Abstract

It has been shown both experimentally and numerically that the phenomenon of extraordinary transmission through subwavelength hole arrays is generally associated with a drop in transmission located very close to it. Paradoxically, this antiresonant drop occurs at the wavelength that, at first glance, should provoke a resonant excitation of a surface plasmon propagating along the metallic surface of the screen. The present paper gives a theoretical demonstration of this phenomenon, which dispels the paradox. Our theory is supported by numerical calculations.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
    [CrossRef]
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  6. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
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  35. P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
    [CrossRef]

2009

2008

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

2007

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

2006

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

E. Popov, M. Nevière, J. Wenger, P.-F. Lenne, H. Rigneault, P. C. Chaumet, N. Bonod, J. Dintinger, and T. W. Ebbesen, “Field enhancement in single subwavelength apertures,” J. Opt. Soc. Am. A 23, 2342–2348 (2006).
[CrossRef]

2005

E. Popov, M. Neviere, A. L. Fehrembach, and N. Bonod, “Optimization of plasmon excitation at structured apertures,” Appl. Opt. 44, 6141–6154 (2005).
[CrossRef] [PubMed]

E. Popov, M. Neviere, A. L. Fehrembach, and N. Bonod, “Enhanced light transmission through a circular structured aperture,” Appl. Opt. 44, 6898–6904 (2005).
[CrossRef] [PubMed]

E. Popov, M. Nevière, P. Boyer, and N. Bonod, “Light transmission through single apertures,” Opt. Commun. 255, 338–348(2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

2004

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

2003

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

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

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003).
[CrossRef] [PubMed]

2002

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, 820–823 (2002).
[CrossRef] [PubMed]

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

Q. Cao and P. Lalanne, “Negative role of suface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

2001

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
[CrossRef]

2000

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

1999

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[CrossRef]

1997

1996

1986

E. Popov, L. Mashev and D. Maystre, “Theoretical study of the anomalies of coated diffraction gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Baida, F. I.

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

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

Bonod, N.

Boyer, P.

E. Popov, M. Nevière, P. Boyer, and N. Bonod, “Light transmission through single apertures,” Opt. Commun. 255, 338–348(2005).
[CrossRef]

Bravo-Abad, J.

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

Cao, Q.

Q. Cao and P. Lalanne, “Negative role of suface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Chaumet, P. C.

Chavel, P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Degiron, A.

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[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, 820–823 (2002).
[CrossRef] [PubMed]

Dereux, A.

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

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (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, 820–823 (2002).
[CrossRef] [PubMed]

Dintinger, J.

E. Popov, M. Nevière, J. Wenger, P.-F. Lenne, H. Rigneault, P. C. Chaumet, N. Bonod, J. Dintinger, and T. W. Ebbesen, “Field enhancement in single subwavelength apertures,” J. Opt. Soc. Am. A 23, 2342–2348 (2006).
[CrossRef]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

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

E. Popov, M. Nevière, J. Wenger, P.-F. Lenne, H. Rigneault, P. C. Chaumet, N. Bonod, J. Dintinger, and T. W. Ebbesen, “Field enhancement in single subwavelength apertures,” J. Opt. Soc. Am. A 23, 2342–2348 (2006).
[CrossRef]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[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, 820–823 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743–1748 (1999).
[CrossRef]

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[CrossRef]

Enoch, S.

N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003).
[CrossRef] [PubMed]

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

Fehrembach, A. L.

Garcia-Vidal, F. J.

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[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, 820–823 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Garcia-Vidal, F. T.

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

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

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

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

Ghaemi, H. F.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743–1748 (1999).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Grupp, D. E.

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[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, 902 (2005).
[CrossRef]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Kim, T. J.

Kuipers, L.

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, 902 (2005).
[CrossRef]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Q. Cao and P. Lalanne, “Negative role of suface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Lee, K. G.

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

Lenne, P.-F.

Lezec, H. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[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, 820–823 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743–1748 (1999).
[CrossRef]

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Lezec, H. Z.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[CrossRef]

Li, L.

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, 820–823 (2002).
[CrossRef] [PubMed]

Liu, H.

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

Martin-Moreno, L.

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[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, 820–823 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Mashev, L.

E. Popov, L. Mashev and D. Maystre, “Theoretical study of the anomalies of coated diffraction gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Maystre, D.

