Abstract

Optical metamaterial consisting of metal-dielectric composites creates a complicated system that is not amenable to analytical solutions. This presents a challenge in optimizing these intricate systems. We present the application of three nature-inspired stochastic optimization techniques in conjunction with fast numerical electromagnetic solvers to yield a metamaterial that satisfies a required design criterion. In particular, three stochastic optimization tools (genetic algorithm, particle swarm optimization, and simulated annealing) are used for designing a low-loss optical negative index metamaterial. A negative refractive index around 0.8+0.2i is obtained at a wavelength of 770nm. The particle swarm optimization algorithm is found to be the most efficient in this case.

© 2007 Optical Society of America

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  1. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2002).
    [CrossRef]
  2. W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based on metal-dielectric composites," Phys. Rev. B 72, 193101 (2005).
    [CrossRef]
  3. N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
    [CrossRef]
  4. D. Melville and R. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005).
    [CrossRef] [PubMed]
  5. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  6. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
    [CrossRef]
  7. U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
    [CrossRef] [PubMed]
  8. T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
    [CrossRef]
  9. A. V. Kildishev, U. K. Chettiar, H.-K. Yuan, W. Cai, and V. M. Shalaev, "Optimizing optical negative index materials: feedback from fabrication," in Proceedings of the 23rd International Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society, 2007), pp. 11-16.
  10. T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
    [CrossRef]
  11. J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE, 1998).
    [CrossRef]
  12. L. Li and D. H. Werner, "Design of all-dielectric frequency selective surfaces using genetic algorithms combined with the finite element-boundary integral method," in Proceedings of the Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting, Vol. 4A, (IEEE, 2005), pp. 376-379.
  13. A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," J. Appl. Comput. Electromagnetics Soc. 22, 172-183 (2007).
  14. D. T. Pham and D. Karaboga, Intelligent Optimization Techniques (Springer-Verlag, 2000).
    [CrossRef]
  15. R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley-Interscience, 2004).
  16. Y. Rahmat-Samii and E. Michelssen, eds., Electromagnetic Optimization by Genetic Algorithms (Wiley-Interscience, 1999).
  17. D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
    [CrossRef]
  18. D. J. Kern, D. H. Werner, and M. Lisovich, "Metaferrites: using electromagnetic bandgap structures to synthesize metamaterial ferrites," IEEE Trans. Antennas Propag. 53, 1382-1389 (2005).
    [CrossRef]
  19. M. A. Gingrich and D. H. Werner, "Synthesis of low/zero index of refraction metamaterials from frequency selective surfaces using genetic algorithms," Electron. Lett. 41, 1266-1267 (2005).
    [CrossRef]
  20. J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
    [CrossRef]
  21. J. Kennedy and R. C. Eberhart, Swarm Intelligence (Academic, 2001).
  22. D. W. Boeringer and D. H. Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propag. 52, 771-779 (2004).
    [CrossRef]
  23. D. W. Boeringer and D. H. Werner, "Efficiency-constrained particle swarm optimization of a modified Bernstein polynomial for conformal array excitation amplitude synthesis," IEEE Trans. Antennas Propag. 53, 2662-2673 (2005).
    [CrossRef]
  24. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  25. A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, "Negative refractive index in optics of metal-dielectric composites," J. Opt. Soc. Am. B 23, 423-433 (2006).
    [CrossRef]
  26. S. Chakravarty, R. Mittra, and N. R. Williams, "Application of a micro-genetic algorithm (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screens buried in dielectrics," IEEE Trans. Antennas Propag. 50, 284-296 (2002).
    [CrossRef]
  27. H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, "A negative permeability material at red light," Opt. Express 15, 1076-1083 (2007).
    [CrossRef] [PubMed]

2007 (2)

A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," J. Appl. Comput. Electromagnetics Soc. 22, 172-183 (2007).

