Abstract

We investigate the difference between analytic predictions, numerical simulations, and experiments measuring the transmission of energy through subwavelength, periodically arranged holes in a metal film. At normal incidence, theory predicts a sharp transmission minimum when the wavelength is equal to the periodicity, and sharp transmission maxima at one or more nearby wavelengths. In experiments, the sharpest maximum from the theory is not observed, while the others appear less sharp. In numerical simulations using commercial electromagnetic field solvers, we find that the sharpest maximum appears and approaches our predictions as the computational resources are increased. To determine possible origins of the destruction of the sharp maximum, we incorporate additional features in our model. Incorporating imperfect conductivity and imperfect periodicity in our model leaves the sharp maximum intact. Imperfect collimation, on the other hand, incorporated into the model causes the destruction of the sharp maximum as happens in experiments. We provide analytic support through an asymptotic calculation for both the existence of the sharp maximum and the destructive impact of imperfect collimation.

© 2013 Optical Society of America

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  1. F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
    [CrossRef]
  2. 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, 667–669 (1998).
    [CrossRef]
  3. L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
    [CrossRef]
  4. A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
    [CrossRef]
  5. F. Medina, F. Mesa, and R. Marques, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Tech. 56, 3108–3120 (2008).
    [CrossRef]
  6. L. Martín-Moreno, F. J. García-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, 1114–1117 (2001).
    [CrossRef]
  7. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
    [CrossRef]
  8. J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
    [CrossRef]
  9. H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12, 3664–3672 (2004).
    [CrossRef]
  10. Z. Tian, R. Singh, J. Han, J. Gu, Q. Xing, J. Wu, and W. Zhang, “Terahertz superconducting plasmonic hole array,” Opt. Lett. 35, 3586–3588 (2010).
    [CrossRef]
  11. F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2774 (2004).
    [CrossRef]
  12. B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
    [CrossRef]
  13. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
    [CrossRef]
  14. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
    [CrossRef]
  15. C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory Tech. 21, 1–6 (1973).
    [CrossRef]
  16. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
    [CrossRef]
  17. T. Weiss, G. Granet, N. A. Gippius, S. G. Tikhodeev, and H. Giessen, “Matched coordinates and adaptive spatial resolution in the Fourier modal method,” Opt. Express 17, 8051–8061 (2009).
    [CrossRef]
  18. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, “Normal vector method for convergence improvement using the RCWA for crossed gratings,” J. Opt. Soc. Am. A 24, 2758–2767 (1997).
  19. R. Antos, “Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures,” Opt. Express 17, 7269–7274 (2009).
    [CrossRef]
  20. H. Liu and P. Lalanne, “Comprehensive microscopic model of the extraorginary optical transmission,” J. Opt. Soc. Am. A 27, 2542–2550 (2010).
    [CrossRef]
  21. S. Venakides and S. P. Shipman, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
    [CrossRef]
  22. F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
    [CrossRef]
  23. L. Martín-Moreno and F. J. García-Vidal, “Optical transmission through circular hole arrays in optically thick metal films,” Opt. Express 12, 3619–3628 (2004).
    [CrossRef]
  24. E. Snitzer, “Cylindrical dielectric waveguide modes,” J. Opt. Soc. Am. 51, 491–498 (1961).
    [CrossRef]
  25. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 1983), pp. 248–259.
  26. S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008).
    [CrossRef]

2010

2009

2008

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

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[CrossRef]

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

F. Medina, F. Mesa, and R. Marques, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008).
[CrossRef]

2007

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

2006

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[CrossRef]

2005

S. Venakides and S. P. Shipman, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[CrossRef]

2004

F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2774 (2004).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[CrossRef]

L. Martín-Moreno and F. J. García-Vidal, “Optical transmission through circular hole arrays in optically thick metal films,” Opt. Express 12, 3619–3628 (2004).
[CrossRef]

H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12, 3664–3672 (2004).
[CrossRef]

2003

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[CrossRef]

2002

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

2001

L. Martín-Moreno, F. J. García-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, 1114–1117 (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, 667–669 (1998).
[CrossRef]

1997

1973

C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory Tech. 21, 1–6 (1973).
[CrossRef]

1961

Antos, R.

