Abstract

We analyze the progressive introduction of disorder in periodic subwavelength hole arrays. Two models of disorder are discussed from their associated Fourier transforms and correlation functions. The optical transmission properties of the corresponding arrays are closely related with the evolutions of structure factors, as experimentally detailed. Remarkably, the optical properties of random arrays are not in general equal to those of the single hole as a result of short-range correlations corresponding to hole-to-hole interactions. These correlations are due to packing constraints that are controlled through the careful generation of random patterns. For high density pattern, short-range order can take over long-range order associated with the periodic array.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. M. Soukoulis, M. J. Velgakis, and E. N. Economou, “One-dimensional localization with correlated disorder,” Phys. Rev. B 50, 5110–5118 (1994).
    [CrossRef]
  2. A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102–153105 (2005).
    [CrossRef]
  3. D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
    [CrossRef]
  4. N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
    [CrossRef]
  5. B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
    [CrossRef] [PubMed]
  6. J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
    [CrossRef]
  7. C. Genet, M. P. van Exter, and J. P. Woerdman, “Huygens description of resonance phenomena in subwavelength hole arrays,” J. Opt. Soc. Am. A 22, 998–1002 (2005).
    [CrossRef]
  8. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
    [CrossRef] [PubMed]
  9. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
    [CrossRef]
  10. F. van Beijnum, C. Rétif, C. B. Smiet, and M. P. van Exter, “Transmission processes in random patterns of subwavelength holes,” Opt. Lett. 36, 3666–3668 (2011).
    [CrossRef] [PubMed]
  11. A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
    [CrossRef]
  12. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
    [CrossRef] [PubMed]
  13. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
    [CrossRef] [PubMed]
  14. F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
    [CrossRef]
  15. J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
    [CrossRef]
  16. F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett. 89, 121115 (2006).
    [CrossRef]
  17. A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105, 073902 (2010).
    [CrossRef] [PubMed]
  18. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  19. 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 (2004).
    [CrossRef] [PubMed]
  20. K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
    [CrossRef]
  21. M. C. Hughes and R. Gordon, “Optical transmission properties and enhanced loss for randomly positioned apertures in a metal film,” Appl. Phys. B 87, 239–242 (2007).
    [CrossRef]
  22. C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
    [CrossRef]
  23. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
    [CrossRef] [PubMed]
  24. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
    [CrossRef]
  25. J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
    [CrossRef]

2011 (1)

2010 (2)

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105, 073902 (2010).
[CrossRef] [PubMed]

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

2009 (2)

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (2)

J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
[CrossRef]

M. C. Hughes and R. Gordon, “Optical transmission properties and enhanced loss for randomly positioned apertures in a metal film,” Appl. Phys. B 87, 239–242 (2007).
[CrossRef]

2006 (4)

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

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

2005 (5)

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102–153105 (2005).
[CrossRef]

C. Genet, M. P. van Exter, and J. P. Woerdman, “Huygens description of resonance phenomena in subwavelength hole arrays,” J. Opt. Soc. Am. A 22, 998–1002 (2005).
[CrossRef]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

2004 (3)

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

2003 (1)

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

2000 (1)

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

1994 (1)

C. M. Soukoulis, M. J. Velgakis, and E. N. Economou, “One-dimensional localization with correlated disorder,” Phys. Rev. B 50, 5110–5118 (1994).
[CrossRef]

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

’t Hooft, G. W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Ahn, Y. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Alkemade, P. F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Auguié, B.

Barnes, W. L.

Bauer, C.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Bravo-Abad, J.

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
[CrossRef]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

Christ, A.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

de Léon-Pérez, F.

Degiron, A.

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Duch, A. C.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

Ebbesen, T. W.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

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

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Economou, E. N.

C. M. Soukoulis, M. J. Velgakis, and E. N. Economou, “One-dimensional localization with correlated disorder,” Phys. Rev. B 50, 5110–5118 (1994).
[CrossRef]

Eliel, E. R.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Enoch, S.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

Fedotov, V. A.

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

Feldmann, J.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

Fernández-Domínguez, A. I.

J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
[CrossRef]

Fu, Y.

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105, 073902 (2010).
[CrossRef] [PubMed]

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
[CrossRef]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

Gbur, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Genet, C.

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

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

C. Genet, M. P. van Exter, and J. P. Woerdman, “Huygens description of resonance phenomena in subwavelength hole arrays,” J. Opt. Soc. Am. A 22, 998–1002 (2005).
[CrossRef]

Giessen, H.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Gordon, R.

