Abstract

We investigate the influence of array order in the optical transmission properties of subwavelength hole arrays, by comparing the experimental spectral transmittance of periodic and quasiperiodic hole arrays as a function of frequency. We find that periodicity and long-range order are not necessary requirements for obtaining enhanced and suppressed optical transmission, provided short-range order is maintained. Transmission maxima and minima are shown to result, respectively, from constructive and destructive interference at each hole, between the light incident upon and exiting from a given hole, and surface plasmon polaritons (SPPs) arriving from individual neighboring holes. These SPPs are launched along both illuminated and exit surfaces, by diffraction of the incident and emerging light at the neighboring individual subwavelength holes. By characterizing the optical transmission of a pair of subwavelength holes as a function of hole-hole distance, we demonstrate that a subwavelength hole can launch SPPs with an efficiency up to 35%, and with an experimentally determined launch phase φ=π/2, for both input-side and exit-side SPPs. This characteristic phase has a crucial influence on the shape of the transmission spectra, determining transmission minima in periodic arrays at those frequencies where grating coupling arguments would instead predict maxima.

© 2008 Optical Society of America

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  1. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
    [CrossRef]
  2. C. J. Bouwkamp, "On Bethe???s theory of diffraction by small holes," Philips Res. Rep. 5, 321-332 (1950).
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]
  4. 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 58, 6779-6782 (1998).
    [CrossRef]
  5. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Tracts in Mod. Phys., Vol. 111, New York, 1988).
  6. M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999).
    [CrossRef]
  7. M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  8. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
    [CrossRef] [PubMed]
  9. S.-H. Chang, S. K. Gray, and G. C. Schatz, "Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films," Opt. Express 13, 3150-3165 (2005).
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  10. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005).
    [CrossRef] [PubMed]
  11. 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]
  12. 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]
  13. F. Przybilla, C. Genet, and T. W. Ebbesen, "Enhanced transmission through Penrose subwavelength hole arrays," Appl. Phys. Lett. 89, 121115 (2006).
    [CrossRef]
  14. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
    [CrossRef]
  15. G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
    [CrossRef] [PubMed]
  16. D. Pacifici, H. J. Lezec, and H. A. Atwater, "All-optical modulation by plasmonic excitation of CdSe quantum dots," Nature Photon. 1, 402-406 (2007).
    [CrossRef]
  17. F. Kalkum, G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, "Surface-wave interferometry on single subwavelength slit-groove structures fabricated on gold films," Opt. Express 15, 2613-2621 (2007).
    [CrossRef] [PubMed]
  18. D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
    [CrossRef]
  19. A.-L. Baudrion, F. de Leon-Perez, O. Mahboub, A. Hohenau,  et al., "Coupling efficiency of light to surface plasmon polariton for single subwavelength holes in a gold film," Opt. Express 16, 3420-3429 (2008).
    [CrossRef] [PubMed]
  20. N. G. de Bruijn, "Algebraic theory of Penrose???s non-periodic tilings of the plane. I-II," Mathematics Proc. A 84, 39-66 (1981).
  21. O. T. A. Janssen, H. P. Urbach, G. W. 't Hooft, "On the phase of plasmons excited by slits in a metal film," Opt. Express 14, 11823-11832 (2006).
    [CrossRef] [PubMed]
  22. 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, 820-822 (2002).
    [CrossRef] [PubMed]
  23. P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006).
    [CrossRef]
  24. G. Leveque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B 76, 155418 (2007).
    [CrossRef]
  25. F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
    [CrossRef]
  26. 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]
  27. H. Gao, J. Henzie, and T. W. Odom, "Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays," Nano Lett. 6, 2104-2108 (2006).
    [CrossRef] [PubMed]

2008 (2)

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
[CrossRef]

A.-L. Baudrion, F. de Leon-Perez, O. Mahboub, A. Hohenau,  et al., "Coupling efficiency of light to surface plasmon polariton for single subwavelength holes in a gold film," Opt. Express 16, 3420-3429 (2008).
[CrossRef] [PubMed]

2007 (5)

G. Leveque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B 76, 155418 (2007).
[CrossRef]

F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

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]

D. Pacifici, H. J. Lezec, and H. A. Atwater, "All-optical modulation by plasmonic excitation of CdSe quantum dots," Nature Photon. 1, 402-406 (2007).
[CrossRef]

F. Kalkum, G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, "Surface-wave interferometry on single subwavelength slit-groove structures fabricated on gold films," Opt. Express 15, 2613-2621 (2007).
[CrossRef] [PubMed]

2006 (7)

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]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

H. Gao, J. Henzie, and T. W. Odom, "Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays," Nano Lett. 6, 2104-2108 (2006).
[CrossRef] [PubMed]

O. T. A. Janssen, H. P. Urbach, G. W. 't Hooft, "On the phase of plasmons excited by slits in a metal film," Opt. Express 14, 11823-11832 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

2002 (2)

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

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, 820-822 (2002).
[CrossRef] [PubMed]

1999 (1)

M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999).
[CrossRef]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[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 58, 6779-6782 (1998).
[CrossRef]

1981 (1)

N. G. de Bruijn, "Algebraic theory of Penrose???s non-periodic tilings of the plane. I-II," Mathematics Proc. A 84, 39-66 (1981).

