Abstract

The optical response of sub-wavelength silver lamellar gratings has been theoretically investigated. Two distinct types of resonance have been predicted for incident radiation with E-field perpendicular to the long axis of the wires. The first resonance has been identified as a cavity mode resonance that is associated with transmission enhancement. The second resonance has been identified as an entirely new horizontal plasmon resonance on the incident (and transmission) surfaces of the wires of the grating. Normal surface plasmon modes are investigated on discontinuous gratings, and their relation to those found on continuous gratings is highlighted by focusing on the perturbation effect of the discontinuities. It is shown that the new horizontal plasmon mode is in no way related to the well known diffractively coupled surface plasmon, and is shown to have a particle plasmon-like nature. It is therefore termed a horizontal particle plasmon, and may be either an uncoupled horizontal particle plasmon resonance (a 1-dimensional particle plasmon) or a coupled horizontal particle plasmon resonance (a 2-dimensional particle plasmon) depending on the height of the grating. It is shown that this resonance may result in a reflection efficiency that is very high, even when the grating would be optically thin if it were a homogeneous film, therefore, it behaves as an inverse wire grid polariser as it reflects more TM than TE incident radiation.

©2008 Optical Society of America

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References

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  1. R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London A 18, 269–275 (1902).
  2. U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfelds Waves),” J. Opt. Soc. Am. 31, 213–222 (1941).
    [Crossref]
  3. H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).
  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]
  5. A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (2003).
    [Crossref]
  6. D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express. 13, 7760–7771 (2005).
    [Crossref] [PubMed]
  7. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
    [Crossref]
  8. S. Collin, F. Pardo, R. Teissier, and J. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 13, S154–S160 (2002).
    [Crossref]
  9. H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B 53, 10289–10295 (1996).
    [Crossref]
  10. A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
    [Crossref]
  11. 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]
  12. I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
    [Crossref]
  13. G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
    [Crossref]
  14. 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]
  15. E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539–554 (1969).
    [Crossref]
  16. J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express.  8, 655–663 (2001).
    [Crossref] [PubMed]
  17. 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]
  18. J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
    [Crossref]
  19. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
    [Crossref]
  20. C. Y. Chen and E. Burstein, “Giant Raman Scattering by Molecules at Metal-Island Films,” Phys. Rev. Lett. 45, 1287–1291 (1980).
    [Crossref]
  21. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
    [Crossref]
  22. 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]
  23. D. Nash and J. R. Sambles, “Surface plasmon - polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81–91 (1996).
  24. M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
    [Crossref]
  25. J. A. StrattonElectromagnetic Theory, (John Wiley and Sons Inc, New Jersey, 2007).
  26. R. F. Harrington and D. T. Auckland, “Electromagnetic Transmission Through Narrow Slots in Thick Conducting Screens,” IEEE Trans. Antennas Propag.  AP-28, 616–622 (1980).
    [Crossref]
  27. Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
    [Crossref] [PubMed]

2005 (1)

D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express. 13, 7760–7771 (2005).
[Crossref] [PubMed]

2004 (1)

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 (1)

A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (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]

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

S. Collin, F. Pardo, R. Teissier, and J. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 13, S154–S160 (2002).
[Crossref]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

2001 (5)

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]

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[Crossref]

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[Crossref] [PubMed]

J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express.  8, 655–663 (2001).
[Crossref] [PubMed]

1999 (2)

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[Crossref]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[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).

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B 53, 10289–10295 (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]

1986 (2)

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
[Crossref]

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]

1985 (1)

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[Crossref]

1980 (2)

C. Y. Chen and E. Burstein, “Giant Raman Scattering by Molecules at Metal-Island Films,” Phys. Rev. Lett. 45, 1287–1291 (1980).
[Crossref]

R. F. Harrington and D. T. Auckland, “Electromagnetic Transmission Through Narrow Slots in Thick Conducting Screens,” IEEE Trans. Antennas Propag.  AP-28, 616–622 (1980).
[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 the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London A 18, 269–275 (1902).

Auckland, D. T.

R. F. Harrington and D. T. Auckland, “Electromagnetic Transmission Through Narrow Slots in Thick Conducting Screens,” IEEE Trans. Antennas Propag.  AP-28, 616–622 (1980).
[Crossref]

Aussenegg, F. R.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Barbara, A.

A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (2003).
[Crossref]

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]

Burstein, E.

C. Y. Chen and E. Burstein, “Giant Raman Scattering by Molecules at Metal-Island Films,” Phys. Rev. Lett. 45, 1287–1291 (1980).
[Crossref]

Bustarret, E.

A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (2003).
[Crossref]

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]

Chen, C. Y.

C. Y. Chen and E. Burstein, “Giant Raman Scattering by Molecules at Metal-Island Films,” Phys. Rev. Lett. 45, 1287–1291 (1980).
[Crossref]

Collin, S.

