Abstract

By numerically calculating the relevant electromagnetic fields and charge current densities, we show how local charges and currents near subwavelength structures govern light transmission through subwavelength apertures in a real metal film. The illumination of a single aperture generates surface waves; and in the case of slits, generates them with high efficiency and with a phase close to –π with respect to a reference standing wave established at the metal film front facet. This phase shift is due to the direction of induced charge currents running within the slit walls. The surface waves on the entrance facet interfere with the standing wave. This interference controls the profile of the transmission through slit pairs as a function of their separation. We compare the calculated transmission profile for a two-slit array to simple interference models and measurements [Phys. Rev. B 77(11), 115411 (2008)].

© 2011 OSA

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  1. 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(11), 115411 (2008).
    [CrossRef]
  2. J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72(6), 064401 (2009).
    [CrossRef]
  3. M. W. Kim, T. T. Kim, J. E. Kim, and H. Y. Park, “Surface plasmon polariton resonance and transmission enhancement of light through subwavelength slit arrays in metallic films,” Opt. Express 17(15), 12315–12322 (2009).
    [CrossRef] [PubMed]
  4. I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
    [CrossRef]
  5. S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
    [CrossRef]
  6. J. S. White, G. Veronis, Z. F. Yu, E. S. Barnard, A. Chandran, S. H. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34(5), 686–688 (2009).
    [CrossRef] [PubMed]
  7. P. B. Catrysse and S. H. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
    [CrossRef]
  8. R. Marques, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17(7), 5571–5579 (2009).
    [CrossRef] [PubMed]
  9. J. Fiala and I. Richter, “Interaction of light with subwavelength apertures: a comparison of approximate and rigorous approaches,” Opt. Quantum Electron. 41(5), 409–427 (2009).
    [CrossRef]
  10. V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41(4), 299–313 (2009).
    [CrossRef]
  11. X. F. Li and S. F. Yu, “Long-wavelength optical transmission of extremely narrow slits via hybrid surface-plasmon and Fabry-Perot modes,” J. Appl. Phys. 108(1), 013302 (2010).
    [CrossRef]
  12. R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12(6), 065101 (2010).
    [CrossRef]
  13. Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
    [CrossRef]
  14. M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton. 4, 043504 (2010).
    [CrossRef]
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  17. Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
    [CrossRef]
  18. Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. X. R. Huang and R. W. Peng, “General mechanism involved in subwavelength optics of conducting microstructures: charge-oscillation-induced light emission and interference,” J. Opt. Soc. Am. A 27(4), 718–729 (2010).
    [CrossRef]
  23. M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
    [CrossRef]
  24. P. B. Catrysse and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
    [CrossRef]
  25. F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
    [CrossRef]
  26. E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
    [CrossRef] [PubMed]
  27. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
    [CrossRef]
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    [CrossRef]
  30. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
    [CrossRef]
  31. E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, 1999).
  32. S.-H. Chang, S. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13, 3150–3165 (2005).
    [CrossRef] [PubMed]
  33. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
    [CrossRef]
  34. M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1993).
  35. J. Weiner and F. D. Nunes, “High-frequency response of subwavelength-structured metals in the petahertz domain,” Opt. Express 16(26), 21256–21270 (2008).
    [CrossRef] [PubMed]
  36. H. Raether, Surface Plasmons (Springer-Verlag, 1988).
  37. G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
    [CrossRef]

2010 (14)

X. F. Li and S. F. Yu, “Long-wavelength optical transmission of extremely narrow slits via hybrid surface-plasmon and Fabry-Perot modes,” J. Appl. Phys. 108(1), 013302 (2010).
[CrossRef]

R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12(6), 065101 (2010).
[CrossRef]

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton. 4, 043504 (2010).
[CrossRef]

B. Wang and P. Lalanne, “Surface plasmon polaritons locally excited on the ridges of metallic gratings,” J. Opt. Soc. Am. A 27(6), 1432–1441 (2010).
[CrossRef]

P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express 18(10), 10896–10904 (2010).
[CrossRef] [PubMed]

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
[CrossRef]

