Abstract

Low-index metamaterial designs in the visible spectrum that are impedance matched to free space are presented. The unit cell of the periodic metamaterial design incorporates a magnetic resonator and silver meshes for respective control of the effective permeability and permittivity. A genetic algorithm is employed to optimize the metamaterial design to achieve a desired set of values for the index of refraction and the intrinsic impedance. Two example GA optimized designs are provided which target the important special cases of a zero and unity index of refraction.

© 2007 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metaldielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
    [CrossRef]
  5. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  6. R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).
    [CrossRef]
  7. B. T. Schwartz and R. Piestun, "Total external reflection from metamaterials with ultralow refractive index," J. Opt. Soc. Am. B 20, 2448-2453 (2003).
    [CrossRef]
  8. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef] [PubMed]
  9. 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).
  10. D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
    [CrossRef]
  11. R. L. Haupt and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, N J, 2007).
    [CrossRef]
  12. 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. 53, 284-296 (2002).
    [CrossRef]
  13. J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE Press, Piscataway, NJ, 1998).
    [CrossRef]
  14. D. R. Smith, S. Schultz, P. Markoˇs, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  15. 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]
  16. T. Koschny, P. Markoˇs, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
    [CrossRef]
  17. A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
    [CrossRef]
  18. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
    [CrossRef]
  19. E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
    [CrossRef]
  20. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth- Heinemann, Oxford, 1984).
  21. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  22. G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
    [CrossRef] [PubMed]

2007

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[CrossRef]

E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
[CrossRef] [PubMed]

2006

2005

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).

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]

2004

R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).
[CrossRef]

A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
[CrossRef]

2003

2002

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

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. 53, 284-296 (2002).
[CrossRef]

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

1972

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Bossard, J. A.

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[CrossRef]

Bray, M. G.

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[CrossRef]

Brueck, S. R. J.

Cai, W.

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. 53, 284-296 (2002).
[CrossRef]

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[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]

Dolling, G.

Drachev, V. P.

Efros, A. L.

A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
[CrossRef]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Fan, W.

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).

Gonzalo, R.

E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Ikonen, P. M. T.

E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[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]

Kildishev, A. V.

Koschny, T.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
[CrossRef]

Kwon, D.-H.

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[CrossRef]

Li, L.

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[CrossRef]

Linden, S.

Malloy, K. J.

Marko?s, P.

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

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
[CrossRef]

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. 53, 284-296 (2002).
[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]

Osgood, R. M.

Panoiu, N. C.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (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]

Piestun, R.

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Saenz, E.

E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Sarychev, A. K.

Schultz, S.

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

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (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]

Schwartz, B. T.

Shalaev, V. M.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (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]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
[CrossRef]

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

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
[CrossRef]

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

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Tretyakov, S. A.

E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Wegener, M.

Werner, D. H.

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[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).

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. 53, 284-296 (2002).
[CrossRef]

Yuan, H.-K.

Zhang, S.

Ziolkowski, R. W.

R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).
[CrossRef]

Electron. Lett.

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).

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 319-320 (2007).
[CrossRef]

IEEE Trans. Antennas Propag.

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. 53, 284-296 (2002).
[CrossRef]

J. Appl. Phys.

E. Saenz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. B

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

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

Phys. Rev. E

A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Reply to comments on "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,"Phys. Rev. E 70, 048603 (2004).
[CrossRef]

R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).
[CrossRef]

Phys. Rev. Lett.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (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]

Other

R. L. Haupt and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, N J, 2007).
[CrossRef]

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

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

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth- Heinemann, Oxford, 1984).

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Figures (3)

Fig. 1.
Fig. 1.

Unit cell geometry of a doubly-periodic metamaterial slab on a thick glass substrate: (a) A view from the +ŷ direction. (b) A perspective view.

Fig. 2.
Fig. 2.

Effective parameters of the LIM design optimized for a zero index of refraction and a free-space matched impedance: (a) n and z. (b) The reflectance (R), transmittance (T), and absorbance (A) spectra.

Fig. 3.
Fig. 3.

Effective parameters of the LIM design optimized for a unity index of refraction and a free-space matched impedance: (a) n and z. (b) The reflectance (R), transmittance (T), and absorbance (A) spectra.

Equations (3)

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

n = μ ε , z = μ ε ,
f = 1 n 2 + z 1 2 .
f = 1 n 1 2 + z 1 2 .

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