OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 14 — Jul. 14, 2003
  • pp: 1677–1688
« Show journal navigation

Optimal design of DFG-based wavelength conversion based on hybrid genetic algorithm

Xueming Liu and Yanhe Li  »View Author Affiliations


Optics Express, Vol. 11, Issue 14, pp. 1677-1688 (2003)
http://dx.doi.org/10.1364/OE.11.001677


View Full Text Article

Acrobat PDF (279 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A hybrid genetic algorithm (GA) is proposed. Simulating two test functions shows that the proposed GA can effectively solve the multimodal optimization problems, and the three movies demonstrate the detailed procedure of each generation. The conversion efficiency and bandwidth, based on quasi-phase-matching (QPM) difference frequency generation (DFG), are optimized by the matrix operator and our GA. Optimized examples for five-, six- and seven-segment QPM gratings are given, respectively. The optimal results show that adding the segment number of QPM can obviously broaden the conversion bandwidth, which is sensitive to the fluctuation of bandwidth and the variation of QPM grating period.

© 2003 Optical Society of America

1. Introduction

All-optical wavelength conversion is widely recognized as a key technology for future wavelength division multiplexed (WDM) networks and as an important method of enhancing routing optical and network properties such as reconfigurability, nonblocking capability, and wavelength reuse. Among various strategies, quasi-phase-matching (QPM) wavelength converters based on difference frequency generation (DFG) or cascaded second-order nonlinear interactions have attracted much attention [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

17

17. X. M. Liu and M. D. Zhang, “Theoretical studies for the special states of the cascaded quadratic nonlinear effects”, J. Opt. Soc. Am. B 18, 1659–1666 (2001). [CrossRef]

], because they offer potential advantages such as strict transparency, simultaneous multichannel conversion, wide bandwidth, high efficiency, and low noise. Efficient DFG-based wavelength conversion was realized in periodically poled LiNbO3 waveguides [4

4. G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998). [CrossRef]

6

6. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of ngineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999). [CrossRef]

]. In the experiments, a normalization conversion efficiency as high as 790%/W was obtained from a LiNbO3 QPM-DFG device [14

14. D. Sato, T. Morita, T. Suhara, and M. Fujimura, “Efficiency improvement by high-index cladding in LiNbO3 waveguide quasi-phase-matched wavelength converter for optical communication,” IEEE Photon. Technol. Lett. 15, 569–571 (2003). [CrossRef]

], and a fiber-to-fiber conversion efficiency of -8 dB was demonstrated by using cascaded nonlinear interactions [16

16. M. H. Chou, I. Brener, M.M. Fejer, E. E. Chabass, and S. B. Christman, “1.5-µm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999). [CrossRef]

].

In the uniform QPM grating, however, the conversion bandwidth is <90 nm for the nonlinear length L>25 mm [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

3

3. X. M. Liu, H. Y. Zhang, and M. D. Zhang, “Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium,” Opt. Express 10, 83–97 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-83 [CrossRef] [PubMed]

]. To broaden QPM bandwidth, all kinds of techniques were theoretically proposed and/or experimentally realized, e.g., chirped [18

18. T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990). [CrossRef]

] and segmented [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

, 7

7. X. M. Liu, H. Y. Zhang, and Y. H Li, “Optimal design for the quasi-phase-matching three-wave mixing,” Opt. Express 9, 631–636 (2001), http://www.opticsexpress.org/oearchive/source/37804.htm [CrossRef] [PubMed]

, 9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

, 19

19. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Eletron. 30, 1596–1604 (1994). [CrossRef]

] grating method, phase shift method [9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

, 15

15. W. Liu, J. Q. Sun, and J. Kurz, “Bandwidth and tunability enhancement of wavelength conversion by quasi-phase-matching difference frequency generation,” Opt. Commun. 216, 239–246 (2003). [CrossRef]

, 20

20. K. Mizuuchi and K. Yamamoto, “Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts,” Opt. Lett. 23, 1880–1882 (1998). [CrossRef]

], pump detuning [2

2. M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFM)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999). [CrossRef]

], multiple QPM [6

6. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of ngineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999). [CrossRef]

,10

10. M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,” Opt. Lett. 28, 558–560 (2003). [CrossRef] [PubMed]

] and employing nonlinear coefficient d 31 [21

21. N. E. Yu, H. Ro, M. Cha, S. Kurimura, and T. Taira, “Broadband quasi-phase-matched second-harmonic generatio in MgO-doped periodically poled LiNbO3 at the communications band,” Opt. Lett. 27, 1046–1048 (2002). [CrossRef]

]. To optimize QPM structure, the matrix operator [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

,7

7. X. M. Liu, H. Y. Zhang, and Y. H Li, “Optimal design for the quasi-phase-matching three-wave mixing,” Opt. Express 9, 631–636 (2001), http://www.opticsexpress.org/oearchive/source/37804.htm [CrossRef] [PubMed]

,9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

] and simulated annealing method [22

22. X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002). [CrossRef]

25

25. J. Wu, T. Kondo, and R. Ito, “Optimal design for broadband quasi-phase-matched second-harmonic generation using simulated annealing”, J. Lightwave Technol. 13, 456–460 (1995). [CrossRef]

] were demonstrated.