1950 (1)

C. J. Bouwkamp, "On Bethe???s theory of diffraction by small holes," Philips Res. Rep. 5, 321-332 (1950).

1944 (1)

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

Agrawal, A.

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]

Alloschery, O.

F. Kalkum, G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, "Surface-wave interferometry on single subwavelength slit-groove structures fabricated on gold films," Opt. Express 15, 2613-2621 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

Atwater, H. A.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, and H. A. Atwater, "All-optical modulation by plasmonic excitation of CdSe quantum dots," Nature Photon. 1, 402-406 (2007).
[CrossRef]

Baudrion, A.-L.

Bethe, H. A.

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

Bouwkamp, C. J.

C. J. Bouwkamp, "On Bethe???s theory of diffraction by small holes," Philips Res. Rep. 5, 321-332 (1950).

Chang, S.-H.

Cheng, B.-Y.

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]

de Bruijn, N. G.

N. G. de Bruijn, "Algebraic theory of Penrose???s non-periodic tilings of the plane. I-II," Mathematics Proc. A 84, 39-66 (1981).

de Leon-Perez, F.

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, 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, 820-822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

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

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, 820-822 (2002).
[CrossRef] [PubMed]

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 58, 6779-6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Gao, H.

H. Gao, J. Henzie, and T. W. Odom, "Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays," Nano Lett. 6, 2104-2108 (2006).
[CrossRef] [PubMed]

García de Abajo, F. J.

F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Garcia-Vidal, F. 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, 820-822 (2002).
[CrossRef] [PubMed]

Gay, G.

F. Kalkum, G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, "Surface-wave interferometry on single subwavelength slit-groove structures fabricated on gold films," Opt. Express 15, 2613-2621 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

Genet, C.

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]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[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 58, 6779-6782 (1998).
[CrossRef]

Gray, S. K.

Grupp, D. E.

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 58, 6779-6782 (1998).
[CrossRef]

Henzie, J.

H. Gao, J. Henzie, and T. W. Odom, "Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays," Nano Lett. 6, 2104-2108 (2006).
[CrossRef] [PubMed]

Hohenau, A.

Hugonin, J. P.

Janssen, O. T. A.

Jin, A.-Z.

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]

Kalkum, F.

Lalanne, P.

Leveque, G.

G. Leveque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B 76, 155418 (2007).
[CrossRef]

Lezec, H. J.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, and H. A. Atwater, "All-optical modulation by plasmonic excitation of CdSe quantum dots," Nature Photon. 1, 402-406 (2007).
[CrossRef]

F. Kalkum, G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, "Surface-wave interferometry on single subwavelength slit-groove structures fabricated on gold films," Opt. Express 15, 2613-2621 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (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, 820-822 (2002).
[CrossRef] [PubMed]

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 58, 6779-6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Li, Z.-Y.

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]

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, 820-822 (2002).
[CrossRef] [PubMed]

Mahboub, O.

Mansuripur, M.

Martin, O. J. F.

G. Leveque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B 76, 155418 (2007).
[CrossRef]

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, 820-822 (2002).
[CrossRef] [PubMed]

Matsui, T.

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]

Moloney, J. V.

Nahata, A.

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]

O???Dwyer, C.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

Odom, T. W.

H. Gao, J. Henzie, and T. W. Odom, "Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays," Nano Lett. 6, 2104-2108 (2006).
[CrossRef] [PubMed]

Pacifici, D.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, and H. A. Atwater, "All-optical modulation by plasmonic excitation of CdSe quantum dots," Nature Photon. 1, 402-406 (2007).
[CrossRef]

Przybilla, F.

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

Rodier, J. C.

Schatz, G. C.

Sun, M.

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]

't Hooft, G. W.

Thio, T.

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
[CrossRef] [PubMed]

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 58, 6779-6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Tian, J.

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]

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

M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999).
[CrossRef]

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van Exter, M. P.

Vardeny, Z. V.

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]

Viaris de Lesegno, B.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

Weiner, J.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
[CrossRef]

G. Leveque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B 76, 155418 (2007).
[CrossRef]

F. Kalkum, G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, "Surface-wave interferometry on single subwavelength slit-groove structures fabricated on gold films," Opt. Express 15, 2613-2621 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

Woerdman, J. P.

Wolff, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Xie, Y.

