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

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References

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  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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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).
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    [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]

Adv. Eng. Software (2)

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

P. Siarry, A. Petrowski, M. Bessaou, �??A multipopulation genetic algorithm aimed at multimodal optimization,�?? Adv. Eng. Software 33, 207-213 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

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]

Comput. Oper. Res. (1)

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]

Electron. Lett. (1)

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]

Eng. Optimize (1)

J. M. Yang, C. J. Lin, C. Y. Kao, �??A robust evolutionary algorithm for global optimization,�?? Eng. Optimize 34, 405-425 (2002).
[CrossRef]

Evol. Comput. (1)

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]

IEEE J. Quantum Electron. (3)

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]

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]

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]

IEEE Photon. Technol. Lett. (5)

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]

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]

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]

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]

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

IEEE T. Evolut. Comput. (1)

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]

IEEE T. Syst. Man. Cy. B (1)

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]

IEEE. J. Quantum Electron. (1)

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]

Ind. Eng. Chem. Res. (1)

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]

Inform. Process Manag. (1)

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

J. Appl. Phys. (1)

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

J. Comput. Sci. Technol. (1)

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

J. Heuristics (2)

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

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

J. Hydraul. Res. (1)

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]

J. Lightwave Technol. (3)

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]

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]

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

J. Mater. Process Tech. (1)

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]

J. Opt. Soc. Am. B (1)

Math. Comput. Simulat. (1)

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]

Opt Quantum Electron. (1)

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

Opt. Commun. (3)

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]

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]

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]

Opt. Express (2)

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]

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]

Opt. Lett. (5)

Other (6)

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

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).

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).

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.

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).

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

Supplementary Material (3)

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Figures (5)

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.

Fig. 2.
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.
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.

Fig. 4.
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.

Fig. 5.
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).

Tables (3)

Tables Icon

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

Tables Icon

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

Tables Icon

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

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

p c = { p ch ( p ch p cl ) ( f m 2 f ave ) ( f max f ave ) , if f m 2 > f ave , p ch , otherwise
p m = { p mh ( p mh p ml ) ( f max f ) ( f max f ave ) , if f > f ave , p mh , otherwise
f = a · f + b ,
{ { a = ( C m 1 ) f ave ( f max f ave ) b = ( f max C m f ave ) f ave ( f max f ave ) , if f min > C m f ave f max C m 1 { a = f ave ( f ave f min ) b = a · f min , otherwise
[ E 1 ( L ) E 2 * ( L ) ] = [ N 1 N 2 N 3 N 4 ] [ E 1 ( 0 ) E 2 * ( 0 ) ] ,
[ N 1 N 2 N 3 N 4 ] = N m N m 1 N l N 1
N l = [ N l , 1 N l , 2 N l , 3 * N l , 1 * ] , l = 1 , 2 , , m
N l , 1 = [ cosh ( Q l L l ) + i Δ k 2 Q l sinh ( Q l L l ) ] e 1
N l , 2 = i ( M 1 Q l ) sinh ( Q l L l ) e 2 ,
N l , 3 = i ( M 2 Q l ) sinh ( Q l L l ) e 2 ,
y ( x ) = x + 10 · sin ( 5 x ) + 7 · cos ( 4 x ) , x [ 2.3 , 5.8 ] .
z ( x , y ) = { H i R i 2 R ¯ 2 ( R ¯ 2 R i 2 2 ) + H i , if R ¯ 2 R i 2 , x [ 0 , 10 ] and y [ 0 , 10 ] 0 , otherwise

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