Abstract

We developed an extended Fano model describing the Extraordinary Electromagnetic Transmission (EET) through arrays of subwavelength apertures, based on terahertz transmission measurements of arrays of various hole size and shapes. Considering a frequency-dependent coupling between resonant and non-resonant pathways, this model gives access to a simple analytical description of EET, provides good agreement with experimental data, and offers new parameters describing the influence of the hole size and shape on the transmitted signal.

© 2009 Optical Society of America

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
    [CrossRef]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  3. E. Ozbay, "Plasmonic: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  4. H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008).
    [CrossRef] [PubMed]
  5. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  6. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007).
    [CrossRef] [PubMed]
  7. 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(6), 1114-1117 (2001).
    [CrossRef]
  8. P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of Surface Plasmon Generation at Nanoslit Apertures," Phys. Rev. Lett. 95, 263,902 (2005).
    [CrossRef]
  9. J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
    [CrossRef]
  10. G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
    [CrossRef]
  11. K. G. Lee and Q. H. Park, "Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits," Phys. Rev. Lett. 95, 103,902 (2005). Now with Institut Pasteur, CNRS URA 2171, Unit In Silico Genetics, 75724 Paris Cedex 15, France
    [CrossRef]
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  13. J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Exp. 14(7), 2552-2572 (2006).
    [CrossRef]
  14. A. Agrawal, Z. V. Vardeny, and A. Nahata, "Engineering the dielectric function of plasmonic lattices," Opt. Exp. 16(13), 9601-9613 (2008).
    [CrossRef]
  15. A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, "Squeezing MillimeterWaves into Microns," Phys. Rev. Lett. 92(14), 143,904 (2004).
  16. 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. Comm. 225(4-6), 331-336 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. J.-B. Masson and G. Gallot, "Coupling between surface plasmons in subwavelength hole arrays," Phys. Rev. B 73, 121,401(R) (2006).
    [CrossRef]
  21. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124(6), 1866-1875 (1961).
    [CrossRef]
  22. J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
    [CrossRef]
  23. S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, "Understanding the Fano Resonance : through Toy Models," Am. J. Phys. 72, 1501 (2004).
    [CrossRef]
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    [CrossRef]
  25. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66(7-8), 163-182 (1944).
    [CrossRef]
  26. C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
    [CrossRef]
  27. D. Grischkowsky, S. R. Keiding, M. van Exter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7(10), 2006-2015 (1990).
    [CrossRef]
  28. C.-C. Chen, "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theo. Tech. 21(1), 1-6 (1973).
    [CrossRef]
  29. J.-B. Masson, A. Podzorov, and G. Gallot, "Anomalies in the disappearance of the extraordinary electromagnetic transmission in subwavelength hole arrays," Opt. Exp. 16(7), 4719-4730 (2008).
    [CrossRef]
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2008

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

A. Agrawal, Z. V. Vardeny, and A. Nahata, "Engineering the dielectric function of plasmonic lattices," Opt. Exp. 16(13), 9601-9613 (2008).
[CrossRef]

J.-B. Masson, A. Podzorov, and G. Gallot, "Anomalies in the disappearance of the extraordinary electromagnetic transmission in subwavelength hole arrays," Opt. Exp. 16(7), 4719-4730 (2008).
[CrossRef]

2007

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
[CrossRef]

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

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

2006

E. Ozbay, "Plasmonic: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Exp. 14(7), 2552-2572 (2006).
[CrossRef]

2005

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of Surface Plasmon Generation at Nanoslit Apertures," Phys. Rev. Lett. 95, 263,902 (2005).
[CrossRef]

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. Exp. 13(8), 3150-3165 (2005).
[CrossRef]

2004

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, "Understanding the Fano Resonance : through Toy Models," Am. J. Phys. 72, 1501 (2004).
[CrossRef]

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. Comm. 225(4-6), 331-336 (2003).
[CrossRef]

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085,415 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[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(6), 1114-1117 (2001).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

C.-M. Ryu and S. Y. Cho, "Phase evolution of the transmission coefficient in an Aharonov-Bohm ring with Fano resonance," Phys. Rev. B 58(7), 3572 (1998).
[CrossRef]

1993

D. G. Duffy, "On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications," ACM Trans. Math Soft. 19(3), 333-359 (1993).
[CrossRef]

1990

1973

C.-C. Chen, "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theo. Tech. 21(1), 1-6 (1973).
[CrossRef]

1961

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124(6), 1866-1875 (1961).
[CrossRef]

1954

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
[CrossRef]

1944

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66(7-8), 163-182 (1944).
[CrossRef]

Agrawal, A.

A. Agrawal, Z. V. Vardeny, and A. Nahata, "Engineering the dielectric function of plasmonic lattices," Opt. Exp. 16(13), 9601-9613 (2008).
[CrossRef]

Alloschery, O.