V. Delgado, R. Marques, and L. Jelinek, “Analytical theory of extraordinary optical transmission through realistic metallic screens,” Opt. Express 18(7), 6506–6515 (2010).
[CrossRef] [PubMed]

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4(2), 311–335 (2010).
[CrossRef]

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

X. R. Huang and R. W. Peng, “General mechanism involved in subwavelength optics of conducting microstructures: charge-oscillation-induced light emission and interference,” J. Opt. Soc. Am. A 27(4), 718–729 (2010).
[CrossRef]

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

2009 (11)

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72(6), 064401 (2009).
[CrossRef]

M. W. Kim, T. T. Kim, J. E. Kim, and H. Y. Park, “Surface plasmon polariton resonance and transmission enhancement of light through subwavelength slit arrays in metallic films,” Opt. Express 17(15), 12315–12322 (2009).
[CrossRef] [PubMed]

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

J. S. White, G. Veronis, Z. F. Yu, E. S. Barnard, A. Chandran, S. H. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34(5), 686–688 (2009).
[CrossRef] [PubMed]

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

P. B. Catrysse and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

R. Marques, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17(7), 5571–5579 (2009).
[CrossRef] [PubMed]

J. Fiala and I. Richter, “Interaction of light with subwavelength apertures: a comparison of approximate and rigorous approaches,” Opt. Quantum Electron. 41(5), 409–427 (2009).
[CrossRef]

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41(4), 299–313 (2009).
[CrossRef]

2008 (3)

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(11), 115411 (2008).
[CrossRef]

J. Weiner and F. D. Nunes, “High-frequency response of subwavelength-structured metals in the petahertz domain,” Opt. Express 16(26), 21256–21270 (2008).
[CrossRef] [PubMed]

P. B. Catrysse and S. H. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

2007 (1)

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

2006 (1)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

2005 (1)

2000 (1)

1999 (2)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

1993 (1)

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1993).

1988 (1)

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

1982 (1)

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings–application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[CrossRef]

Akozbek, N.

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

Atwater, H. A.

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

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(11), 115411 (2008).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Babicheva, V. E.

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41(4), 299–313 (2009).
[CrossRef]

Baida, F. I.

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Banzer, P.

Barnard, E. S.

Bezuglyi, E. V.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

Billaudeau, C.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Blair, S.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton. 4, 043504 (2010).
[CrossRef]

Bloemer, M. J.

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1993).

Brolo, A. G.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4(2), 311–335 (2010).
[CrossRef]

Brongersma, M. L.

Buncick, M.

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

Cao, Y.

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

Catrysse, P. B.

P. B. Catrysse and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

P. B. Catrysse and S. H. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

Chandran, A.

Chang, S.-H.

Chern, R. L.

R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12(6), 065101 (2010).
[CrossRef]

Collin, S.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Davis, M.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton. 4, 043504 (2010).
[CrossRef]

de Ceglia, D.

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

Delgado, V.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Diwekar, M.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton. 4, 043504 (2010).
[CrossRef]

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Fakhraai, Z.

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

Fan, S. H.

P. B. Catrysse and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

J. S. White, G. Veronis, Z. F. Yu, E. S. Barnard, A. Chandran, S. H. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34(5), 686–688 (2009).
[CrossRef] [PubMed]

P. B. Catrysse and S. H. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

Feigenbaum, E.

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

Fiala, J.

J. Fiala and I. Richter, “Interaction of light with subwavelength apertures: a comparison of approximate and rigorous approaches,” Opt. Quantum Electron. 41(5), 409–427 (2009).
[CrossRef]

Fu, J. X.

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

Ghosh, G.

E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

Gordon, R.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4(2), 311–335 (2010).
[CrossRef]

Gray, S.

Gu, B. Y.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
[CrossRef]

Guizal, B.

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Hong, W. T.

R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12(6), 065101 (2010).
[CrossRef]

Hua, Y. L.

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

Huang, X. R.

Ip, S.

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

Jelinek, L.

Kats, A. V.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

Kavanagh, K. L.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4(2), 311–335 (2010).
[CrossRef]

Kim, J. E.

Kim, M. W.

Kim, T. T.