In this paper, we propose an effective hybrid GA, which includes such techniques as clustering, sharing, crowding, adaptive genetic operators, elitist replacement, and fitness scaling. Two test functions prove the proposed GA, and three simulation movies are also included. By means of our GA, DFG-based wavelength converters of nonuniform QPM grating structure are optimized.

2. Hybrid GA

Step 0 (initialization): Initialize the number of peak centers n, the shortest niche radius r, the number of elitist set M and the number k. Generate N individuals randomly. Set the number of generation, g=1. Go to Step 6.

Step 1 (clustering): Sort individuals according to the descending order of the fitness. Find out n peak centers (see RULE I). Allocate individuals to the nearest peak center (see RULE II).

RULE II: ① For each individual without being marked as selected, calculate its distances to n confirmed peak centers. ② Select the shortest distance and allocate the individual to the corresponding peak center. ③ Repeat ① and ② until N individuals are allocated.

Step 2 (sharing): Calculate the niche count mi of each individual (mi is equal to the individual count in each peak center). Calculate the shared fitness f′i of an individual i, i.e., f′i=fi/mi (fi is its genuine fitness). Each peak can be considered as a niche in the multimodal domain. Sharing, one of niching techniques, can maintain population diversity effectively.

Step 3 (selection): Perform a Roulette wheel selection scheme, which is the traditional selection function with the probability of surviving.

Step 4 (crossover): Implement a single-point crossover and employ an adaptive probability of crossover pc, i.e.,

pc={pch(pchpcl)(fm2fave)(fmaxfave),iffm2>fave,pch,otherwise
(1)

where fm2 is the maximum fitness of the two chromosomes being crossed, fmax and fave are the maximum fitness and average fitness of the entire population, and pch and pcl are the probability of highest crossover and lowest crossover, respectively.

Step 5 (mutation): Implement a single mutation and employ an adaptive probability of mutation pm, i.e.,

pm={pmh(pmhpml)(fmaxf)(fmaxfave),iff>fave,pmh,otherwise
(2)

where f is the fitness of the chromosome, and pmh and pml are the probability of the adaptive mutation, the highest mutation and the lowest mutation, respectively. pch=0.99, pcl=0.7, pmh=0.02 and pml=0.005 in this paper.

Step 6: Calculate the object value of each individual, and its corresponding fitness f.

Step 7 (crowding): If g>2, implement the deterministic crowding, which is described in [29

29. S. W. Mahfoud, “Crowding and preselection revisited,” In R. Manner and B. Manderick (Eds.), Parallel Problem Solving from Nature (Amsterdam, Elsevier Science.1992) (pp. 27–36).

].

Step 8 (elitist replacement): If g>2, replace M individuals of the population with the lowest fitness from the elitist set. If g>1, select M individuals as elitist set in order of fitness in each niche uniformly.

Step 9 (fitness scaling): Employ a linear scaling to scale the fitness function, i.e.,

f=a·f+b,
(3)
{{a=(Cm1)fave(fmaxfave)b=(fmaxCmfave)fave(fmaxfave),iffmin>CmfavefmaxCm1{a=fave(favefmin)b=a·fmin,otherwise
(4)

where Cm is a constant, and Cm=1.2 in our simulation; fmin is the minimum fitness of the entire population; other parameters are the same as Eqs. (1) and (2).

Step 10: If the terminating criteria is satisfied, then stop and output optimal results, else, g=g+1 and go to step 1.

3. Matrix operator for QPM-DFG

Reference [9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

] shows that, although the propagation loss of the waveguide is sensitive to the conversion efficiency η, it is insensitive to the conversion bandwidth Δλ. In periodically poled crystal waveguides (e.g., LiNbO3), the loss, group velocity mismatch, and dispersion of the material can normally be ignored for lengths L~20 mm [6

6. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of ngineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999). [CrossRef]

10

10. M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,” Opt. Lett. 28, 558–560 (2003). [CrossRef] [PubMed]

,19

19. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Eletron. 30, 1596–1604 (1994). [CrossRef]

]. When the three waves propagate collinearly in a nonlinear medium with periodic structures (e.g., periodically poled LiNbO3), each wave is coupled to the other two waves through the second-order nonlinear polarizability. This process is governed by the coupled-mode equations of QPM three-wave mixing, which can be derived from Maxwell’s equations by invoking the slowly varying envelope approximation, and assuming a plane-wave interaction and a first-order diffraction effect of the grating perturbation [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

,3

3. X. M. Liu, H. Y. Zhang, and M. D. Zhang, “Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium,” Opt. Express 10, 83–97 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-83 [CrossRef] [PubMed]

,9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

,11

11. T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron. 39, 166–171 (2003). [CrossRef]

,17

17. X. M. Liu and M. D. Zhang, “Theoretical studies for the special states of the cascaded quadratic nonlinear effects”, J. Opt. Soc. Am. B 18, 1659–1666 (2001). [CrossRef]

19

19. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Eletron. 30, 1596–1604 (1994). [CrossRef]

]. Because the pump power is far greater than the signal and idler power, in the typical DFG process, the pump is regarded as undepleting (i.e., the small-signal approximation). By means of the matrix operator [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

, 7

7. X. M. Liu, H. Y. Zhang, and Y. H Li, “Optimal design for the quasi-phase-matching three-wave mixing,” Opt. Express 9, 631–636 (2001), http://www.opticsexpress.org/oearchive/source/37804.htm [CrossRef] [PubMed]

