Extraordinary optical reflection from sub-wavelength cylinder arrays

Raquel Gomez-Medina; Marine Laroche; Juan José Sáenz

doi:10.1364/OE.14.003730

Optics Express
Vol. 14,
Issue 9,
pp. 3730-3737
(2006)
•https://doi.org/10.1364/OE.14.003730

Extraordinary optical reflection from sub-wavelength cylinder arrays

Raquel Gomez-Medina, Marine Laroche, and Juan José Sáenz

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Raquel Gomez-Medina, Marine Laroche, and Juan José Sáenz, "Extraordinary optical reflection from sub-wavelength cylinder arrays," Opt. Express 14, 3730-3737 (2006)

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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.

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References

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Year
Author
Publication

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).
R.W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 15, 928 (1935).
[Crossref]
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]
Lord Rayleigh, “On the dynamical theory of gratings,” Proc. Roy. Soc. (London) A79, 399 (1907).
A. Hessel and A.A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275 (1965)
[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).
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]
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]
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]
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 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]
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 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, J.J. Sáenz, I Campillo, and J.S. Dolado, “Site and Lattice Resonances in Metallic Hole Arrays,” Opt. Express 14, 7 (2006).
[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]
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]
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]
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]
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]
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]
V. Twersky, “Multiple scattering of waves and optical phenomena,” J. Opt. Soc. Am 52, 145 (1962).
[Crossref] [PubMed]
K. Ohtaka and H. Numata, “Multiple scattering effects in photon diffraction for an array of cylindrical dielectric,” Phys. Lett. 73A, 411 (1979).
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]
P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.
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]
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).
U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961).
[Crossref]
J.U. Nöckel and A.D. Stone, “Resonance line shapes in quasi-one-dimensional scattering,” Phys. Rev. B 50, 17415 (1994).
[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]
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]
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)

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]

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)

A. Hessel and A.A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275 (1965)
[Crossref]

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)

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]

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.

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

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]

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.

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.

Dintinger, J.

Dolado, J.S.

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]

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.

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.

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.

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

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]

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 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]

García-Martín, A.

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]

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]

Hessel, A.

A. Hessel and A.A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275 (1965)
[Crossref]

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.

Klein Koerkamp, K. J.

Kuipers, L.

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.

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.

Lezec, H.

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]

Lezec, H. J.

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]

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.

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.

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.

A. Hessel and A.A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275 (1965)
[Crossref]

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.

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]

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.

Saénz, J.J.

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 subwave-lenght 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]

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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.

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Fig. 2. (s-polarization) (a) Plot of ℜ{G_b } 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.

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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.

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Equations (28)

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k_{0} = k \sin θ u_{x} + k \cos θ u_{y} \equiv 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} \approx π a^{2} (ε - 1) {[1 - i \frac{π}{4} {(ka)}^{2} (ε - 1)]}^{- 1},

E^{scatt} (r) = (α_{zz} E_{in} (r_{0})) k^{2} G (r)

G (r) \equiv \sum_{n = - \infty}^{+ \infty} e^{i Q_{0} x_{n}} G_{0} (r, r_{n}) = \frac{1}{D} \sum_{m = - \infty}^{\infty} e^{i (Q_{0} - K_{m}) x} (\frac{i}{2 q_{m}} e^{i q_{m} ∣ y ∣})

E_{in} (r_{0}) = E^{0} + α_{zz} k^{2} \sum_{m \neq 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 {\frac{1}{2 D q_{0}} - \frac{1}{4}} + \frac{1}{2 D} \sum_{m = 1}^{\infty} (\frac{i}{q_{m}} + \frac{i}{q_{- m}} - \frac{2}{K_{m}}) + \frac{1}{2 π} (\ln {\frac{kD}{4 π}} + γ_{E}) .

E^{scatt} (r) = {\hat{α}}_{zz} E^{0} k^{2} G (r)

k^{2} {\hat{α}}_{zz} = {(\frac{1}{k^{2} α_{zz}} - G_{b})}^{- 1} .

