Abstract

We demonstrate that the resonantly enhanced transmission spectrum associated with a periodic array of subwavelength apertures is dependent upon the shape of the apertures. This is demonstrated using coherent terahertz radiation and aperture arrays fabricated in 75 µm thick stainless steel foils. We examine rectangular apertures with different aspect ratios as well as circular apertures. In the absence of periodicity in the arrays, no resonance features are present. For periodic arrays, we show that the ratio of the transmission coefficients for the two lowest order resonances can be directly related to the ratio of the appropriate aperture dimensions. From the time-domain waveforms, we find two independent, yet phase-coherent, transmission processes: non-resonant transmission related to the simple transmission through subwavelength apertures and a time-delayed resonant transmission related to the interaction of the THz pulse with the periodic aperture array. In these waveforms, we also observe a sign inversion for the primary bipolar pulse relative to the reference. This is shown to be a simple consequence of diffraction.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

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.

Y.-H. Ye and J.-Y. Zhang, ???Middle-infrared transmission enhancement through periodically perforated metal films,??? Appl. Phys. Lett. 84, 2977-2979 (2004).
[CrossRef]

F. Miyamaru and M. Hangyo, ???Finite size effect of transmission property for metal hole arrays in subterahertz region,??? Appl. Phys. Lett. 84, 2742-2744 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Nahata and T.F. Heinz, ???Reshaping of freely propagating terahertz pulses by diffraction,??? IEEE J. Sel. Top. Quantum Electron. 2, 701-708 (1996).
[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. Express

Opt. Lett.

Phys. Rev.

H. Bethe, ???Theory of diffraction by small holes,??? Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Phys. Rev. B

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]

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

Phys. Rev. Lett.

R. Gordon, A.G. Brolo, A. McKinnon, A. Rajora, B. Leatham, and K.L. Kavanagh, ???Strong polarization in the optical transmission through elliptical nanohole arrays,??? Phys. Rev. Lett. 92, 037401 (2004).
[CrossRef] [PubMed]

K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, and L. Kuipers, ???Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,??? Phys. Rev. Lett. 92, 183901/1-4 (2004).
[CrossRef]

Proc. Roy. Soc. A

Lord Rayleigh, ???On the passage of waves through fine slits in thin opaque screens,??? Proc. Roy. Soc. A 89, 194-219 (1913).
[CrossRef]

Rep. Prog. Phys.

C.J. Bouwkamp, ???Diffraction theory,??? Rep. Prog. Phys. 17, 35-100 (1954).
[CrossRef]

Science

H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, ???Beaming light from a subwavelength aperture,??? Science 297, 220-222 (2002).
[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.

Supplementary Material (3)

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Figures (5)

Fig. 1.
Fig. 1.

The four different aperture shapes used in this investigation and the polarization direction of the normally incident THz pulses. Array A consists of 400 µm diameter circular apertures, Array B consists of 400 µm×400 µm square apertures, Array C consists of 400 µm×300 µm rectangular apertures, Array D consists of 400 µm×200 µm rectangular apertures, and Array E consists of 400 µm×400 µm square apertures. In Arrays A-D, the apertures are periodically spaced by 1 mm. In Array E, the spacing is designed to yield a non-resonant transmission behavior. The dashed lines correspond to the aperture dimension at 45° with respect to the polarization direction, along the (+1, +1) axis. This last dimension is necessary for Fig. 5.

Fig. 2.
Fig. 2.

Measured time-domain THz waveforms transmitted through five different aperture arrays fabricated in 75 µm thick free-standing stainless steel foils. [Expanded Fig. 2 (a), (b), (c)]

Fig. 3.
Fig. 3.

Magnitude of the normalized amplitude transmission spectra for (upper) Arrays A and B and (lower) Arrays B-E.

Fig. 4.
Fig. 4.

Phase of the normalized amplitude transmission spectra for (upper) Arrays A and B and (lower) Arrays B-E.

Fig. 5.
Fig. 5.

The ratio of the normalized amplitude transmission coefficients versus the ratio of relevant aperture dimensions. See text for details of the definitions of these ratios. The filled markers correspond to data points for the four periodic arrays. The dashed line is a linear least squares fit to the data for Arrays B-D.

Equations (2)

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t N ( f ) = E transmitted ( f ) E reference ( f ) = t N ( f ) exp [ i φ N ( f ) ] .
λ peak = P i 2 + j 2 n sp = P i 2 + j 2 ε d .

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