Abstract

The dispersion diagrams of surface plasmon polaritons have been calculated for rectangular gratings, with very narrow wires, of varying depths. For gratings with a moderate height a family of vertical-standing-wave resonances may be excited, which consist of surface plasmons, oscillating on either vertical surface, coupling together through the metal wires. These modes evolve similarly to the manner in which shallow-grating surface-plasmon dispersion curves evolve into cavity modes in the grooves of the structure. However, on further increase in grating height these vertical standing waves evolve into a second resonant feature, which is independent of yet further increases in height. This new mode is shown to be equivalent to the resonances found on infinite multilayer metal/dielectric structures illuminated at normal incidence.

© 2009 Optical Society of America

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  1. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396-400 (1902).
  2. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves),” J. Opt. Soc. Am. 31, 213-222 (1941).
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  4. M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
    [CrossRef]
  5. W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
    [CrossRef]
  6. I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
    [CrossRef]
  7. I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings,” Phys. Rev. B 66, 205408 (2002).
    [CrossRef]
  8. I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
    [CrossRef]
  9. M. Scalora, M. J. Bloemer, and C. M. Bowden, “Laminated photonic band structures with high conductivity and high transparency: Metals under a new light,” Opt. Photonics News 10, 23-27 (1998).
  10. M. R. Gadsdon, J. Parsons, and J. R. Sambles, “Electromagnetic resonances of a multilayer metal-dielectric stack,” J. Opt. Soc. Am. B 26, 734-742 (2009).
    [CrossRef]
  11. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
    [CrossRef]
  12. M. C. Larciprete, C. Sibilia, S. Paolini, and M. Bertolotti, “Accessing the optical limiting properties of metallo-dielectric photonic band gap structures,” J. Appl. Phys. 93, 5013-5017 (2003).
    [CrossRef]
  13. M. Scalora, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, “Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks,” Opt. Express 15, 508-523 (2007).
    [CrossRef] [PubMed]
  14. A. Bichri, J. Lafait, and H. Welsch, “Visible and infrared optical properties of Ag/SiO2 multilayers: radiative virtual modes and coupling effects,” J. Phys.: Condens. Matter 5, 7361-7374 (1993).
    [CrossRef]
  15. A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
    [CrossRef]
  16. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068-1076 (1995).
    [CrossRef]
  17. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024-1035 (1996).
    [CrossRef]
  18. D. Nash and J. R. Sambles, “Surface plasmon -polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81-91 (1996).
  19. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
    [CrossRef]
  20. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
    [CrossRef] [PubMed]
  21. J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
    [CrossRef] [PubMed]
  22. M. R. Gadsdon, I. R. Hooper, and J. R. Sambles, “Optical resonances on sub-wavelength silver lamellar gratings,” Opt. Express 16, 22003-22028 (2008).
    [CrossRef] [PubMed]
  23. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  24. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).
    [CrossRef]
  25. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
    [CrossRef]
  26. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  27. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
    [CrossRef]
  28. A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to 'designer' surface plasmons,” Opt. Express 16, 20441-20447 (2008).
    [CrossRef] [PubMed]
  29. M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009).
    [CrossRef] [PubMed]

2009 (2)

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009).
[CrossRef] [PubMed]

M. R. Gadsdon, J. Parsons, and J. R. Sambles, “Electromagnetic resonances of a multilayer metal-dielectric stack,” J. Opt. Soc. Am. B 26, 734-742 (2009).
[CrossRef]

2008 (2)

2007 (1)

2005 (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

2004 (2)

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

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

2003 (2)

M. C. Larciprete, C. Sibilia, S. Paolini, and M. Bertolotti, “Accessing the optical limiting properties of metallo-dielectric photonic band gap structures,” J. Appl. Phys. 93, 5013-5017 (2003).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
[CrossRef]

2002 (2)

I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings,” Phys. Rev. B 66, 205408 (2002).
[CrossRef]

2001 (2)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

1999 (1)

W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

1998 (2)

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, and C. M. Bowden, “Laminated photonic band structures with high conductivity and high transparency: Metals under a new light,” Opt. Photonics News 10, 23-27 (1998).

1997 (1)

A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
[CrossRef]

1996 (3)

D. Nash and J. R. Sambles, “Surface plasmon -polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81-91 (1996).

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024-1035 (1996).
[CrossRef]

1995 (1)

1993 (1)

A. Bichri, J. Lafait, and H. Welsch, “Visible and infrared optical properties of Ag/SiO2 multilayers: radiative virtual modes and coupling effects,” J. Phys.: Condens. Matter 5, 7361-7374 (1993).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1981 (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1941 (1)

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396-400 (1902).

Abd-Lefdil, M.

A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
[CrossRef]

Akozbek, N.

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Bertolotti, M.

M. C. Larciprete, C. Sibilia, S. Paolini, and M. Bertolotti, “Accessing the optical limiting properties of metallo-dielectric photonic band gap structures,” J. Appl. Phys. 93, 5013-5017 (2003).
[CrossRef]

Bichri, A.