Kindler, J.

Kofke, M. J.

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

Kuipers, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Lalanne, P.

B. Wang and P. Lalanne, “Surface plasmon polaritons locally excited on the ridges of metallic gratings,” J. Opt. Soc. Am. A 27(6), 1432–1441 (2010).
[CrossRef]

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Leuchs, G.

Levchenko, A.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

Lévêque, G.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76(15), 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(11), 115411 (2008).
[CrossRef]

Li, H. Q.

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

Li, J. Y.

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

Li, X. F.

X. F. Li and S. F. Yu, “Long-wavelength optical transmission of extremely narrow slits via hybrid surface-plasmon and Fabry-Perot modes,” J. Appl. Phys. 108(1), 013302 (2010).
[CrossRef]

Li, Z. Y.

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

Lozovik, Y. E.

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41(4), 299–313 (2009).
[CrossRef]

Marques, R.

Martin, O. J. F.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Medina, F.

Mesa, F.

Neviere, M.

Nikitin, A. Y.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

Nunes, F. D.

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(11), 115411 (2008).
[CrossRef]

Palik, E.

E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

Pardo, F.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Park, H. Y.

Pelouard, J. L.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Pendry, J. B.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

Peng, R. W.

Peschel, U.

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Popov, E.

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

Poujet, Y.

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Quabis, S.

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

Richter, I.

J. Fiala and I. Richter, “Interaction of light with subwavelength apertures: a comparison of approximate and rigorous approaches,” Opt. Quantum Electron. 41(5), 409–427 (2009).
[CrossRef]

Rodier, J. C.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Salvi, J.

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Sanda, P. N.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings–application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[CrossRef]

Sauvan, C.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Scalora, M.

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

Schatz, G.

Sheng, P.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings–application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[CrossRef]

Sinton, D.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4(2), 311–335 (2010).
[CrossRef]

Spevak, I. S.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

Stepleman, R. S.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings–application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Van Labeke, D.

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Veronis, G.

Vincenti, M. A.

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

Waldeck, D. H.

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

Walker, G. C.

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

Wang, B.

Wang, H. Y.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
[CrossRef]

Wei, Z. Y.

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

Weiner, J.

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72(6), 064401 (2009).
[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(11), 115411 (2008).
[CrossRef]

J. Weiner and F. D. Nunes, “High-frequency response of subwavelength-structured metals in the petahertz domain,” Opt. Express 16(26), 21256–21270 (2008).
[CrossRef] [PubMed]

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

White, J. S.

Wolf, E.

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1993).

Wu, C.

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

Yang, H. F.

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

Yu, S. F.

X. F. Li and S. F. Yu, “Long-wavelength optical transmission of extremely narrow slits via hybrid surface-plasmon and Fabry-Perot modes,” J. Appl. Phys. 108(1), 013302 (2010).
[CrossRef]

Yu, Z. F.

Zhao, L. M.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
[CrossRef]

Zhou, Y. S.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

M. J. Kofke, D. H. Waldeck, Z. Fakhraai, S. Ip, and G. C. Walker, “The effect of periodicity on the extraordinary optical transmission of annular aperture arrays,” Appl. Phys. Lett. 94(2), 023104 (2009).
[CrossRef]

P. B. Catrysse and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

Chin. Phys. B (1)

Y. L. Hua, J. X. Fu, J. Y. Li, Z. Y. Li, and H. F. Yang, “Experimental studies of extraordinary light transmission through periodic arrays of subwavelength square and rectangular holes in metal films,” Chin. Phys. B 19(4), 047309 (2010).
[CrossRef]

J. Appl. Phys. (2)

X. F. Li and S. F. Yu, “Long-wavelength optical transmission of extremely narrow slits via hybrid surface-plasmon and Fabry-Perot modes,” J. Appl. Phys. 108(1), 013302 (2010).
[CrossRef]

M. A. Vincenti, D. de Ceglia, M. Buncick, N. Akozbek, M. J. Bloemer, and M. Scalora, “Extraordinary transmission in the ultraviolet range from subwavelength slits on semiconductors,” J. Appl. Phys. 107(5), 053101 (2010).
[CrossRef]

