Abstract

We present a structure exhibiting a negative index of refraction at visible or near infrared frequencies using a single metal layer. This contrasts with recently developed structures based on metal-dielectric-metal composites. The proposed metamaterial consists of periodically arranged thick stripes interacting with each other to give rise to a negative permeability. Improved designs that allow for a negative index for both polarizations are also presented. The structures are numerically analyzed and it is shown that the dimensions can be engineered to shift the negative index band within a region ranging from telecommunication wavelengths down to blue light.

© 2007 Optical Society of America

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  1. RicardoA. Depine and Akhlesh Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
    [CrossRef]
  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 Technol. 47, 2075-2084 (1999).
    [CrossRef]
  3. R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  4. CostasM.  Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
    [CrossRef] [PubMed]
  5. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
    [CrossRef] [PubMed]
  6. Michael Scalora et al., "Negative refraction and sub-wavelength focusing in the visible range using transparent metallodielectric stacks," Opt. Express 15, 508-529 (2007).
    [CrossRef] [PubMed]
  7. G. Dolling, M. Wegener, C. M. Soukoulis, S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  8. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: Double-negative at 813 nm and single-negative at 772 nm," http://arxiv.org/ftp/physics/papers/0612/0612247.pdf.
  9. Zhiming Huang, Jianqiang Xue, Yun Hou, Junhao Chu, and D.H. Zhang, "Optical magnetic response from parallel plate metamaterials," Phys. Rev. B 74, 193105 (2006).
    [CrossRef]
  10. VladimirM. Shalaev, Wenshan Cai, Uday K. Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
    [CrossRef]
  11. P.B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  12. D. R. Smith, S. Schultz, P. Markos, and C.M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  13. Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco, Jr., and Jin Au Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
    [CrossRef]
  14. 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 (2003).
    [CrossRef]

2007

2006

Zhiming Huang, Jianqiang Xue, Yun Hou, Junhao Chu, and D.H. Zhang, "Optical magnetic response from parallel plate metamaterials," Phys. Rev. B 74, 193105 (2006).
[CrossRef]

2005

VladimirM. Shalaev, Wenshan Cai, Uday K. Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[CrossRef] [PubMed]

2004

RicardoA. Depine and Akhlesh Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco, Jr., and Jin Au Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

2003

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 (2003).
[CrossRef]

2002

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

2001

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

1999

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

1972

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

Soukoulis, M.

CostasM.  Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Christy, R. W.

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

Costas,

CostasM.  Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Dolling, G.

Economou, E. N.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[CrossRef] [PubMed]

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 Technol. 47, 2075-2084 (1999).
[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]

Kafesaki, M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[CrossRef] [PubMed]

Koschny, T.

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 (2003).
[CrossRef]

Koschny, Th.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[CrossRef] [PubMed]

Linden, Stefan

CostasM.  Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Linden, S.

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 (2003).
[CrossRef]

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

Pendry, J. B.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[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 Technol. 47, 2075-2084 (1999).
[CrossRef]

Ricardo,

RicardoA. Depine and Akhlesh Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

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 Technol. 47, 2075-2084 (1999).
[CrossRef]

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 coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

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 (2003).
[CrossRef]

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

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

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

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[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 (2003).
[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 coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

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 Technol. 47, 2075-2084 (1999).
[CrossRef]

Vladimir,

Wegener, M.

Wegener, Martin

CostasM.  Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Technol.

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

Microwave Opt. Technol. Lett.

RicardoA. Depine and Akhlesh Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

Zhiming Huang, Jianqiang Xue, Yun Hou, Junhao Chu, and D.H. Zhang, "Optical magnetic response from parallel plate metamaterials," Phys. Rev. B 74, 193105 (2006).
[CrossRef]

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. Markos, 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

Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco, Jr., and Jin Au Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[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 (2003).
[CrossRef]

Phys. Rev. Lett.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95,223902 (2005).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

CostasM.  Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Other

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: Double-negative at 813 nm and single-negative at 772 nm," http://arxiv.org/ftp/physics/papers/0612/0612247.pdf.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Basic metamaterial lattice. All other designs are derived from this one. (b) Double stripe metamaterial. (c) Square rings metamaterial (double stripes crossing in normal directions). (d) Cross-hair metamaterial (adding perpendicular stripes to structure in (a). (e) Unit cell of (c) and incident wave (same orientation for all structures).

Fig. 2.
Fig. 2.

Calculated currents and fields near the gap for design 1(a). Dimensions are the same as in Fig. 3. (a) Currents below magnetic resonance (450 THz). (b) Currents above magnetic resonance (510 THz) for the same phase of the incident wave. (c) Electric field (510 THz). (d) Magnetic field (510 THz). In all cases, the incident wave has the direction drawn in (c)

Fig. 3.
Fig. 3.

S parameters and real parts of the permittivity and permeability of structures in Fig. 1.

Fig. 4.
Fig. 4.

(a) Dependence of fres and fp on scaling. The base structure (S=1) has dimensions t=w=220 nm, s=60 nm and a total stripe length equal to 440 nm. (b) Dependence of fres and fp on s. Dimensions are t=w=110 nm and 220 nm stripe length.

Fig. 5.
Fig. 5.

Retrieved parameters for structure 1(a) with t=w=110 nm, s=60 nm and length 220 nm. Left: Factor of merit and real part of the refractive index. Right: Real parts of permittivity and permeability.

Fig. 6.
Fig. 6.

Proposed 3D metamaterial.

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