Abstract

Under light illumination, metallic gratings present unexpected and fascinating phenomena, which are due to the complex charge patterns generated on the grating surfaces. The moving electrons are due to the launching of surface plasmon polaritons (SPPs), but only in part. We derive analytical expressions quantifying the plasmonic character of the surface charge patterns, i.e. the contribution of SPPs to its formation. The expressions have a general significance, in the sense that they may be applied to a variety of geometries and spectral ranges, irrespective of whether the grating absorbs, transmits, reflects, or how strongly it resonates.

© 2013 OSA

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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, 396–402 (1902).
  2. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
    [CrossRef] [PubMed]
  3. M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
    [CrossRef]
  4. F. Pardo, P. Bouchon, R. Haïdar, and J. L. Pelouard, “Light funneling mechanism explained by magnetoelectric interference,” Phys. Rev. Lett.107(9), 093902 (2011).
    [CrossRef] [PubMed]
  5. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
    [CrossRef] [PubMed]
  6. X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett.105(24), 243901 (2010).
    [CrossRef] [PubMed]
  7. W. Wang, S. M. Wu, R. J. Knize, K. Reinhardt, Y. L. Lu, and S. C. Chen, “Enhanced photon absorption and carrier generation in nanowire solar cells,” Opt. Express20(4), 3733–3743 (2012).
    [CrossRef] [PubMed]
  8. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves),” J. Opt. Soc. Am.31(3), 213–222 (1941).
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    [CrossRef]
  10. P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep.64(10), 453–469 (2009).
    [CrossRef]
  11. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
    [CrossRef]
  12. F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
    [CrossRef] [PubMed]
  13. G. A. Zheng, X. Q. Cui, and C. H. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” Proc. Natl. Acad. Sci. U.S.A.107(20), 9043–9048 (2010).
    [CrossRef] [PubMed]
  14. X. P. Huang and M. L. Brongersma, “Rapid computation of light scattering from aperiodic plasmonic structures,” Phys. Rev. B84(24), 245120 (2011).
    [CrossRef]
  15. T. Tanemura, P. Wahl, S. H. Fan, and D. A. B. Miller, “Modal source radiator model for arbitrary two-dimensional arrays of subwavelength apertures on metal films,” IEEE J. Sel. Top. Quantum Electron.19(3), 4601110 (2013).
    [CrossRef]
  16. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
    [CrossRef] [PubMed]
  17. In this work, we use the values tabulated in E. D. Palik, Handbook of Optical Constants of Solids, Part II (Academic, 1985), for the refractive index nm of gold for λ<10 µm. For λ>10 µm we use a Drude model, nm(λ)2 = ε∞−λp−2/[λ−1(λ−1 + iλγ−1)], with ε∞ = 8.842, λp = 0.164 µm and λγ = 20.689 µm.
  18. X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett.102(15), 153903 (2009).
    [CrossRef] [PubMed]
  19. H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
    [CrossRef]
  20. This is the reason why, in relation with Fig. 1(c), the polarization of the source used to calculate F has not been specified.
  21. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83(14), 2845–2848 (1999).
    [CrossRef]
  22. 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. A12(5), 1068–1076 (1995).
    [CrossRef]
  23. P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45, 1357–1374 (1998). See the free software downloadable at http://www.lp2n.institutoptique.fr/Membres-Services/Responsables-d-equipe/LALANNE-Philippe
  24. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett.88(5), 057403 (2002).
    [CrossRef] [PubMed]
  25. D. Maystre, A. L. Fehrembach, and E. Popov, “Plasmonic antiresonance through subwavelength hole arrays,” J. Opt. Soc. Am. A28(3), 342–355 (2011).
    [CrossRef] [PubMed]
  26. M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B66(19), 195105 (2002).
    [CrossRef]
  27. N. Garcia and M. Nieto-Vesperinas, “Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits,” J. Opt. A, Pure Appl. Opt.9(5), 490–495 (2007).
    [CrossRef]
  28. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

2013 (1)

T. Tanemura, P. Wahl, S. H. Fan, and D. A. B. Miller, “Modal source radiator model for arbitrary two-dimensional arrays of subwavelength apertures on metal films,” IEEE J. Sel. Top. Quantum Electron.19(3), 4601110 (2013).
[CrossRef]

2012 (2)

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

W. Wang, S. M. Wu, R. J. Knize, K. Reinhardt, Y. L. Lu, and S. C. Chen, “Enhanced photon absorption and carrier generation in nanowire solar cells,” Opt. Express20(4), 3733–3743 (2012).
[CrossRef] [PubMed]

2011 (3)