, 9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

], the QPM-DFG process can be described as

[E1(L)E2*(L)]=[N1N2N3N4][E1(0)E2*(0)],
(5a)
[N1N2N3N4]=NmNm1NlN1
(5b)
Nl=[Nl,1Nl,2Nl,3*Nl,1*],l=1,2,,m
(5c)
Nl,1=[cosh(QlLl)+iΔk2Qlsinh(QlLl)]e1
(5d)
Nl,2=i(M1Ql)sinh(QlLl)e2,
(5e)
Nl,3=i(M2Ql)sinh(QlLl)e2,
(5f)

where N*l,2 and N*l,3 are the conjugate of N l, 2 and N l, 3, respectively, Ll is the length of the l-th segment (i.e., L l=zl-zl -1), and zl -1 and zl are the input and output places of this segment, respectively (See Fig. 1). e 1=exp(-iΔklLl/2), e 2=exp(-iΔkl(zl -1+Ll)/2), and Ql=M1M2*(Δkl2)2 for the phase mismatching Δkl of the l-th segment. Δkl=k 3-k 2-k 1-2π/Λl under the approximation of the first-order periodic perturbation effect. Mj=ωjdeffE3(0)/(njc) (j=1, 2). Λ and c are the grating period and the speed of light in the vacuum, respectively. kj, nj and Ej are the wave vector, the index of refraction, and the electric field under light-frequencies ωj (j=1,2,3; and ω 1, ω 2 and ω 3 denote the signal, idler and pump waves), respectively. E 3(0) is the electric field of pump at the input port (See Fig. 1).

Fig.1. Model of nonuniform grating structure. Directions of the arrows represent those of the nonlinear coefficient. E2(L) accounts for the idler wave.

4. Test function

y(x)=x+10·sin(5x)+7·cos(4x),x[2.3,5.8].
(6)

This test function consists of three unequally spaced peaks with nonuniform height, which is demonstrated in Fig.2. Maxima are located at approximate x values of 2.9213, 4.1903, and 5.2468. Maxima are of approximate heights 16.2937, 9.3492, and 10.4057, respectively. Other test function is

z(x,y)={HiRi2R¯2(R¯2Ri22)+Hi,ifR¯2Ri2,x[0,10]andy[0,10]0,otherwise
(7)

where 2=X 2+Y 2, X=x-xci, Y=y-yci, ci=(xci, yci), and Ri={1.5, 2.5, 1, 0.75, 3}, Hi={2, 4.4, 3, 4.5, 4}, ci={(2, 8), (3, 4), (5, 7), (7, 8.5), (7, 4)}. This test function consists of five peaks (center ci, radius Ri and height Hi), which are displayed in Fig.3. The value of five peaks are 4.5 at (7, 8.5), 4.4 at (3, 4), 4 at (7, 4), 3 at (5, 7), and 2 at (2, 8). Fig.3 shows that the area of the second highest peak is much larger than that of the global peak and its local peak value of 4.4 is very close to the global peak value of 4.5. It results in the difficulty in finding the global peak without special technique.

Each symbol “*” in Figs. 2 and 3 corresponds to each individual in the last generation of GA, and different color symbols in Figs. 2 and 3 represent the population of different peaks, respectively. In the simulation, n=k=3, r=0.2, N=45, g=35 and M=3 for Fig. 2; and n=k=5, r=0.25, N=300, g=25 and M=50 for Fig.3. Fig. 2(a) shows the curve of y(x) and the distribution of all individuals in the 35-th generation, and Fig.2(b) demonstrates the procedure how our hybrid GA finds the global maximum and two local maxima of Eq. (6) in each generation. Fig. 3(a) exhibits the three-dimension figure of z(x, y) and the distribution of all individuals in the 25-th generation, Fig. 3(b) illustrates the contour of z(x, y) and the projection of all individuals of Fig. 3(a) in the xy-plane, and Fig. 3(c) and (d) demonstrate the procedure how our hybrid GA finds the global maximum and four local maxima of Eq. (7) in each generation.

Fig. 2. Curve of y(x) and the distribution of all individuals. (a) for the 35-th generation. (b) (298 KB) Film showing the procedure of each generation.
Fig. 3. Test function z(x, y) and the entire population in the 25-th generation. (a) For the three-dimension figure of z(x, y) and the distribution of all individuals. (b) For the contour of z(x, y) and the projection of all individuals of (a) in the xy-plane. (c) (1120 KB) Film showing the procedure of each generation in the three-dimension figure. (d) (1193 KB) Film showing the procedure of each generation in the contour of z(x, y). Five different color symbols represent the population of five peaks, respectively.