S. Collin, F. Pardo, R. Teissier, and J. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 13, S154–S160 (2002).
[Crossref]

Crouse, D.

D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express. 13, 7760–7771 (2005).
[Crossref] [PubMed]

Ditlbacher, H.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Economou, E. N.

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Fano, U.

Fournier, T.

A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (2003).
[Crossref]

Garcia-Vidal, F. J.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[Crossref]

Gaylord, T. K.

Gotschy, W.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Harrington, R. F.

R. F. Harrington and D. T. Auckland, “Electromagnetic Transmission Through Narrow Slots in Thick Conducting Screens,” IEEE Trans. Antennas Propag.  AP-28, 616–622 (1980).
[Crossref]

Hibbins, A. P.

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]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

Honkanen, M.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[Crossref]

Hooper, I. R.

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

Keshavareddy, P.

D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express. 13, 7760–7771 (2005).
[Crossref] [PubMed]

Kettunen, V.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[Crossref]

Kottmann, J. P.

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[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]

J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express.  8, 655–663 (2001).
[Crossref] [PubMed]

Krenn, J. R.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Kuittinen, M.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[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]

Lamprecht, B.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Lautanen, J.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[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]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

Leitner, A.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Li, L.

Lochbihler, H.

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B 53, 10289–10295 (1996).
[Crossref]

Lockyear, M. J.

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]

López-Rios, T.

A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (2003).
[Crossref]

Martin, O. J. F.

J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express.  8, 655–663 (2001).
[Crossref] [PubMed]

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[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]

Moharam, M. G.

Moskovits, M.

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[Crossref]

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).

Pardo, F.

S. Collin, F. Pardo, R. Teissier, and J. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 13, S154–S160 (2002).
[Crossref]

Pelouard, J.

S. Collin, F. Pardo, R. Teissier, and J. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 13, S154–S160 (2002).
[Crossref]

Pendry, J. B.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[Crossref]

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[Crossref]

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]

Quémerais, P.

A. Barbara, E. Bustarret, T. López-Rios, P. Quémerais, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D 23, 143–154 (2003).
[Crossref]

Raether, H.

H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).

Sambles, 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]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[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]

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

Schider, G.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90, 3825–3830 (2001).
[Crossref]

Schnabel, B.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[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]

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]

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]

Stratton, J. A.

J. A. StrattonElectromagnetic Theory, (John Wiley and Sons Inc, New Jersey, 2007).

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]

Teissier, R.

S. Collin, F. Pardo, R. Teissier, and J. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 13, S154–S160 (2002).
[Crossref]

Turunen, J.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[Crossref]

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Wyrowski, F.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[Crossref]

Appl. Phys. B (2)

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[Crossref]

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, “Inverse metal-stripe polarizers,” Appl. Phys. B 68, 81–85 (1999).
[Crossref]

Appl. Phys. Lett. (1)

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Figures (22)

Fig. 1.
Fig. 1. Schematic representation of the theoretical model.

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Fig. 2.
Fig. 2. Reflection efficiency as a function of grating height, h, for the parameters d=144 nm, f=0.45, λ=550 nm. The inset gives an enlarged view of the region 0 nm≤h≤5 nm. The solid line gives the response to radiation with E-field parallel to the grating vector, while the dashed line gives the response to radiation with E-field perpendicular to the grating vector.

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Fig. 3.
Fig. 3. Reflection efficiency response of the grating as a function of both the incident frequency and grating height. The fixed grating parameters are d=144 nm, f=0.45. The wavelength range is 370 nm≤λ≤850 nm, which equates to a frequency range of 2.22×1015 rad.s -1≤ω≤5.10×1015 rad.s -1. The grating height is in the range 20 nm≤h≤240 nm.

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Fig. 4.
Fig. 4. Reflection efficiency response of the grating as a function of both the incident frequency and grating height. The fixed grating parameters are d=144 nm, f=0.45. The frequency range is 2.22×1015 rad.s -1≤ω≤4.7×1015 rad.s -1, which equates to a wavelength range of 400 nm≤λ≤850 nm. The grating height is in the range 5 nm≤h≤40 nm.

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Fig. 5.
Fig. 5. |Hz | for the two reflection peaks at low grating thickness in Fig. 2, with d=144 nm, f=0.45, λ=550 nm.

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Fig. 6.
Fig. 6. Reflection efficiency as a function of grating height for two high f values. The grating parameters are d=144 nm, f=0.9 and f=0.98, λ=550 nm.

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Fig. 7.
Fig. 7. |Hz | for the two reflection minima of Fig. 6, with d=144 nm, f=0.9, λ=550 nm.

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Fig. 8.
Fig. 8. Reflection efficiency response of the cavity mode resonance as a function of both the incident frequency and slit width, for a constant wire width of 64.8 nm. The grating height is h=91 nm. The frequency is in the same range as in Fig. 4 and the slit width is in the range 10 nm≤slit width≤100 nm.