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, "A negative permeability material at red light," Opt. Express 15, 1076-1083 (2007).
[CrossRef] [PubMed]

2006 (4)

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, "Negative refractive index in optics of metal-dielectric composites," J. Opt. Soc. Am. B 23, 423-433 (2006).
[CrossRef]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
[CrossRef] [PubMed]

2005 (7)

D. Melville and R. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

D. W. Boeringer and D. H. Werner, "Efficiency-constrained particle swarm optimization of a modified Bernstein polynomial for conformal array excitation amplitude synthesis," IEEE Trans. Antennas Propag. 53, 2662-2673 (2005).
[CrossRef]

W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based on metal-dielectric composites," Phys. Rev. B 72, 193101 (2005).
[CrossRef]

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

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

M. A. Gingrich and D. H. Werner, "Synthesis of low/zero index of refraction metamaterials from frequency selective surfaces using genetic algorithms," Electron. Lett. 41, 1266-1267 (2005).
[CrossRef]

2004 (1)

D. W. Boeringer and D. H. Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propag. 52, 771-779 (2004).
[CrossRef]

2003 (1)

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

2002 (3)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2002).
[CrossRef]

S. Chakravarty, R. Mittra, and N. R. Williams, "Application of a micro-genetic algorithm (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screens buried in dielectrics," IEEE Trans. Antennas Propag. 50, 284-296 (2002).
[CrossRef]

1999 (2)

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

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
[CrossRef]

Blaikie, R.

Boeringer, D. W.

D. W. Boeringer and D. H. Werner, "Efficiency-constrained particle swarm optimization of a modified Bernstein polynomial for conformal array excitation amplitude synthesis," IEEE Trans. Antennas Propag. 53, 2662-2673 (2005).
[CrossRef]

D. W. Boeringer and D. H. Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propag. 52, 771-779 (2004).
[CrossRef]

Boltasseva, A.

Bossard, J. A.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

Cai, W.

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, "A negative permeability material at red light," Opt. Express 15, 1076-1083 (2007).
[CrossRef] [PubMed]

A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, "Negative refractive index in optics of metal-dielectric composites," J. Opt. Soc. Am. B 23, 423-433 (2006).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based on metal-dielectric composites," Phys. Rev. B 72, 193101 (2005).
[CrossRef]

A. V. Kildishev, U. K. Chettiar, H.-K. Yuan, W. Cai, and V. M. Shalaev, "Optimizing optical negative index materials: feedback from fabrication," in Proceedings of the 23rd International Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society, 2007), pp. 11-16.

Chakravarty, S.

S. Chakravarty, R. Mittra, and N. R. Williams, "Application of a micro-genetic algorithm (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screens buried in dielectrics," IEEE Trans. Antennas Propag. 50, 284-296 (2002).
[CrossRef]

Chatterjee, A.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE, 1998).
[CrossRef]

Chettiar, U. K.

Drachev, V. P.

Drupp, R.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

Eberhart, R. C.

J. Kennedy and R. C. Eberhart, Swarm Intelligence (Academic, 2001).

Eibert, T. F.

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
[CrossRef]

Fang, N.

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Genov, D. A.

W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based on metal-dielectric composites," Phys. Rev. B 72, 193101 (2005).
[CrossRef]

Gingrich, M. A.

M. A. Gingrich and D. H. Werner, "Synthesis of low/zero index of refraction metamaterials from frequency selective surfaces using genetic algorithms," Electron. Lett. 41, 1266-1267 (2005).
[CrossRef]

Haupt, R. L.

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley-Interscience, 2004).

Haupt, S. E.

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley-Interscience, 2004).

Holden, A. J.

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

Jackson, D. R.

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
[CrossRef]

Karaboga, D.

D. T. Pham and D. Karaboga, Intelligent Optimization Techniques (Springer-Verlag, 2000).
[CrossRef]

Kempel, L. C.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE, 1998).
[CrossRef]

Kennedy, J.

J. Kennedy and R. C. Eberhart, Swarm Intelligence (Academic, 2001).

Kern, D. J.

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

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

Kildishev, A. V.

