Abstract

A three-dimensional, isotropic metamaterial with double-negative behavior is proposed. The material comprises metallic spheres coated in a high-permittivity shell and dispersed in a host medium. In stark contrast to other Mie resonance-based metamaterial designs, ours relies on the metallic phase behaving as a near-perfect electric conductor, rather than a plasmonic. As such, by tuning the particle dimensions, double-negative behavior can be achieved at any frequency where one can find high-conductivity and high-permittivity materials.

© 2014 Optical Society of America

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  1. Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
    [CrossRef]
  2. O. Sigmund and S. Torquato, J. Mech. Phys. Solids 45, 1037 (1997).
    [CrossRef]
  3. D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
    [CrossRef]
  4. Y. Lai, H. Chen, Z.-Q. Zhang, and C. Chan, Phys. Rev. Lett. 102, 093901 (2009).
    [CrossRef]
  5. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
    [CrossRef]
  6. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  7. S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 34, 3478 (2009).
    [CrossRef]
  8. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 32, 1671 (2007).
    [CrossRef]
  9. D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef]
  10. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 32, 53 (2007).
    [CrossRef]
  11. S. Zhou, S. Townsend, Y. M. Xie, X. Huang, J. Shen, and Q. Li, Opt. Lett. 39, 2415 (2014).
    [CrossRef]
  12. I. Vendik, O. Vendik, and M. Odit, Microw. Opt. Technol. Lett. 48, 2553 (2006).
    [CrossRef]
  13. V. Yannopapas, Phys. Rev. B 75, 035112 (2007).
    [CrossRef]
  14. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
    [CrossRef]
  15. R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
    [CrossRef]
  16. D. Wu, S. Jiang, Y. Cheng, and X. Liu, Opt. Express 21, 1076 (2013).
    [CrossRef]
  17. J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, Science 305, 847 (2004).
    [CrossRef]
  18. R. Ruppin, Opt. Commun. 182, 273 (2000).
    [CrossRef]
  19. W. Yang, Appl. Opt. 42, 1710 (2003).
    [CrossRef]
  20. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).
  21. G. Gaunaurd, H. Überall, and P. J. Moser, J. Appl. Phys. 52, 35 (1981).
    [CrossRef]
  22. P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
    [CrossRef]
  23. M. Schall, H. Helm, and S. Keiding, Int. J. Infrared Millim. Waves 20, 595 (1999).
    [CrossRef]
  24. F. Grant, Rev. Mod. Phys. 31, 646 (1959).
    [CrossRef]
  25. E. V. Loewenstein, D. R. Smith, and R. L. Morgan, Appl. Opt. 12, 398 (1973).
    [CrossRef]
  26. I. Trelea, Inform. Process. Lett. 85, 317 (2003).
    [CrossRef]

2014 (1)

2013 (1)

2011 (1)

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
[CrossRef]

2009 (2)

2007 (5)

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 32, 1671 (2007).
[CrossRef]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 32, 53 (2007).
[CrossRef]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
[CrossRef]

V. Yannopapas, Phys. Rev. B 75, 035112 (2007).
[CrossRef]

2006 (2)

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

I. Vendik, O. Vendik, and M. Odit, Microw. Opt. Technol. Lett. 48, 2553 (2006).
[CrossRef]

2004 (1)

J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

2003 (2)

W. Yang, Appl. Opt. 42, 1710 (2003).
[CrossRef]

I. Trelea, Inform. Process. Lett. 85, 317 (2003).
[CrossRef]

2000 (4)

R. Ruppin, Opt. Commun. 182, 273 (2000).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

1999 (1)

M. Schall, H. Helm, and S. Keiding, Int. J. Infrared Millim. Waves 20, 595 (1999).
[CrossRef]

1997 (1)

O. Sigmund and S. Torquato, J. Mech. Phys. Solids 45, 1037 (1997).
[CrossRef]

1981 (2)

G. Gaunaurd, H. Überall, and P. J. Moser, J. Appl. Phys. 52, 35 (1981).
[CrossRef]

P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
[CrossRef]

1973 (1)

1959 (1)

F. Grant, Rev. Mod. Phys. 31, 646 (1959).
[CrossRef]

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Cai, W.

Chan, C.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. Chan, Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Chen, H.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. Chan, Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Cheng, Y.

Chettiar, U. K.

Ding, Y.

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
[CrossRef]

Dolling, G.

Drachev, V. P.

Garcia-Vidal, F.

J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Gaunaurd, G.

G. Gaunaurd, H. Überall, and P. J. Moser, J. Appl. Phys. 52, 35 (1981).
[CrossRef]

Grant, F.

F. Grant, Rev. Mod. Phys. 31, 646 (1959).
[CrossRef]

Helm, H.

M. Schall, H. Helm, and S. Keiding, Int. J. Infrared Millim. Waves 20, 595 (1999).
[CrossRef]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Huang, X.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Jiang, S.

Keiding, S.

M. Schall, H. Helm, and S. Keiding, Int. J. Infrared Millim. Waves 20, 595 (1999).
[CrossRef]

Kildishev, A. V.

Kroll, N.

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

Lai, Y.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. Chan, Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Li, Q.

Linden, S.

Liu, X.

Liu, Z.

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
[CrossRef]

Loewenstein, E. V.

López-Tejeira, F.

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
[CrossRef]

Marqués, R.

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
[CrossRef]

Martin-Moreno, L.

J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Mojahedi, M.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Morgan, R. L.

Moser, P.

P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
[CrossRef]

Moser, P. J.

G. Gaunaurd, H. Überall, and P. J. Moser, J. Appl. Phys. 52, 35 (1981).
[CrossRef]

Murphy, J.

P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
[CrossRef]

Nagl, A.