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Fig. 9.
Fig. 9. Reflection efficiency response of the cavity mode resonance as a function of both the incident frequency and in-plane momentum. The grating parameters are h=91 nm, d=144 nm and f=0.9. The frequency is in the same range as in Fig. 4 and the in-plane momentum is in the range 0≤2kx/kg ≤1.

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Fig. 10.
Fig. 10. Reflection efficiency response of coupled horizontal particle plasmon resonance as a function of both the incident frequency and slit width, for a constant wire width of 64.8 nm. The grating height is h=9.5 nm. The frequency is in the same range as in Fig. 4. The slit width is in the range 0.2 nm≤(1-f)d≤100.2 nm.

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Fig. 11.
Fig. 11. Reflection efficiency response of the coupled horizontal particle plasmon resonance as a function of both the incident frequency and wire width, for a constant slit width of 79.2 nm. The grating height is h=9.5 nm. The frequency is in the same range as in Fig. 4. The wire width is in the range 40 nm≤fd≤184 nm.

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Fig. 12.
Fig. 12. Reflection efficiency response of the coupled horizontal particle plasmon resonance as a function of both the incident frequency and mark-to-space ratio, for a constant grating period of 144nm. The grating height is h=9.5 nm. The frequency is in the same range as in Fig. 4. The mark-to-space ratio is in the range 0.2≤f≤0.8, giving a slit width that is always ≥28.8 nm.

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Fig. 13.
Fig. 13. Reflection efficiency response of the coupled horizontal particle plasmon resonance as a function of both the incident frequency and in-plane momentum. The grating parameters are d=144 nm, f=0.45 and h=9.5 nm. The frequency is in the same range as in Fig. 4 and the in-plane momentum is in the range 0≤2kx/kg ≤1.

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Fig. 14.
Fig. 14. Poles of the S matrix of a silver rectangular grating as a function of both the incident frequency and in-plane momentum for decreasing t. The fixed grating parameters are d=500 nm, fd=480 nm, h=10 nm and the substrate is vacuum. The frequency is in the range 0<ω≤6.28×1015 rad.s -1, giving a wavelength range of 300 nm≤λ<∞, and the in-plane momentum is in the range 0≤2kx/kg ≤1. The dotted line indicates the light and diffracted lines.

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Fig. 15.
Fig. 15. Poles of the S matrix of a silver lamellar grating as a function of both the incident frequency and in-plane momentum for increasing slit widths. The fixed grating parameters are d=500 nm, h=10 nm and the substrate is vacuum. The frequency and in-plane momentum ranges are the same as in Fig. 14.

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Fig. 16.
Fig. 16. Reflection efficiency response of a silver lamellar grating as a function of both the incident frequency and in-plane momentum for the same increasing slit widths as Fig. 15. The fixed grating parameters are d=500 nm, h=10 nm and the substrate is vacuum. The frequency and in-plane momentum ranges are the same as in Fig. 14.

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Fig. 17.
Fig. 17. Poles of the S matrix and reflection efficiency response of a silver lamellar grating as a function of both the incident frequency and in-plane momentum. The fixed grating parameters are d=140 nm, f=0.5, h=10 nm and the substrate is vacuum. The frequency and in-plane momentum ranges are the same as in Fig. 14.

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Fig. 18.
Fig. 18. Poles of the S matrix of a silver lamellar grating as a function of both the incident frequency. The fixed grating parameters are d=140 nm, f=0.5, h=10 nm and the substrate is vacuum. The frequency range is the same as in Fig. 14 and the in-plane momentum is kx =0.

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Fig. 19.
Fig. 19. Poles of the S matrix of a silver rectangular grating as a function of both the incident frequency and in-plane momentum for decreasing t. The fixed grating parameters are d=140 nm, f=0.5, h=10 nm and the substrate is vacuum. The frequency and inplane momentum ranges are the same as in Fig. 14.

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Fig. 20.
Fig. 20. Reflection and transmission efficiency responses of a silver rectangular grating as a function of both the incident frequency and in-plane momentum. The fixed grating parameters are d=140 nm, f=0.5, h=10 nm and the substrate is vacuum. The frequency and in-plane momentum ranges are the same as in Fig. 14, and t=2 nm.

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Fig. 21.
Fig. 21. Experimental data published in Fig. 8(c) of Schider et. al. [13] (points), with theoretical calculations using the present model (line). Experimental parameters are given as d=350 nm, h=25 nm, f=0.43; theoretical parameters are d=356 nm, h=27 nm, f=0.43.

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Fig. 22.
Fig. 22. Reflection efficiency as a function of grating height, for the parameters d=356 nm, f=0.43, λ=601 nm.

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Equations (1)

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k sp = k 0 sin ( θ ) ± q k g

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