E. Popov, L. Mashev and D. Maystre, “Theoretical study of the anomalies of coated diffraction gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

D. Maystre, Diffraction Gratings, SPIE Milestones Series (SPIE, 1993), Vol. MS83.

D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” Electromagnetic Surface Modes, A.D.Boardman, ed. (Wiley, 1982), Chap. 17.

D. Maystre, “Rigorous vector theories of diffraction gratings,” Progress in Optics 21, E.Wolf, ed. (1984), Chap. 1, 1–67.
[CrossRef]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Neviere, M.

Nevière, M.

Park, Q. H.

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

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

Polman, A.

Popov, E.

E. Popov, M. Nevière, J. Wenger, P.-F. Lenne, H. Rigneault, P. C. Chaumet, N. Bonod, J. Dintinger, and T. W. Ebbesen, “Field enhancement in single subwavelength apertures,” J. Opt. Soc. Am. A 23, 2342–2348 (2006).
[CrossRef]

E. Popov, M. Neviere, A. L. Fehrembach, and N. Bonod, “Enhanced light transmission through a circular structured aperture,” Appl. Opt. 44, 6898–6904 (2005).
[CrossRef] [PubMed]

E. Popov, M. Nevière, P. Boyer, and N. Bonod, “Light transmission through single apertures,” Opt. Commun. 255, 338–348(2005).
[CrossRef]

E. Popov, M. Neviere, A. L. Fehrembach, and N. Bonod, “Optimization of plasmon excitation at structured apertures,” Appl. Opt. 44, 6141–6154 (2005).
[CrossRef] [PubMed]

N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003).
[CrossRef] [PubMed]

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

E. Popov, L. Mashev and D. Maystre, “Theoretical study of the anomalies of coated diffraction gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Porto, J. A.

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

Przybilla, F.

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

Reinisch, R.

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

Rigneault, H.

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Sauvan, C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743–1748 (1999).
[CrossRef]

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[CrossRef]

Van Exter, M. P.

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

Van Labeke, D.

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

Verhagen, E.

Wenger, J.

Woerdman, J. P.

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

Wolff, P. A.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743–1748 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Appl. Opt.

J. Opt. A Pure Appl. Opt.

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

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

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

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

Nature Phys.

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

Opt. Acta

E. Popov, L. Mashev and D. Maystre, “Theoretical study of the anomalies of coated diffraction gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Opt. Commun.

E. Popov, M. Nevière, P. Boyer, and N. Bonod, “Light transmission through single apertures,” Opt. Commun. 255, 338–348(2005).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phys. Rev. B

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Z. Lezec, “Surface plasmons enhanced optical transmission through subwavelengths holes,” Phys. Rev. B 58, 6779–6782(1998).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

Phys. Rev. Lett.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Q. Cao and P. Lalanne, “Negative role of suface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 902 (2005).
[CrossRef]

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

Science

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, 820–823 (2002).
[CrossRef] [PubMed]

Other

D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” Electromagnetic Surface Modes, A.D.Boardman, ed. (Wiley, 1982), Chap. 17.

D. Maystre, Diffraction Gratings, SPIE Milestones Series (SPIE, 1993), Vol. MS83.

D. Maystre, “Rigorous vector theories of diffraction gratings,” Progress in Optics 21, E.Wolf, ed. (1984), Chap. 1, 1–67.
[CrossRef]

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Figures (20)

Fig. 1
Fig. 1

Experimental transmission spectrum of a gold film of thickness 200 nm with periods d = d = 700 nm , the radius of the holes being equal to 70 nm . The smooth curve shows a theoretical curve obtained by adjusting freely the parameters in a formula proposed by Fano. The arrow shows the location of the drop given by Eq. (1). The inset shows the experimental transmission spectrum for the same array, but in a film 100 nm thick. Reprinted from Ref. [26], p. 335, with permission from Elsevier.

Fig. 2
Fig. 2

Calculated transmission of the inductive grid corresponding to Fig. 1, for various values of the radius of the holes.

Fig. 3
Fig. 3

Perforated metallic screen, scheme and notations. (a) Inductive grid, (b) lamellar grating.

Fig. 4
Fig. 4

Interfaces between the different regions and fields of the nonperforated screen. The screen is illuminated in normal incidence by an electromagnetic plane wave of wavelength λ = 2 π / k in vacuum and wavevector k 1 propagating in region 1 (arrow 1 in Fig. 4), thus | k 1 | = k 1 = 2 π λ 1 = ν 1 k , λ 1 being the wavelength in region 1.