ψ (r) = ψ^{0} e^{i Q_{0} x} e^{i q_{0} y} + ψ^{0} \sum_{m}^{Prop} i \frac{\hat{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 \frac{ℑ {\hat{4 πf} (q_{0}, q_{0})}}{2 D q_{0}} + \frac{1}{D^{2}} \sum_{n}^{Prop} (\frac{{∣ \hat{4 πf} (q_{0}, q_{0}) ∣}^{2}}{4 q_{n} q_{0}})

R = \frac{1}{D^{2}} \sum_{n}^{Prop} (\frac{{∣ \hat{4 πf} (- q_{n}, q_{0}) ∣}^{2}}{4 q_{n} q_{0}}) .

R = \frac{ℑ {G (0)}}{2 D q_{0}} {∣ {\hat{α}}_{zz} k^{2} ∣}^{2} .

R = \frac{ℑ G (0)}}{2 D q_{0}} {(ℜ^{2} {\frac{1}{k^{2} α_{zz}} - G_{b}} + ℑ^{2} G (0)})}^{- 1}

R (ω ≲ ω_{m}) \approx R_{max} {(\frac{1}{γ^{2}} {(1 - \sqrt{\frac{ω_{m}^{2} - ω_{m}^{2}}{ω_{m}^{2} - ω^{2}}})}^{2} + 1)}^{- 1}

H_{n}^{scatt} (r) = - {α_{yy} \partial_{x} H_{in} (r)}_{r = r_{n}} \partial_{x} G_{0} (r, r_{n}) - {α_{xx} \partial_{y} H_{in} (r)}_{r = r_{n}} \partial_{y} G_{0} (r, r_{n})

α_{xx} = α_{yy} \approx 2 π a^{2} \frac{ε - 1}{ε + 1} {[1 - i \frac{π}{4} {(ka)}^{2} \frac{ε - 1}{ε + 1}]}^{- 1}

α_{xy} = α_{yx} = 0

lim_{r \to r_{0}} \partial_{x} H_{in} (r) = i Q_{0} H^{0} - α_{yy} \partial_{x} H_{in} (r ∣_{r = r_{0}} \partial_{x}^{2} G_{b} = i Q_{0} H^{0} {(1 + α_{yy} \partial_{x}^{2} G_{b})}^{- 1}

\partial_{x}^{2} G_{b} = - \frac{1}{2 D} \sum_{m = 1}^{\infty} {\frac{i {(K_{m} - Q_{0})}^{2}}{q_{m}} + \frac{i {(K_{m} + Q_{0})}^{2}}{q - m} - 2 K_{m} - \frac{k^{2}}{K_{m}}}

- \frac{k^{2}}{4 π} (\ln {\frac{kD}{4 π}} + γ_{E} - \frac{1}{2}) + \frac{1}{6} \frac{π}{D^{2}} + i (\frac{k^{2}}{8} - \frac{Q_{0}^{2}}{2 D q_{0}})

\partial_{y}^{2} G_{b} = - \frac{1}{2 D} \sum_{m = 1}^{\infty} {i q_{m} + i q_{- m} + 2 K_{m} - \frac{k^{2}}{K_{m}}}

- \frac{k^{2}}{4 π} (\ln {\frac{kD}{4 π}} + γ_{E} + \frac{1}{2}) + \frac{1}{6} \frac{π}{D^{2}} + i (\frac{k^{2}}{8} - \frac{q_{0}^{2}}{2 D q_{0}})

H_{n}^{scatt} (r) = - i H^{0} {\hat{α}}_{yy} Q_{0} \partial_{x} G (r) - i H^{0} {\hat{α}}_{xx} q_{0} \partial_{y} G (r)

{\hat{α}}_{xx} = {(1 + α_{xx} \partial_{y}^{2} G_{b})}^{- 1} α_{xx}

{\hat{α}}_{yy} = {(1 + α_{yy} \partial_{x}^{2} G_{b})}^{- 1} α_{yy} .

\hat{4 πf} (q_{m}, q_{0}) = {\hat{α}}_{yy} Q_{0} (Q_{0} - K_{m}) + {\hat{α}}_{xx} q_{0} q_{m} .