A and Medvedkov O I 2002 Long-period refractiveindex fiber gratings: properties, applications and fabricationtechniques Proc. SPIE 4083 212–23
[13] Chiang K S, Lor K P, Chow C K, Chan H P, Rastogi V andChu Y M 2003 Widely tunable long-period gratingfabricated in polymer-clad ion-exchanged glass waveguideIEEE Photon. Technol. Lett. 15 1094–6
[14] Kin Q L, Chiang K S and Lor K P 2005 Tailoring thetransmission characteristics of polymer long-periodwaveguide gratings by UV irradiation IEEE Photon.Technol. Lett. 17 2340–2
[15] Bhaskar S, Zheng R T, Alphones A, Ngo N Q andSuganthan P N 2005 Particle swarm optimization for thedesign of low dispersion fiber Bragg grating IEEE Photon.Technol. Lett. 17 615–7
[16] Gao J Q, Liu Y H and Di J H 2009 Improved intelligentparticle swarm optimization algorithms for designing thesampling period profile of the sampled fiber Bragg gratingsProc. 8th Int. Conf. on Machine Learning and Cybernetics(Baoding, July) pp 1374–9
[17] Yu X, Sun Y, Yao Y, Tian J and Cong S 2011 Quantumbehaved particle swarm optimization for the synthesis offiber Bragg grating filter SPIE-OSA-IEEE AsiaCommunications and Photonics vol 8307, pp 1–5
[18] Liu Y, Yu Z, Zhang J, Yang B and Zhang X 2004Optimization design of flat-band long period grating Chin.Opt. Lett. 2 200–2
[19] Liu Y and Yu Z 2006 Optimal designing of EDFA gainflattening long period fiber grating by intelligent particleswarm optimization algorithms SEAL vol 4247 (Berlin:Springer) pp 221–7
[20] Guan B, Zhang A, Tam H, Chan L W, Choy C L, Tao X M andDemokan M S 2002 Step-changed long period fibergratings IEEE Photon. Technol. Lett. 14 657–9
[21] Chan F Y M and Chiang K S 2005 Analysis of apodized phaseshifted long period fiber grating Opt. Commun. 244 233–43
[22] Liu Q and Chiang K S 2006 Design of long period waveguidegrating filter by control of waveguide cladding profileJ. Lightwave Technol. 24 3540–6
[23] Hassan R, Cohanim B and Weck O 2005 A comparison ofparticle swarm optimization and the genetic algorithm 46thAIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics, and Materials Conf. pp 1–13
[24] Das S, Abraham A and Konar A 2008 Particle swarmoptimization and differential evolution algorithms:technical analysis, applications and hybridizationperspectives Advances of Comput. Intelligencevol 38 (Berlin: Springer) pp 1–38
[25] Zhan Z H, Xiao J, Zhang J and Chen W N 2007 Adaptivecontrol of acceleration coefficients for particle swarmoptimization based on clustering analysis CEC2007: IEEECongr. Evol. Comput. pp 3276–82
[26] Zhan Z H, Zhang J, Li Y and Chung H S 2009 Adaptiveparticle swarm optimization IEEE Trans. Syst. Man Cybern.B 39 1362–82
[27] Huang T and Mohan A S 2005 A hybrid boundary conditionfor robust particle swarm optimization IEEE AntennasWirel. Propag. Lett. 4 112–7
[28] Kennedy J and Eberhart R 1995 Particle swarm optimizationProc. IEEE Int. Conf. Neural Networks vol 4, pp 1942–8
[29] Eberhart R and Kennedy J 1995 A new optimizer usingparticle swarm theory Proc. 6th Symp. Micro MachineHuman Sci. (Nagoya) pp 39–43