Bravo-Abad, J.

Cao, H.

Cao, Q.

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

Chan, C. T.

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[CrossRef]

Chen, C. C.

C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory Tech. 21, 1–6 (1973).
[CrossRef]

de Léon-Pérez, F.

Degiron, A.

Ebbesen, T. W.

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

L. Martín-Moreno, F. J. García-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, 1114–1117 (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, 667–669 (1998).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

García-Vidal, F. J.

S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008).
[CrossRef]

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[CrossRef]

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

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

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[CrossRef]

L. Martín-Moreno and F. J. García-Vidal, “Optical transmission through circular hole arrays in optically thick metal films,” Opt. Express 12, 3619–3628 (2004).
[CrossRef]

L. Martín-Moreno, F. J. García-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, 1114–1117 (2001).
[CrossRef]

Genet, C.

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, 667–669 (1998).
[CrossRef]

Giessen, H.

Gippius, N. A.

Gómez Rivas, J.

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Gordon, R.

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

Granet, G.

Gu, J.

Han, J.

Hang, Z. H.

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[CrossRef]

Hangyo, M.

F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2774 (2004).
[CrossRef]

Haring Bolivar, P.

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Hou, B.

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[CrossRef]

Hurz, H.

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Kerwien, N.

Kumar, L. K. S.

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

Lalanne, P.

H. Liu and P. Lalanne, “Comprehensive microscopic model of the extraorginary optical transmission,” J. Opt. Soc. Am. A 27, 2542–2550 (2010).
[CrossRef]

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

Lezec, H. J.

L. Martín-Moreno, F. J. García-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, 1114–1117 (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, 667–669 (1998).
[CrossRef]

Li, L.

Liu, H.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 1983), pp. 248–259.

Marques, R.

F. Medina, F. Mesa, and R. Marques, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

Martín-Moreno, L.

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[CrossRef]

S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008).
[CrossRef]

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

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

L. Martín-Moreno and F. J. García-Vidal, “Optical transmission through circular hole arrays in optically thick metal films,” Opt. Express 12, 3619–3628 (2004).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[CrossRef]

L. Martín-Moreno, F. J. García-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, 1114–1117 (2001).
[CrossRef]

Medina, F.

F. Medina, F. Mesa, and R. Marques, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

Mesa, F.

F. Medina, F. Mesa, and R. Marques, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

Miyamaru, F.

F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2774 (2004).
[CrossRef]

Moreno, Esteban

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

Nahata, A.

Nikitin, A. Y.

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

Osten, W.

Pellerin, K. M.

L. Martín-Moreno, F. J. García-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, 1114–1117 (2001).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[CrossRef]

L. Martín-Moreno, F. J. García-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, 1114–1117 (2001).
[CrossRef]

Przybilla, F.

Rafler, S.

Rodrigo, S. G.

S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008).
[CrossRef]

Ruoff, J.

Schotsch, C.

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Schuster, T.

Sheng, P.

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[CrossRef]

Shipman, S. P.

S. Venakides and S. P. Shipman, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[CrossRef]

Singh, R.

Snitzer, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 1983), pp. 248–259.

Thio, T.

L. Martín-Moreno, F. J. García-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, 1114–1117 (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, 667–669 (1998).
[CrossRef]

Tian, Z.

Tikhodeev, S. G.

Venakides, S.

S. Venakides and S. P. Shipman, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[CrossRef]

Weiss, T.

Wen, W.

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[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, 667–669 (1998).
[CrossRef]

Wu, J.

Xing, Q.

Zhang, W.

Zueco, D.

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

Appl. Phys. Lett.

F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2774 (2004).
[CrossRef]

B. Hou, Z. H. Hang, W. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89, 131917 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

F. Medina, F. Mesa, and R. Marques, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microw. Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory Tech. 21, 1–6 (1973).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Condens. Matter

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[CrossRef]

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, 667–669 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008).
[CrossRef]

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Hurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

Phys. Rev. E

S. Venakides and S. P. Shipman, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[CrossRef]

Phys. Rev. Lett.