F. Pardo, P. Bouchon, R. Haïdar, and J. L. Pelouard, “Light funneling mechanism explained by magnetoelectric interference,” Phys. Rev. Lett.107(9), 093902 (2011).
[CrossRef] [PubMed]

X. P. Huang and M. L. Brongersma, “Rapid computation of light scattering from aperiodic plasmonic structures,” Phys. Rev. B84(24), 245120 (2011).
[CrossRef]

D. Maystre, A. L. Fehrembach, and E. Popov, “Plasmonic antiresonance through subwavelength hole arrays,” J. Opt. Soc. Am. A28(3), 342–355 (2011).
[CrossRef] [PubMed]

2010 (3)

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

G. A. Zheng, X. Q. Cui, and C. H. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” Proc. Natl. Acad. Sci. U.S.A.107(20), 9043–9048 (2010).
[CrossRef] [PubMed]

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett.105(24), 243901 (2010).
[CrossRef] [PubMed]

2009 (2)

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep.64(10), 453–469 (2009).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett.102(15), 153903 (2009).
[CrossRef] [PubMed]

2008 (1)

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

2007 (2)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, “Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits,” J. Opt. A, Pure Appl. Opt.9(5), 490–495 (2007).
[CrossRef]

2006 (2)

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys.2(8), 551–556 (2006).
[CrossRef]

2005 (1)

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

2002 (2)

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B66(19), 195105 (2002).
[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(5), 057403 (2002).
[CrossRef] [PubMed]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83(14), 2845–2848 (1999).
[CrossRef]

1995 (1)

1976 (1)

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[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, 396–402 (1902).

Alloschery, O.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

Anderton, C. R.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Bouchon, P.

F. Pardo, P. Bouchon, R. Haïdar, and J. L. Pelouard, “Light funneling mechanism explained by magnetoelectric interference,” Phys. Rev. Lett.107(9), 093902 (2011).
[CrossRef] [PubMed]

Brongersma, M. L.

X. P. Huang and M. L. Brongersma, “Rapid computation of light scattering from aperiodic plasmonic structures,” Phys. Rev. B84(24), 245120 (2011).
[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(5), 057403 (2002).
[CrossRef] [PubMed]

Chen, S. C.

Cui, X. Q.

G. A. Zheng, X. Q. Cui, and C. H. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” Proc. Natl. Acad. Sci. U.S.A.107(20), 9043–9048 (2010).
[CrossRef] [PubMed]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Fan, R. H.

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett.105(24), 243901 (2010).
[CrossRef] [PubMed]

Fan, S. H.

T. Tanemura, P. Wahl, S. H. Fan, and D. A. B. Miller, “Modal source radiator model for arbitrary two-dimensional arrays of subwavelength apertures on metal films,” IEEE J. Sel. Top. Quantum Electron.19(3), 4601110 (2013).
[CrossRef]

Fano, U.

Fehrembach, A. L.

Garcia, N.

N. Garcia and M. Nieto-Vesperinas, “Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits,” J. Opt. A, Pure Appl. Opt.9(5), 490–495 (2007).
[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(14), 2845–2848 (1999).
[CrossRef]

Gay, G.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

Gaylord, T. K.

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Grann, E. B.

Gray, S. K.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Haïdar, R.

F. Pardo, P. Bouchon, R. Haïdar, and J. L. Pelouard, “Light funneling mechanism explained by magnetoelectric interference,” Phys. Rev. Lett.107(9), 093902 (2011).
[CrossRef] [PubMed]

Huang, X. P.

X. P. Huang and M. L. Brongersma, “Rapid computation of light scattering from aperiodic plasmonic structures,” Phys. Rev. B84(24), 245120 (2011).
[CrossRef]

Huang, X. R.

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett.105(24), 243901 (2010).
[CrossRef] [PubMed]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep.64(10), 453–469 (2009).
[CrossRef]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys.2(8), 551–556 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

Hutley, M. C.

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[CrossRef]

Knize, R. J.

Lalanne, P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett.102(15), 153903 (2009).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep.64(10), 453–469 (2009).
[CrossRef]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys.2(8), 551–556 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[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(5), 057403 (2002).
[CrossRef] [PubMed]

Lezec, H. J.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

Liu, H. T.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett.102(15), 153903 (2009).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep.64(10), 453–469 (2009).
[CrossRef]

Lu, Y. L.

Maria, J.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Maystre, D.

D. Maystre, A. L. Fehrembach, and E. Popov, “Plasmonic antiresonance through subwavelength hole arrays,” J. Opt. Soc. Am. A28(3), 342–355 (2011).
[CrossRef] [PubMed]

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[CrossRef]

Miller, D. A. B.