A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," J. Appl. Comput. Electromagnetics Soc. 22, 172-183 (2007).

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, "A negative permeability material at red light," Opt. Express 15, 1076-1083 (2007).
[CrossRef] [PubMed]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
[CrossRef] [PubMed]

A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, "Negative refractive index in optics of metal-dielectric composites," J. Opt. Soc. Am. B 23, 423-433 (2006).
[CrossRef]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

A. V. Kildishev, U. K. Chettiar, H.-K. Yuan, W. Cai, and V. M. Shalaev, "Optimizing optical negative index materials: feedback from fabrication," in Proceedings of the 23rd International Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society, 2007), pp. 11-16.

Klar, T. A.

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
[CrossRef] [PubMed]

Lanuzza, L.

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

Li, L.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

L. Li and D. H. Werner, "Design of all-dielectric frequency selective surfaces using genetic algorithms combined with the finite element-boundary integral method," in Proceedings of the Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting, Vol. 4A, (IEEE, 2005), pp. 376-379.

Lisovich, M.

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

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Mayer, T. S.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

Melville, D.

Michelssen, E.

Y. Rahmat-Samii and E. Michelssen, eds., Electromagnetic Optimization by Genetic Algorithms (Wiley-Interscience, 1999).

Mittra, R.

S. Chakravarty, R. Mittra, and N. R. Williams, "Application of a micro-genetic algorithm (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screens buried in dielectrics," IEEE Trans. Antennas Propag. 50, 284-296 (2002).
[CrossRef]

Monorchio, A.

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2002).
[CrossRef]

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

Pham, D. T.

D. T. Pham and D. Karaboga, Intelligent Optimization Techniques (Springer-Verlag, 2000).
[CrossRef]

Rahmat-Samii, Y.

Y. Rahmat-Samii and E. Michelssen, eds., Electromagnetic Optimization by Genetic Algorithms (Wiley-Interscience, 1999).

Robbins, D. J.

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

Sarychev, A. K.

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Shalaev, V. M.

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, "A negative permeability material at red light," Opt. Express 15, 1076-1083 (2007).
[CrossRef] [PubMed]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
[CrossRef] [PubMed]

A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, "Negative refractive index in optics of metal-dielectric composites," J. Opt. Soc. Am. B 23, 423-433 (2006).
[CrossRef]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based on metal-dielectric composites," Phys. Rev. B 72, 193101 (2005).
[CrossRef]

A. V. Kildishev, U. K. Chettiar, H.-K. Yuan, W. Cai, and V. M. Shalaev, "Optimizing optical negative index materials: feedback from fabrication," in Proceedings of the 23rd International Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society, 2007), pp. 11-16.

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Smith, J. A.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Steward, W. J.

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

Tang, Y. U.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

Volakis, J. L.

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
[CrossRef]

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE, 1998).
[CrossRef]

Werner, D. H.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

M. A. Gingrich and D. H. Werner, "Synthesis of low/zero index of refraction metamaterials from frequency selective surfaces using genetic algorithms," Electron. Lett. 41, 1266-1267 (2005).
[CrossRef]

D. W. Boeringer and D. H. Werner, "Efficiency-constrained particle swarm optimization of a modified Bernstein polynomial for conformal array excitation amplitude synthesis," IEEE Trans. Antennas Propag. 53, 2662-2673 (2005).
[CrossRef]

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

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

D. W. Boeringer and D. H. Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propag. 52, 771-779 (2004).
[CrossRef]

L. Li and D. H. Werner, "Design of all-dielectric frequency selective surfaces using genetic algorithms combined with the finite element-boundary integral method," in Proceedings of the Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting, Vol. 4A, (IEEE, 2005), pp. 376-379.

Wilhelm, M.

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

Williams, N. R.

S. Chakravarty, R. Mittra, and N. R. Williams, "Application of a micro-genetic algorithm (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screens buried in dielectrics," IEEE Trans. Antennas Propag. 50, 284-296 (2002).
[CrossRef]

Wilton, D. R.

