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

Optics Express, Vol. 11, Issue 14, pp. 1677-1688 (2003)

http://dx.doi.org/10.1364/OE.11.001677

Acrobat PDF (279 KB)

### 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

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. 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]

_{3}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. 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]

_{3}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]

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]

*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. 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]

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]

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. 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. 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. 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]

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. 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. 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]

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]

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. 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]

*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]

**19**, 1785–1792 (2001). [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]

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]

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. 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]

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

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

## 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).

*selected*. ② Select

*k*(usually

*k*=

*n*) individuals orderly from the population, which satisfy the following conditions: the individuals are not marked as

*selected*; the Euclidean distance from the individual to all of the confirmed peak centers is larger than

*r*. ③ Calculate the sum of distances between each of

*k*individuals and all of confirmed peak centers, assign the individual with the largest sum of distance as the next confirmed peak center, and mark it as

*selected*. ④ Repeat ② and ③ until

*n*peak centers are found.

*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 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

*p*, i.e.,

_{c}*f*is the maximum fitness of the two chromosomes being crossed,

_{m2}*f*and

_{max}*f*are the maximum fitness and average fitness of the entire population, and

_{ave}*p*and

_{ch}*p*are the probability of highest crossover and lowest crossover, respectively.

_{cl}*Step 5*(mutation): Implement a single mutation and employ an adaptive probability of mutation

*p*, i.e.,

_{m}*f*is the fitness of the chromosome, and

*p*and

_{mh}*p*are the probability of the adaptive mutation, the highest mutation and the lowest mutation, respectively.

_{ml}*p*=0.99,

_{ch}*p*=0.7,

_{cl}*p*=0.02 and

_{mh}*p*=0.005 in this paper.

_{ml}*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].

*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.,

*C*is a constant, and

_{m}*C*=1.2 in our simulation;

_{m}*f*is the minimum fitness of the entire population; other parameters are the same as Eqs. (1) and (2).

_{min}*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

**38**, 1225–1233 (2002). [CrossRef]

*λ*. In periodically poled crystal waveguides (e.g., LiNbO

_{3}), 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. 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. 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]

_{3}), 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

**19**, 1785–1792 (2001). [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]

**38**, 1225–1233 (2002). [CrossRef]

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. 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. 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]

**19**, 1785–1792 (2001). [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]

**38**, 1225–1233 (2002). [CrossRef]

*N**

_{l,2}and

*N**

_{l,3}are the conjugate of

*N*

_{l, 2}and

*N*

_{l, 3}, respectively,

*L*is the length of the

_{l}*l*-th segment (i.e.,

*L*

_{l}=

*z*-

_{l}*z*

_{l}_{-1}), and

*z*

_{l}_{-1}and

*z*are the input and output places of this segment, respectively (See Fig. 1).

_{l}*e*

_{1}=exp(-

*i*Δ

*k*/2),

_{l}L_{l}*e*

_{2}=exp(-

*i*Δ

*k*(

_{l}*z*

_{l}_{-1}+

*L*)/2), and

_{l}*k*of the

_{l}*l*-th segment. Δ

*k*=

_{l}*k*

_{3}-

*k*

_{2}-

*k*

_{1}-2π/Λ

*under the approximation of the first-order periodic perturbation effect.*

_{l}*M*=

_{j}*ω*(0)/(

_{j}d_{eff}E_{3}*n*) (

_{j}c*j*=1, 2). Λ and

*c*are the grating period and the speed of light in the vacuum, respectively.

*k*,

_{j}*n*and

_{j}*E*are the wave vector, the index of refraction, and the electric field under light-frequencies

_{j}*ω*(

_{j}*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).

## 4. Test function

*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

*R̄*

^{2}=

*X*

^{2}+

*Y*

^{2},

*X*=

*x*-

*x*,

_{ci}*Y*=

*y*-

*y*,

_{ci}*c*=(

_{i}*x*,

_{ci}*y*), and

_{ci}*R*={1.5, 2.5, 1, 0.75, 3},

_{i}*H*={2, 4.4, 3, 4.5, 4},

_{i}*c*={(2, 8), (3, 4), (5, 7), (7, 8.5), (7, 4)}. This test function consists of five peaks (center

_{i}*c*, radius

_{i}*R*and height

_{i}*H*), 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.

_{i}*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.

*T*of our GA is obviously shortened in comparison with the traditional sharing GA. The reason is that

*T*∝(

*kN*) for our GA, but

*T*∝(

*N*

^{2}) for the traditional sharing GA [27].