5. Optimized results by means of hybrid GA

Although two-, three-, and four-segment QPM structures were optimized by the exhaustion method in [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

, 9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

], more effective algorithms have to be implemented when the segment number m≥5. Fortunately, our proposed GA can availably overcome these difficulties. In the simulation calculations, we employ the representative data of periodically poled LiNbO3 [1

1. X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

, 3

3. X. M. Liu, H. Y. Zhang, and M. D. Zhang, “Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium,” Opt. Express 10, 83–97 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-83 [CrossRef] [PubMed]

, 9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

, 17

17. X. M. Liu and M. D. Zhang, “Theoretical studies for the special states of the cascaded quadratic nonlinear effects”, J. Opt. Soc. Am. B 18, 1659–1666 (2001). [CrossRef]

]: the pump power P 3=200 mW and wavelength λ 3=775nm; deff=15 pm/V and L=20 mm; the signal channels spaced 1 nm/channel are from 1440 nm to 1660 nm, and each input signal power P 1=1 mW; the effective channel waveguide cross section is 30µm2; the lengths of all segments are assumed to be equal, i.e., L 1=L 2=…=Lm. The relation between the light intensity I and the electric field E is that I=ε 0 cn|E|2/2, and ε 0 is the dielectric permittivity in the vacuum. Additionally, N=1500, M=150, n=k=5, g=100 and r=0.1 (here r is the normalized Euclidean distance).

Figures 4 (a)(c) show the optimal results of the conversion efficiency η and its corresponding bandwidth Δλ versus the signal wavelength λ 1 in five-, six- and seven-segment structures, respectively. Their corresponding optimal values of Λ are tabularized in tables 13. pl (l=1, 2, …, 5) in figures and tables represents the l-th peak center, and Δλ is the corresponding optimal conversion bandwidth. In the optimal simulation of Tables 13 and Fig. 4, we assume that: the conversion efficiency is >-6 dB, the fluctuation of the conversion bandwidth is <1dB; and The variation of the grating period Λ is 1 nm [see Fig. 4 (a)].

It is easily seen, from Tables 13 and Fig. 4, that ① the optimal bandwidth Δλ is broadened with an increase in the segment number m, e.g., Δλ=192 nm for seven segments against Δλ=150 nm for five segments; ② there are the same or approximately the same Δλ for each peak center for a given segment number; ③ to realize the fixed Δλ in the experiments, therefore, there are several candidates by the optimization of our GA, and this result has important applications in the design of QPM structure; ④ our proposed GA can effectively avoid the local trap during the optimal procedure; ⑤ the global maximum value Δλ lies in the first peak center p 1, as is determined in the assumption of our GA.

Table 1. Optimized Bandwidth Δλ for Five-Segment QPM structure

table-icon
View This Table
| View All Tables

Table 2. Optimized Bandwidth Δλ for Six-Segment QPM structure

table-icon
View This Table
| View All Tables

Table 3. Optimized Bandwidth Δλ for Seven-Segment QPM structure

table-icon
View This Table
| View All Tables
Fig. 4. Optimal results for the conversion efficiency η and bandwidth Δλ of signal wavelength λ 1 in five-, six-, and seven-segment QPM grating: (a) five-segment, (b) six-segment, and (c) seven-segment. η is assumed to be>-6 dB, the fluctuation of Δλ is <1 dB, and the variation in the grating period Λ is 1 nm.

Although Tables 13 and Fig. 4 are obtained from Eq. (5), which is valid under the condition of loss free (corresponding nonlinear length L<20 mm [9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

]), the optimized conversion bandwidth Δλ is still right by use of Eq. (5) when the waveguide loss is taken into account for 20<L<50 mm. But, for this case, the conversion efficiency η decreases. These results are consistent with [9

9. X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

]. The reasons are that, with the waveguide loss, the depletion of signals and pumps leads to the decrease of converted waves, and the approximately same decrease of signals and converted waves makes Δλ be almost unchanged. For the practicable design of QPM devices, the experimental conditions limit the variation of Λ and the tolerance of phase mismatch. In the following parts, we give an example under the condition of the Λ variation of 10 nm instead of 1 nm. Of course, our proposed algorithm can effectively optimize the nonuniform QPM grating structures at any value of the Λ variations.

To clearly understand the relationships of the conversion efficiency η and bandwidth Δλ with the fluctuation of Δλ and the variation of Λ, we give two optimized examples for η and Δλ versus λ 1 under the conditions of the Δλ fluctuation of <2 nm and the Λ variation of 10 nm in five-segment QPM structure, respectively. The optimized results are illustrated in Fig. 5. By comparing Fig. 4(a) with Fig. 5, it is found that ① Δλ=168 nm in the Δλ fluctuation of <2 nm against Δλ=150 nm in that of <1 nm and ② Δλ decreases from 150 nm to 117 nm when the variation of Λ is from 1 nm to 10 nm under the same other conditions. The simulated results also show that ① improving the property of the Δλ fluctuation (i.e., decreasing the Δλ fluctuation) is at the cost of narrowing the conversion bandwidth Δλ and 2 extending the variation of Λ also makes Δλ narrowed.

Fig. 5. Optimal results for the conversion efficiency η and bandwidth Δλ of signal wavelength λ 1 in five-segment QPM grating: Red and blue curves account for the Δλ fluctuation of <2 nm and the Λ variation of 10 nm, respectively. Other parameters and assumptions in Fig. 5 are consistent with those in Fig. 4(a).

Although Figs. 4 and 5 and Tables 13 only denote some specific examples, e.g., five-, six-, and seven-segment QPM grating structures, our proposed hybrid GA can provide powerful tool for all kinds of the nonuniform QPM grating structures. In virtue of the inherent merits of GA [27

27. S. W. Mahfoud, “Niching methods for genetic algorithms,” Ph.D. dissertation, Univ. of Illinois, Urbana-Champaign, 1995.