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

L. Martín-Moreno, F. J. García-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, 1114–1117 (2001).
[CrossRef]

Rev. Mod. Phys.

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

Science

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[CrossRef]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 1983), pp. 248–259.

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Figures (8)

Fig. 1.
Fig. 1.

Plane wave is incident on a metal film of thickness h, with holes of width (in the case of rectangular holes) or radius (in the case of circular holes) a periodically placed with period L. Some of the incident energy is reflected, and some enters the hole, exiting through to the other side.

Fig. 2.
Fig. 2.

Transmission for a normally incident plane wave on a two-dimensionally periodic array of square holes. The period L=Lx=Ly is arbitrary, and the thickness of the metal is h=0.2L. The solid line depicts transmission for square holes with side length a=0.4L, and the dotted line depicts transmission for circular holes of the same area. The number λ is the wavelength λ=2πc/ω. For both square and circular holes, there are several minima present at λ/L=1, at λ/L=(1/2)1/2, etc. Inset: closeup of the double maximum.

Fig. 3.
Fig. 3.

Transmission profile of a square-hole array using different approximation methods. The solid profile uses the same physical parameters as in Fig. 2, except that only one waveguide mode is included in the calculations. This has the effect of shifting the broad maximum to higher wavelengths, as seen in Fig. 3 of [3], but this shift is slight. The dotted profile, in addition, replaces all nonsingular terms from Eq. (1) with their constant values at λ=L, finding that this simplification shifts the broad maximum noticeably more to the right. In the dashed line we instead replace nonsingular terms with their linear expansions about λ=L and find that the locations of both peaks match those calculated using only the single-mode simplification. Between λ=0.95L and λ=1.05L, the dashed and solid curves are practically indistinguishable. Inset: closer view of the peaks.

Fig. 4.
Fig. 4.

Transmission profiles using the same parameters as Fig. 2 for the case of finite conductivity. The solid line is for ϵ2=7·104+i5·107, a typical value of the dielectric constant of copper in the microwave range [26]. The values for Al, Cu, and Ag do not differ enough to produce visible change in the transmission profile. It is also indistinguishable from the profile produced by circular holes in a PEC, as in Fig. 2. (In reality, the value of ϵ2 changes with λ, but again this dependence does not produce any visible difference.) The dashed line is for ϵ2=1.7×104+i2×104, a typical value of the dielectric constant of silver in the infrared range. The primary difference is that the height of the narrow peak has decreased to near 90%. Finally, the dash-dotted line is for ϵ2=40+i12, a typical value of the dielectric constant of aluminum in the visible range. Inset: closeup of the narrow maximum.

Fig. 5.
Fig. 5.

Transmission profile calculated using the same parameters Fig. 4 produced by COMSOL Multiphysics instead of our model. (a) A plane wave is incident from one boundary, and transmitted energy is calculated at the other. Because we assume normal incidence, periodic boundary conditions are enforced on the four sides of the period cell. (b) Two different films are simulated, one that is a perfect electric conductor (PEC), and another that is Al at a frequency of 10 GHz. The transmission profiles of both metals agree. The Rayleigh anomaly and the narrower transmission maxima, however, are not captured exactly. The transmission profile becomes closer to the one simulated by the modal method as the number of mesh points increases.

Fig. 6.
Fig. 6.

Transmission calculated using the same parameters as Fig. 4 produced in Microwave Studio. In both pictures, the solid line is the true transmission profile, and the dashed line is the profile produced by Microwave Studio. (a) Compared to our simulations and the COMSOL results, the transmission is overestimated almost everywhere. (b) Closeup of the double maximum. The narrow maximum is only hinted at, and the broad maximum is more closely captured. As with the COMSOL simulations, in the range tested, increasing the calculation density causes the transmission profile to become closer to the one simulated by the modal method. However, it is too computationally expensive to increase the density further.

Fig. 7.
Fig. 7.