Fig. 5
Fig. 5

Decimal logarithm of the transmission (left) and of the modulus of B ± 1 (right) for a perfectly conducting lamellar grating [Fig. 3b] having a period d = 1. , a width t of the holes equal to 0.05 and a depth h = 0.3 . The indices ν 1 , ν 2 and ν 3 of the dielectric regions are equal to unity.

Fig. 6
Fig. 6

Same as Fig. 5, but with a hole width t equal to 0.6.

Fig. 7
Fig. 7

Asymptotic values when η of the logarithm of the transmission and of the modulus of the amplitude in the first order with the same other parameters as in Figs. 5, 6.

Fig. 8
Fig. 8

Variation of the asymptotic value of the transmission of a perfectly conducting lamellar grating as the wavelength tends to one ( η ), versus the screen depth h. The period is equal to 1, the width t of the holes is equal to 0.05. The indices ν 1 , ν 2 and ν 3 are equal to unity.

Fig. 9
Fig. 9

Decimal logarithm of the transmission and of the modulus of B ± 1 for a perfectly conducting inductive grid [Fig. 3a] having periods d = d = 1 , with a radius R of the circular holes equal to 0.1 and a depth h = 0.3 . The indices ν 1 , ν 2 and ν 3 are equal to unity.

Fig. 10
Fig. 10

Same as Fig. 7, but R = 0.3 .

Fig. 11
Fig. 11

Variations of the asymptotic values of the logarithm of the transmission and of | B ± 1 , 0 | with R / d . The other parameters are the same as in Fig. 9.

Fig. 12
Fig. 12

Variations of the asymptotic values of the logarithm of the transmission with h / d . The other parameters are the same as in Fig. 9.

Fig. 13
Fig. 13

Decimal logarithm of the transmission (left) and of the modulus of B ± 1 (right) for a metallic lamellar grating with optical index 4.2 i having a period d = 1 , a width t of the holes equal to 0.05 and a depth h = 0.3 . The indices ν 1 , ν 2 and ν 3 are equal to unity.

Fig. 14
Fig. 14

Same as Fig. 13 (left) but with a width t of the holes equal to 0.6.

Fig. 15
Fig. 15

Values of the logarithm of the transmission and of the amplitude in the first order at the wavelength λ = 1.0296 given by Eq. (35), keeping the same other parameters as in Figs. 13, 14. The horizontal dotted lines represent the theoretical values of the real and imaginary parts of B ± 1 .

Fig. 16
Fig. 16

Variation of the values of the logarithm of the transmission and of the amplitude in the ± 1 order at the wavelength λ = 1.0296 , keeping the same other parameters as in Figs. 13 ( t / d = 0.05 ). The horizontal dotted lines represent the theoretical values of the real and imaginary parts of B ± 1 . The indices ν 1 , ν 2 and ν 3 are equal to unity.

Fig. 17
Fig. 17

Values of the logarithm of the transmission and of the amplitude in the first order for a 2D inductive grid with periods d = d = 1 , with a radius R of the circular holes equal to 0.2 and a depth h = 0.3 . The indices ν 1 , ν 2 and ν 3 are equal to unity and the index of metal is equal to 4.2 i . The vertical dotted line shows the location (1.0296) of the drop in transmission predicted by theory, the horizontal dotted lines represent the theoretical values of the real and imaginary parts of B ± 1 , 0 at wavelength 1.0296.

Fig. 18
Fig. 18

Variations of the asymptotic values of the logarithm of the transmission and of B ± 1 , 0 with R / d . The other parameters are the same as in Fig. 17.

Fig. 19
Fig. 19

Variations of the asymptotic values of the logarithm of the transmission and of B ± 1 , 0 with h / d for R / d = 0.1 . The other parameters are the same as in Fig. 17.

Fig. 20
Fig. 20

Same as the left-hand side of Fig. 11, but with the index of silver ( ν M = 0.7 + i 4.2 ) instead of ν M = i 4.2 .

