Abstract

A multiple scattering analysis of the reflectance of a periodic array of sub-wavelength cylinders is presented. The optical properties and their dependence on wavelength, geometrical parameters and cylinder dielectric constant are analytically derived for both s- and p-polarized waves. In absence of Mie resonances and surface (plasmon) modes, and for positive cylinder polarizabilities, the reflectance presents sharp peaks close to the onset of new diffraction modes (Rayleigh frequencies). At the lowest resonance frequency, and in the absence of absorption, the wave is perfectly reflected even for vanishingly small cylinder radii.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R.W. Wood, "On the remarkable case of uneven distribution of light in a diffraction grating spectrum," Proc. R. Soc. London A 18, 269 (1902).
  2. R.W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 15, 928 (1935).
    [CrossRef]
  3. U. Fano, "The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves)," J. Opt. Soc. Am. 31, 213 (1941).
    [CrossRef]
  4. Lord Rayleigh, "On the dynamical theory of gratings," Proc. Roy. Soc. (London) A79, 399 (1907).
  5. A. Hessel and A.A. Oliner, "A new theory of Wood’s anomalies on optical gratings," Appl. Opt. 4, 1275 (1965)
    [CrossRef]
  6. M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).
  7. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio and P.A. Wolf, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667 (1998).
    [CrossRef]
  8. E. Popov, M. Nevière, S. Enoch and R. Reinisch,"Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100 (2000).
    [CrossRef]
  9. 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 (2001).
    [CrossRef] [PubMed]
  10. M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
    [CrossRef]
  11. F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005).
    [CrossRef]
  12. J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
    [CrossRef] [PubMed]
  13. F. J. García de Abajo, and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005).
    [CrossRef]
  14. F. J. García de Abajo, J.J. Sáenz, I Campillo and J.S. Dolado, "Site and Lattice Resonances in Metallic Hole Arrays," Opt. Express 14, 7 (2006).
    [CrossRef] [PubMed]
  15. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999).
    [CrossRef]
  16. Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601 (2001).
    [CrossRef] [PubMed]
  17. F. Yang and J.R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901 (2002).
    [CrossRef] [PubMed]
  18. F. J. García-Vidal and L. Martín -Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002)
    [CrossRef]
  19. M. M. J. Treacy,"Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  20. H. Lezec and T. Thio,"Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629 (2004).
    [CrossRef] [PubMed]
  21. 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]
  22. 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] [PubMed]
  23. 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]
  24. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
    [CrossRef]
  25. H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).
  26. C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (JohnWiley & Sons, New York, 1998).
    [CrossRef]
  27. V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am 52, 145 (1962).
    [CrossRef] [PubMed]
  28. K. Ohtaka and H. Numata, "Multiple scattering effects in photon diffraction for an array of cylindrical dielectric," Phys. Lett. 73A, 411 (1979).
  29. Ch. Kunze, and R. Lenk, "A single scatter in a quantum wire: compact reformulation of scattering and transmission," Sol. State Comm. 84, 457 (1992).
    [CrossRef]
  30. P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.
  31. R.E. Collin and W.H. Eggimann,"Dynamic Interaction Fields in a Two-Dimensional Lattice," IRE Trans.On Microwave Theory and Techniques, MTT- 9, 110 (1961).
    [CrossRef]
  32. H. Feshbach,"Unified theory of nuclear reactions, I", Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19, 287 (1962).
  33. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866 (1961).
    [CrossRef]
  34. J.U. Nöckel and A.D. Stone, "Resonance line shapes in quasi-one-dimensional scattering," Phys. Rev. B 50, 17415 (1994).
    [CrossRef]
  35. R. G Gómez-Medina, P. San Jose, A. García- Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Sáenz, "Resonant radiation pressure on neutral particles in a waveguide," Phys. Rev. Lett. 86, 4275 (2001).
    [CrossRef] [PubMed]
  36. R. Gómez-Medina, and J.J. Sáenz, "Unusually strong optical interactions between particles in quasi-onedimensional geometries," Phys. Rev. Lett. 93, 243602 (2004).
    [CrossRef]
  37. M. Olshanii, "Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons," Phys. Rev. Lett. 81, 938 (1998).
    [CrossRef]
  38. P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (2003).
    [CrossRef]