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

Azad, A. K.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

Bandopadhyay, S.

S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, "Understanding the Fano Resonance : through Toy Models," Am. J. Phys. 72, 1501 (2004).
[CrossRef]

Barnes, W. L.

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

Bethe, H. A.

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66(7-8), 163-182 (1944).
[CrossRef]

Bouwkamp, C. J.

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
[CrossRef]

Bravo-Abad, J.

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
[CrossRef]

Brok, J. M.

J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Exp. 14(7), 2552-2572 (2006).
[CrossRef]

Brown, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, "Squeezing MillimeterWaves into Microns," Phys. Rev. Lett. 92(14), 143,904 (2004).

Chang, S.-H.

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. Exp. 13(8), 3150-3165 (2005).
[CrossRef]

Chen, C.-C.

C.-C. Chen, "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theo. Tech. 21(1), 1-6 (1973).
[CrossRef]

Chen, J.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

Cho, S. Y.

C.-M. Ryu and S. Y. Cho, "Phase evolution of the transmission coefficient in an Aharonov-Bohm ring with Fano resonance," Phys. Rev. B 58(7), 3572 (1998).
[CrossRef]

de Lesegno, B. V.

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

Dereux, A.

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

Duffy, D. G.

D. G. Duffy, "On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications," ACM Trans. Math Soft. 19(3), 333-359 (1993).
[CrossRef]

Dutta-Roy, B.

S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, "Understanding the Fano Resonance : through Toy Models," Am. J. Phys. 72, 1501 (2004).
[CrossRef]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007).
[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, 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(6), 1114-1117 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

Fano, U.

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124(6), 1866-1875 (1961).
[CrossRef]

Fattinger, C.

Fernandez-Dominguez, A. I.

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
[CrossRef]

Gallot, G.

J.-B. Masson, A. Podzorov, and G. Gallot, "Anomalies in the disappearance of the extraordinary electromagnetic transmission in subwavelength hole arrays," Opt. Exp. 16(7), 4719-4730 (2008).
[CrossRef]

J.-B. Masson and G. Gallot, "Coupling between surface plasmons in subwavelength hole arrays," Phys. Rev. B 73, 121,401(R) (2006).
[CrossRef]

Garcia-Vidal, F. J.

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[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(6), 1114-1117 (2001).
[CrossRef]

Gay, G.

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

Genet, C.

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

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Comm. 225(4-6), 331-336 (2003).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

Gong, M.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

Gray, S. K.

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. Exp. 13(8), 3150-3165 (2005).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, S. R. Keiding, M. van Exter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7(10), 2006-2015 (1990).
[CrossRef]

D. Qu and D. Grischkowsky, "Observation of a New Type of THz Resonance of Surface Plasmons Propagating on Metal-Film Hole Arrays," Phys. Rev. Lett. 93(19), 196,804 (2004).

Han, J.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, "Squeezing MillimeterWaves into Microns," Phys. Rev. Lett. 92(14), 143,904 (2004).

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of Surface Plasmon Generation at Nanoslit Apertures," Phys. Rev. Lett. 95, 263,902 (2005).
[CrossRef]

Keiding, S. R.

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, 263,902 (2005).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, "Squeezing MillimeterWaves into Microns," Phys. Rev. Lett. 92(14), 143,904 (2004).

Lee, K. G.

K. G. Lee and Q. H. Park, "Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits," Phys. Rev. Lett. 95, 103,902 (2005). Now with Institut Pasteur, CNRS URA 2171, Unit In Silico Genetics, 75724 Paris Cedex 15, France
[CrossRef]

Lezec, H. J.

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

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(6), 1114-1117 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

Liu, H.

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

Lu, X.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

Mani, H. S.

S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, "Understanding the Fano Resonance : through Toy Models," Am. J. Phys. 72, 1501 (2004).
[CrossRef]

Martin-Moreno, L.

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[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(6), 1114-1117 (2001).
[CrossRef]

Masson, J.-B.

J.-B. Masson, A. Podzorov, and G. Gallot, "Anomalies in the disappearance of the extraordinary electromagnetic transmission in subwavelength hole arrays," Opt. Exp. 16(7), 4719-4730 (2008).
[CrossRef]

J.-B. Masson and G. Gallot, "Coupling between surface plasmons in subwavelength hole arrays," Phys. Rev. B 73, 121,401(R) (2006).
[CrossRef]

Nahata, A.

A. Agrawal, Z. V. Vardeny, and A. Nahata, "Engineering the dielectric function of plasmonic lattices," Opt. Exp. 16(13), 9601-9613 (2008).
[CrossRef]

O’Dwyer, C.

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

Ozbay, E.

