Abstract

Recent demonstrations have shown that the transmission through a subwavelength aperture in metal film placed in a periodic lattice or an aperiodic structure is significantly increased relative to a bare aperture. Using terahertz time-domain spectroscopy, we analyze the enhanced transmission properties of aperiodic and corresponding random 2D aperture arrays perforated in metallic films, which include quasicrystals and quasicrystal approximates. We demonstrate that the transmission enhancement phenomenon occurs for aperture arrays having discrete Fourier components in the 2D geometrical structure factor. We further show that the phenomenon is valid for a larger class of 2D aperture array designs that can be tailored to exhibit desired resonances and hence is more general. The inherent relationship between various features observed in the measured time-domain electric field, calculated transmission spectra, and the real and reciprocal space representation of the aperture array is discussed in detail. The results are interpreted in terms of Fano-type interference mechanism. The importance of antiresonance features observed in the transmission spectra is also discussed.

© 2007 Optical Society of America

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References

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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, 667-669 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. M. Sun, J. Tian, Z. Y. Li, B.-Y. Cheng, D.-Z. Zhang, A.-Z. Jin, and H.-F. Yang, "The role of periodicity in enhanced transmission through subwavelength hole arrays," Chin. Phys. Lett. 23, 486-488 (2006).
    [CrossRef]
  14. F. Przybilla, C. Genet, and T. W. Ebbesen, "Enhanced transmission through Penrose subwavelength hole arrays," Appl. Phys. Lett. 89, 121115 (2006).
    [CrossRef]
  15. N. Papasimakis, V. A. Fedotov, F. J. Garcia de Abajo, A. S. Schwanecke, and N. I. Zheludev, "Enhanced microwave transmission through quasicrystal hole arrays," arXiv:0704.2552v1 (2007).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  21. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
    [CrossRef] [PubMed]
  22. B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  26. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
    [CrossRef] [PubMed]
  27. P. A. Stampfli, "Dodecagonal quasiperiodic lattice in two dimensions," Helv. Phys. Acta 59, 1260-1263 (1986).
  28. M. Oxborrow and L. C. Henley, "Random square-triangle tilings: a model for twelve-fold symmetric quasicrystals," Phys. Rev. B 48, 6966-6998 (1993).
    [CrossRef]
  29. 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]
  30. H. Cao and A. Nahata, "Influence of aperture shape on transmission properties of a periodic array of subwavelength apertures," Opt. Express 12, 3664-3672 (2004).
    [CrossRef] [PubMed]
  31. J. E. S. Socolar, "Simple octagonal and dodecagonal quasicrystals," Phys. Rev. B 39, 10519 (1989).
    [CrossRef]
  32. T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, "Surface plasmon enhanced transmission through hole arrays in Cr films," J. Opt. Soc. Am. B 16, 1743-1748 (1999).
    [CrossRef]
  33. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
    [CrossRef]
  34. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1873 (1961).
    [CrossRef]
  35. C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003).
    [CrossRef]
  36. R. Österbacka, X. M. Jiang, C. P. An, B. Horovitz, and Z. V. Vardeny, "Photoinduced quantum interference antiresonances in π-conjugated polymers," Phys. Rev. Lett. 88, 226401 (2002).
    [CrossRef] [PubMed]
  37. T. D. M. Lee, G. J. Parker, M. E. Zoorob, S. J. Cox, and M. D. B. Charlton, "Design and simulation of highly symmetric photonic quasi-crystals," Nanotechnology 16, 2703-2706 (2005).
    [CrossRef]

2007 (1)

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

2006 (4)

M. Sun, J. Tian, Z. Y. Li, B.-Y. Cheng, D.-Z. Zhang, A.-Z. Jin, and H.-F. Yang, "The role of periodicity in enhanced transmission through subwavelength hole arrays," Chin. Phys. Lett. 23, 486-488 (2006).
[CrossRef]

F. Przybilla, C. Genet, and T. W. Ebbesen, "Enhanced transmission through Penrose subwavelength hole arrays," Appl. Phys. Lett. 89, 121115 (2006).
[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

F. J. Garcia de Abajo, J. J. Saenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express 14, 7-18 (2006).
[CrossRef] [PubMed]

2005 (2)

A. Agrawal, H. Cao, and A. Nahata, "Time-domain analysis of enhanced transmission through a single subwavelength aperture," Opt. Express 13, 3535-3542 (2005).
[CrossRef] [PubMed]

T. D. M. Lee, G. J. Parker, M. E. Zoorob, S. J. Cox, and M. D. B. Charlton, "Design and simulation of highly symmetric photonic quasi-crystals," Nanotechnology 16, 2703-2706 (2005).
[CrossRef]

2004 (6)

2003 (5)

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]

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

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003).
[CrossRef]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
[CrossRef]

2002 (2)

