Abstract

Using terahertz (THz) transmission measurements through two-dimensional Fibonacci deterministic subwavelength hole arrays fabricated in metal foils, we find that the surface plasmon-polariton (SPP) correlation lengths for aperiodic resonances are smaller than those associated with the underlying grid. The enhanced transmission spectra associated with these arrays contain two groups of Fano-type resonances: those related to the two-dimensional Fibonacci structure and those related to the underlying hole grid array upon which the aperiodic Fibonacci array is built. For both groups the destructive interference frequencies at which transmission minima occur closely match prominent reciprocal vectors in the hole array (HA) structure-factor in reciprocal space. However the Fibonacci-related transmission resonances are much weaker than both their calculated Fourier intensity in k space and the grid-related resonances. These differences may arise from the complex, multi-fractal dispersion relations and scattering from the underlying grid arrays. We also systematically studied and compared the transmission resonance strength of Fibonacci HA and periodic HA lattices as a function of the number of holes in the array structure. We found that the Fibonacci-related resonance strengths are an order of magnitude weaker than that of the periodic HA, consistent with the smaller SPP correlation length for the aperiodic structure.

© 2012 OSA

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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. 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]
  3. 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]
  4. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
    [CrossRef] [PubMed]
  5. A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
    [CrossRef] [PubMed]
  6. M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
    [CrossRef] [PubMed]
  7. D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
    [CrossRef] [PubMed]
  8. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
    [CrossRef] [PubMed]
  9. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
    [CrossRef] [PubMed]
  10. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
    [CrossRef]
  11. R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008).
    [CrossRef] [PubMed]
  12. A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic aperiodic arrays of metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009).
    [CrossRef] [PubMed]
  13. R. Lifshitz, “The square Fibonacci tiling,” J. Alloy. Comp. 342(1-2), 186–190 (2002).
    [CrossRef]
  14. X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
    [CrossRef] [PubMed]
  15. L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
    [CrossRef]
  16. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
    [CrossRef]
  17. A. Miroshnichenko, S. Flach, and Y. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
    [CrossRef]
  18. A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
    [CrossRef] [PubMed]
  19. F. Przybilla, C. Genet, and T. W. Ebbesen, “Long vs. short-range orders in random subwavelength hole arrays,” Opt. Express 20(4), 4697–4709 (2012).
    [CrossRef] [PubMed]

2012 (1)

2010 (1)

A. Miroshnichenko, S. Flach, and Y. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

2009 (2)

2008 (3)

2007 (1)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

2004 (1)

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]

2002 (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]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

R. Lifshitz, “The square Fibonacci tiling,” J. Alloy. Comp. 342(1-2), 186–190 (2002).
[CrossRef]

2001 (1)

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (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(6668), 667–669 (1998).
[CrossRef]

1994 (1)

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[CrossRef] [PubMed]

1993 (1)

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[CrossRef] [PubMed]

1991 (1)

X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
[CrossRef] [PubMed]

1987 (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Agrawal, A.

A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
[CrossRef] [PubMed]

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Berger, C.

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[CrossRef] [PubMed]

Bergman, D. J.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[CrossRef] [PubMed]

Boriskina, S. V.

Cheng, B.

X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
[CrossRef] [PubMed]

Cyrot-Lackmann, F.

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[CrossRef] [PubMed]

Dal Negro, L.

Dallapiccola, R.

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]

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.

F. Przybilla, C. Genet, and T. W. Ebbesen, “Long vs. short-range orders in random subwavelength hole arrays,” Opt. Express 20(4), 4697–4709 (2012).
[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]

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Feng, N.

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Flach, S.

A. Miroshnichenko, S. Flach, and Y. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Fu, X.

X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

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]

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[CrossRef] [PubMed]

Genet, C.

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]

Gopinath, A.

Hu, A.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

Huang, X. Q.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

Jiang, S. S.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

Kivshar, Y.

A. Miroshnichenko, S. Flach, and Y. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Klein, T.

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[CrossRef] [PubMed]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[CrossRef] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

Lanco, P.

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[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]

Lifshitz, R.

R. Lifshitz, “The square Fibonacci tiling,” J. Alloy. Comp. 342(1-2), 186–190 (2002).
[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, Y.

X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
[CrossRef] [PubMed]

Martin-Moreno, L.

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]

Matsui, T.

A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Mayou, D.

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[CrossRef] [PubMed]

Mazzer, M.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

Miroshnichenko, A.