2006 (1)

2005 (3)

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

F. J. García de Abajo, and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005).
[CrossRef]

2004 (4)

J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
[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]

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

R. Gómez-Medina, and J.J. Sáenz, "Unusually strong optical interactions between particles in quasi-onedimensional geometries," Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

2003 (3)

P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (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]

M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
[CrossRef]

2002 (4)

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] [PubMed]

F. Yang and J.R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

F. J. García-Vidal and L. Martín -Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002)
[CrossRef]

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

2001 (3)

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 (2001).
[CrossRef] [PubMed]

Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601 (2001).
[CrossRef] [PubMed]

R. G Gómez-Medina, P. San Jose, A. García- Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Sáenz, "Resonant radiation pressure on neutral particles in a waveguide," Phys. Rev. Lett. 86, 4275 (2001).
[CrossRef] [PubMed]

2000 (1)

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

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

1998 (2)

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

M. Olshanii, "Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons," Phys. Rev. Lett. 81, 938 (1998).
[CrossRef]

1994 (1)

J.U. Nöckel and A.D. Stone, "Resonance line shapes in quasi-one-dimensional scattering," Phys. Rev. B 50, 17415 (1994).
[CrossRef]

1992 (1)

Ch. Kunze, and R. Lenk, "A single scatter in a quantum wire: compact reformulation of scattering and transmission," Sol. State Comm. 84, 457 (1992).
[CrossRef]

1979 (1)

K. Ohtaka and H. Numata, "Multiple scattering effects in photon diffraction for an array of cylindrical dielectric," Phys. Lett. 73A, 411 (1979).

1977 (1)

M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).

1965 (1)

1962 (1)

V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am 52, 145 (1962).
[CrossRef] [PubMed]

1961 (2)

R.E. Collin and W.H. Eggimann,"Dynamic Interaction Fields in a Two-Dimensional Lattice," IRE Trans.On Microwave Theory and Techniques, MTT- 9, 110 (1961).
[CrossRef]

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

1941 (1)

1935 (1)

R.W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 15, 928 (1935).
[CrossRef]

1907 (1)

Lord Rayleigh, "On the dynamical theory of gratings," Proc. Roy. Soc. (London) A79, 399 (1907).

1902 (1)

R.W. Wood, "On the remarkable case of uneven distribution of light in a diffraction grating spectrum," Proc. R. Soc. London A 18, 269 (1902).

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]

Campillo, I

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] [PubMed]

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]

Collin, R.E.

R.E. Collin and W.H. Eggimann,"Dynamic Interaction Fields in a Two-Dimensional Lattice," IRE Trans.On Microwave Theory and Techniques, MTT- 9, 110 (1961).
[CrossRef]

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]

Dintinger, J.

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]

Dolado, J.S.

Domokos, P.

P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (2003).
[CrossRef]

Ebbesen, T. W.

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.

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

Eggimann, W.H.

R.E. Collin and W.H. Eggimann,"Dynamic Interaction Fields in a Two-Dimensional Lattice," IRE Trans.On Microwave Theory and Techniques, MTT- 9, 110 (1961).
[CrossRef]

Enoch, S.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

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

Fano, U.

García, F. J.

F. J. García-Vidal and L. Martín -Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (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 (2001).
[CrossRef] [PubMed]

García, F.J.

J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

García de Abajo, F. J.