R. Österbacka, X. M. Jiang, C. P. An, B. Horovitz, and Z. V. Vardeny, "Photoinduced quantum interference antiresonances in π-conjugated polymers," Phys. Rev. Lett. 88, 226401 (2002).
[CrossRef] [PubMed]

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

2001 (2)

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]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, "Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals," J. Phys.: Condens. Matter 13, 10459-10470 (2001).
[CrossRef]

2000 (2)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

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]

1999 (1)

1998 (2)

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]

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]

1993 (1)

M. Oxborrow and L. C. Henley, "Random square-triangle tilings: a model for twelve-fold symmetric quasicrystals," Phys. Rev. B 48, 6966-6998 (1993).
[CrossRef]

1989 (1)

J. E. S. Socolar, "Simple octagonal and dodecagonal quasicrystals," Phys. Rev. B 39, 10519 (1989).
[CrossRef]

1986 (1)

P. A. Stampfli, "Dodecagonal quasiperiodic lattice in two dimensions," Helv. Phys. Acta 59, 1260-1263 (1986).

1984 (2)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

1974 (1)

R. Penrose, "The role of aesthetics in pure and applied mathematical research," Bull. Inst. Math. Appl. 10, 266-271 (1974).

1961 (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1873 (1961).
[CrossRef]

Appl. Phys. Lett. (2)

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]

F. Przybilla, C. Genet, and T. W. Ebbesen, "Enhanced transmission through Penrose subwavelength hole arrays," Appl. Phys. Lett. 89, 121115 (2006).
[CrossRef]

Bull. Inst. Math. Appl. (1)

R. Penrose, "The role of aesthetics in pure and applied mathematical research," Bull. Inst. Math. Appl. 10, 266-271 (1974).

Chin. Phys. Lett. (1)

M. Sun, J. Tian, Z. Y. Li, B.-Y. Cheng, D.-Z. Zhang, A.-Z. Jin, and H.-F. Yang, "The role of periodicity in enhanced transmission through subwavelength hole arrays," Chin. Phys. Lett. 23, 486-488 (2006).
[CrossRef]

Helv. Phys. Acta (1)

P. A. Stampfli, "Dodecagonal quasiperiodic lattice in two dimensions," Helv. Phys. Acta 59, 1260-1263 (1986).

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

J. Phys.: Condens. Matter (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, "Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals," J. Phys.: Condens. Matter 13, 10459-10470 (2001).
[CrossRef]

Nanotechnology (1)

T. D. M. Lee, G. J. Parker, M. E. Zoorob, S. J. Cox, and M. D. B. Charlton, "Design and simulation of highly symmetric photonic quasi-crystals," Nanotechnology 16, 2703-2706 (2005).
[CrossRef]

Nature (5)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature 440, 1166-1169 (2006).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. 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]

Opt. Commun. (1)

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1873 (1961).
[CrossRef]

Phys. Rev. B (7)

J. E. S. Socolar, "Simple octagonal and dodecagonal quasicrystals," Phys. Rev. B 39, 10519 (1989).
[CrossRef]

M. Oxborrow and L. C. Henley, "Random square-triangle tilings: a model for twelve-fold symmetric quasicrystals," Phys. Rev. B 48, 6966-6998 (1993).
[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]

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
[CrossRef]

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]

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[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. (6)

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]

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

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]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

R. Österbacka, X. M. Jiang, C. P. An, B. Horovitz, and Z. V. Vardeny, "Photoinduced quantum interference antiresonances in π-conjugated polymers," Phys. Rev. Lett. 88, 226401 (2002).
[CrossRef] [PubMed]

Other (3)

N. Papasimakis, V. A. Fedotov, F. J. Garcia de Abajo, A. S. Schwanecke, and N. I. Zheludev, "Enhanced microwave transmission through quasicrystal hole arrays," arXiv:0704.2552v1 (2007).

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

C. Janot, Quasicrystals: A Primer, 2nd ed. (Oxford U. Press, 1994).

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Figures (6)

Fig. 1
Fig. 1

THz transmission properties of random aperture arrays. (a) Real- and (b) reciprocal-space representations of an 800-hole random aperture array used in our study. (c) The transmission spectrum through a random aperture array of 2500 holes with 400 μ m diameter and 12% fractional aperture area. The dotted curve in the spectrum shows the fit using the individual aperture transmission model of [24] with D = 0.42 mm . (d) Dependence of transmittance on the number of holes in the film for a fixed aperture diameter. (e) Dependence of the peak transmission wavelength on the aperture diameter D for constant fractional aperture area.