A. Miroshnichenko, S. Flach, and Y. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Nahata, A.

A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
[CrossRef] [PubMed]

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Negro, L. D.

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Pendry, J. B.

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]

Peng, R. W.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

Przybilla, F.

Qiu, F.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

Reinhard, B. M.

Stellacci, F.

Stockman, M. I.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[CrossRef] [PubMed]

Sutherland, B.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[CrossRef] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

Taylor, P. C.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[CrossRef] [PubMed]

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]

Vardeny, Z. V.

A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
[CrossRef] [PubMed]

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Wang, M.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[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]

Zheng, D.

X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
[CrossRef] [PubMed]

Zhu, W.

A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80(17), 3063–3065 (2002).
[CrossRef]

J. Alloy. Comp. (1)

R. Lifshitz, “The square Fibonacci tiling,” J. Alloy. Comp. 342(1-2), 186–190 (2002).
[CrossRef]

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

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[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]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B Condens. Matter 43(13), 10808–10814 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009).
[CrossRef] [PubMed]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?” Phys. Rev. Lett. 87(16), 167401 (2001).
[CrossRef] [PubMed]

D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, “Evidence for unconventional electronic transport in quasicrystals,” Phys. Rev. Lett. 70(25), 3915–3918 (1993).
[CrossRef] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Hole array geometries and corresponding FFT spectra. (a) Fibonacci hole array and (c) random hole array on a square grid array; aperture diameter d = 0.44 mm, nearest neighbor spacing a = 0.8 mm with 173 holes. The structure factor of the Fibonacci (b) and random-hole-on-grid array (d) calculated using a 2D FFT. The Fibonacci-related reciprocal vectors, (F)(i) and grid-related reciprocal vectors, (G)(i) that correspond to Miller indices (1,0) and (1,1), respectively are denoted.

Fig. 2
Fig. 2

THz time-domain spectroscopy studies of HA structures described in Fig. 1. (a) THz transmission spectrum, tF(ω) of the 2D Fibonacci HA (300 holes) and its corresponding tRG(ω) spectrum of random-on-grid HA (RG) array. The transmission minima F1-F3 associated with the Fibonacci structure, and those associated with G1 related to the underlying grid are assigned. (b) The spectrum of the transmission ratio tF(ω)/tRG(ω). (c) THz transmission spectrum tF(ω) of Fibonacci HA structures fabricated with the same nearest neighbor distance a = 0.8 mm and number of holes (800 holes), but different hole diameters d as denoted. The Fibonacci-related transmission minimum frequencies are indicated by dashed vertical lines. (d) Real and imaginary parts of the effective dielectric constant of the Fibonacci HA structure with d = 0.68 mm obtained from the transmission amplitude and phase spectra. The transmission minima are denoted.

Fig. 3
Fig. 3

The dependence of THz transmission resonance strength on the number of holes for the Fibonacci and periodic HA structures. (a) THz transmission spectrum of a typical Fibonacci HA structure, and (c) periodic HA lattice, compared to the spectrum of the corresponding random HAs (all structures have 800 holes). The Fibonacci resonance F2 and periodic resonance G1 strengths are shaded. The integration of (b) F2 and (d) G2 resonance strengths is plotted versus the number of holes in the structure. The corresponding strengths in the structure factor in k-space are calculated (blue symbols). (b) The inset shows an intensity profile which is formed by cutting the reciprocal lattice shown in Fig. 1(b) along the line that connects the origin with the F2 reciprocal vector.

Fig. 4
Fig. 4

Calculation of the correlation length, R. (a) DFT spectra calculated at two different correlation lengths around (1,0) peak of a periodic structure with a period of 1 mm. (b) The integration of (1,0) peaks as a function of R in a log-log scale. The fit line shows that the DFT intensity increases quadratic with R. (c) Transmission spectra of a Fibonacci HA with d = 0.68 mm hole diameter (dash blue line) and a periodic HA with d = 0.4 mm (red line). The blue solid line shows a Fibonacci spectrum normalized to the same hole area with the periodic HA. The dash dark line is a cut-off line above which we calculate the transmission strength of the Fibonacci F2 and periodic G1 peaks. (d) Hole-to-hole correlation function calculation, g of periodic, RG and Fibonacci HAs with 800 holes and the nearest neighbor distance of 0.8 mm.

Equations (1)

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t(ω)=| t(ω) |exp[iφ(ω)]= E transmitted (ω) E incident (ω) ,

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