T. Tanemura, P. Wahl, S. H. Fan, and D. A. B. Miller, “Modal source radiator model for arbitrary two-dimensional arrays of subwavelength apertures on metal films,” IEEE J. Sel. Top. Quantum Electron.19(3), 4601110 (2013).
[CrossRef]

Moharam, M. G.

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas, “Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits,” J. Opt. A, Pure Appl. Opt.9(5), 490–495 (2007).
[CrossRef]

Nuzzo, R. G.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

O’Dwyer, C.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

Pardo, F.

F. Pardo, P. Bouchon, R. Haïdar, and J. L. Pelouard, “Light funneling mechanism explained by magnetoelectric interference,” Phys. Rev. Lett.107(9), 093902 (2011).
[CrossRef] [PubMed]

Pelouard, J. L.

F. Pardo, P. Bouchon, R. Haïdar, and J. L. Pelouard, “Light funneling mechanism explained by magnetoelectric interference,” Phys. Rev. Lett.107(9), 093902 (2011).
[CrossRef] [PubMed]

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(14), 2845–2848 (1999).
[CrossRef]

Peng, R. W.

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett.105(24), 243901 (2010).
[CrossRef] [PubMed]

Pommet, D. A.

Popov, E.

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(14), 2845–2848 (1999).
[CrossRef]

Reinhardt, K.

Rétif, C.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

Rogers, J. A.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Smiet, C. B.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

Stewart, M. E.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Tanemura, T.

T. Tanemura, P. Wahl, S. H. Fan, and D. A. B. Miller, “Modal source radiator model for arbitrary two-dimensional arrays of subwavelength apertures on metal films,” IEEE J. Sel. Top. Quantum Electron.19(3), 4601110 (2013).
[CrossRef]

Thompson, L. B.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Treacy, M. M. J.

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B66(19), 195105 (2002).
[CrossRef]

van Beijnum, F.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

van Exter, M. P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature492(7429), 411–414 (2012).
[CrossRef] [PubMed]

Viaris de Lesegno, B.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

Wahl, P.

T. Tanemura, P. Wahl, S. H. Fan, and D. A. B. Miller, “Modal source radiator model for arbitrary two-dimensional arrays of subwavelength apertures on metal films,” IEEE J. Sel. Top. Quantum Electron.19(3), 4601110 (2013).
[CrossRef]

Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep.64(10), 453–469 (2009).
[CrossRef]

Wang, W.

Weiner, J.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys.2(4), 262–267 (2006).
[CrossRef]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag.4, 396–402 (1902).

Wu, S. M.

Yang, C. H.

G. A. Zheng, X. Q. Cui, and C. H. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” Proc. Natl. Acad. Sci. U.S.A.107(20), 9043–9048 (2010).
[CrossRef] [PubMed]

Yang, X. Y.

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett.102(15), 153903 (2009).
[CrossRef] [PubMed]

Zheng, G. A.

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Other (4)

In this work, we use the values tabulated in E. D. Palik, Handbook of Optical Constants of Solids, Part II (Academic, 1985), for the refractive index nm of gold for λ<10 µm. For λ>10 µm we use a Drude model, nm(λ)2 = ε∞−λp−2/[λ−1(λ−1 + iλγ−1)], with ε∞ = 8.842, λp = 0.164 µm and λγ = 20.689 µm.

This is the reason why, in relation with Fig. 1(c), the polarization of the source used to calculate F has not been specified.

P. Lalanne and M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization,” J. Mod. Opt. 45, 1357–1374 (1998). See the free software downloadable at http://www.lp2n.institutoptique.fr/Membres-Services/Responsables-d-equipe/LALANNE-Philippe

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Figures (5)

Fig. 1
Fig. 1

(a) Sketch of the one-dimensional grating geometry considered in this work. The actual indentation shape (square grooves in the figure) is unimportant. The grating is illuminated under TM polarization. The point A(x = a/2, z = 0), located just in the middle of the flat surface, will be used to quantify the plasmonic character of the grating. (b) Field scattered by an isolated subwavelength indentation under TM illumination. The total field HTOT(x) on the metal surface (z = 0) is composed of a SPP (HSPP(x) sketched in blue) and a QCW (HQCW(x) sketched in red). (c) Spectral evolution of the dimensionless parameter F used to quantify the SPP-contribution weight to HTOT at a one-wavelength distance from the indentation.