, 33

33. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (New York: Addison-Wesley, 1989).

], our GA can be implemented into all sorts of practical tolerances and requirements after little modification. Therefore, our proposed GA can effectively offer the optimal tool for the practical design of QPM grating under the determinate conditions.

6. Conclusions

In the paper, we have proposed a hybrid GA, which includes such techniques as clustering, sharing, crowding, adaptive genetic operators, elitist replacement, and fitness scaling. Simulating two test functions shows that our GA can obtain the global and all local peak values in parallel, and three movies demonstrate the detailed procedure of each generation. By means of the matrix operator and hybrid GA, DFG-based wavelength converters in nonuniform QPM grating structures are optimized. Three examples (i.e., five-, six- and seven-segment QPM gratings) and five peak values are obtained in parallel, respectively. The optimal results show that ① increasing the segment number of QPM grating can availably broaden the conversion bandwidth Δλ, ② decreasing the fluctuation of Δλ (i.e., improving the properties of the fluctuation of Δλ) is at the cost of Δλ, e.g., Δλ=168 nm in the Δλ fluctuation of <2 nm against Δλ=150 nm in that of <1 nm, and ③ extending the variation of Λ decreases Δλ, e.g., Δλ=150 nm in the Λ variation of 1 nm against Δλ=117 nm in that of 10 nm. Our proposed GA has important applications in the practical design of nonuniform QPM grating structure.

Acknowledgment

This work was supported by the National Natural Science Foundation of China (60132020). The authors would like to thank Dr. Xin-Jun Liu and Dr. Xinjie Yu, Tsinghua Univ., for helping to make three movies and fruitful discussions on the GA, respectively.

Xueming Liu is currently engaged in postdoctoral work at School of Electrical Engineering, Seoul National University, Seoul 151-744, Korea.

References and links

1.

X. M. Liu, H. Y. Zhang, and Y. L. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001). [CrossRef]

2.

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and bandwidth enhancement of difference frequency generation (DFM)-based wavelength conversion by pump detuning,” Electron. Lett. 35, 978–980 (1999). [CrossRef]

3.

X. M. Liu, H. Y. Zhang, and M. D. Zhang, “Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium,” Opt. Express 10, 83–97 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-83 [CrossRef] [PubMed]

4.

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998). [CrossRef]

5.

M.H. Chou, I. Brenner, G. Lenz, R. Scotti, E.E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K.R. parameswaran, and M.M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 12, 82–84 (2000). [CrossRef]

6.

M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of ngineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999). [CrossRef]

7.

X. M. Liu, H. Y. Zhang, and Y. H Li, “Optimal design for the quasi-phase-matching three-wave mixing,” Opt. Express 9, 631–636 (2001), http://www.opticsexpress.org/oearchive/source/37804.htm [CrossRef] [PubMed]

8.

M. H. Chou, J. Hauden, M. A. Arbore, I. Brener, and M. M. Fejer, “1.5-um-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23, 1004–1006 (1998). [CrossRef]

9.

X. M. Liu, H. Y. Zhang, Y. L. Guo, and Y. H. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE. J. Quantum Elecron. 38, 1225–1233 (2002). [CrossRef]

10.

M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,” Opt. Lett. 28, 558–560 (2003). [CrossRef] [PubMed]

11.

T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron. 39, 166–171 (2003). [CrossRef]

12.

Y. Q. Qin and E. Wintner, “Optical filtering and switching using counter-propagating wavelength converter,” Opt. Quantum Electron. 35, 35–46 (2003). [CrossRef]

13.

M. C. Cardakli, A. B. Sahin, O. H. Adamczyk, A. E. Willner, K. R. Parameswaran, and M. M. Fejer, “Wavelength conversion of subcarrier channels using difference frequency generation in a PPLN waveguide,” IEEE Photon. Technol. Lett. 14, 1327–1329 (2002). [CrossRef]

14.

D. Sato, T. Morita, T. Suhara, and M. Fujimura, “Efficiency improvement by high-index cladding in LiNbO3 waveguide quasi-phase-matched wavelength converter for optical communication,” IEEE Photon. Technol. Lett. 15, 569–571 (2003). [CrossRef]

15.

W. Liu, J. Q. Sun, and J. Kurz, “Bandwidth and tunability enhancement of wavelength conversion by quasi-phase-matching difference frequency generation,” Opt. Commun. 216, 239–246 (2003). [CrossRef]

16.

M. H. Chou, I. Brener, M.M. Fejer, E. E. Chabass, and S. B. Christman, “1.5-µm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999). [CrossRef]

17.

X. M. Liu and M. D. Zhang, “Theoretical studies for the special states of the cascaded quadratic nonlinear effects”, J. Opt. Soc. Am. B 18, 1659–1666 (2001). [CrossRef]

18.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990). [CrossRef]

19.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Eletron. 30, 1596–1604 (1994). [CrossRef]

20.

K. Mizuuchi and K. Yamamoto, “Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts,” Opt. Lett. 23, 1880–1882 (1998). [CrossRef]

21.

N. E. Yu, H. Ro, M. Cha, S. Kurimura, and T. Taira, “Broadband quasi-phase-matched second-harmonic generatio in MgO-doped periodically poled LiNbO3 at the communications band,” Opt. Lett. 27, 1046–1048 (2002). [CrossRef]

22.