P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
[CrossRef]

Nemat-Nasser, S.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Odit, M.

I. Vendik, O. Vendik, and M. Odit, Microw. Opt. Technol. Lett. 48, 2553 (2006).
[CrossRef]

Padilla, W.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Paniagua-Domínguez, R.

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
[CrossRef]

Pendry, J.

J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Qiu, C.

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
[CrossRef]

Ruppin, R.

R. Ruppin, Opt. Commun. 182, 273 (2000).
[CrossRef]

Sánchez-Gil, J. A.

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
[CrossRef]

Schall, M.

M. Schall, H. Helm, and S. Keiding, Int. J. Infrared Millim. Waves 20, 595 (1999).
[CrossRef]

Schultz, S.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Shalaev, V. M.

Shen, J.

Shi, J.

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
[CrossRef]

Sigmund, O.

O. Sigmund and S. Torquato, J. Mech. Phys. Solids 45, 1037 (1997).
[CrossRef]

Smith, D.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Smith, D. R.

Soukoulis, C. M.

Torquato, S.

O. Sigmund and S. Torquato, J. Mech. Phys. Solids 45, 1037 (1997).
[CrossRef]

Townsend, S.

Trelea, I.

I. Trelea, Inform. Process. Lett. 85, 317 (2003).
[CrossRef]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Überall, H.

P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
[CrossRef]

G. Gaunaurd, H. Überall, and P. J. Moser, J. Appl. Phys. 52, 35 (1981).
[CrossRef]

Vendik, I.

I. Vendik, O. Vendik, and M. Odit, Microw. Opt. Technol. Lett. 48, 2553 (2006).
[CrossRef]

Vendik, O.

I. Vendik, O. Vendik, and M. Odit, Microw. Opt. Technol. Lett. 48, 2553 (2006).
[CrossRef]

Vier, D.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Wegener, M.

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Wu, D.

Xiao, S.

Xie, Y. M.

Yang, W.

Yannopapas, V.

V. Yannopapas, Phys. Rev. B 75, 035112 (2007).
[CrossRef]

Yuan, H.-K.

Zhang, Z.-Q.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. Chan, Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Zhou, S.

Appl. Opt. (2)

Inform. Process. Lett. (1)

I. Trelea, Inform. Process. Lett. 85, 317 (2003).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

M. Schall, H. Helm, and S. Keiding, Int. J. Infrared Millim. Waves 20, 595 (1999).
[CrossRef]

J. Appl. Phys. (1)

G. Gaunaurd, H. Überall, and P. J. Moser, J. Appl. Phys. 52, 35 (1981).
[CrossRef]

J. Mech. Phys. Solids (1)

O. Sigmund and S. Torquato, J. Mech. Phys. Solids 45, 1037 (1997).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

I. Vendik, O. Vendik, and M. Odit, Microw. Opt. Technol. Lett. 48, 2553 (2006).
[CrossRef]

Nature (1)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

New J. Phys. (1)

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, New J. Phys. 13, 123017 (2011).
[CrossRef]

Opt. Commun. (1)

R. Ruppin, Opt. Commun. 182, 273 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. B (2)

V. Yannopapas, Phys. Rev. B 75, 035112 (2007).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007).
[CrossRef]

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. Chan, Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Radio Sci. (1)

P. Moser, J. Murphy, A. Nagl, and H. Überall, Radio Sci. 16, 279 (1981).
[CrossRef]

Rev. Mod. Phys. (1)

F. Grant, Rev. Mod. Phys. 31, 646 (1959).
[CrossRef]

Science (1)

J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Other (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

High-conductivity spheres are coated in a high-permittivity shell (left). The spheres are dispersed in a host medium to create a slab of metamaterial (right) which has double-negative behavior.

Fig. 2.
Fig. 2.

For a conducting sphere coated in a dielectric shell, the size parameter of the shell xres at which the electric (a1) and magnetic (b1) dipole modes become resonant is highly dependent on the ratio of the radii.

Fig. 3.
Fig. 3.

(a)–(b) Homogeneous spheres with sufficiently high permittivity have separate electric and magnetic dipole resonance frequencies. (c)–(d) The addition of a conducting core can draw the dipole resonances together, producing double-negative behavior. Note that the conducting core does not have a resonance of its own. The above was calculated with ϵshell=43+0.3i, rcore/rshell=0.43, f=0.5.

Fig. 4.
Fig. 4.

1 THz plane wave E⃗=z^Eeik0x is incident on the core-shell particle from Fig. 3. By visualizing the local electric field strength and direction, the (a) TE (electric) and (b) TM (magnetic) dipole resonance modes are revealed.

Fig. 5.
Fig. 5.

Results of the FOM design optimization at 1 THz and f=0.5. Radii dimensions are micrometers.

Equations (6)

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

ϵ=ϵ+iϵ=ϵhx3+3ifa1x33ifa1/2,
μ=μ+iμ=x3+3ifb1x33ifb1/2,
a1=[H1a/n2+1/x2]ψ1(x2)ψ0(x2)[H1a/n2+1/x2]ζ1(x2)ζ0(x2);H1a=ψ1(n2y)ζ1(n2x)ζ1(n2y)ψ1(n2x)ψ1(n2y)ζ1(n2x)ζ1(n2y)ψ1(n2x),
b1=[n2H1b+1/x2]ψ1(x2)ψ0(x2)[n2H1b+1/x2]ζ1(x2)ζ0(x2);H1b=ψ1(n2y)ζ1(n2x)ζ1(n2y)ψ1(n2x)ψ1(n2y)ζ1(n2x)ζ1(n2y)ψ1(n2x),
a1=2ix33(n121n12+2)+O(x5).
maxrshell,rcoreFOM=nn.

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