Abstract

Using terahertz time-domain spectroscopy, we have measured the optical properties of metallic films perforated with arrays of subwavelength apertures that possess short-range order (SRO), but lack long-range orientational order (LRO). We demonstrate that extraordinary transmission enhancement still occurs through the SRO aperture structures, despite the absence of LRO. The dielectric response of these arrays is characterized by a superposition of a broad principal resonance that is due to the random rotations of the building block (BB) units, and discrete resonances arising from well-defined reciprocal vectors in the structure factor that result from a virtual lattice associated with the BB units.

© 2008 Optical Society of America

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  1. R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films," Phys. Rev. Lett. 55, 1117-1120 (1985).
    [CrossRef] [PubMed]
  2. R. Gruhlke, W. Hod, and D. Hall, "Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film," Phys. Rev. Lett. 56, 2838-2841 (1986).
    [CrossRef] [PubMed]
  3. 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, 667-669 (1998).
    [CrossRef]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  5. E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189 (2006).
    [CrossRef] [PubMed]
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
    [CrossRef] [PubMed]
  7. 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]
  8. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
    [CrossRef] [PubMed]
  9. A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (R) (2002).
    [CrossRef]
  10. C. Janot, Quasicrystals: A Primer (Oxford University Press, New York, 1994).
  11. T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
    [CrossRef] [PubMed]
  12. A. Agrawal, T. Matsui, Z. Valy Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545 (2007).
    [CrossRef]
  13. V. M. Nield and D. A. Keen, Diffuse Neutron Scattering from Crystalline Materials (Oxford University Press, New York, 2001).
  14. T. R. Welberry, Diffuse x-ray scattering and models of disorder (Oxford University Press, New York, 2004).
  15. Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
    [CrossRef]
  16. D. Grischkowsky, in Frontiers in Nonlinear Optics, H. Walther, N. Koroteev, and M. O. Scully, eds., (Institute of Physics Publishing, Philadelphia, 1992).

2007 (3)

T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
[CrossRef] [PubMed]

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

A. Agrawal, T. Matsui, Z. Valy Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545 (2007).
[CrossRef]

2006 (2)

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2001 (1)

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]

1998 (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, 667-669 (1998).
[CrossRef]

1986 (1)

R. Gruhlke, W. Hod, and D. Hall, "Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

1985 (1)

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films," Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
[CrossRef] [PubMed]

A. Agrawal, T. Matsui, Z. Valy Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545 (2007).
[CrossRef]

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

Cheng, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Dou, J.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Dragila, R.

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films," Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

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]

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, 667-669 (1998).
[CrossRef]

Garcia-Vidal, F. J.

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]

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, 667-669 (1998).
[CrossRef]

Gruhlke, R.

R. Gruhlke, W. Hod, and D. Hall, "Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Hall, D.

R. Gruhlke, W. Hod, and D. Hall, "Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Hod, W.

R. Gruhlke, W. Hod, and D. Hall, "Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

Lezec, H. J.

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]

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, 667-669 (1998).
[CrossRef]

Luther-Davies, B.

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films," Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

Ma, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Martin-Moreno, L.

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]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
[CrossRef] [PubMed]

A. Agrawal, T. Matsui, Z. Valy Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545 (2007).
[CrossRef]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Nahata, A.

A. Agrawal, T. Matsui, Z. Valy Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545 (2007).
[CrossRef]

T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
[CrossRef] [PubMed]

Ozbay, E.

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189 (2006).
[CrossRef] [PubMed]

Pellerin, K. M.

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]

Pendry, J. B.

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]

Sheng, Y.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Thio, T.

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]

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, 667-669 (1998).
[CrossRef]

Valy Vardeny, Z.

T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
[CrossRef] [PubMed]

A. Agrawal, T. Matsui, Z. Valy Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545 (2007).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

Vukovic, S.

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films," Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

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, 667-669 (1998).
[CrossRef]

Zhang, D.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (4)

T. Matsui, A. Agrawal, A. Nahata, and Z. Valy Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature 446, 517-521 (2007).
[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, 667-669 (1998).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508 (2006).
[CrossRef] [PubMed]

Phys Rev. Lett. (1)

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. Lett. (3)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films," Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

R. Gruhlke, W. Hod, and D. Hall, "Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film," Phys. Rev. Lett. 56, 2838-2841 (1986).
[CrossRef] [PubMed]

Science (1)

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189 (2006).
[CrossRef] [PubMed]

Other (5)

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (R) (2002).
[CrossRef]

C. Janot, Quasicrystals: A Primer (Oxford University Press, New York, 1994).

V. M. Nield and D. A. Keen, Diffuse Neutron Scattering from Crystalline Materials (Oxford University Press, New York, 2001).

T. R. Welberry, Diffuse x-ray scattering and models of disorder (Oxford University Press, New York, 2004).

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

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Figures (3)

Fig. 1.
Fig. 1.

(a). Schematic of the design procedure for fabricating a SRO structure. Randomly rotated squares of side length a are placed at the vertices of a virtual lattice having lattice constant b. (b) A 5×5 unit cell subset of an actual SRO structure, where the black circles correspond to the apertures. (c) The reciprocal space representation of the SRO aperture in (b), where the individual reciprocal vectors, RVs, are assigned.

Fig. 2.
Fig. 2.

(a). The THz transmission spectra through SRO structures with two different aperture diameters D=500 µm (red curve) and D=600 µm (blue curve), along with spectra for the corresponding random aperture structures (dotted lines). Resonances are assigned corresponding to RVs in reciprocal space shown in Fig. 1(c). (b) Spectra of the real and imaginary components of the effective dielectric constant obtained from (a) for SRO structure with D=600 µm (red curves). The modeled ε(ω) of the effective medium (blue line) is based on a fit using Eq. (2) with parameters given in the text.

Fig. 3.
Fig. 3.

(a). The reciprocal space representation of a SRO aperture with orientation angles limited by θmax=π/6; the RVs are as in Fig. 1(b). The localization of the diffuse band at RVD is clearly evident. (b) THz transmission spectra through such SRO structures with a=0.75 mm and D=400 µm (red curve) and a=1 mm and D=500 µm (blue curve).

Equations (3)

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t ( v ) = t ( v ) exp [ i φ ( v ) ] = E transmitted ( v ) E incident ( v )
ε m ( ω ) = ε ( 1 ω ~ p 2 ω 2 + i γ ω ) + j ω Lj 2 ω 2 ω Tj 2 ω 2 i γ j ω + ω 1 ω h ω L 2 ( ω ~ T ) ω 2 ω ~ T 2 ω 2 i γ ω d ω ~ T
ω Tj = 2 π c b m 2 + n 2 ,

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