J. Nanophoton. (2)

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton. 4, 043504 (2010).
[CrossRef]

P. B. Catrysse and S. H. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

J. Opt. (1)

R. L. Chern and W. T. Hong, “Transmission resonances and antiresonances in metallic arrays of compound subwavelength holes,” J. Opt. 12(6), 065101 (2010).
[CrossRef]

J. Opt. Soc. Am. A (3)

Laser Photon. Rev. (1)

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4(2), 311–335 (2010).
[CrossRef]

Opt. Commun. (1)

F. I. Baida, Y. Poujet, J. Salvi, D. Van Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-lambda annular aperture arrays,” Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Opt. Quantum Electron. (2)

J. Fiala and I. Richter, “Interaction of light with subwavelength apertures: a comparison of approximate and rigorous approaches,” Opt. Quantum Electron. 41(5), 409–427 (2009).
[CrossRef]

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41(4), 299–313 (2009).
[CrossRef]

Photonics Nanostruct. (1)

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photonics Nanostruct. 8(2), 94–101 (2010).
[CrossRef]

Phys. Rev. A (1)

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and L. M. Zhao, “Enhancement of the extraordinary optical transmission in a subwavelength metal slit dressed by a metal grating,” Phys. Rev. A 81(3), 035803 (2010).
[CrossRef]

Phys. Rev. B (6)

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[CrossRef]

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[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(11), 115411 (2008).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings–application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[CrossRef]

Phys. Rev. Lett. (2)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72(6), 064401 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Other (3)

E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1993).

Supplementary Material (3)

» Media 1: AVI (3760 KB)     
» Media 2: AVI (3017 KB)     
» Media 3: AVI (3404 KB)     

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Figures (15)

Fig. 1
Fig. 1

Schematic of the one- and two-slit structures: (a) Incident surface XY plane with 50 nm slit milled in a 200 nm thick Ag film. (b) Section cut in the XZ plane. (c) Incident surface XY plane of two-slit structure separated by a variable pitch ranging over 3 to 4 wavelengths of the characteristic surface wave generated by light incident normal to the XY plane. (d) Section cut in the XZ plane of the two-slit structure. The dielectric index of refraction surrounding the structures and within the slits is taken to be that of the glass microscope slides used in experiments [1], n = 1.46. The plane-wave illumination is taken to be single-frequency at the Ar-ion laser green line, 514.5 nm.

Fig. 2
Fig. 2

(a) Reference field amplitude Re [ H ref norm ] , normalized to maximum amplitude Re [ H ref max ] . (b) Total field amplitude Re [ H tot norm ] normalized as in (a). (c) Net scattered field amplitude Re [ H scat norm ] normalized as in (a). Note opposite amplitude color code (deep red vs deep blue) between H ref norm adjacent to the front Ag facet in panel (a) and H scat norm at the slit entrance in panel (c), consistent with phase map in Fig. 4. Length spans on each panel: X = 3.2 μm, Z = 1.335 μm.

Fig. 3
Fig. 3

Frame fromMedia 1. Left panel shows amplitude Re [ H ref norm ] and the right panel amplitude of H-field, Re [ H scat norm ] . The surface waves propagate along the two dielectric-metal interfaces. After about two optical cycles they appear to stabilize in amplitude and phase. Length span X = 3.2μm, Z = 1.335μm.

Fig. 4
Fig. 4

Phase map of H scat relative to H ref. The color bar limits are ±π radians. Along the slit centerline the point of maximum phase is 10 nm to the left of the vertical surface line. At that point φ scat = −3.1405 radians. The map also shows the phase variation of the waves propagating on the incident and exit surfaces and the spatial variation of the phase within the slit volume. Spatial dimensions: vertical, X = 3.2μm; horizontal, Z = 0.300μm.

Fig. 5
Fig. 5

Calculated transmission T norm through a single subwavelength slit as a function of metal film thickness. The peaks are due to Fabry-Perot cavity resonances set up within the slit volume.