(a) Transmission profile for a plane wave normally incident on a one-dimensionally periodic array of slits in a perfectly conducting film, with distance L between neighboring holes, width 0.4L, and film width 0.2L. (b) Closeup comparison of the previous profile (solid line) near λ/L=1 with the transmission profile produced from a finite array of 30 holes repeated periodically with distance 300L between arrays, and also with a normally incident plane wave (dashed line). The latter curve is indistinguishable from the curve in (a), and it is also indistinguishable from one produced using distance 1500L between arrays with no other change in parameters.

Fig. 8.
Fig. 8.

Transmission profiles for square holes periodically repeated with period L and hole width a=0.4L in a perfectly conducting film of width h=0.2L, illuminated by plane waves at various angles. (a) Incident waves vary from 0.1° to +0.1° in both the x and y directions. (b) Incident waves vary from 0.2° to +0.2°. (c) Incident waves vary from 1° to +1°. The thinner of the two transmission maxima diminishes in height until it is no longer apparent, and the single remaining maximum decreases in magnitude more slowly.

Tables (1)

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Table 1. Transmission Maxima Compared to Approximate Values of Resonances λleft and λright Using Only One Waveguide Mode with Increasing Degrees of Accuracy

Equations (28)

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(GS)XGVX=I,GVX(GS)X=0,
iYk,p=ω/c((2πL)2(ωc)2)1/2=1((λL1)(λL+1))1/2,iYk,s=((2πL)2(ωc)2)1/2ω/c=((λL1)(λL+1))1/2,
(GS)2(GV)2=0.
(Jn(aλ1)aλ1Jn(aλ1)+Kn(aλ2)aλ2Kn(aλ2))(ω2μϵ1Jn(aλ1)aλ1Jn(aλ1)+ω2μϵ2Kn(aλ2)aλ2Kn(aλ2))=n2kα2(1(aλ1)2+1(aλ22))2,
kαk0+C1ϵ21/2+C2ϵ2
(GSGVGVGS)(XX)=(I0).
Gαβ=ikYk(Mα,Wk)(Wk,Mα),
(U,V)=period cellUx*Vx+Uy*Vydxdy.
Sα=iYαeα2+eα2eα2eα2,GαV=2iYαeα2eα2,
Iα=2iYk0(Wk0,Mα),
tk=α(Wk,Mα)Xα,rk=δk,k0+α(Wk,Mα)Xα.
T=kR(Yk)|tk|2/Yk0.
(kxky)=(kx0ky0)+2π(j1/Lxj2/Ly)
Wk,p=(kxky)ei(kxx+kyy)LxLy|kt|,Wk,s=(kykx)ei(kxx+kyy)LxLy|kt|
Sα=iYζeα2+eα2eα2eα2,GαV=2iYζeα2eα2,
Yζ=ϵ1ωckα(Wk,Mα,holeTE)+ϵ2ωckα(Wk,Mα,metalTE)+ckαμω(Wk,Mα,holeTM)+ckαμω(Wk,Mα,metalTM).
Δ=eα(GiYα),Γ=eα1(G+iYα),
T=|2iYαIΔ2Γ2|2I(G)Yk0.
G=iYαeα±eα1eαeα1.
G=Gc+iω/c((ω/c)2(2π/L)2)1/2Gp+i((ω/c)2(2π/L)2)1/2ω/cGs.
GpGs(λL1)(λL+1)+((λL1)(λL+1))1/2(GciYαeα±eα1eαeα1)=0.
GpGsδ2(δ2+2)+δ2(1+δ24+O(δ4))(γ0±+γ1±δ2+O(δ4))=0,
δ=Gp2γ0±,
kαk0+C1ϵ21/2+C2ϵ2.
C1TE=Jn(up)αa(ω2μ)1/2Jn(up)k0(1+n2k02a2α2),
C2TE=Jn(up)αk0Jn(up)(1+n2k02a2α2)[1a2ω2μ(12+n2k02a2α2+Jn(up)n2Jn(up)a2α(2+4k02α))],
C1TM=ϵ1(ω2μ)1/2ak0,
C2TM=ϵ1ω2μ2k0(1a2k021a2β+Jn(up)Jn(up)a(β1/2))+ϵ12a2k0,

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