F. J. García de Abajo, J.J. Sáenz, I Campillo and J.S. Dolado, "Site and Lattice Resonances in Metallic Hole Arrays," Opt. Express 14, 7 (2006).
[CrossRef] [PubMed]

F. J. García de Abajo, and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005).
[CrossRef]

F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

García-Vidal, F. J.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Ghaemi, H.F.

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

Gómez-Medina, R.

F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

R. Gómez-Medina, and J.J. Sáenz, "Unusually strong optical interactions between particles in quasi-onedimensional geometries," Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

Gómez-Medina, R. G

R. G Gómez-Medina, P. San Jose, A. García- Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Sáenz, "Resonant radiation pressure on neutral particles in a waveguide," Phys. Rev. Lett. 86, 4275 (2001).
[CrossRef] [PubMed]

Hessel, A.

Horak, P.

P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (2003).
[CrossRef]

Hugonin, J. 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]

Klein Koerkamp, K. J.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

Kuipers, L.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

Kunze, Ch.

Ch. Kunze, and R. Lenk, "A single scatter in a quantum wire: compact reformulation of scattering and transmission," Sol. State Comm. 84, 457 (1992).
[CrossRef]

Lalanne, 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]

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] [PubMed]

Lenk, R.

Ch. Kunze, and R. Lenk, "A single scatter in a quantum wire: compact reformulation of scattering and transmission," Sol. State Comm. 84, 457 (1992).
[CrossRef]

Lezec, H.

Lezec, H.J.

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

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

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 (2001).
[CrossRef] [PubMed]

Maystre, D.

M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).

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]

Nevière, M.

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

M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).

Nöckel, J.U.

J.U. Nöckel and A.D. Stone, "Resonance line shapes in quasi-one-dimensional scattering," Phys. Rev. B 50, 17415 (1994).
[CrossRef]

Numata, H.

K. Ohtaka and H. Numata, "Multiple scattering effects in photon diffraction for an array of cylindrical dielectric," Phys. Lett. 73A, 411 (1979).

Ohtaka, K.

K. Ohtaka and H. Numata, "Multiple scattering effects in photon diffraction for an array of cylindrical dielectric," Phys. Lett. 73A, 411 (1979).

Oliner, A.A.

Olshanii, M.

M. Olshanii, "Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons," Phys. Rev. Lett. 81, 938 (1998).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Popov, E.

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

Porto, J. A.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, "On the dynamical theory of gratings," Proc. Roy. Soc. (London) A79, 399 (1907).

Reinisch, R.

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

Ritsch, H.

P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (2003).
[CrossRef]

Rodier, J. 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]

Sáenz, J. J.

F. J. García de Abajo, and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005).
[CrossRef]

F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

Sáenz, J.J.

F. J. García de Abajo, J.J. Sáenz, I Campillo and J.S. Dolado, "Site and Lattice Resonances in Metallic Hole Arrays," Opt. Express 14, 7 (2006).
[CrossRef] [PubMed]

R. Gómez-Medina, and J.J. Sáenz, "Unusually strong optical interactions between particles in quasi-onedimensional geometries," Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

Sambles, J.R.

F. Yang and J.R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

San Jose, P.

R. G Gómez-Medina, P. San Jose, A. García- Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Sáenz, "Resonant radiation pressure on neutral particles in a waveguide," Phys. Rev. Lett. 86, 4275 (2001).
[CrossRef] [PubMed]

Sarrazin, M.

M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (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]

Segerink, F. B.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

Stone, A.D.

J.U. Nöckel and A.D. Stone, "Resonance line shapes in quasi-one-dimensional scattering," Phys. Rev. B 50, 17415 (1994).
[CrossRef]

Takakura, Y.

Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601 (2001).
[CrossRef] [PubMed]

Thio, T.

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

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

Treacy, M. M. J.

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

Twersky, V.

V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am 52, 145 (1962).
[CrossRef] [PubMed]

van der Molen, K. L.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

van Hulst, N. F.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

Vigneron, J.-P.

M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
[CrossRef]

Vigoureux, J.-M.

