Abstract

We present comprehensive investigations of the electromagnetic enhancement by a periodic array of rectangular nanogrooves in a metallic substrate. The impacts of array parameters and of illumination conditions on the enhanced electric-field intensity are explored using fully vectorial methods. The calculations are performed mainly for gold and for the visible and infrared wavelengths. The fully vectorial results are reproduced and explained by a simple Fabry–Perot model. Compared with the case of a single groove, the electric-field enhancement of the groove array is found to be much higher by almost 1 order of magnitude, which is shown to be related to the excitation of surface plasmon polaritons with the aid of the model. Practical considerations of a finite groove number and of a finite groove length are also provided.

© 2011 Optical Society of America

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  5. Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
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    [CrossRef]
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    [CrossRef]
  27. 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]
  28. 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]
  29. H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
    [CrossRef] [PubMed]
  30. L. F. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
  31. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  32. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  33. H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82, 115418(2010).
    [CrossRef]
  34. 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, 453–469 (2009).
    [CrossRef]
  35. J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

2010 (3)

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, 453–469 (2009).
[CrossRef]

Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
[CrossRef]

2008 (6)

D. Lau and S. Furman, “Fabrication of nanoparticle micro-arrays patterned using direct write laser photo reduction,” Appl. Surf. Sci. 255, 2159–2161 (2008).
[CrossRef]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude?” IEEE J. Sel. Top. Quantum Electron. 14, 1565–1576 (2008).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

H. T. Miyazaki and Y. Kurokawa, “Controlled plasmon resonance in closed metal insulator metal nanocavities,” Appl. Phys. Lett. 89, 211126 (2006).
[CrossRef]

2005 (1)

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

2004 (1)

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

2003 (2)

M. Culha, D. Stokes, Leonardo R. Allain, and T. Vo-Dinh, “Surface-enhanced Raman scattering substrate based on a self-assembled monolayer for use in gene diagnostics,” Anal. Chem. 75, 6196–6201 (2003).
[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]

2002 (2)

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]

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]

2001 (1)

2000 (3)

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

H. X. Xu, J. Aizpirua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

M. Kahl and E. Voges, “Analysis of plasmon resonance and surface-enhanced Raman scattering on periodic silver structures,” Phys. Rev. B 61, 14078–14088 (2000).
[CrossRef]

1999 (1)

1998 (1)

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

1997 (1)

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

1996 (2)

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166(1996).
[CrossRef] [PubMed]

L. F. 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)

1991 (1)

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

1988 (1)

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

1986 (1)

A. Wirgin and A. A. Maradudin, “Resonant response of a bare metallic grating to S-polarized light,” Prog. Surf. Sci. 22, 1–99(1986).
[CrossRef]

1985 (2)

E. D. Palik, Handbook of Optical Constants of Solids Part II (Academic, 1985).

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[CrossRef]

1984 (1)

T. López-Ríos and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[CrossRef]

Aizpirua, J.

H. X. Xu, J. Aizpirua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Allain, Leonardo R.

M. Culha, D. Stokes, Leonardo R. Allain, and T. Vo-Dinh, “Surface-enhanced Raman scattering substrate based on a self-assembled monolayer for use in gene diagnostics,” Anal. Chem. 75, 6196–6201 (2003).
[CrossRef] [PubMed]

Apell, P.

H. X. Xu, J. Aizpirua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Arctander, E.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

Astilean, S.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Barbara, A.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Bonod, Nicolas

Brolo, A. G.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

Bustarret, E.

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]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of gratings theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
[CrossRef]

Chavel, P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Culha, M.

M. Culha, D. Stokes, Leonardo R. Allain, and T. Vo-Dinh, “Surface-enhanced Raman scattering substrate based on a self-assembled monolayer for use in gene diagnostics,” Anal. Chem. 75, 6196–6201 (2003).
[CrossRef] [PubMed]

Dechelette, A.

Dieringer, J. A.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Emory, S. R.

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Enoch, S.

Fournier, T.

Furman, S.