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002). [CrossRef]

23.

Y. Zhang and B. Y. Gu, “Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification,” Opt. Commun. 192, 417–425 (2001). [CrossRef]

24.

B. Y. Gu, Y. Zhang, and B. Z. Dong, “Investigations of harmonic generations in aperiodic optical superlattices,” J. Appl. Phys. 87, 7629–7637 (2000). [CrossRef]

25.

J. Wu, T. Kondo, and R. Ito, “Optimal design for broadband quasi-phase-matched second-harmonic generation using simulated annealing”, J. Lightwave Technol. 13, 456–460 (1995). [CrossRef]

26.

X. M. Liu and B. Lee, “Optimal design of fiber Raman amplifier based on hybrid genetic algorithm,” (submitted to IEEE Photon. Technol. Lett.)

27.

S. W. Mahfoud, “Niching methods for genetic algorithms,” Ph.D. dissertation, Univ. of Illinois, Urbana-Champaign, 1995.

28.

X. M. Liu and B. Lee, “Optimal design for ultrabroad-band amplifier,” (submitted to J. Lightwave Technol.)

29.

S. W. Mahfoud, “Crowding and preselection revisited,” In R. Manner and B. Manderick (Eds.), Parallel Problem Solving from Nature (Amsterdam, Elsevier Science.1992) (pp. 27–36).

30.

B. L. Miller and M. J. Shaw, “Genetic algorithms with dynamic niche sharing for multimodal function optimization,” in Proc. 1996 IEEE Int.Conf. Evolutionary Computation. Piscataway (NJ: IEEE Press, 1996).

31.

D. Thierens and D. E. Goldberg, “Elitist recombination: An integrated selection recombination GA,” Proceedings of the First IEEE Conference on Evolutionary Computation, 1994, pp.508–512.

32.

Yin and N. Germay, “A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization,” in R. F. Albrecht, C. R. Reeves, and N. C. Steele, editors, Proceedings of the International Conference on Artificial Neural Nets and Genetic Algorithms (Berlin, Springer-Verlag, 1993).

33.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (New York: Addison-Wesley, 1989).

34.

C. Y. Lin and W. H. Wu, “Niche identification techniques in multimodal genetic search with sharing scheme,” Adv. Eng. Software 33, 779–791 (2002). [CrossRef]

35.

J. P. Li, M. E. Balazs, G. T. Parks, and P. J. Clarkson, “A species conserving genetic algorithm for multimodal function optimization,” Evol. Comput. 10, 207–234 (2002). [CrossRef] [PubMed]

36.

P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software 33, 207–213 (2002). [CrossRef]

37.

L. X. Guo and M. Y. Zhao, “A parallel search genetic algorithm based on multiple peak values and multiple rules,” J. Mater. Process Tech. 129, 539–544 (2002). [CrossRef]

38.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE T. Evolut. Comput. 6, 182–197 (2002). [CrossRef]

39.

R. B. Kasat, D. Kunzru, D. N. Saraf, and S. K. Gupta, “Multiobjective optimization of industrial FCC units using elitist nondominated sorting genetic algorithm,” Ind. Eng. Chem. Res. 41, 4765–4776 (2002). [CrossRef]

40.

J. K. Cochran, S. M. Horng, and J. W. Fowler, “A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines,” Comput. Oper. Res. 30, 1087–1102 (2003). [CrossRef]

41.

R. Q. Lu and Z. Jin, “Formal ontology: Foundation of domain knowledge sharing and reusing,” J. Comput. Sci. Technol. 17, 535–548 (2002). [CrossRef]

42.

L. Tamine, C. Chrisment, and M. Boughanem, “Multiple query evaluation based on an enhanced genetic algorithm,” Inform. Process Manag. 39, 215–231 (2003). [CrossRef]

43.

J. Kivijarvi, P. Franti, and O. Nevalainen, “Self-adaptive genetic algorithm for clustering,” J. Heuristics 9, 113–129 (2003). [CrossRef]

44.

K. G. Khoo and P. N. Suganthan, “Structural pattern recognition using genetic algorithms with specialized operators,” IEEE T. Syst. Man. Cy. B 33, 156–165 (2003). [CrossRef]

45.

J. M. Yang, C. J. Lin, and C. Y. Kao, “A robust evolutionary algorithm for global optimization,” Eng. Optimize 34, 405–425 (2002). [CrossRef]

46.

X. H. Yuan, Y. B. Yuan, and Y. C. Zhang, “A hybrid chaotic genetic algorithm for short-term hydro system scheduling,” Math. Comput. Simulat. 59, 319–327 (2002). [CrossRef]

47.

Z. Y. Wu and A. R. Simpson, “A self-adaptive boundary search genetic algorithm and its application to water distribution systems,” J. Hydraul. Res. 40, 191–203 (2002). [CrossRef]

48.