M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
[CrossRef]

Vincent, P.

M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).

Wolf, P.A.

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

Wood, R.W.

R.W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 15, 928 (1935).
[CrossRef]

R.W. Wood, "On the remarkable case of uneven distribution of light in a diffraction grating spectrum," Proc. R. Soc. London A 18, 269 (1902).

Yang, F.

F. Yang and J.R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

Appl. Opt. (1)

Europhys. Lett. (1)

P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (2003).
[CrossRef]

J. Opt. (Paris) (1)

M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).

J. Opt. Soc. Am (1)

V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am 52, 145 (1962).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Nature (1)

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

On Microwave Theory and Techniques, MTT (1)

R.E. Collin and W.H. Eggimann,"Dynamic Interaction Fields in a Two-Dimensional Lattice," IRE Trans.On Microwave Theory and Techniques, MTT- 9, 110 (1961).
[CrossRef]

Opt. Express (2)

Phys. Lett. (1)

K. Ohtaka and H. Numata, "Multiple scattering effects in photon diffraction for an array of cylindrical dielectric," Phys. Lett. 73A, 411 (1979).

Phys. Rev. (2)

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

R.W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 15, 928 (1935).
[CrossRef]

Phys. Rev. B (7)

F. J. García-Vidal and L. Martín -Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002)
[CrossRef]

M. M. J. Treacy,"Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (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 (2000).
[CrossRef]

M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003).
[CrossRef]

J.U. Nöckel and A.D. Stone, "Resonance line shapes in quasi-one-dimensional scattering," Phys. Rev. B 50, 17415 (1994).
[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]

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005).
[CrossRef]

Phys. Rev. E (1)

F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

Phys. Rev. Lett. (10)

F. J. García de Abajo, and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005).
[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 (2001).
[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]

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] [PubMed]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601 (2001).
[CrossRef] [PubMed]

F. Yang and J.R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

R. G Gómez-Medina, P. San Jose, A. García- Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Sáenz, "Resonant radiation pressure on neutral particles in a waveguide," Phys. Rev. Lett. 86, 4275 (2001).
[CrossRef] [PubMed]

R. Gómez-Medina, and J.J. Sáenz, "Unusually strong optical interactions between particles in quasi-onedimensional geometries," Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

M. Olshanii, "Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons," Phys. Rev. Lett. 81, 938 (1998).
[CrossRef]

Proc. R. Soc. London A (1)

R.W. Wood, "On the remarkable case of uneven distribution of light in a diffraction grating spectrum," Proc. R. Soc. London A 18, 269 (1902).

Proc. Roy. Soc. (London) (1)

Lord Rayleigh, "On the dynamical theory of gratings," Proc. Roy. Soc. (London) A79, 399 (1907).

Science (1)

J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

Sol. State Comm. (1)

Ch. Kunze, and R. Lenk, "A single scatter in a quantum wire: compact reformulation of scattering and transmission," Sol. State Comm. 84, 457 (1992).
[CrossRef]

Other (4)

P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.

H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).

C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (JohnWiley & Sons, New York, 1998).
[CrossRef]

H. Feshbach,"Unified theory of nuclear reactions, I", Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19, 287 (1962).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

(s-polarization) Calculated reflectance R in a frequency ω versus in-plane wave number Q 0 = (ω/c)sin(θ). The reflectance along the vertical lines is shown in the inset.

Fig. 2.
Fig. 2.

(s-polarization) (a) Plot of ℜ{Gb } and ℜ{1/(k 2α zz } versus frequency along the constant Q 0 line in Fig. 1 (Q 0 = 0.8π/D)). The crossing points (open circles) correspond to different resonant frequencies ω 0m . (b) Calculated reflectance R versus ω. The inset shows a zoom-out of the ω 01 resonance. Dashed lines corresponds to the approximate expression given in eq. 15 with no fitting parameters.

Fig. 3.
Fig. 3.

