Abstract

We demonstrate resonantly enhanced transmission of freely propagating coherent terahertz radiation through free-standing metal foils perforated with periodic arrays of sub-wavelength apertures. These arrays consist of 400 µm diameter apertures periodically spaced by 1 mm and 600 µm diameter apertures periodically spaced by 1.5 mm. We measure absolute amplitude transmission coefficients of ~0.6 at the resonance wavelength. Correspondingly, the ratio of the absolute amplitude transmission coefficient to the fractional aperture area at these resonance frequencies is ~5. This value at terahertz frequencies is significantly larger than equivalent values measured at optical frequencies.

© 2004 Optical Society of America

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  1. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, �??Extraordinary optical transmission through subwavelength hole arrays,�?? Nature 391, 667-669 (1998).
    [CrossRef]
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  3. D.E. Grupp, H.J. Lezec, T. Thio, T.W. Ebbesen, �??Beyond the Bethe limit: tunable enhanced light transmission through a single sub-wavelength aperture,�?? Adv. Mater. 11, 860-862 (1999).
    [CrossRef]
  4. 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]
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    [CrossRef]
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    [CrossRef]
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Adv. Mater.

D.E. Grupp, H.J. Lezec, T. Thio, T.W. Ebbesen, �??Beyond the Bethe limit: tunable enhanced light transmission through a single sub-wavelength aperture,�?? Adv. Mater. 11, 860-862 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. B

A. Dogariu, A. Nahata, R.A. Linke, L.J. Wang, and R. Trebino, �??Optical pulse propagation through metallic nano-apertures,�?? Appl. Phys. B 74, s69-s73 (2002).
[CrossRef]

Appl. Phys. Lett.

D.E. Grupp, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, and T.Thio, �??Crucial role of metal surface in enhanced transmission through subwavelength apertures,�?? Appl. Phys. Lett. 77, 1569-1571 (2000).
[CrossRef]

A. Nahata, J.T. Yardley and T.F. Heinz, �??Free-space electro-optic detection of continuous-wave terahertz radiation,�?? Appl. Phys. Lett. 75, 2524-2526 (1999).
[CrossRef]

M.M.J. Treacy, �??Dynamical diffraction in metallic optical gratings,�?? Appl. Phys. Lett. 75, 606-608 (1999).
[CrossRef]

Nature

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, �??Extraordinary optical transmission through subwavelength hole arrays,�?? Nature 391, 667-669 (1998).
[CrossRef]

Opt. Commun.

A. Krishnan, T. Thio, T.J. Kim, H.J. Lezec, T.W. Ebbesen, P.A. Wolff, J. Pendry, L. Martin-Moreno, and F.J. Garcia-Vidal, �??Evanescently coupled resonance in surface plasmon enhanced transmission,�?? Opt. Commun. 200, 1-7 (2001).
[CrossRef]

Opt. Lett.

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, 1114-1117 (2001).
[CrossRef] [PubMed]

Phys. Rev. B

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, �??Theory of light transmission through subwavelength periodic hole arrays,�?? Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, �??Surface plasmons enhance optical transmission through subwavelength holes,�?? Phys. Rev. B 83, 6779-6782 (1998).
[CrossRef]

F. Yang, J.R. Sambles, and G.W. Bradberry, �??Long-range surface modes supported by thin films,�?? Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

Phys. Rev. Lett.

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]

Springer Tracts in Modern Physics

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Vol. 111 of Springer Tracts in Modern Physics, Springer-Verlag, Berlin, 1988).

Other

D. Grischkowsky, in Frontiers in Nonlinear Optics, edited by H. Walther, N. Koroteev, and M.O. Scully (Institute of Physics Publishing, Philadelphia, 1992) and references therein.

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Figures (3)

Fig. 1.
Fig. 1.

Measured time-domain THz waveforms transmitted through an aperture array fabricated in (a) a 75 µm thick free-standing stainless steel foil and (b) a 75 µm thick free-standing stainless steel foil with 3 µm of silver deposited on both surfaces. Sample A consists of 400 µm diameter apertures periodically spaced by 1 mm. Sample B consists of 600 µm diameter apertures periodically spaced by 1.5 mm.

Fig. 2.
Fig. 2.

(a) Magnitude and (b) phase of the amplitude transmission coefficient obtained using a 75 µm free-standing stainless steel foil.

Fig. 3.
Fig. 3.

(a) Magnitude and (b) phase of the amplitude transmission coefficient obtained using a 75 µm free-standing stainless steel foil coated on both sides with 3 µm of silver.

Equations (8)

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

k sp = k x + i G x + j G y ,
k sp = ω c ( ε d ε m ε d + ε m ) 1 2 ,
k spr = ω c ( ε d ( ε mr + ε d ) 2 + ε mi 2 ) 1 2 ( ε e 2 + ( ε e 4 + ε d 2 ε mi 2 ) 1 2 2 ) 1 2 = ω c n sp
k spi = ω c ( ε d ( ε mr + ε d ) 2 + ε mi 2 ) 1 2 ε d ε mi [ 2 ( ε e 2 + ( ε e 4 + ε d 2 ε mi 2 ) 1 2 ) ] 1 2
k spr = ω c n sp ω c ε d
k spi = ω c ε d 3 2 2 ε mi .
λ peak = P i 2 + j 2 n sp = P i 2 + j 2 ε d
E transmitted ( f ) E incident ( f ) = t ( f ) = t ( f ) exp [ φ ( f ) ] .

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