Equations (40)

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

λ = Re { d ν M p 1 + ν M 2 } ,
H i = H i z ^ = exp ( i k 1 y ) z ^ ,
E i = Z 1 exp ( i k 1 y ) x ^ , Z 1 = μ 0 ν 1 2 ε 0 = Z 0 ν 1 ,
H r = H r z ^ = exp ( + i k 1 y ) z ^ ,
E r = Z 1 exp ( + i k 1 y ) x ^ .
H = 2 cos ( k 1 y ) z ^ ,
E = Z 1 [ exp ( i k 1 y ) exp ( + i k 1 y ) ] x ^ = 2 i Z 1 sin ( k 1 y ) x ^ .
H = [ exp ( i k 1 x ) + exp ( i k 1 x ) ] z ^ = 2 cos ( k 1 x ) z ^ ,
E = Z 1 [ exp ( i k 1 x ) exp ( i k 1 x ) ] y ^ = 2 i Z 1 sin ( k 1 x ) y ^ .
H z C = 2 ( 1 + a cos ( k 1 x ) ) ,
E y C = 2 i Z 1 a sin ( k 1 x ) .
k 1 = p K , with K = 2 π / d ,
t λ 1 / 2 = λ / 2 ν 1 .
λ 1 / d = 1. + 10 η .
α n = n 2 π d , β m = m 2 π d .
H r = H r z ^ = ρ exp ( i k 1 y ) z ^ ,
E r = ρ Z 1 exp ( i k 1 y ) x ^ ,
H t = τ exp ( i k M y ) z ^ , k M = k ν M ,
E t = Z M τ exp ( i k M y ) x ^ , Z M = μ 0 ε M ,
ρ = ( ν M ν 1 ) / ( ν M + ν 1 ) ,
τ = 2 ν M / ( ν M + ν 1 ) .
E = { E i + E r for y > 0 E t for y < 0 , H = { H i + H r for y > 0 H t for y < 0 .
for y > 0 , H = exp [ i k ( α x + β y ) ] + exp [ i k ( α x + β y ) ] z ^ = 2 cos ( k α x ) exp ( i k β y ) z ^ ,
for y < 0 , H = exp [ i k ( α x γ y ) ] + exp [ i k ( α x γ y ) ] z ^ = 2 cos ( k α x ) exp ( i k γ y ) z ^ ,
α = ν M 1 + ( ν M / ν 1 ) 2 , β = ν 1 1 + ( ν M / ν 1 ) 2 , γ = ν M 2 / ν 1 1 + ( ν M / ν 1 ) 2 .
for y > 0 , E = 2 Z 1 ν 1 [ β cos ( k α x ) x ^ + i α sin ( k α x ) y ^ ] exp ( i k β y ) ,
for y < 0 , E = 2 Z M ν M [ γ cos ( k α x ) x ^ + i α sin ( k α x ) y ^ ] exp ( i k γ y ) .
( E , H ) = { ( E C , H C ) in D 1 ( 0 , 0 ) in D 2
h δ .
H C = [ 1 + ρ + 2 a cos ( k α x ) ] z ^ ,
E C = Z 1 { [ ( 1 ρ ) 2 a β ν 1 cos ( k α x ) ] x ^ + 2 i α a ν 1 sin ( k α x ) y ^ } ,
H C = [ τ exp ( i k ν M y ) + 2 a cos ( k α x ) exp ( i k γ y ) ] z ^ ,
E C = Z M { [ τ exp ( i k ν M y ) + 2 γ a cos ( k α x ) exp ( i k γ y ) / ν M ] x ^ + 2 i α a sin ( k α x ) exp ( i k γ y ) y ^ / ν M } .
a = 1 + ρ 2 = ν M ν M + ν 1 ,
k α = p 2 π d λ = d ν M p 1 + ( ν M / ν 1 ) 2 ,
t 2 π / k α = λ / α .
H C 2 ν M ν M + ν 1 [ 1 cos ( k ν 1 x ) ] z ^ ,
E C = 2 Z M ν M ν M + ν 1 { [ 1 cos ( k ν 1 x ) ] x ^ i ν M ν 1 sin ( k ν 1 x ) y ^ } ,
H C = 2 exp ( i k ν M y ) ν M ( ν M + ν 1 ) [ 1 cos ( k ν 1 x ) ] z ^ ,
E C = 2 Z M exp ( i k ν M y ) ν M ( ν M + ν 1 ) { [ 1 cos ( k ν 1 x ) ] x ^ i ν 1 ν M sin ( k ν 1 x ) y ^ } .

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