Abstract

In this article, we present a genetic algorithm (GA) as one branch of artificial intelligence (AI) for the optimization-design of the artificial magnetic metamaterial whose structure is automatically generated by computer through the filling element methodology. A representative design example, metamaterials with permeability of negative unity, is investigated and the optimized structures found by the GA are presented. It is also demonstrated that our approach is effective for the synthesis of functional magnetic and electric metamaterials with optimal structures. This GA-based optimization-design technique shows great versatility and applicability in the design of functional metamaterials.

© 2008 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  4. D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  5. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  6. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  7. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602-1-4 (2003).
    [CrossRef]
  8. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
    [CrossRef] [PubMed]
  9. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  10. W. Zhu, X. Zhao, and N. Ji, "Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects," Appl. Phys. Lett. 90, 011911-1-3 (2007).
    [CrossRef]
  11. H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
    [CrossRef]
  12. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
    [CrossRef]
  13. K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
    [CrossRef]
  14. X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, "Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials," Opt. Express 14, 7188-7197 (2006).
    [CrossRef] [PubMed]
  15. M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
    [CrossRef]
  16. F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
    [CrossRef]
  17. D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites using electromagnetic bandgap structures to synthesis metamaterial ferrites," IEEE Trans. Antenna Propag. 53, 1382-1389 (2005).
    [CrossRef]
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  21. D. H. Kwon and D. H. Werner, "Low-index metamaterial designs in visible spectrum," Opt. Express 14, 9267-9272 (2007)
    [CrossRef]
  22. G. Mumcu, M. Valerio, K. Sertel, and J. L. Volakis, "Applications of the finite element method to designing composite metamaterials," International conference on electromagnetic in advanced applications, 818-821 (2007)
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  26. F. Bilotti, L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave Opt. Technol. Lett. 48, 2171-2175 (2006).
    [CrossRef]
  27. S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
    [CrossRef]
  28. D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109-1-3 (2006).
    [CrossRef]

2007 (3)

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

D. H. Kwon and D. H. Werner, "Low-index metamaterial designs in visible spectrum," Opt. Express 14, 9267-9272 (2007)
[CrossRef]

J. Goh, I. Fushman, D. Englund, and J. Vuckovic, "Genetic optimization of photonic band structures," Opt. Express 15, 8218-8230 (2007).
[CrossRef] [PubMed]

2006 (4)

F. Bilotti, L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave Opt. Technol. Lett. 48, 2171-2175 (2006).
[CrossRef]

X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, "Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials," Opt. Express 14, 7188-7197 (2006).
[CrossRef] [PubMed]

J. W. Rinne and P. Wiltzis, "Design of holographic structures using Genetic Algorithm," Opt. Express 14, 9909-9916 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites using electromagnetic bandgap structures to synthesis metamaterial ferrites," IEEE Trans. Antenna Propag. 53, 1382-1389 (2005).
[CrossRef]

2004 (1)

F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (3)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Aydin, K.

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

Bilotti, F.

F. Bilotti, L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave Opt. Technol. Lett. 48, 2171-2175 (2006).
[CrossRef]

Chen, C. H.

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, "Optimal design of integrally gated CNT field-emission devices using a genetic algorithm," Nanotechnology 18, 395203-1-10 (2007).

Chen, H.

H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
[CrossRef]

Chen, P. Y.

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, "Optimal design of integrally gated CNT field-emission devices using a genetic algorithm," Nanotechnology 18, 395203-1-10 (2007).

Chen, X.

X. Chen, Tomasz, M.  Grzegorczyk, B. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608-1-7 (2004).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Cwik, T.

F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
[CrossRef]

Economou, E. N.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
[CrossRef] [PubMed]

Englund, D.

Enoch, S.

S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
[CrossRef]

Fu, Q. H.

Fushman, I.

Goh, J.

Grzegorczyk, T. M.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

Guerin, N.

S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
[CrossRef]

Gundogdu, T. F.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Huangfu, J

H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
[CrossRef]

Huangfu, J.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

Hudli??ka, M.

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

Ji, N.

W. Zhu, X. Zhao, and N. Ji, "Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects," Appl. Phys. Lett. 90, 011911-1-3 (2007).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
[CrossRef] [PubMed]

Kern, D. J.

D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites using electromagnetic bandgap structures to synthesis metamaterial ferrites," IEEE Trans. Antenna Propag. 53, 1382-1389 (2005).
[CrossRef]

Kong, J. A.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

Koschny, T.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602-1-4 (2003).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Kwon, D. H.