M. C. Hughes and R. Gordon, “Optical transmission properties and enhanced loss for randomly positioned apertures in a metal film,” Appl. Phys. B 87, 239–242 (2007).
[CrossRef]

Hanarp, P.

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

Hohng, S. C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Hughes, M. C.

M. C. Hughes and R. Gordon, “Optical transmission properties and enhanced loss for randomly positioned apertures in a metal film,” Appl. Phys. B 87, 239–242 (2007).
[CrossRef]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Käll, M.

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

Kim, D. S.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Kim, J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Koch, M.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102–153105 (2005).
[CrossRef]

Koerkamp, K. J. K.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

Kuhl, J.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Kuipers, L.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lagendijk, A.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102–153105 (2005).
[CrossRef]

Lalanne, P.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Laluet, J. Y.

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lezec, H. J.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Lienau, C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Liu, H.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Malyarchuk, V.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105, 073902 (2010).
[CrossRef] [PubMed]

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
[CrossRef]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

Nau, D.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Nikitin, A. Y.

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105, 073902 (2010).
[CrossRef] [PubMed]

Olofsson, L.

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

Papasimakis, N.

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

Park, J. W.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Park, Q. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Prikulis, J.

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

Przybilla, F.

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef] [PubMed]

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

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

Rétif, C.

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Schönhardt, A.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Segerink, F. B.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

Smiet, C. B.

Sönnichsen, C.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, M. J. Velgakis, and E. N. Economou, “One-dimensional localization with correlated disorder,” Phys. Rev. B 50, 5110–5118 (1994).
[CrossRef]

Steininger, G.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

Sutherland, D.

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

Tsai, D. P.

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

van Beijnum, F.

van der Molen, K. L.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

van Exter, M. P.

van Hulst, N. F.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

Velgakis, M. J.

C. M. Soukoulis, M. J. Velgakis, and E. N. Economou, “One-dimensional localization with correlated disorder,” Phys. Rev. B 50, 5110–5118 (1994).
[CrossRef]

Visser, T. D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

von Plessen, G.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

Vos, W. L.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102–153105 (2005).
[CrossRef]

Woerdman, J. P.

Yamamoto, N.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Yee, K. J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Yoon, Y. C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Zentgraf, T.

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Zheludev, N. I.

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

Appl. Phys. B (1)

M. C. Hughes and R. Gordon, “Optical transmission properties and enhanced loss for randomly positioned apertures in a metal film,” Appl. Phys. B 87, 239–242 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

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

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

F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[CrossRef]

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

Nano Lett. (1)

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4, 1003–1008 (2004).
[CrossRef]

Nat. Phys. (1)

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120–123 (2006).
[CrossRef]

Nature (1)

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Phys. Rev. B (4)

C. M. Soukoulis, M. J. Velgakis, and E. N. Economou, “One-dimensional localization with correlated disorder,” Phys. Rev. B 50, 5110–5118 (1994).
[CrossRef]

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102–153105 (2005).
[CrossRef]

N. Papasimakis, V. A. Fedotov, Y. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and the order-disorder transitions,” Phys. Rev. B 80, 041102(R) (2009).
[CrossRef]

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

J. Bravo-Abad, A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” Phys. Rev. Lett. 99, 203905 (2007).
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105, 073902 (2010).
[CrossRef] [PubMed]

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

D. Nau, A. Schönhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, and H. Giessen, “Disorder issues in metallic photonic crystals,” Phys. Status Solidi B 243, 231–2343 (2006).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

SEM images of two-dimensional arrays of sub-wavelength holes with increasing degree of disorder (only the top left quarter of each structure is displayed). Starting from a N = 900 holes periodic array (a) disorder is introduced by moving R = 300 holes (b), R = 600 holes (c) and R = 900 holes (d) around their original position in a sub-unit cell of size χ = 300 nm. Alternatively, we move all the holes by increasing the amplitude of the displacement, χ = 100 nm (e), χ = 200 nm (f), χ = 300 nm (g) and χ = 450 nm (h). For each case, we also show the associated Fourier spectrum Imax(k) = max(I(k)) and pair correlation function g(r).