Fig. 6
Fig. 6

(a) Filled red circles: calculated E-field intensity; filled blue squares: calculated H-field intensity along Z on the slit centerline (see Fig. 1(b)) for Ag film thickness of 162 nm. Dashed vertical lines indicate the position of the incident and exit Ag film XY planes. (b) Same plot as (a) but for Ag film thickness of 272 nm. The out-of-phase intensity distribution between E- and H-fields indicates a standing wave within the slit.

Fig. 7
Fig. 7

Media 2 frame showing: (a) standing wave resulting from reflection of an incident plane wave on a plane Ag surface. (b) A component of the induced current density running near the incident surface in the positive X direction. (c) Current density components running in the slit wall along the Z direction. (d) Amplitudes of H scat, normalized to the maximum amplitude of H ref, produced by the current density components. Color code: red, green, blue; positive, null, negative amplitudes, respectively.

Fig. 8
Fig. 8

Amplitude of H scat, normalized to H ref at the surface plotted against the distance on either side of the slit centerline. The plot corresponds to a vertical cut in Fig. 7(d), 2 nm to the left of the front facet.

Fig. 9
Fig. 9

Log (base 10) of transmission as a function of slit separation for a two-slit array. The transmission is normalized to that of a single slit. Slit dimensions are the same as in the one-slit studies. The intensity modulation pattern shows minima very close to integral numbers of the Raether λ spp = 309.4 nm.

Fig. 10
Fig. 10

Phase map of the scattered H-field (H scat) relative to the phase of the standing wave H-field (H ref) for a two-slit structure separated by 618 nm, twice the spp wavelength of λ surf = 309 nm. The color bar limits are ±π radians. The map shows that the surface wave phase is very close to −π radians at the position of the slits, that a standing wave sets up between the slits, and that surface waves propagate away from the slits on the sides exterior to the slit pair. Spatial dimensions same as in Fig. 4

Fig. 11
Fig. 11

Panel (a): H-field amplitude of the reference standing wave, H ref, on the plane Ag surface. Color bar spans maximum and minimum field amplitude. The two vertical black lines denote the Ag film thickness, 200 nm. Note that H ref has maximum amplitude adjacent to the surface and penetrates the metal to the skin depth. Panels (b), (c): Amplitude of the total H-field (H tot) and scattered H-field H scat, respectively, with slit pitch equal to 2λ spp. Note relatively strong scattered field on incident surface, weak field within slits, and minimal transmission at this slit pitch. Panels (d), (e): H tot, H scat with slit pitch 2.5λ spp near transmission maximum. Length span X = 3.2 μm, Z = 0.300 μm.

Fig. 12
Fig. 12

Frame from Media 3. Left panel: H scat on two-slit structure with slit pitch of 2λ spp. Note strong amplitude of scattered surface waves on the incident facet propagating away from the slits in ±X direction and relatively weak transmitted propagation to the exit side. Right panel: H scat on two-slit structure with slit pitch of 2.5λ spp. Note large standing wave on entrance facet between slits, strong field in the slit and relatively strong amplitude of transmitted propagating wave. Color code: red, green, blue; positive, null, negative amplitudes, respectively.

Fig. 13
Fig. 13

Plot of FDTD results for far-field transmission through two slits (solid circles) and a fit of Eq. (7) to the FDTD calculation (solid line).

Fig. 14
Fig. 14

Lossy multiple reflection model fit, Eq. (8), to FDTD results (solid circles).

Fig. 15
Fig. 15

Comparison of measured transmission [1] to FDTD numerical simulations.

Equations (8)

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

H tot = H ref + H scat
T = A det P z d A det A s P z d A s
T norm = P z d A det / A slit P z d A s / A s = T A s A slit
τ = ( 1 𝒜 1 ) 2
= π 1
J x = σ E x and J z = σ E z
n ( ) ( p ) = { 1 + ( β 0 β 0 ) 2 2 β 0 β 0 cos [ ( 2 π λ spp ) p + φ ] } 2
η mod ( p ) = { ( 1 + k 0 e k 1 p ) 2 e 2 k Ag p ( β β ) 2 2 ( 1 + k 0 e k 1 p ) ( e k Ag p ) β β cos ( 2 π k 2 p + φ ) } 2

Metrics