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
[CrossRef]

Yuan, H.-K.

Zhang, X.

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Electron. Lett. (1)

M. A. Gingrich and D. H. Werner, "Synthesis of low/zero index of refraction metamaterials from frequency selective surfaces using genetic algorithms," Electron. Lett. 41, 1266-1267 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Negative-index metamaterials: going optical," IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (7)

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag. 47, 843-850 (1999).
[CrossRef]

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. Drupp, and L. Li, "The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications," IEEE Trans. Antennas Propag. 54, 1265-1276 (2006).
[CrossRef]

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, "The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces," IEEE Trans. Antennas Propag. 53, 8-17 (2005).
[CrossRef]

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

D. W. Boeringer and D. H. Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propag. 52, 771-779 (2004).
[CrossRef]

D. W. Boeringer and D. H. Werner, "Efficiency-constrained particle swarm optimization of a modified Bernstein polynomial for conformal array excitation amplitude synthesis," IEEE Trans. Antennas Propag. 53, 2662-2673 (2005).
[CrossRef]

S. Chakravarty, R. Mittra, and N. R. Williams, "Application of a micro-genetic algorithm (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screens buried in dielectrics," IEEE Trans. Antennas Propag. 50, 284-296 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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

J. Appl. Comput. Electromagnetics Soc. (1)

A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," J. Appl. Comput. Electromagnetics Soc. 22, 172-183 (2007).

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (2)

W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based on metal-dielectric composites," Phys. Rev. B 72, 193101 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficient," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2002).
[CrossRef]

Other (7)

J. Kennedy and R. C. Eberhart, Swarm Intelligence (Academic, 2001).

D. T. Pham and D. Karaboga, Intelligent Optimization Techniques (Springer-Verlag, 2000).
[CrossRef]

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley-Interscience, 2004).

Y. Rahmat-Samii and E. Michelssen, eds., Electromagnetic Optimization by Genetic Algorithms (Wiley-Interscience, 1999).

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE, 1998).
[CrossRef]

L. Li and D. H. Werner, "Design of all-dielectric frequency selective surfaces using genetic algorithms combined with the finite element-boundary integral method," in Proceedings of the Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting, Vol. 4A, (IEEE, 2005), pp. 376-379.

A. V. Kildishev, U. K. Chettiar, H.-K. Yuan, W. Cai, and V. M. Shalaev, "Optimizing optical negative index materials: feedback from fabrication," in Proceedings of the 23rd International Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society, 2007), pp. 11-16.

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Figures (7)

Fig. 1
Fig. 1

Unit cell structure of the 2D periodic NIM grating geometry. The structure is illuminated by a monochromatic plane wave at normal incidence from air.

Fig. 2
Fig. 2

Brute-force test of the SA approach to a NFL optimization. The grayscale contour plot indicates the values of the objective function. The values of wavelength (numbered lines of a second contour plot) are shown superimposed on top of the plot.

Fig. 3
Fig. 3

Reflectance (R), transmittance (T), and absorbance (A) spectra of the GA-optimized NIM structure.

Fig. 4
Fig. 4

Real and imaginary parts of the effective index of refraction n of the optimized structure.

Fig. 5
Fig. 5

Real and imaginary parts of the recovered effective permittivity of the optimized structure.

Fig. 6
Fig. 6

Real and imaginary parts of the recovered effective permeability of the optimized structure.

Fig. 7
Fig. 7

Comparison of convergence properties of the SA, GA, and PSO optimization methods.

Equations (4)

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

V i , m n e x t = ( ω V i , m c u r r e n t ) + c 1 r a n d ( p i , m b e s t X i , m c u r r e n t ) + c 2 r a n d ( g m b e s t X i , m c u r r e n t ) ,
X i , m n e x t = X i , m c u r r e n t + ( Δ t × V i , m n e x t ) ,
o b j = 10 max λ ( n n ) ,
f i t n e s s = c o s t = max λ { n n } .

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