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

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  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).
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  8. E. Popov, M. Neviére, S. Enoch, and R. Reinisch,“Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).
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  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).
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  16. Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601 (2001).
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    [CrossRef]
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    [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]
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  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. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “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-one-dimensional 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]
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    [CrossRef]

2006 (1)

2005 (3)

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 subwave-lenght hole arrays,” Phys. Rev. E,  72, 016608, (2005).
[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]

2004 (4)

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]

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]

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

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

2003 (3)

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]

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]

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

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275 (2001).
[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]

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

2000 (1)

E. Popov, M. Neviére, 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. Neviére, D. Maystre, and 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 (2)

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

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).

1961 (2)

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

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]

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]

Bohren, C.F.

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

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]

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]

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

Fano, U.

Feshbach, H.

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).

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

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, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwave-lenght 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]

García-Martín, A.

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

García-Vidal, 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]

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]

García-Vidal, F.J.

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

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 subwave-lenght hole arrays,” Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

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

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “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]

Huffman, D.R.

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

Lester, M.

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

Lezec, H.

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 (2001).
[CrossRef] [PubMed]

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, and F.J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004).
[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]

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. Neviére, D. Maystre, and 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).

Morse, P.M.

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

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]

Neviére, M.

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

M. Neviére, D. Maystre, and 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).

Nieto-Vesperinas, M.

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

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]

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 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and 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]

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. Neviére, 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. Neviére, 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]

Saénz, J.J.

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

Sáenz, J. J.

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwave-lenght 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]

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-one-dimensional 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 José, P.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “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]

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]

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 de Hulst, H.C.

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

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. Neviére, D. Maystre, and 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]

Ann. Phys. (1)

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).

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]

IRE Trans. on Microwave Theory and Techniques (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]

J. Opt. (1)

M. Neviére, D. Maystre, and 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]

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)

E. Popov, M. Neviére, 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]

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]

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 subwave-lenght hole arrays,” Phys. Rev. E,  72, 016608, (2005).
[CrossRef]

Phys. Rev. Lett. (10)

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]

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]

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “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-one-dimensional 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]

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]

F. J. García de Abajo and J. J. Sáenz, “Electromagnetic surface states in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901 (2005).
[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. (1)

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

Science (1)

J. B. Pendry, L. Martín-Moreno, and 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 (3)

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 (John Wiley & Sons, New York, 1998).
[CrossRef]

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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 .

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