M. Kirley, “A cellular genetic algorithm with disturbances: Optimization using dynamic spatial interactions,” J. Heuristics 8, 321–342 (2002). [CrossRef]

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(230.1150) Optical devices : All-optical devices

ToC Category:
Research Papers

History
Original Manuscript: June 9, 2003
Revised Manuscript: July 1, 2003
Published: July 14, 2003

Citation
Xueming Liu and Yanhe Li, "Optimal design of DFG-based wavelength conversion based on hybrid genetic algorithm," Opt. Express 11, 1677-1688 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-14-1677


Sort:  Journal  |  Reset  

References

  1. X. M. Liu, H. Y. Zhang, Y. L. Guo, "Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation," J. Lightwave Technol. 19, 1785-1792 (2001). [CrossRef]
  2. M. H. Chou, I. Brener, K. R. Parameswaran, M. M. Fejer, "Stability and bandwidth enhancement of difference frequency generation (DFM)-based wavelength conversion by pump detuning," Electron. Lett. 35, 978-980 (1999). [CrossRef]
  3. X. M. Liu, H. Y. Zhang, and M. D. Zhang, �??Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium,�?? Opt. Express 10, 83�??97 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-83">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-83</a>. [CrossRef] [PubMed]
  4. G. P. Banfi, P. K. Datta, V. Degiorgio, D. Fortusini, "Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate," Appl. Phys. Lett. 73, 136-138 (1998). [CrossRef]
  5. M.H.Chou, I.Brenner, G.Lenz, R.Scotti, E.E. Chaban, J.Shmulovich, D.Philen, S.Kosinski, K.R.parameswaran, and M.M.Fejer, �??Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,�?? IEEE Photon. Technol. Lett. 12, 82-84 (2000). [CrossRef]
  6. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, "Multiple-channel wavelength conversion by use of ngineered quasi-phase-matching structures in LiNbO3 waveguides," Opt. Lett. 24, 1157-1159 (1999). [CrossRef]
  7. X. M. Liu, H. Y. Zhang, Y. H Li, "Optimal design for the quasi-phase-matching three-wave mixing," Opt. Express 9, 631-636 (2001), <a href="http://www.opticsexpress.org/oearchive/source/37804.htm">http://www.opticsexpress.org/oearchive/source/37804.htm</a>. [CrossRef] [PubMed]
  8. M. H. Chou, J. Hauden, M. A. Arbore, I.Brener, M. M. Fejer, "1.5-um-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures," Opt. Lett. 23, 1004-1006 (1998). [CrossRef]
  9. X. M. Liu, H. Y. Zhang, Y. L. Guo, Y. H. Li, �??Optimal design and applications for quasi-phase-matching three-wave mixing,�?? IEEE. J. Quantum Electron. 38, 1225-1233 (2002). [CrossRef]
  10. M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, H. Suzuki, �??Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,�?? Opt. Lett. 28, 558-560 (2003). [CrossRef] [PubMed]
  11. T. Suhara, Y. Avetisyan, H. Ito, �??Theoretical analysis of laterally emitting terahertz-wave generation by difference-frequency generation in channel waveguides,�?? IEEE J. Quantum Electron. 39, 166-171 (2003). [CrossRef]
  12. Y. Q. Qin, E. Wintner, �??Optical filtering and switching using counter-propagating wavelength converter,�?? Opt Quantum Electron. 35, 35-46 (2003). [CrossRef]
  13. M. C. Cardakli, A. B. Sahin, O. H. Adamczyk, A. E. Willner, K. R. Parameswaran, M. M. Fejer, �??Wavelength conversion of subcarrier channels using difference frequency generation in a PPLN waveguide,�?? IEEE Photon. Technol. Lett. 14, 1327-1329 (2002). [CrossRef]
  14. D. Sato, T. Morita, T. Suhara, M. Fujimura, �??Efficiency improvement by high-index cladding in LiNbO3 waveguide quasi-phase-matched wavelength converter for optical communication,�?? IEEE Photon. Technol. Lett. 15, 569-571 (2003). [CrossRef]
  15. W. Liu, J. Q. Sun, J. Kurz, �??Bandwidth and tunability enhancement of wavelength conversion by quasi-phase-matching difference frequency generation,�?? Opt. Commun. 216, 239-246 (2003). [CrossRef]
  16. M. H. Chou, I. Brener,M.M. Fejer, E. E. Chabass, and S. B. Christman, �??1.5-m-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO waveguides,�?? IEEE Photon. Technol. Lett. 11, 653�??655 (1999). [CrossRef]
  17. X. M. Liu and M. D. Zhang, "Theoretical studies for the special states of the cascaded quadratic nonlinear effects", J. Opt. Soc. Am. B 18, 1659-1666 (2001). [CrossRef]
  18. T. Suhara and H. Nishihara, "Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings," IEEE J. Quantum Electron. 26, 1265-1276 (1990). [CrossRef]
  19. K. Mizuuchi, K.Yamamoto, M.Kato, and H.Sato, �??Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,�?? IEEE J. Quantum Eletron. 30, 1596-1604 (1994). [CrossRef]
  20. K. Mizuuchi and K. Yamamoto, "Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts," Opt. Lett. 23, 1880-1882 (1998). [CrossRef]
  21. N. E. Yu, H. Ro, M. Cha, S. Kurimura, T. Taira, �??Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band,�?? Opt. Lett. 27, 1046-1048 (2002). [CrossRef]
