Abstract

We show that a metallic plate with periodic fractal-shaped slits can be homogenized as a plasmonic metamaterial with plasmon frequency dictated by the fractal geometry. Owing to the all-dimensional subwavelength nature of the fractal pattern, our system supports both transverse-electric and transverse-magnetic surface plasmons. As a result, this structure can be employed to focus light sources with all-dimensional subwavelength resolution and enhanced field strengths. Microwave experiments reveal that the best achievable resolution is onlyλ/15, and finite-difference-time-domain simulations demonstrate that similar effects can be realized at infrared frequencies with appropriate designs.

©2010 Optical Society of America

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References

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
    [Crossref]
  2. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very Narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
    [Crossref]
  3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
    [Crossref] [PubMed]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  5. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
    [Crossref] [PubMed]
  6. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
    [Crossref]
  7. J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
    [Crossref]
  8. W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
    [Crossref]
  9. X. Yang, Y. Liu, J. Ma, J. Cui, H. Xing, W. Wang, C. Wang, and X. Luo, “Broadband super-resolution imaging by a superlens with unmatched dielectric medium,” Opt. Express 16(24), 19686–19694 (2008).
    [Crossref] [PubMed]
  10. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [Crossref] [PubMed]
  11. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
    [Crossref] [PubMed]
  12. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
    [Crossref]
  13. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
    [Crossref] [PubMed]
  14. J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
    [Crossref]
  15. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
    [Crossref] [PubMed]
  16. C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
    [Crossref]
  17. K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
    [Crossref]
  18. D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antenn. Propag. Mag. 45(1), 38–57 (2003).
    [Crossref]
  19. W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
    [Crossref]
  20. W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
    [Crossref]
  21. F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
    [Crossref]
  22. A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
    [Crossref]
  23. P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73(3), 033108 (2006).
    [Crossref]
  24. X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
    [Crossref]
  25. S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96(3), 1293–1300 (2004).
    [Crossref]
  26. P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
    [Crossref]
  27. C. Mateo-Segura, C. R. Simovski, G. Goussetis, and S. Tretyakov, “Subwavelength resolution for horizontal and vertical polarization by coupled arrays of oblate nanoellipsoids,” Opt. Lett. 34(15), 2333–2335 (2009).
    [Crossref] [PubMed]
  28. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
    [Crossref]
  29. Free FDTD package MIT Electromagnetic Equation Propagation (MEEP). To calculate the SPP band structures, we put an x-polarized point source as an excitation in a plane just above the structure, at a position deviating slightly from the center. One unit cell was used as the computation domain with periodic boundary conditions imposed, and the mesh size was taken as 0.02*0.02*0.02μm. Convergences of the calculations were carefully examined
  30. In the frequency domain of interest in this work (e.g., from microwave to infra-red), the SPP characteristics of the designed system are mainly determined by the geometry of the structure, rather than the dielectric properties of the constitutional material that we used. However, at higher frequencies (e.g. visible), material loss and dispersions play more important roles.
  31. H. Raether, Surface Plasmons (ed. G. Hohler) (Springer, Berlin, 1988).
  32. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref] [PubMed]
  33. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
    [Crossref] [PubMed]
  34. A drawback of our lens is that it only works for sources with definite in-plane electric polarization. This problem can be remedied by replacing the fractal shape by some isotropic patterns.
  35. In our experiments, we only measured the one-dimensional field distributions along the line perpendicular to the antenna on the image planes.
  36. CONCERTO 7.0, Vector Fields Limited, England, (2008). The basic mesh size was taken as 0.5*0.5*1mm for microwave calculations, and 0.02*0.02*0.02μm for infrared calculations, and finer meshes were adopted in the regions wherever necessary. Convergences of the calculations were carefully examined.
  37. Here, the experimentally measured field enhancement is not obvious (about 2 times comparing with the air case). This is because the source dipole antenna adopted in experiment is too long so that the efficiency of coupling with SPP is relatively low. In addition, since the receiver antenna is also too long, the received signal actually represents an averaged field over the area covered by the antenna, and therefore, the strong local field enhancement is smeared.
  38. FDTD simulations revealed that similar behaviors exist when we shift the source along y direction inside a unit cell, and the formed image consists of two peaks when the source is right at the y-direction boundary of two adjacent unit cells.
  39. L. Zhou and C. T. Chan, “Relaxation mechanisms in three-dimensional metamaterial lens focusing,” Opt. Lett. 30(14), 1812–1814 (2005).
    [Crossref] [PubMed]
  40. The transmittance cannot reach 1 due to the material losses.

2009 (2)

2008 (2)

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

X. Yang, Y. Liu, J. Ma, J. Cui, H. Xing, W. Wang, C. Wang, and X. Luo, “Broadband super-resolution imaging by a superlens with unmatched dielectric medium,” Opt. Express 16(24), 19686–19694 (2008).
[Crossref] [PubMed]

2007 (3)

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
[Crossref]

2006 (3)

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73(3), 033108 (2006).
[Crossref]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[Crossref]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

2005 (6)

W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

L. Zhou and C. T. Chan, “Relaxation mechanisms in three-dimensional metamaterial lens focusing,” Opt. Lett. 30(14), 1812–1814 (2005).
[Crossref] [PubMed]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[Crossref]

2004 (3)

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96(3), 1293–1300 (2004).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

2003 (4)

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antenn. Propag. Mag. 45(1), 38–57 (2003).
[Crossref]

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

2001 (2)

K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

2000 (2)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very Narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
[Crossref]

Alitalo, P.

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[Crossref]

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96(3), 1293–1300 (2004).
[Crossref]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Belov, P. A.

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73(3), 033108 (2006).
[Crossref]

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

Cai, W.

W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[Crossref]

Cardama, A.

C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
[Crossref]

Chan, C. T.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

L. Zhou and C. T. Chan, “Relaxation mechanisms in three-dimensional metamaterial lens focusing,” Opt. Lett. 30(14), 1812–1814 (2005).
[Crossref] [PubMed]

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Chen, Y.

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Cui, J.

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Ganguly, S.

D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antenn. Propag. Mag. 45(1), 38–57 (2003).
[Crossref]

Garcia-Vidal, F. J.

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very Narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Ge, W.

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Genov, D. A.

W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[Crossref]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Gomez Rivas, J.

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
[Crossref]

Goussetis, G.

Hao, Y.

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73(3), 033108 (2006).
[Crossref]

Haring Bolivar, P.

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
[Crossref]

He, S.

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
[Crossref]

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

Hou, B.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

Jang, K. H.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

Jin, Y.

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
[Crossref]

Jose, K. A.

K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
[Crossref]

Jung, J.

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

Kato, J.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[Crossref]

Kawata, S.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[Crossref]

Kurz, H.

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
[Crossref]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Li, X.

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
[Crossref]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Liu, L.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Liu, Y.

Luo, X.

Ma, J.

Martin-Moreno, L.

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Maslovski, S.

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96(3), 1293–1300 (2004).
[Crossref]

Mateo-Segura, C.

Miyamaru, F.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Ono, A.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[Crossref]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Park, G. S.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

Pendry, J. B.

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very Narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very Narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Pous, R.

C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
[Crossref]

Puente-Baliarda, C.

C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
[Crossref]

Romeu, J.

C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
[Crossref]

Saito, Y.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Schotsch, C.

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Shalaev, V. M.

W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[Crossref]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Sheng, P.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Shin, Y. M.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Simovski, C.

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[Crossref]

Simovski, C. R.

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

So, J. K.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

Soukoulis, C. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

Srivastava, A.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

Sudhakaran, S.

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73(3), 033108 (2006).
[Crossref]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Takeda, M. W.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Tretyakov, S.

C. Mateo-Segura, C. R. Simovski, G. Goussetis, and S. Tretyakov, “Subwavelength resolution for horizontal and vertical polarization by coupled arrays of oblate nanoellipsoids,” Opt. Lett. 34(15), 2333–2335 (2009).
[Crossref] [PubMed]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[Crossref]

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96(3), 1293–1300 (2004).
[Crossref]

Varadan, V. K.

K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
[Crossref]

Varadan, V. V.

K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
[Crossref]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Viitanen, A.

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[Crossref]

Vinoy, K. J.

K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
[Crossref]

Wang, C.

Wang, W.

Wen, W.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Werner, D. H.

D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antenn. Propag. Mag. 45(1), 38–57 (2003).
[Crossref]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Won, J. H.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

Xing, H.

Xu, G.

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Yang, X.

Yang, Z.

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Zhou, L.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

L. Zhou and C. T. Chan, “Relaxation mechanisms in three-dimensional metamaterial lens focusing,” Opt. Lett. 30(14), 1812–1814 (2005).
[Crossref] [PubMed]

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

Appl. Phys. Lett. (1)

W. Wen, Z. Yang, G. Xu, Y. Chen, L. Zhou, W. Ge, C. T. Chan, and P. Sheng, “Infrared passbands from fractal slit patterns on a metal plate,” Appl. Phys. Lett. 83(11), 2106–2108 (2003).
[Crossref]

IEEE Antenn. Propag. Mag. (1)

D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antenn. Propag. Mag. 45(1), 38–57 (2003).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antenn. Propag. 46(4), 517–524 (1998).
[Crossref]

J. Appl. Phys. (1)

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96(3), 1293–1300 (2004).
[Crossref]

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

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

Microw. Opt. Technol. Lett. (1)

K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,” Microw. Opt. Technol. Lett. 29(4), 215–219 (2001).
[Crossref]

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (9)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[Crossref]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[Crossref]

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73(3), 033108 (2006).
[Crossref]

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
[Crossref]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[Crossref]

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68(20), 201306 (2003).
[Crossref]

W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

Phys. Rev. Lett. (4)

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[Crossref] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very Narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Science (6)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Other (9)

A drawback of our lens is that it only works for sources with definite in-plane electric polarization. This problem can be remedied by replacing the fractal shape by some isotropic patterns.

In our experiments, we only measured the one-dimensional field distributions along the line perpendicular to the antenna on the image planes.

CONCERTO 7.0, Vector Fields Limited, England, (2008). The basic mesh size was taken as 0.5*0.5*1mm for microwave calculations, and 0.02*0.02*0.02μm for infrared calculations, and finer meshes were adopted in the regions wherever necessary. Convergences of the calculations were carefully examined.

Here, the experimentally measured field enhancement is not obvious (about 2 times comparing with the air case). This is because the source dipole antenna adopted in experiment is too long so that the efficiency of coupling with SPP is relatively low. In addition, since the receiver antenna is also too long, the received signal actually represents an averaged field over the area covered by the antenna, and therefore, the strong local field enhancement is smeared.

FDTD simulations revealed that similar behaviors exist when we shift the source along y direction inside a unit cell, and the formed image consists of two peaks when the source is right at the y-direction boundary of two adjacent unit cells.

Free FDTD package MIT Electromagnetic Equation Propagation (MEEP). To calculate the SPP band structures, we put an x-polarized point source as an excitation in a plane just above the structure, at a position deviating slightly from the center. One unit cell was used as the computation domain with periodic boundary conditions imposed, and the mesh size was taken as 0.02*0.02*0.02μm. Convergences of the calculations were carefully examined

In the frequency domain of interest in this work (e.g., from microwave to infra-red), the SPP characteristics of the designed system are mainly determined by the geometry of the structure, rather than the dielectric properties of the constitutional material that we used. However, at higher frequencies (e.g. visible), material loss and dispersions play more important roles.

H. Raether, Surface Plasmons (ed. G. Hohler) (Springer, Berlin, 1988).

The transmittance cannot reach 1 due to the material losses.

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Figures (8)

Fig. 1
Fig. 1 Geometry of the fractal plasmonic metamaterial (MTM). Unit cell strcuture: l1=l2=0.5μm, l3=l4=0.25μm, w=0.06μm, H=0.5μm.
Fig. 2
Fig. 2 SPP band structures of the fractal plate calculated by FDTD simulations for (a) ΓX and (b) ΓX' directions; Under the conditions of (c) kx=π/a and (d) ky=π/a, FDTD calculated transmission spectra under incident plane evanescent waves with different polarizations. Insets: SPP band structures of rectangle hole plate calculated by FDTD simulations, with structural details d=1μm,s=4.2d,a=0.3d,L=0.5d (see Ref. [15]).
Fig. 3
Fig. 3 FDTD calculated plasmon wavelength λp as functions of the slit width w when the fractal is 3-level (solid squares) and 4-level (open circles). Inset shows the calculated λp as a function of the periodicity a of the fractal array.
Fig. 4
Fig. 4 (a). Picture of a 63mm-thick fractal plasmonic metamaterial and its unit cell structure (all lengths are measured in mm). Here the periodicity is 18mm (32mm) in x (y) direction. (b)-(c) Electric field distributions along the line perpendicular to the antenna on the image plane obtained by experiments (open circles) and FDTD simulations (solid lines) for different lens thickness, referenced by the experimental results measured without any lens (solid squares). Here, the maximum electric field is normalized to 1 in the presence of a lens.
Fig. 5
Fig. 5 Field distributions along the line perpendicular to the antenna on the image plane formed by the 63mm-thick lens when the source is placed at (a) Δx=1mm , (b) Δx=7mm , and (c) Δx=9mm , obtained by measurements (open circles) and FDTD simulations (lines). Here the E field is normalized such that its maximum value is 1. The FDTD calculated two-dimensional patterns of the images for (d) Δx=1mm , (e) Δx=7mm , (f) Δx=9mm .
Fig. 6
Fig. 6 FDTD calculated E-field patterns on the image planes obtained without a lens (a) + (d), with a rectangle-hole structure lens (b) + (e), and with our fractal structure lens (c) + (f). Here, the two x-polarized dipole sources are separated by 1μm in x direction for (a), (b), and (c), and in y direction for (d), (e) and (f). Both the rectangle-hole structure and fractal structure are the same as those in Fig. 2.
Fig. 7
Fig. 7 FDTD calculated phase change of the transmitted wave through our fractal lens (blue stars) and an air layer of the same thickness (red circles) as functions of the incident angle for TM- (a) and TE-polarized (b) incident waves. Here, the working frequency is 41THz.
Fig. 8
Fig. 8 Electric field distributions along the line perpendicular to the fractal structure for a TM-polarized incident evanescent wave with kx=π/(2a) (a) and a TE-polarized one with ky=π/a (b). Blue diamonds represent FDTD simulations while red lines reprent appropriate fitting functions ( eαz in air and straight lines in slab). Here, the working frequency is 41THz.

Equations (1)

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Ex(x,y)=iμ0P08π2eik||(xcosϕ+ysinϕ)eikzdkz[TTE(k||)sin2ϕ+kz2k02TTM(k||)cos2ϕ] kdkdϕ

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