E. Ozbay, "Plasmonic: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Park, Q. H.

K. G. Lee and Q. H. Park, "Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits," Phys. Rev. Lett. 95, 103,902 (2005). Now with Institut Pasteur, CNRS URA 2171, Unit In Silico Genetics, 75724 Paris Cedex 15, France
[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(6), 1114-1117 (2001).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[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(6), 1114-1117 (2001).
[CrossRef]

Podzorov, A.

J.-B. Masson, A. Podzorov, and G. Gallot, "Anomalies in the disappearance of the extraordinary electromagnetic transmission in subwavelength hole arrays," Opt. Exp. 16(7), 4719-4730 (2008).
[CrossRef]

Qu, D.

D. Qu and D. Grischkowsky, "Observation of a New Type of THz Resonance of Surface Plasmons Propagating on Metal-Film Hole Arrays," Phys. Rev. Lett. 93(19), 196,804 (2004).

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of Surface Plasmon Generation at Nanoslit Apertures," Phys. Rev. Lett. 95, 263,902 (2005).
[CrossRef]

Ryu, C.-M.

C.-M. Ryu and S. Y. Cho, "Phase evolution of the transmission coefficient in an Aharonov-Bohm ring with Fano resonance," Phys. Rev. B 58(7), 3572 (1998).
[CrossRef]

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, "Squeezing MillimeterWaves into Microns," Phys. Rev. Lett. 92(14), 143,904 (2004).

Sarrazin, M.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085,415 (2003).
[CrossRef]

Schatz, G. C.

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. Exp. 13(8), 3150-3165 (2005).
[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(6), 1114-1117 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

Urbach, H. P.

J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Exp. 14(7), 2552-2572 (2006).
[CrossRef]

van Exter, M.

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. Comm. 225(4-6), 331-336 (2003).
[CrossRef]

Vardeny, Z. V.

A. Agrawal, Z. V. Vardeny, and A. Nahata, "Engineering the dielectric function of plasmonic lattices," Opt. Exp. 16(13), 9601-9613 (2008).
[CrossRef]

Vigneron, J.-P.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085,415 (2003).
[CrossRef]

Vigoureux, J.-M.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085,415 (2003).
[CrossRef]

Weiner, J.

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

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. Comm. 225(4-6), 331-336 (2003).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

Xu, J.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

Zhang, W.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

Zhang, X.-C.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

ACM Trans. Math Soft.

D. G. Duffy, "On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications," ACM Trans. Math Soft. 19(3), 333-359 (1993).
[CrossRef]

Am. J. Phys.

S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, "Understanding the Fano Resonance : through Toy Models," Am. J. Phys. 72, 1501 (2004).
[CrossRef]

Appl. Phys. Lett.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, "Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies," Appl. Phys. Lett. 91, 071,122 (2007).
[CrossRef]

IEEE Trans. Microwave Theo. Tech.

C.-C. Chen, "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theo. Tech. 21(1), 1-6 (1973).
[CrossRef]

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Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-668 (1998).
[CrossRef]

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

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

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

Nature Physics

G. Gay, O. Alloschery, B. V. 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 Physics 2, 262-267 (2006).
[CrossRef]

Opt. Comm.

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. Comm. 225(4-6), 331-336 (2003).
[CrossRef]

Opt. Exp.

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. Exp. 13(8), 3150-3165 (2005).
[CrossRef]

J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Exp. 14(7), 2552-2572 (2006).
[CrossRef]

A. Agrawal, Z. V. Vardeny, and A. Nahata, "Engineering the dielectric function of plasmonic lattices," Opt. Exp. 16(13), 9601-9613 (2008).
[CrossRef]

J.-B. Masson, A. Podzorov, and G. Gallot, "Anomalies in the disappearance of the extraordinary electromagnetic transmission in subwavelength hole arrays," Opt. Exp. 16(7), 4719-4730 (2008).
[CrossRef]

Phys. Rev.

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124(6), 1866-1875 (1961).
[CrossRef]

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[CrossRef]

Phys. Rev. B

C.-M. Ryu and S. Y. Cho, "Phase evolution of the transmission coefficient in an Aharonov-Bohm ring with Fano resonance," Phys. Rev. B 58(7), 3572 (1998).
[CrossRef]

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085,415 (2003).
[CrossRef]

Phys. Rev. Lett.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, "Direct Observation of a Transition of a Surface Plasmon Resonance from a Photonic Crystal Effect," Phys. Rev. Lett. 98, 183,901 (2007).
[CrossRef]

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(6), 1114-1117 (2001).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of Surface Plasmon Generation at Nanoslit Apertures," Phys. Rev. Lett. 95, 263,902 (2005).
[CrossRef]

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of Extraordinary Transmission of Light through Quasiperiodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 99, 203,905 (2007).
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J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

E. Ozbay, "Plasmonic: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Other

J.-B. Masson and G. Gallot, "Coupling between surface plasmons in subwavelength hole arrays," Phys. Rev. B 73, 121,401(R) (2006).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, "Squeezing MillimeterWaves into Microns," Phys. Rev. Lett. 92(14), 143,904 (2004).