Yang, H.-F.

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]

Zakharian, A. R.

Zhang, D.-Z.

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]

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M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999).
[CrossRef]

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[CrossRef]

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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]

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[CrossRef] [PubMed]

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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 H. J. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

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D. Pacifici, H. J. Lezec, and H. A. Atwater, "All-optical modulation by plasmonic excitation of CdSe quantum dots," Nature Photon. 1, 402-406 (2007).
[CrossRef]

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G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O???Dwyer, J. Weiner, and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nature Phys. 2, 262-267 (2006).
[CrossRef]

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[CrossRef]

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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 58, 6779-6782 (1998).
[CrossRef]

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

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, "Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits," Phys. Rev. B 77, 115411 (2008).
[CrossRef]

G. Leveque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B 76, 155418 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

SEM images of hole arrays milled in a Ag film according to (a) square, (b) triangular, (c) Penrose, and (d) dodecagonal tilings of the plane. The nearest neighbor distance (for square and triangular arrays) and side of the tiling rhombi (for quasiperiodic arrays, shown as red lines) is a=400nm. The insets show the power spectra of computed 2D discrete Fourier transforms of each array type, in a logarithmic color map scale; the superimposed gray disk has a constant radius equal to 2π/a as reference length for the reciprocal space vectors.

Fig. 2.
Fig. 2.

Optical transmission through hole arrays with hole-hole distance a=400 nm (red line) and a=500 nm (green line), normalized to the measured optical transmission through random arrays with same hole diameter and number of holes.

Fig. 3.
Fig. 3.

Mode refractive index for surface plasmon polaritons at a Ag/SiO2 interface, as a function of free space wavelength. Insets: top panel, real part of the dielectric constants of Ag and SiO2 as experimentally determined by spectroscopic ellipsometry; bottom panel, SPP propagation lengths at a flat Ag/SiO2 interface.

Fig. 4.
Fig. 4.

Experimental universal transmission spectra for various types of hole arrays as a function of normalized wavelength.

Fig. 5.
Fig. 5.

Optical transmission through two holes milled in a Ag film, index matched with an optical fluid and a glass slide (both with n=1.46 at 514.5 nm) measured by uniformly illuminating the structures with a gaussian TM-polarized laser at 514.5 nm. The hole diameter is 50 nm and it is kept constant as a function of hole-hole distance a. The transmission data were opportunely normalized to extract the per-hole intensity η.

Fig. 6.
Fig. 6.

Blue lines: universal transmission spectra calculated within the interference model developed in the present manuscript, using a number of holes N=49. For comparison, the red solid lines represent experimental transmission data taken from Fig. 4.

Fig. 7.
Fig. 7.

Normalized optical transmission measured at λ=514.5nm for various types of hole arrays. A coherent Ar laser source and an incandescent lamp have been used. The coherence length of the lamp and spectrometer system was experimentally determined to be ~2µm.

Equations (17)

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n SPP ( λ ) λ λ SPP = Re [ ( ε 1 ( λ ) ε 2 ( λ ) ε 1 ( λ ) + ε 2 ( λ ) ) 1 2 ] ,
Λ SPP ( λ ) 4 π κ SPP λ = 4 π λ Im [ ( ε 1 ( λ ) ε 2 ( λ ) ε 1 ( λ ) + ε 2 ( λ ) ) 1 2 ] ,
k SPP = k + G ,
k SPP = G .
G ij = 2 π a i 2 + j 2 ,
( λ max n SPP a ) ij = 1 i 2 + j 2 ,
G ij = 4 π a 3 i 2 + j 2 + ij ,
( λ max n SPP a ) ij = 3 2 i 2 + j 2 + ij ,
H N = 2 = ( H 0 + β β a e ik SPP a H 0 ) T ( 1 + β β a e ik SPP a ) = H 0 T ( 1 + β β a e ik SPP a ) 2 ,
H N = 1 = H 0 T ,
η N = 2 = H N = 2 2 H N = 1 2 = ( 1 + β β a e ik SPP a ) 2 2 ,
β β = β 0 β 0 e i φ ,
η N = 2 = H N = 2 2 H N = 1 2 = ( 1 + β 0 β 0 a e i φ e ik SPP a ) 2 2 = [ 1 + ( β 0 β 0 ) 2 a + 2 β 0 β 0 a cos ( k SPP a + φ ) ] 2 ,
β 0 β 0 = 0.12 , φ = π 2 ,
H m , top = 1 + j m β 0 β 0 cos 2 ( θ jm θ p ) a jm exp [ i ( k SPP a jm + φ ) ] ,
H m , bot = H m , top + j m β 0 β 0 cos 2 ( θ jm θ p ) a jm H j , top exp [ i ( k SPP a jm + φ ) ]
η N = m = 1 N H m , bot 2 N 2 .

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