Fig. 2
Fig. 2

THz transmission properties of 2D aperture arrays in the form of Penrose-type quasicrystals. (a) Real-space representation of a 2D Penrose-type quasicrystal constructed of fat and skinny rhomb tiles with apertures fabricated at the vertices, where d 3 corresponds to the length of the rhomb side. (b) Reciprocal-space representation (or structure factor) of the 2D aperture array shown in (a). The tenfold rotational symmetry is apparent from the RVs in the Fourier-space representation. (c) Electric field transmission spectrum, T ( ν ) of a Penrose quasicrystal with d 3 = 1.5 mm and D = 540 μ m . The resonance bands F ( i ) in the spectrum correspond to the RVs in the structure factor representation of the Penrose-type lattice in (b). The AR features are assigned and correspond to dips in T ( ν ) that occur at the high-frequency side of each resonant band. (d) The transient field amplitude in the THz-TDS measurements of the Penrose quasicrystal aperture array with d 3 = 1.5 mm compared with that of a random aperture array. E T denotes the single-cycle electric field of the incident THz pulse. The inset is an enlarged version of the quasicrystal oscillatory transient response with an internal period δ τ = 5 ps , and envelope period Δ τ = 28 ps . (e) The dependence of the resonance peak wavelength, λ 0 ( i ) on the quasicrystal rhomb side length, d 3 for the three main resonances F ( i ) , shown in (c), for four Penrose structures having different values of d 3 but the same fractional aperture area.

Fig. 3
Fig. 3

Real-space representation of dodecagonal or 12-fold quasicrystal aperture array fabricated using square and triangular tiles with same side length d 5 . The apertures were fabricated at the vertices of the tiles. (b) The corresponding reciprocal-space representation for the sample shown in (a). The discrete T ( i ) vectors in the reciprocal space exhibit the underlying structure factor, and local 12-fold rotational symmetry. (c) The transmission spectra of two quasicrystals with 12-fold rotational symmetry with hole diameter D = 0.35 mm ( 2 × ) and 0.58 mm , respectively. For both spectra the side length d 5 = 1.5 mm , and the resonances T ( i ) and ARs AR i are shown. (d) The electric field transmission spectra of the perforated film with D = 0.58 mm at various angles θ between the incident beam and the surface normal. The inset summarizes the split and change of resonance frequency ν ( T ( 1 ) ) with θ. The lines through the data points are guides to the eye.

Fig. 4
Fig. 4

Real- and (b) reciprocal-space representations of quasicrystal aperture array with eightfold local rotational symmetry. The discrete peaks E ( i ) in reciprocal space exhibit the underlying geometrical structure factor associated with the aperture array in (a). (c) Amplitude transmission spectra of the eightfold rotational symmetry aperture array structures measured in samples with different aperture diameters D, but same lattice spacing d i . The resonance bands E ( i ) are assigned. (d) The shift in resonance frequency ν ( E ( 2 ) ) and the corresponding antiresonance frequency ν ( AR 2 ) as a function of aperture diameter, D.

Fig. 5
Fig. 5

Dependence of resonant peak frequency ν ( E ( 2 ) ) and the corresponding AR frequency ν ( AR 2 ) on the aperture diameter for the octagonal quasicrystal shown in Fig 4. (b) The dependence of the wavelength, λ, that corresponds to the resonance E ( 2 ) and AR 2 on the quasicrystal rhomb side length, d 4 for octagonal quasicrystal structures, as shown in Fig. 4.

Fig. 6
Fig. 6

Real- and reciprocal-space representations of “approximate” quasicrystal aperture array with (a) 40-fold and (b) 120-fold rotational symmetry. The discrete peaks RV n ( i ) in reciprocal space exhibits the desired n = 40 - and 120-fold rotational symmetry. (c) Amplitude transmission spectra of the aperiodic aperture array structures with local 40-fold (red curve) and 120-fold (blue curve) rotational symmetry (the spectra were offset for clarity).

Tables (3)

Tables Icon

Table 1 Numerical Relations between Various Ratios of Real-Space Distances, d i ; Corresponding RV Distances, F ( i ) ; Resonant Frequencies, ν ( i ) ; and ARs, AR i , Feature in the Transmission Spectrum of 2D Penrose-Type Quasicrystal Aperture Arrays Structure with d 3 = 2.0 mm and D = 720 μ m a

Tables Icon

Table 2 Numerical Relations between Various Ratios of Real-Space Distances, d i ; Corresponding RV Magnitudes, T ( i ) ; Resonant Frequencies, ν ( i ) ; and ARs, AR i , in the Transmission Spectra of Dodecagonal Quasicrystal Aperture Arrays Structure with D = 0.35 and 0.58 mm a

Tables Icon

Table 3 Relations between Various Ratios of Real-Space Distances, d i ; Corresponding RVs, E ( i ) ; Resonant Frequencies, ν ( i ) ; and ARs, AR i , Feature in the Transmission Spectrum of Octagonal Quasicrystal Aperture Arrays Structure a

Equations (2)

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T ( ν ) = T ( ν ) exp [ φ ( ν ) ] = E transmitted ( ν ) E incident ( ν ) .
k + k SPP = G ( i ) .

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