  22. X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, Y. L. Chen, �??Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,�?? Opt. Commun. 204, 407-411 (2002). [CrossRef]
  23. Y. Zhang, B. Y. Gu, �??Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification,�?? Opt. Commun. 192, 417-425 (2001). [CrossRef]
  24. B. Y. Gu, Y. Zhang, B. Z. Dong, �??Investigations of harmonic generations in aperiodic optical superlattices,�?? J. Appl. Phys. 87, 7629-7637 (2000). [CrossRef]
  25. J. Wu, T. Kondo, and R. Ito, �??Optimal design for broadband quasi-phase-matched second-harmonic generation using simulated annealing�??, J. Lightwave Technol. 13, 456-460 (1995). [CrossRef]
  26. X. M. Liu, and B. Lee, �??Optimal design of fiber Raman amplifier based on hybrid genetic algorithm,�?? (submitted to IEEE Photon. Technol. Lett.)
  27. S. W. Mahfoud, �??Niching methods for genetic algorithms,�?? Ph.D. dissertation, Univ. of Illinois, Urbana-Champaign, 1995.
  28. X. M. Liu, and B. Lee, �??Optimal design for ultrabroad-band amplifier,�?? (submitted to J. Lightwave Technol.)
  29. S. W. Mahfoud, �??Crowding and preselection revisited,�?? In Manner, R., & Manderick, B. (Eds.), Parallel Problem Solving from Nature (Amsterdam, Elsevier Science. 1992) (pp. 27-36).
  30. B. L. Miller and M. J. Shaw, �??Genetic algorithms with dynamic niche sharing for multimodal function optimization,�?? in Proc. 1996 IEEE Int.Conf. Evolutionary Computation. Piscataway (NJ: IEEE Press, 1996).
  31. D. Thierens, D. E. Goldberg, �??Elitist recombination: An integrated selection recombination GA,�?? Proceedings of the First IEEE Conference on Evolutionary Computation, 1994, pp.508-512.
  32. Yin and N. Germay, �??A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization,�?? in R. F. Albrecht, C. R. Reeves, and N. C. Steele, editors, Proceedings of the International Conference on Artificial Neural Nets and Genetic Algorithms (Berlin, Springer-Verlag, 1993).
  33. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (New York: Addison-Wesley, 1989).
  34. C. Y. Lin, W. H. Wu, �??Niche identification techniques in multimodal genetic search with sharing scheme,�?? Adv. Eng. Software 33, 779-791 (2002). [CrossRef]
  35. J. P. Li, M. E. Balazs, G. T. Parks, P. J. Clarkson, �??A species conserving genetic algorithm for multimodal function optimization,�?? Evol. Comput. 10, 207-234 (2002). [CrossRef] [PubMed]
  36. P. Siarry, A. Petrowski, M. Bessaou, �??A multipopulation genetic algorithm aimed at multimodal optimization,�?? Adv. Eng. Software 33, 207-213 (2002). [CrossRef]
  37. L. X. Guo, M. Y. Zhao, �??A parallel search genetic algorithm based on multiple peak values and multiple rules,�?? J. Mater. Process Tech. 129, 539-544 (2002). [CrossRef]
  38. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, �??A fast and elitist multiobjective genetic algorithm: NSGA-II,�?? IEEE T. Evolut. Comput. 6, 182-197 (2002). [CrossRef]
  39. R. B. Kasat, D. Kunzru, D. N. Saraf, S. K. Gupta, �??Multiobjective optimization of industrial FCC units using elitist nondominated sorting genetic algorithm,�?? Ind. Eng. Chem. Res. 41, 4765-4776 (2002). [CrossRef]
  40. J. K. Cochran, S. M. Horng, J. W. Fowler, �??A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines,�?? Comput. Oper. Res. 30, 1087-1102 (2003). [CrossRef]
  41. R. Q. Lu, Z. Jin, �??Formal ontology: Foundation of domain knowledge sharing and reusing,�?? J. Comput. Sci. Technol. 17, 535-548 (2002). [CrossRef]
  42. L. Tamine, C. Chrisment, M. Boughanem, �??Multiple query evaluation based on an enhanced genetic algorithm,�?? Inform. Process Manag. 39, 215-231(2003). [CrossRef]
  43. J. Kivijarvi, P. Franti, O. Nevalainen, �??Self-adaptive genetic algorithm for clustering,�?? J. Heuristics 9, 113-129 (2003). [CrossRef]
  44. K. G. Khoo, P. N. Suganthan, �??Structural pattern recognition using genetic algorithms with specialized operators,�?? IEEE T. Syst. Man. Cy. B 33, 156-165 (2003). [CrossRef]
  45. J. M. Yang, C. J. Lin, C. Y. Kao, �??A robust evolutionary algorithm for global optimization,�?? Eng. Optimize 34, 405-425 (2002). [CrossRef]
  46. X. H. Yuan, Y. B. Yuan, Y. C. Zhang, �??A hybrid chaotic genetic algorithm for short-term hydro system scheduling,�?? Math. Comput. Simulat. 59, 319-327 (2002). [CrossRef]
  47. Z. Y. Wu, A. R. Simpson, �??A self-adaptive boundary search genetic algorithm and its application to water distribution systems,�?? J. Hydraul. Res. 40, 191-203 (2002). [CrossRef]
  48. M. Kirley, �??A cellular genetic algorithm with disturbances: Optimization using dynamic spatial interactions,�?? J. Heuristics 8, 321-342 (2002). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: AVI (291 KB)     
» Media 2: AVI (1094 KB)     
» Media 3: AVI (1165 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited