Abstract

We report on perfect transmission in two-dimensional plasmonic matamaterials in the terahertz frequency range, in which zeroth order transmittance becomes essentially unity near specific resonance frequencies. Perfect transmission may occur when the plasmonic metamaterials are perfectly impedance matched to vacuum, which is equivalent to designing an effective dielectric constant around εr=-2 . When the effective dielectric constant of the metamaterial is tuned towards εr and the hole coverage is larger than 0.2, strong evanescent field builds up in the near field, making perfect transmission possible.

© 2005 Optical Society of America

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  1. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), p. 356.
  2. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396 (1902).
  3. R. W. Wood, "Anomalous diffraction gratings," Phys. Rev. 48, 928 (1935).
    [CrossRef]
  4. Lord Rayleigh, "On the passage of electric waves through tubes, or the vibrations of dielectric cylinders," Phil. Mag. 14, 60 (1907).
  5. Lord Rayleigh, "On the dynamical theory of gratings," Proc. R. Soc. A 79, 399 (1907).
    [CrossRef]
  6. R. Ulrich, "Interference filters for the far infrared," Appl. Opt. 7, 1987 (1968).
    [CrossRef] [PubMed]
  7. R. Ulrich, "Preparation of grids for far infrared filters," Appl. Opt. 8, 319 (1969).
    [CrossRef] [PubMed]
  8. C. C. Chen, "Transmission through a conducting screen perforated periodically with apertures." IEEE trans. Microwave Theory Tech. 18, 627 (1970).
    [CrossRef]
  9. P. J. Bliek, L. C. Botten, R. Deleuil, R. C. MC Phedran, and D. Maystre, "Inductive grids in the region of diffraction anomalies: theory, experiment, and applications," IEEE trans. Microwave Theory Tech. 28, 1119 (1980).
    [CrossRef]
  10. T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667- 669 (1998).
    [CrossRef]
  11. H. Cao and A. Nahata, "Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures," Opt. Express 12, 3664-3672 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3664">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3664</a>
    [CrossRef] [PubMed]
  12. D. Qu, D. Grischkowsky, and W. Zhang, "Terahertz transmission properties of thin, subwavelength metallic hole arrays," Opt. Lett. 29, 896 (2004).
    [CrossRef] [PubMed]
  13. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  14. S. Astilean, Ph. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265 (2000).
    [CrossRef]
  15. M.M.J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  16. F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
    [CrossRef]
  17. J. T. Shen, Peter B. Catrysse, and Shanhui Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197401 (2005).
    [CrossRef] [PubMed]
  18. F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, "Tunneling mechanism of light transmission through metallic films," Phys. Rev. Lett. 95, 067403 (2005).
    [CrossRef]
  19. L. M. Moreno and F. J. García-Vidal, "Optical transmission through circular hole arrays in optically thick metal films," Opt. Express 12, 3619-3628 (2004),
    [CrossRef] [PubMed]
  20. F. J. Garcia de Abajo, R. Gomez-Medina, and J. J. Saenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016608 (2005).
    [CrossRef]
  21. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114 (2001).
    [CrossRef] [PubMed]
  22. M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, E. Sano, "Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays," Opt. Lett. 30, 1210 (2005).
    [CrossRef] [PubMed]
  23. V. Schmidt, W. Husinsky, and G. Betz, "Dynamics of laser desorption and ablation of metals at the threshold on the femtosecond time scale," Phys. Rev. Lett. 85, 3516 (2000).
    [CrossRef] [PubMed]
  24. G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulation GaAs emitter," Rev. Sci. Instrum. 73, 1715 (2002).
    [CrossRef]
  25. G. Zhao, R. N. Schouten, N van der Valk, W. Th. Wenckebach and P. C. M. Planken, "A terahertz system using semi-large emitters: noise and performance characteristics," Phys. Med. Biol. 47, 3699 (2002).
    [CrossRef] [PubMed]
  26. J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, "Tunable terahertz generation using femtosecond pulse shaping," Appl. Phys. Lett. 81, 13 (2002).
    [CrossRef]
  27. E. D. Palik (Ed.), "Handbook of Optical Constants of Solids" (Academic Press, San Diego, 1985).
  28. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
    [CrossRef] [PubMed]
  29. 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, S97 (2005).
    [CrossRef]
  30. K. G. Lee, and Q-Han Park, "Coupling of surface plasmon polaritions and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902 (2005).
    [CrossRef] [PubMed]
  31. H. Lochbihler and R. Depine, "Highly conducting wire gratings in the resonance region," Appl. Opt. 32, 3459 (1993).
    [CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, "Tunable terahertz generation using femtosecond pulse shaping," Appl. Phys. Lett. 81, 13 (2002).
[CrossRef]

IEEE trans. Microwave Theory Tech.

C. C. Chen, "Transmission through a conducting screen perforated periodically with apertures." IEEE trans. Microwave Theory Tech. 18, 627 (1970).
[CrossRef]

P. J. Bliek, L. C. Botten, R. Deleuil, R. C. MC Phedran, and D. Maystre, "Inductive grids in the region of diffraction anomalies: theory, experiment, and applications," IEEE trans. Microwave Theory Tech. 28, 1119 (1980).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

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, S97 (2005).
[CrossRef]

Nature (London)

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667- 669 (1998).
[CrossRef]

Opt. Commun.

S. Astilean, Ph. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phil. Mag.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396 (1902).

Lord Rayleigh, "On the passage of electric waves through tubes, or the vibrations of dielectric cylinders," Phil. Mag. 14, 60 (1907).

Phys. Med. Biol.

G. Zhao, R. N. Schouten, N van der Valk, W. Th. Wenckebach and P. C. M. Planken, "A terahertz system using semi-large emitters: noise and performance characteristics," Phys. Med. Biol. 47, 3699 (2002).
[CrossRef] [PubMed]

Phys. Rev.

R. W. Wood, "Anomalous diffraction gratings," Phys. Rev. 48, 928 (1935).
[CrossRef]

Phys. Rev. B

M.M.J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Phys. Rev. E

F. J. Garcia de Abajo, R. Gomez-Medina, and J. J. Saenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016608 (2005).
[CrossRef]

Phys. Rev. Lett.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

K. G. Lee, and Q-Han Park, "Coupling of surface plasmon polaritions and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902 (2005).
[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, 2845-2848 (1999).
[CrossRef]

J. T. Shen, Peter B. Catrysse, and Shanhui Fan, "Mechanism for designing metallic metamaterials with a high index of refraction," Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, "Tunneling mechanism of light transmission through metallic films," Phys. Rev. Lett. 95, 067403 (2005).
[CrossRef]

V. Schmidt, W. Husinsky, and G. Betz, "Dynamics of laser desorption and ablation of metals at the threshold on the femtosecond time scale," Phys. Rev. Lett. 85, 3516 (2000).
[CrossRef] [PubMed]

Proc. R. Soc. A

Lord Rayleigh, "On the dynamical theory of gratings," Proc. R. Soc. A 79, 399 (1907).
[CrossRef]

Rev. Sci. Instrum.

G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulation GaAs emitter," Rev. Sci. Instrum. 73, 1715 (2002).
[CrossRef]

Science

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

Other

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), p. 356.

E. D. Palik (Ed.), "Handbook of Optical Constants of Solids" (Academic Press, San Diego, 1985).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic view of plasmonic meta-materials with periodic arrays of square holes and a SEM image. (b) An effective medium converted by an effective surface impedance in the structure displayed in (a). (c) At a specific frequency, the effective surface impedance becomes equal to the vacuum impedance and this medium has a perfect transmission.

Fig. 2.
Fig. 2.

(a) Schematics of the Femtosecond machining system used for manufacturing our samples. (b) Schematics of our terahertz transmission experiments. (c) Time trace of the incident terahertz beam (black line) and the transmitted beam (red line) for a typical sample. (d) Fourier transform of (c).

Fig. 3.
Fig. 3.

(a) Transmission spectra of the transmitted field amplitude for four samples with different sample coverages of 0.1, 0.17, 0.2 and 0.25, respectively, from top to bottom. At the bottom the sample with the coverage 0.25 is shown. (b) and (c) THz time traces for samples with sample coverage of 0.1 and 0.25 respectively. The source signals (top) are quasi-monochromatic THz waves at 0.66 THz tailored by the pulse shaping.

Fig. 4.
Fig. 4.

(a). The effective dielectric constant plotted versus the frequency for coverages of 0.25 (red line), 0.2 (green line), 0.17 (orange line), and 0.1 (blue line). (b) Peak transmission frequency ft at which the transmittance becomes unity, plotted against the sample coverage (from Eq. 5). Only for a coverage larger than 0.19 is ft smaller than Rayleigh minimum as indicated by the gray line. (c) Transmittance for the hole sample with coverage 0.3, along with the sample image (inset). (d) Peak field amplitude plotted against the coverage for the square hole (filled squares) and the circular hole (filled circles) samples. The gray line represents Eq. (3), truncated at the amplitude of unity, calculated for f=0.66 THz.

Equations (5)

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ε eff = π 2 8 1 β ( 1 f c 2 f 2 )
Z = Z 0 1 1 + ε m
Z eff = Z 0 1 1 + ε eff
Z eff = Z 0 for ε eff = 2
f t = f c 1 + 16 β π 2

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