A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
[CrossRef]

A. Bichri, J. Lafait, and H. Welsch, “Visible and infrared optical properties of Ag/SiO2 multilayers: radiative virtual modes and coupling effects,” J. Phys.: Condens. Matter 5, 7361-7374 (1993).
[CrossRef]

Bloemer, M. J.

Bowden, C. M.

M. Scalora, M. J. Bloemer, and C. M. Bowden, “Laminated photonic band structures with high conductivity and high transparency: Metals under a new light,” Opt. Photonics News 10, 23-27 (1998).

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Cappeddu, M. G.

Centini, M.

D'Aguanno, G.

de Ceglia, D.

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Fano, U.

Fowler, M.

Gadsdon, M. R.

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

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

Gaylord, T. K.

Grann, E. B.

Haus, J. W.

Hendry, E.

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009).
[CrossRef] [PubMed]

A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to 'designer' surface plasmons,” Opt. Express 16, 20441-20447 (2008).
[CrossRef] [PubMed]

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Hooper, I. R.

M. R. Gadsdon, I. R. Hooper, and J. R. Sambles, “Optical resonances on sub-wavelength silver lamellar gratings,” Opt. Express 16, 22003-22028 (2008).
[CrossRef] [PubMed]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings,” Phys. Rev. B 66, 205408 (2002).
[CrossRef]

Kottmann, J. P.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Lafait, J.

A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
[CrossRef]

A. Bichri, J. Lafait, and H. Welsch, “Visible and infrared optical properties of Ag/SiO2 multilayers: radiative virtual modes and coupling effects,” J. Phys.: Condens. Matter 5, 7361-7374 (1993).
[CrossRef]

Larciprete, M. C.

M. C. Larciprete, C. Sibilia, S. Paolini, and M. Bertolotti, “Accessing the optical limiting properties of metallo-dielectric photonic band gap structures,” J. Appl. Phys. 93, 5013-5017 (2003).
[CrossRef]

Lawrence, C. R.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Li, L.

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009).
[CrossRef] [PubMed]

A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to 'designer' surface plasmons,” Opt. Express 16, 20441-20447 (2008).
[CrossRef] [PubMed]

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Mandatori, A.

Martin, O. J. F.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

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

Mattiucci, N.

Moharam, M. G.

Nash, D.

D. Nash and J. R. Sambles, “Surface plasmon -polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81-91 (1996).

Paolini, S.

M. C. Larciprete, C. Sibilia, S. Paolini, and M. Bertolotti, “Accessing the optical limiting properties of metallo-dielectric photonic band gap structures,” J. Appl. Phys. 93, 5013-5017 (2003).
[CrossRef]

Parsons, J.

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

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

Pommet, D. A.

Preist, T. W.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces (Springer-Verlag, 1988).

Sambles, J. R.

M. R. Gadsdon, J. Parsons, and J. R. Sambles, “Electromagnetic resonances of a multilayer metal-dielectric stack,” J. Opt. Soc. Am. B 26, 734-742 (2009).
[CrossRef]

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009).
[CrossRef] [PubMed]

M. R. Gadsdon, I. R. Hooper, and J. R. Sambles, “Optical resonances on sub-wavelength silver lamellar gratings,” Opt. Express 16, 22003-22028 (2008).
[CrossRef] [PubMed]

A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to 'designer' surface plasmons,” Opt. Express 16, 20441-20447 (2008).
[CrossRef] [PubMed]

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings,” Phys. Rev. B 66, 205408 (2002).
[CrossRef]

W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

D. Nash and J. R. Sambles, “Surface plasmon -polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81-91 (1996).

Sarid, D.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Scalora, M.

M. Scalora, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, “Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks,” Opt. Express 15, 508-523 (2007).
[CrossRef] [PubMed]

M. Scalora, M. J. Bloemer, and C. M. Bowden, “Laminated photonic band structures with high conductivity and high transparency: Metals under a new light,” Opt. Photonics News 10, 23-27 (1998).

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Sibilia, C.

Smith, D. R.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Sobnack, M. B.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Suckling, J. R.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Takakura, Y.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Tan, W. C.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Tan, W.-C.

W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

Wanstall, N. P.

W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Welsch, H.

A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
[CrossRef]

A. Bichri, J. Lafait, and H. Welsch, “Visible and infrared optical properties of Ag/SiO2 multilayers: radiative virtual modes and coupling effects,” J. Phys.: Condens. Matter 5, 7361-7374 (1993).
[CrossRef]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396-400 (1902).