D. H. Kwon and D. H. Werner, "Low-index metamaterial designs in visible spectrum," Opt. Express 14, 9267-9272 (2007)
[CrossRef]

Li, Z.

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

Lisovich, M.

D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites using electromagnetic bandgap structures to synthesis metamaterial ferrites," IEEE Trans. Antenna Propag. 53, 1382-1389 (2005).
[CrossRef]

Manteghi, M.

F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
[CrossRef]

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602-1-4 (2003).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109-1-3 (2006).
[CrossRef]

Mumcu, G.

G. Mumcu, M. Valerio, K. Sertel, and J. L. Volakis, "Applications of the finite element method to designing composite metamaterials," International conference on electromagnetic in advanced applications, 818-821 (2007)
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Nucci, L.

F. Bilotti, L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave Opt. Technol. Lett. 48, 2171-2175 (2006).
[CrossRef]

Ozbay, E.

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Penciu, R. S.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Rahmat-Samii, Y.

F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
[CrossRef]

Ran, L.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
[CrossRef]

Rinne, J. W.

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Sabouroux, F.

S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109-1-3 (2006).
[CrossRef]

Sertel, K.

G. Mumcu, M. Valerio, K. Sertel, and J. L. Volakis, "Applications of the finite element method to designing composite metamaterials," International conference on electromagnetic in advanced applications, 818-821 (2007)
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602-1-4 (2003).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109-1-3 (2006).
[CrossRef]

Soukoulis, C. M.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602-1-4 (2003).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Tayeb, G.

S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
[CrossRef]

Tomasz, X.

X. Chen, Tomasz, M.  Grzegorczyk, B. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608-1-7 (2004).
[CrossRef]

Tretyakov, S. A.

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

Valerio, M.

G. Mumcu, M. Valerio, K. Sertel, and J. L. Volakis, "Applications of the finite element method to designing composite metamaterials," International conference on electromagnetic in advanced applications, 818-821 (2007)
[CrossRef]

Vegni, L.

F. Bilotti, L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave Opt. Technol. Lett. 48, 2171-2175 (2006).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Ville, F. J.

F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
[CrossRef]

Volakis, J. L.

G. Mumcu, M. Valerio, K. Sertel, and J. L. Volakis, "Applications of the finite element method to designing composite metamaterials," International conference on electromagnetic in advanced applications, 818-821 (2007)
[CrossRef]

Vuckovic, J.

Wang, W. P.

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, "Optimal design of integrally gated CNT field-emission devices using a genetic algorithm," Nanotechnology 18, 395203-1-10 (2007).

Wen, H. C.

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, "Optimal design of integrally gated CNT field-emission devices using a genetic algorithm," Nanotechnology 18, 395203-1-10 (2007).

Werner, D. H.

D. H. Kwon and D. H. Werner, "Low-index metamaterial designs in visible spectrum," Opt. Express 14, 9267-9272 (2007)
[CrossRef]

D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites using electromagnetic bandgap structures to synthesis metamaterial ferrites," IEEE Trans. Antenna Propag. 53, 1382-1389 (2005).
[CrossRef]

Wiltzis, P.

Wu, J. S.

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, "Optimal design of integrally gated CNT field-emission devices using a genetic algorithm," Nanotechnology 18, 395203-1-10 (2007).

Yang, Y.

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Zhang, X.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
[CrossRef]

Zhao, J.

Zhao, X.

W. Zhu, X. Zhao, and N. Ji, "Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects," Appl. Phys. Lett. 90, 011911-1-3 (2007).
[CrossRef]

Zhao, X. P.

Zhou, X.

Zhu, W.

W. Zhu, X. Zhao, and N. Ji, "Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects," Appl. Phys. Lett. 90, 011911-1-3 (2007).
[CrossRef]

IEEE Trans. Antenna Propag. (2)

F. J. Ville, T. Cwik, Y. Rahmat-Samii, and M. Manteghi, "A parallel electromagnetic genetic-algorithm optimization (EGO) application for patch antenna design," IEEE Trans. Antenna Propag. 52, 2424-2435 (2004).
[CrossRef]

D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites using electromagnetic bandgap structures to synthesis metamaterial ferrites," IEEE Trans. Antenna Propag. 53, 1382-1389 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

F. Bilotti, L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave Opt. Technol. Lett. 48, 2171-2175 (2006).
[CrossRef]

New J. Phys. (1)