Fig. 2
Fig. 2

(a) Transmission spectra of two-dimensional arrays of sub-wavelength hole with increasing degree of disorder. Disorder is introduced by moving R = 0 to 900 holes from their initial position with χ = 300 nm (local disorder). (b) All the holes are displaced from their initial position, amplitude of the displacement is increased from χ = 0 to 500 nm (global disorder). As a reference the spectrum of a single aperture having the same dimensions as the holes within the random arrays is also represented (thick grey line). (c) Intensity of the first peak of the numerical Fourier transform of the different structures as a function of the degree of disorder D. (d) Efficiency of EOT as a function of D and evolution of the SP propagation length SP. This length is evaluated as SP = λ res 2 / ( 2 π n SP F W H M ) from the FWHM of the transmission resonance peaked at λres and the associated SP index n SP = [ ɛ m ɛ d / ɛ m + ɛ d ], with ɛm and ɛd the respective dielectric constants of the metal and dielectric media. Note that the spectra of the arrays with D > 0.45 were too broad to extract FWHM with enough confidence.

Fig. 3
Fig. 3

(a) Ratio of the relative efficiency of EOT to the intensity of the associated Bragg peak on the Fourier spectrum. (b) Efficiency of EOT and intensity of the first Bragg peak on the Fourier spectrum as a function of the mean square displacement of the holes from their initial position in the periodic array. Also represented is the Debye Waller law (dashed line) evaluated for Gi=1,j=0. Note that D and 〈δ2〉 are proportional up to 〈δ2〉 = 15·10−3 μm2.

Fig. 4
Fig. 4

SEM images of random hole arrangements generated for increasing value of σ: (a) σ = 250 nm (ρ ≈ 7.5%), (b) σ = 450 nm (ρ ≈ 2.3%) and (c) σ = 650 nm (ρ ≈ 1.2%). The average hole density per surface area (ρ) was chosen to be equal to a third of the maximum value achievable given the geometrical constraints imposed by σ. The apertures have all the same dimensions (d = 160 nm). Numerical Fourier transforms of the random arrays are also represented. The scale and images contrast are the same in the different panels. (d) SEM images of single apertures milled in the same Au film (t = 275 nm) having the same dimension as the holes within the random arrays. The magnified SEM images display two isolated single apertures with identical geometrical parameters. The white ring surrounding the apertures on the SEM images denotes the rounded edge of the holes.

Fig. 5
Fig. 5

Transmission spectra of random hole arrangements generated for increasing values of σ. The data correspond to the geometrical parameters presented in Fig. 4. As a reference the spectrum of a single aperture having the same dimensions as the holes within the random arrays is also represented (thick grey line). The spectrum of the single hole corresponds to an average of the spectrum of two different isolated single apertures (see Fig. 4(d)).

Fig. 6
Fig. 6

SEM images of compact random hole arrangements generated for increasing value of σ: (a) σ = 250 nm (ρ ≈ 22.6 %), (b) σ = 300 nm (ρ ≈ 15.8 %), (c) σ = 350 nm (ρ ≈ 11.7 %) and (d) σ = 400 nm (ρ ≈ 9.2 %). The average hole density per surface area ρ was chosen to be equal to the maximum value allowed by the constraint imposed by σ. The apertures have all the same dimensions (d = 160 nm). Numerical Fourier transforms of the random arrays are also represented. These diffraction spectra allow to identify short-range order in the arrays (concentric rings). Radial averaged cross sections allow to easily visualise the frequencies of the inner rings, which clearly correspond to the parameter σ. The scale and the images contrast are the same as in Fig. 4.

Fig. 7
Fig. 7

Transmission spectra of random hole arrays generated with increasing values of the minimum hole separation (σ). These data correspond to the geometrical parameters presented in Fig. 6 (arrays with maximum hole density). As a reference the spectrum of a single aperture having the same dimension as the holes within the random arrays is also represented (thick grey line). (Inset) Evolution of the positions of the resonance (black dots) observed on the experimental spectra of the compact random hole arrays as a function of the spatial frequencies krandom dominating the numerical FT shown in Fig. 6 (note that krandom ≈ 2π/σ). These positions are compared to the positions λres estimated from the SP coupling condition (continuous line) considering the spectral structure of the Fourier transform of the random arrays (krandom = kSP with kSP = nSP · 2π/λres).

Fig. 8
Fig. 8

Transmission spectra of random hole arrays having increasing number of holes (N) of constant diameter d = 160 nm. The average hole density has been kept constant (ρ ≈ 10.6 %) with a minimal hole separation σ = 250 nm. Note that the different structures have been generated independently. As a reference the spectrum of a single aperture having the same dimension as the holes within the random arrays is also represented (thick grey line).

Equations (3)

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

I ( k ) | S k | 2
g ( r ) = 1 2 π r N ρ N i = 1 N j = 1 , j i N { 0 if r | r i r j | 1 2 1 if 1 2 < r | r i r j | 1 2 0 if 1 2 < r | r i r j |
I ( G i , j ) I 0 ( G i , j ) = e G i , j 2 δ 2 / 2

Metrics