(p-polarization) Calculated reflectance R in a frequency ω versus in-plane wave number Q 0 = (ω/c)sin(θ). The reflectance along the vertical lines is shown in the inset.

Equations (28)

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

k 0 = k sin θ u x + k cos θ u y Q 0 u x + q 0 u y ,
E n scatt ( r ) = α zz E in ( r n ) k 2 G 0 r r n
α zz π a 2 ( ε 1 ) [ 1 i π 4 ( ka ) 2 ( ε 1 ) ] 1 ,
E scatt ( r ) = ( α zz E in ( r 0 ) ) k 2 G ( r )
G ( r ) n = + e i Q 0 x n G 0 r r n = 1 D m = e i ( Q 0 K m ) x ( i 2 q m e i q m y )
E in ( r 0 ) = E 0 + α zz k 2 m 0 E in ( r m ) G 0 r 0 r m = E 0 + α zz k 2 E in ( r 0 ) G b
= ( 1 α zz k 2 G b ) 1 E 0
G b = i { 1 2 D q 0 1 4 } + 1 2 D m = 1 ( i q m + i q m 2 K m ) + 1 2 π ( ln { kD 4 π } + γ E ) .
E scatt ( r ) = α ̂ zz E 0 k 2 G ( r )
k 2 α ̂ zz = ( 1 k 2 α zz G b ) 1 .
ψ ( r ) = ψ 0 e i Q 0 x e i q 0 y + ψ 0 m Prop i 4 πf ̂ q m q 0 2 D q m e i ( Q 0 K m ) x e i q m y
T = 1 2 { 4 πf ̂ q 0 q 0 } 2 D q 0 + 1 D 2 n Prop ( 4 πf ̂ q 0 q 0 2 4 q n q 0 )
R = 1 D 2 n Prop ( 4 πf ̂ q n q 0 2 4 q n q 0 ) .
R = { G ( 0 ) } 2 D q 0 α ̂ zz k 2 2 .
R = G ( 0 ) } 2 D q 0 ( 2 { 1 k 2 α zz G b } + 2 G ( 0 ) } ) 1
R ( ω ω m ) R max ( 1 γ 2 ( 1 ω m 2 ω m 2 ω m 2 ω 2 ) 2 + 1 ) 1
H n scatt ( r ) = { α yy x H in ( r ) } r = r n x G 0 r r n { α xx y H in ( r ) } r = r n y G 0 r r n
α xx = α yy 2 π a 2 ε 1 ε + 1 [ 1 i π 4 ( ka ) 2 ε 1 ε + 1 ] 1
α xy = α yx = 0
lim r r 0 x H in ( r ) = i Q 0 H 0 α yy x H in ( r r = r 0 x 2 G b = i Q 0 H 0 ( 1 + α yy x 2 G b ) 1
x 2 G b = 1 2 D m = 1 { i ( K m Q 0 ) 2 q m + i ( K m + Q 0 ) 2 q m 2 K m k 2 K m }
k 2 4 π ( ln { kD 4 π } + γ E 1 2 ) + 1 6 π D 2 + i ( k 2 8 Q 0 2 2 D q 0 )
y 2 G b = 1 2 D m = 1 { i q m + i q m + 2 K m k 2 K m }
k 2 4 π ( ln { kD 4 π } + γ E + 1 2 ) + 1 6 π D 2 + i ( k 2 8 q 0 2 2 D q 0 )
H n scatt ( r ) = i H 0 α ̂ yy Q 0 x G ( r ) i H 0 α ̂ xx q 0 y G ( r )
α ̂ xx = ( 1 + α xx y 2 G b ) 1 α xx
α ̂ yy = ( 1 + α yy x 2 G b ) 1 α yy .
4 πf ̂ q m q 0 = α ̂ yy Q 0 ( Q 0 K m ) + α ̂ xx q 0 q m .

Metrics