K. G. Lee and Q. H. Park, "Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits," Phys. Rev. Lett. 95, 103,902 (2005). Now with Institut Pasteur, CNRS URA 2171, Unit In Silico Genetics, 75724 Paris Cedex 15, France
[CrossRef]

D. Qu and D. Grischkowsky, "Observation of a New Type of THz Resonance of Surface Plasmons Propagating on Metal-Film Hole Arrays," Phys. Rev. Lett. 93(19), 196,804 (2004).

K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical methods for physics and engineering (Cambridge University Press, 2006).

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B. D. Fried and S. D. Conte, The plasma dispersion function. The Hilbert transform of the Gaussian (Academic Press, New York, 1961).

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Figures (8)

Fig. 1.
Fig. 1.

Fano model of a subwavelength hole array and the coupling V between a continuum of states {|E〉} and a resonant level Eφ . [i〉 and |ψE 〉 are the initial and final states, respectively.

Fig. 2.
Fig. 2.

Normalized transmission spectra of subwavelength hole arrays (L=600µm), for round holes of diameter 270µm (A) and 350µm (B), and for square holes of effective hole diameter (see text for definition) of 233µm (C) and 273µm (D). The black dots are the experimental data and the red solid lines come from the extended Fano model using eq. 6 and 15, and the parameters A and Δ are found in figures 4 and 5. The arrows show Bloch model frequencies as vi,j0=cLi2+j2 where i and j are integers [1].

Fig. 3.
Fig. 3.

Coupling Hamiltonian matrix element vE (E) calculated from experimental data (dots) and Gaussian fit (solid line), for round (hole diameter: 210 µm, black) and square (effective hole diameter 113 µm, green and 194µm, red) apertures. The Laguerre decomposition used is truncated at fifth order (k=5, n=10, see Appendix A).

Fig. 4.
Fig. 4.

Evolution of the amplitude A of the Gaussian coupling (see Eq. 10) versus effective hole diameter for round (black), pentagon (red), square (green) and triangle (blue) apertures. The inset shows the evolution of the normalized parameter AD for all aperture shapes. Solid lines are fits from equation 12.

Fig. 5.
Fig. 5.

Evolution of the inverse of width of the Gaussian coupling 1/Δ (see Eq. 10) versus effective hole diameter for round (black), pentagon (red), square (green) and triangle (blue) apertures. Solid lines are linear fits.

Fig. 6.
Fig. 6.

Evolution of the amplitude of the coupling A(s,0) and slope α(s) of the inverse of width of the coupling 1/Δ versus aperture rugosity Δr. Solid lines are linear fits. The 4 markers correspond to the 4 different hole shapes.

Fig. 7.
Fig. 7.

Evolution of the frequency ν 1,0 of the first resonance versus effective hole diameter for round holes (black round dots) and square holes (red square dots). Black and red solid lines are the maximum resonance from the extended Fano model for round and square holes, respectively.

Fig. 8.
Fig. 8.

Fano profiles obtained from the extended Fano model (Eq. 6). (A) Δ=3 and A varies from 0.1 to 0.5. (B) the ratio Δ/A remains constant and equal to 5, while A varies from 0.15 to 3.

Equations (24)

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

φH0φ=Eφ
EH0E=E δ (EE) ,
H=H0+V,
EVφ=v (E)
EVE=φVφ=0.
T(E)=ψETi2ETi2=q(E)+ε(E)21+ε2(E),
ε(E)=EEφΓ(E)πv2(E),
q(E)=φTiπv*(E)ψETi.
Γ(E)=πHilb [v(E)2]=P P v(E)2EE d E ,
v(E)=2πAΔeE2Δ2.
A(s,D)=A(s,0)×AD(D),
AD(D)=0.75105(D413),
Δr2=n2π02πn[r(θ)rˉ]2dθwithrˉ=12π02πr(θ)dθ,
1Δ(s,D)=α(s)[DD(s)].
Γ=4A2Δ2 exp [2(EΔ)2] erfi (2EΔ) ,
ϕk(E)=eE2Lk(E)=eE2Σl=0kblEl,
v(E)=Σk=0akφk(E).
Γ(E)=PP0v(u)2Eudu=P P 0 Σk=0akϕk(u)2Eu du
=Σn=0cn0eEunEu du ,
H=HE+Hφ+V,
v(E)=EVφ.
v(E)=EVφ=V0E|φ ,
v (E)V0φ(ρ)eikρdρ.
φ=φ0eρ2Δρ2.

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