J. Appl. Phys. (1)

M. C. Larciprete, C. Sibilia, S. Paolini, and M. Bertolotti, “Accessing the optical limiting properties of metallo-dielectric photonic band gap structures,” J. Appl. Phys. 93, 5013-5017 (2003).
[CrossRef]

J. Mod. Opt. (1)

D. Nash and J. R. Sambles, “Surface plasmon -polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81-91 (1996).

J. Opt. A, Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

J. Phys.: Condens. Matter (2)

A. Bichri, J. Lafait, and H. Welsch, “Visible and infrared optical properties of Ag/SiO2 multilayers: radiative virtual modes and coupling effects,” J. Phys.: Condens. Matter 5, 7361-7374 (1993).
[CrossRef]

A. Bichri, J. Lafait, H. Welsch, and M. Abd-Lefdil, “Characterization of Berreman modes in metal/dielectric and multilayers,” J. Phys.: Condens. Matter 9, 6523-6532 (1997).
[CrossRef]

Opt. Express (3)

Opt. Photonics News (1)

M. Scalora, M. J. Bloemer, and C. M. Bowden, “Laminated photonic band structures with high conductivity and high transparency: Metals under a new light,” Opt. Photonics News 10, 23-27 (1998).

Philos. Mag. (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396-400 (1902).

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B (5)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

W.-C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings,” Phys. Rev. B 66, 205408 (2002).
[CrossRef]

Phys. Rev. E (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Phys. Rev. Lett. (5)

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009).
[CrossRef] [PubMed]

Science (1)

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

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces (Springer-Verlag, 1988).

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Figures (11)

Fig. 1
Fig. 1

Schematic representation of the theoretical model.

Fig. 2
Fig. 2

Reflection efficiency response of the grating as a function of both the incident frequency and f. The fixed grating parameters are d = 200 nm , h = 350 nm , and θ = 4.89 ° . The wavelength range is 370 nm λ 850 nm , which equates to a frequency range of 2.22 × 10 15 rad s 1 ω 5.1 × 10 15 rad s 1 . f is in the range 0.05 f 0.95 . The dotted lines indicate the location of the subsequent field plots (Figs. 3, 5).

Fig. 3
Fig. 3

H z for the two lowest-frequency reflection minima in Fig. 2 for f = 0.93 . The black line indicates the location of the surface of the grating.

Fig. 4
Fig. 4

Reflection efficiency response of the grating as a function of both the incident frequency and wire width, f d . The fixed grating parameters are ( 1 f ) d = 166 nm , h = 350 nm , and θ = 4.89 ° . The frequency range is the same as in Fig. 2. The wire width is in the range 1 nm f d 50 nm .

Fig. 5
Fig. 5

H z for the two lowest-frequency reflection minima in Fig. 2 for f = 0.17 . Both fields are plotted at a phase of ϕ = π 2 relative to the incident radiation at a phase ϕ = 0 . The black line indicates the location of the surface of the grating.

Fig. 6
Fig. 6

Reflection efficiency response of the grating as a function of both the incident frequency and grating height, h. The fixed grating parameters are ( 1 f ) d = 225 nm , f d = 10 nm , and θ = 4.89 ° . The frequency range is the same as in Fig. 2. The height is in the range 10 nm h 1000 nm .

Fig. 7
Fig. 7

Poles of the scattering matrix of a silver rectangular grating as a function of both the incident frequency and in-plane momentum for increasing h. The fixed grating parameters are d = 172.5 nm , f d = 6.5 nm . The frequency is in the range 0 < ω 6.28 × 10 15 rad s 1 , giving a wavelength range > λ 300 nm , and the in-plane momentum is in the range 0 2 k x k g 1 . The dotted lines indicate the light line and the first-order diffracted line.

Fig. 8
Fig. 8

Poles of the scattering matrix of a silver rectangular grating as a function of both the incident frequency and in-plane momentum for increasing h. The fixed grating parameters are d = 172.5 nm , f d = 6.5 nm . The frequency and in-plane momentum ranges are the same as in Fig. 7.

Fig. 9
Fig. 9

Reflection efficiency response of the multilayer structure, comprising ten silver layers of thickness 1 nm b 50 nm , separated by nine 166 nm air layers. The black squares are the limit solutions to Eqs. (2, 3). The incident and transmission materials are also air, and the structure is illuminated at normal incidence. The frequency range is the same as in Fig. 7.

Fig. 10
Fig. 10

Poles of the scattering matrix of a silver rectangular grating as a function of both the incident frequency and wire width for the two extreme values of 2 k x k g . The fixed grating parameters are ( 1 f ) d = 166 nm and h = 320 nm . The frequency and wire width ranges are the same as in Fig. 9. The black squares are the limit solutions to Eqs.(2, 3).

Fig. 11
Fig. 11

The E ̱ fields for an infinite multilayer structure, comprising 20 nm silver layers separated by 150 nm air layers. The permittivity of the silver layers are approximated by the Drude model, using the parameters defined in the main text, with the imaginary part removed. The fields are plotted using the solutions to Eqs. (2, 3), corresponding to the band edges of the bandpass region. The solid lines are the cos standing waves in the dielectric, the dashed curves are the (a) sinh and (b) cosh waves in the metal, and the dotted curves show where the dielectric standing waves would continue if no metal were present. The bold and narrow curves are π out of phase and the vertical dot-dash lines indicate the effective cavity length.

Equations (3)

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δ M + 1 δ M δ M + 1 < 0.001 .
n 1 tan ( n 1 k a 2 ) = k 2 tanh ( k 2 k b 2 ) .
n 1 tan ( n 1 k a 2 ) = k 2 coth ( k 2 k b 2 ) .

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