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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2003 (9)

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]

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]

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

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]

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]

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]

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

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

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]

2002 (16)

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

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]

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]

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

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

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]

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]

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]

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]

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]

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

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]

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]

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]

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]

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]

2001 (4)

2000 (2)

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]

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]

1999 (3)

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]

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]

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]

1998 (3)

1995 (1)

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]

1994 (1)

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]

1990 (1)

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]

Adamczyk, O. H.

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]

Agarwal, S.

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]

Arbore, M. A.

Asobe, M.

Avetisyan, Y.

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]

Balazs, M. E.

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]

Banfi, G. P.

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]

Bessaou, M.

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

Boughanem, M.

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

Brener, I.

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]

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]

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]

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]

Brenner, I.

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]

Cardakli, M. C.

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]

Cha, M.

Chaban, E.E.

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]

Chabass, E. E.

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]

Chen, X. F.

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]

Chen, Y. L.

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]

Chen, Y. P.

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]

Chou, M. H.

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]

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]

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]

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]

Chou, M.H.

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]

Chrisment, C.

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

Christman, S. B.

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]

Clarkson, P. J.

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]

Cochran, J. K.

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]

Datta, P. K.

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]

Deb, K.

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]

Degiorgio, V.

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]

Dong, B. Z.

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]

Fejer, M. M.

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]

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]

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]

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]

Fejer, M.M.

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-µm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[Crossref]

Fortusini, D.

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]

Fowler, J. W.

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]

Franti, P.

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

Fujimura, M.

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]

Germay, N.

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).

Goldberg, D. E.

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

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.

Gu, B. Y.

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]

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]

Guo, L. X.

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]

Guo, Y. L.

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).
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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).
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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]

Hauden, J.

Horng, S. M.

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]

Ito, H.

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]

Ito, R.

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]

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

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

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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]

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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]

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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).
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M. Kirley, “A cellular genetic algorithm with disturbances: Optimization using dynamic spatial interactions,” J. Heuristics 8, 321–342 (2002).
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J. Kivijarvi, P. Franti, and O. Nevalainen, “Self-adaptive genetic algorithm for clustering,” J. Heuristics 9, 113–129 (2003).
[Crossref]

Kondo, T.

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]

Kosinski, S.

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]

Kunzru, D.

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]

Kurimura, S.

Kurz, J.

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

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Lenz, G.

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]

Li, J. P.

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]

Li, Y. H

Li, Y. H.

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]

Lin, C. J.

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

Lin, C. Y.

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]

Liu, W.

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]

Liu, X. M.

Lu, R. Q.

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

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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 R. Manner and B. Manderick (Eds.), Parallel Problem Solving from Nature (Amsterdam, Elsevier Science.1992) (pp. 27–36).

Meyarivan, T.

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]

Miller, B. L.

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).

Miyazawa, H.

Mizuuchi, K.

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]

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]

Morita, T.

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]

Nevalainen, O.

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

Nishida, Y.

Nishihara, H.

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]

Parameswaran, K. R.

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]

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]

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]

parameswaran, K.R.

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]

Parks, G. T.

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]

Petrowski, A.

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

Philen, D.

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]

Pratap, A.

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]

Qin, Y. Q.

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

Ro, H.

Sahin, A. B.

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]

Saraf, D. N.

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]

Sato, D.

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]

Sato, H.

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]

Scotti, R.

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]

Shaw, M. J.

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).

Shmulovich, J.

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]

Siarry, P.

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

Simpson, A. R.

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]

Suganthan, P. N.

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]

Suhara, T.

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]

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]

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]

Sun, J. Q.

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]

Suzuki, H.

Tadanaga, O.

Taira, T.

Tamine, L.

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

Thierens, D.

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.

Willner, A. E.

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]

Wintner, E.

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

Wu, F.

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]

Wu, J.

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]

Wu, W. H.

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]

Wu, Z. Y.

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]

Xia, Y. X.

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]

Yamamoto, K.

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]

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]

Yang, J. M.

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

Yin,

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).

Yu, N. E.

Yuan, X. H.

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]

Yuan, Y. B.

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]

Zeng, X. L.

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]

Zhang, H. Y.

Zhang, M. D.

Zhang, Y.

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]

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]

Zhang, Y. C.

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]

Zhao, M. Y.

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]

Adv. Eng. Software (2)

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]

P. Siarry, A. Petrowski, and 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, 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]

Comput. Oper. Res. (1)

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]

Electron. Lett. (1)

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]

Eng. Optimize (1)

J. M. Yang, C. J. Lin, and 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, and P. J. Clarkson, “A species conserving genetic algorithm for multimodal function optimization,” Evol. Comput. 10, 207–234 (2002).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (2)

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]

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]

IEEE J. Quantum Eletron. (1)

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. (4)

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Supplementary Material (3)

» Media 1: AVI (291 KB)     
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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)

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

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

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

Equations (12)

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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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