K.  Aydin, Z. Li, M.  Hudli�?ka, S. A.  Tretyakov, and E.  Ozbay, "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions," New J. Phys. 9, 326-336 (2007).
[CrossRef]

Opt. Express (4)

Phys. Rev. Lett. (4)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Other (12)

W. Zhu, X. Zhao, and N. Ji, "Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects," Appl. Phys. Lett. 90, 011911-1-3 (2007).
[CrossRef]

H. Chen, L. Ran, J Huangfu, X. Zhang, and K. Chen, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-4 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Negative refraction of a combined double S-shaped metamaterial," Appl. Phys. Lett. 86, 151909-1-3 (2005).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602-1-4 (2003).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
[CrossRef] [PubMed]

G. Mumcu, M. Valerio, K. Sertel, and J. L. Volakis, "Applications of the finite element method to designing composite metamaterials," International conference on electromagnetic in advanced applications, 818-821 (2007)
[CrossRef]

J. Holland, Adaptation in Nature and Artificial System (Ann Arbor: The University of Michigan Press, 1975). CST Microwave Studio 2006.b http://www.CST.com.

X. Chen, Tomasz, M.  Grzegorczyk, B. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608-1-7 (2004).
[CrossRef]

http://www.python.org.

P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, and W. P. Wang, "Optimal design of integrally gated CNT field-emission devices using a genetic algorithm," Nanotechnology 18, 395203-1-10 (2007).

S. Enoch, G. Tayeb, F. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902-1-4 (2002).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109-1-3 (2006).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Illustration of (a) filling square-pixel (FSP) and (b) filling beehive-cell (FBC) method for the structural design of a metamaterial unit cell. The lattice constant ax =ay =az =a is set to 7.5mm. The dimensions of the metallic patches are w1 =0.8 mm, w2 =0.55 mm for Ns =N c=7, and w1 =0.5 mm, w2 =0.35 mm for Ns =Nc =11. The thickness of the substrate (FR4 with εr = 4.4) and the metallic patches are 1.5 mm and 0.035 mm, respectively.

Fig. 2.
Fig. 2.

The best fitness plotted as a function of generation (top). The unit cells show the best structures (elite) at different generations during the evolution process of the GA (bottom).

Fig. 3.
Fig. 3.

GA-optimized unit cell and its corresponding µeff and εeff for the FSP method with (a) Ns =7 and (b) Ns =11, and the FBC method with (c) Nc =7and (d)Nc =11 (desired permeability: µeff =-1 over the range of 4~10 GHz).

Fig. 4.
Fig. 4.

The GA-optimized unit cell for the metamaterial with permeability µeff =-0.5 and its corresponding µeff and εeff .

Fig. 5.
Fig. 5.

The GA-optimized unit cell for the metamaterial with permeability µeff =-2 and its corresponding µeff and εeff .

Fig. 6.
Fig. 6.

The GA-optimized unit cell for the metamaterial with permeability µeff =2+i4 and its corresponding µeff and εeff .

Fig. 7.
Fig. 7.

The GA-optimized unit cell for the metamaterial with permeability µeff =-1 at 5 GHz and its corresponding µeff and εeff .

Fig. 8.
Fig. 8.

The GA-optimized unit cell for the metamaterial with permeability of zero and its corresponding µeff and εeff .

Fig. 9.
Fig. 9.

The GA-optimized unit cell for the metamaterial with permittivity of εeff =-1 and its corresponding εeff and µeff .

Fig. 10.
Fig. 10.

Left-handed side shows the unit cell of a NIM, which is composite material made of the GA-optimized electric and magnetic resonators on the opposite sides of the substrate; the right-handed side shows its corresponding µeff , εeff , n and z.

Equations (8)

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

μ eff ( ω ) = 1 ω mp 2 ω m 0 2 ω 2 ω m 0 2 + i Γ m ω = μ eff ( ω ) + μ eff ( ω ) ,
ε eff ( ω ) = 1 ω p 2 ω 2 ,
fitness = min ( μ eff + R a + μ eff + R b ) | 4 GHz < f < 10 GHz
fitness = min ( μ eff + 1 + μ eff " ) f = 5 GHz
fitness = ( μ eff + μ eff " ) μ eff = min ( μ eff )
ε eff ( ω ) = 1 ω ep 2 ω e 0 2 ω 2 ω e 0 2 + i Γ e ω = ε eff ( ω ) + ε eff " ( ω )
fitness = min ( ε eff + 1 + ε eff " ) 4 GHz < f < 10 GHz
fitness = min ( n eff + 1 + μ eff " ) 4 GHz < f < 10 GHz

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