## 5. Optimized results by means of hybrid GA

**19**, 1785–1792 (2001). [CrossRef]

**38**, 1225–1233 (2002). [CrossRef]

*m*≥5. Fortunately, our proposed GA can availably overcome these difficulties. In the simulation calculations, we employ the representative data of periodically poled LiNbO

_{3}[1

**19**, 1785–1792 (2001). [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]

**38**, 1225–1233 (2002). [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]

*P*

_{3}=200 mW and wavelength

*λ*

_{3}=775nm;

*d*=15 pm/V and

_{eff}*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 30µm

^{2}; the lengths of all segments are assumed to be equal, i.e.,

*L*

_{1}=

*L*

_{2}=…=

*L*. The relation between the light intensity

_{m}*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).

*η*and its corresponding bandwidth Δ

*λ*versus the signal wavelength

*λ*

_{1}in five-, six- and seven-segment structures, respectively. Their corresponding optimal values of Λ are tabularized in tables 1–3.

*pl*(

*l*=1, 2, …, 5) in figures and tables represents the

*l*-th peak center, and Δ

*λ*is the corresponding optimal conversion bandwidth. In the optimal simulation of Tables 1–3 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)].

*λ*is broadened with an increase in the segment number

*m*, e.g., Δ

*λ*=192 nm for seven segments against Δ

*λ*=150 nm for five segments; ② there are the same or approximately the same Δ

*λ*for each peak center for a given segment number; ③ to realize the fixed Δ

*λ*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 Δ

*λ*lies in the first peak center

*p*

_{1}, as is determined in the assumption of our GA.

*L*<20 mm [9

**38**, 1225–1233 (2002). [CrossRef]

*λ*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

**38**, 1225–1233 (2002). [CrossRef]

*λ*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.

*η*and bandwidth Δ

*λ*with the fluctuation of Δ

*λ*and the variation of Λ, we give two optimized examples for

*η*and Δ

*λ*versus

*λ*

_{1}under the conditions of the Δ

*λ*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 Δ

*λ*=168 nm in the Δ

*λ*fluctuation of <2 nm against Δ

*λ*=150 nm in that of <1 nm and ② Δ

*λ*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 Δ

*λ*fluctuation (i.e., decreasing the Δ

*λ*fluctuation) is at the cost of narrowing the conversion bandwidth Δ

*λ*and 2 extending the variation of Λ also makes Δ

*λ*narrowed.

## 6. Conclusions

*λ*, ② decreasing the fluctuation of Δ

*λ*(i.e., improving the properties of the fluctuation of Δ

*λ*) is at the cost of Δ

*λ*, e.g., Δ

*λ*=168 nm in the Δ

*λ*fluctuation of <2 nm against Δ

*λ*=150 nm in that of <1 nm, and ③ extending the variation of Λ decreases Δ

*λ*, e.g., Δ

*λ*=150 nm in the Λ variation of 1 nm against Δ

*λ*=117 nm in that of 10 nm. Our proposed GA has important applications in the practical design of nonuniform QPM grating structure.

## Acknowledgment

## References and links

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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. |

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 |

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. |

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29. | S. W. Mahfoud, “Crowding and preselection revisited,” In R. Manner and B. Manderick (Eds.), |

30. | B. L. Miller and M. J. Shaw, “Genetic algorithms with dynamic niche sharing for multimodal function optimization,” in |

31. | D. Thierens and D. E. Goldberg, “Elitist recombination: An integrated selection recombination GA,” |

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, |

33. | D. E. Goldberg, |

34. | C. Y. Lin and W. H. Wu, “Niche identification techniques in multimodal genetic search with sharing scheme,” Adv. Eng. Software |

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. |

36. | P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software |

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. |

38. | K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE T. Evolut. Comput. |

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. |

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. |

41. | R. Q. Lu and Z. Jin, “Formal ontology: Foundation of domain knowledge sharing and reusing,” J. Comput. Sci. Technol. |

42. | L. Tamine, C. Chrisment, and M. Boughanem, “Multiple query evaluation based on an enhanced genetic algorithm,” Inform. Process Manag. |

43. | J. Kivijarvi, P. Franti, and O. Nevalainen, “Self-adaptive genetic algorithm for clustering,” J. Heuristics |

44. | K. G. Khoo and P. N. Suganthan, “Structural pattern recognition using genetic algorithms with specialized operators,” IEEE T. Syst. Man. Cy. B |

45. | J. M. Yang, C. J. Lin, and C. Y. Kao, “A robust evolutionary algorithm for global optimization,” Eng. Optimize |

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. |

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. |

48. | M. Kirley, “A cellular genetic algorithm with disturbances: Optimization using dynamic spatial interactions,” J. Heuristics |

**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

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