Fig. 2
Fig. 2

Intrinsic behaviour of F + and F for gold gratings in air. (a) F + for normal incidence (θ = 0) and for various grating periods, a = 0.6, 1, 3, 10, 102, 103 µm. The spectral interval changes accordingly from the visible (top) to millimeter waves (bottom). Blue squares show the Rayleigh anomalies at λ = λR = a and red circles show the SPP-phase-matching position at λ = λSPP = aRe(kSPP/k0). (b) F + for λ = λSPP (red-solid curve) and λ = λR (blue-dashed curve) as a function of the period (θ = 0). (c) F + (top) and F (bottom) as a function of λ and θ for a = 1µm. The superimposed blue dashed lines and red dash-dot lines correspond to Rayleigh anomaly λ = λR = a(1 ± sin(θ)) and SPP-phase-matching conditions λ = λSPP = a [Re(kSPP/k0) ± sin(θ)], respectively.

Fig. 3
Fig. 3

Test of the general results in Fig. 2 on a specific example: self-suspended gold membranes in air perforated by subwavelength slit arrays for a = 1 µm (a) and a = 10 µm (b). The slit width is 0.1a and the membrane thickness is 0.15a (θ = 0). (a1)-(b1): Zeroth-order transmittance spectra (blue-solid curves) calculated with the RCWA. (a2)-(b2), (a3)-(b3): Decomposition of the scattered magnetic-field |Hy| (left) into SPP (middle) and direct (right) contributions, at the transmission dip obtained for λ = λSPP (a2)-(b2) and at the transmission peak (a3)-(b3). The incident plane wave has a unitary magnetic-field amplitude. In agreement with the values of F + in Figs. 2(a2) and 2(a4) [also shown with the red-dashed curves in (a1) and (b1)], the anti-resonance is almost only due to SPPs, whereas at the resonance peak, the surface charge pattern possesses a less pronounced plasmonic character.

Fig. 4
Fig. 4

Like in Fig. 3 for a grating exhibiting a strong absorption at θ = 0. The grating is composed of an array of dielectric ridges on a gold surface. The ridge width and height are 0.2a, and the ridge refractive index is 1.5 (nd = 1). (a1)-(b1): Zeroth-order reflectance spectra (blue-solid curves). The magnetic-field distributions |Hy| are calculated at the reflectance dip (a2)-(b2) and at λ = 1.1a (a3)-(b3). In agreement with Figs. 2(a2) and 2(a4) [also shown with the red-dashed curves in (a1) and (b1)], the absorption is dominantly achieved by SPPs for a = 1 µm and is rather balanced for a = 10 µm.

Fig. 5
Fig. 5

Forward-propagating SPP on a metal surface. As sketched in blue, the transversal field components [HSPP(z), ESPP(z)] exp(ikSPPx) decay exponentially away from the metal surface (z = 0). The refractive indices of the dielectric and of the metal are denoted by nd and nm.

Equations (13)

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F + = | H SPP + | | H SPP + |+| H DIR + | .
J(x,z)=iω n= Δε(xna,z) w n Ε(xna,z),
J(x,z)= n= ( j x x+ j z z) w n δ(xna,z) .
H y SPP (x,0)=exp(i k SPP x),
H y QCW (x,0)= ( 2π k SPP 2 k 0 2 ε d ε m ε m ε d ) 1 [ I m (x)+ I d (x) ],
I m (x)= ε d exp(iπ/4) ε m ε d 0 + exp( i k 0 x ε m +it ) t ( 1( ε m +it ) k 0 2 / k SPP 2 ) ε m +it dt,
H TOT + ( x,0 ) n= w n [ H y SPP (xna,0)+ H y QCW (xna,0) ] .
[ H y , E z ]  =  [ H SPP ( z ), E SPP ( z )] exp( i k SPP x ) = [1,  k SPP /( kwe 0 )] exp(i k 0 γ SPP z) exp( i k SPP x ),
H y ( x,z ) = [ β SPP + ( x )+ β SPP ( x )] H SPP ( z ) +  Σ σ a σ H y (σ) ( x,z ),    
E z ( x,z ) = [ β SPP + ( x ) β SPP ( x )] E SPP ( z ) +  Σ σ a σ E z (σ) ( x,z ), 
[ E z (σ) ( x,z ) H SPP ( z ) E SPP ( z ) H y (σ) ( x,z )]dz=0,  
β SPP + ( x )= ( 4 N SPP ) 1 [ E SPP ( z ) H y ( x,z )+ E z ( x,z ) H SPP ( z ) ]dz,
β SPP ( x )= ( 4 N SPP ) 1 [ E SPP ( z ) H y ( x,z ) E z ( x,z ) H SPP ( z )]dz,

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