D. Lau and S. Furman, “Fabrication of nanoparticle micro-arrays patterned using direct write laser photo reduction,” Appl. Surf. Sci. 255, 2159–2161 (2008).
[CrossRef]

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]

F. J. García-Vidal, J. Sánchez-Dehesa, A. Dechelette, E. Bustarret, T. López-Ríos, T. Fournier, and B. Pannetier, “Localized surface plasmons in lamellar metallic gratings,” J. Lightwave Technol. 17, 2191–2195 (1999).
[CrossRef]

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166(1996).
[CrossRef] [PubMed]

Gaylord, T. K.

Golden, G.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

Gordon, R.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

Grann, E. B.

Guan, P.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

Hsu, P. C.

Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
[CrossRef]

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, 453–469 (2009).
[CrossRef]

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

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]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of gratings theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Jakas, M. M.

Kahl, M.

M. Kahl and E. Voges, “Analysis of plasmon resonance and surface-enhanced Raman scattering on periodic silver structures,” Phys. Rev. B 61, 14078–14088 (2000).
[CrossRef]

Käll, M.

H. X. Xu, J. Aizpirua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Kavanagh, K. L.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude?” IEEE J. Sel. Top. Quantum Electron. 14, 1565–1576 (2008).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Controlled plasmon resonance in closed metal insulator metal nanocavities,” Appl. Phys. Lett. 89, 211126 (2006).
[CrossRef]

Lalanne, P.

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82, 115418(2010).
[CrossRef]

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, 453–469 (2009).
[CrossRef]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of gratings theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Lau, D.

D. Lau and S. Furman, “Fabrication of nanoparticle micro-arrays patterned using direct write laser photo reduction,” Appl. Surf. Sci. 255, 2159–2161 (2008).
[CrossRef]

Le Perchec, J.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Leathem, B.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

Li, L. F.

Lin, Y. W.

Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
[CrossRef]

Liu, H. T.

S. W. Zhang, H. T. Liu, and G. G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27, 1555–1560 (2010).
[CrossRef]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82, 115418(2010).
[CrossRef]

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, 453–469 (2009).
[CrossRef]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Llopis, F.

López-Ríos, T.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

F. J. García-Vidal, J. Sánchez-Dehesa, A. Dechelette, E. Bustarret, T. López-Ríos, T. Fournier, and B. Pannetier, “Localized surface plasmons in lamellar metallic gratings,” J. Lightwave Technol. 17, 2191–2195 (1999).
[CrossRef]

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

T. López-Ríos and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[CrossRef]

Maradudin, A. A.

A. Wirgin and A. A. Maradudin, “Resonant response of a bare metallic grating to S-polarized light,” Prog. Surf. Sci. 22, 1–99(1986).
[CrossRef]

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[CrossRef]

Martín-Moreno, L.

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]

Mendoza, D.

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude?” IEEE J. Sel. Top. Quantum Electron. 14, 1565–1576 (2008).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Controlled plasmon resonance in closed metal insulator metal nanocavities,” Appl. Phys. Lett. 89, 211126 (2006).
[CrossRef]

Moharam, M. G.

Möller, K. D.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Mu, G. G.

Nie, S. M.

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Palamaru, M.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids Part II (Academic, 1985).

Pannetier, B.

F. J. García-Vidal, J. Sánchez-Dehesa, A. Dechelette, E. Bustarret, T. López-Ríos, T. Fournier, and B. Pannetier, “Localized surface plasmons in lamellar metallic gratings,” J. Lightwave Technol. 17, 2191–2195 (1999).
[CrossRef]

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

Pendry, J. B.

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166(1996).
[CrossRef] [PubMed]

Pommet, D. A.

Popov, E.

Qin, D.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

Quémerais, P.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Raether, H.

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

Rodier, J. C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Sánchez-Dehesa, J.

F. J. García-Vidal, J. Sánchez-Dehesa, A. Dechelette, E. Bustarret, T. López-Ríos, T. Fournier, and B. Pannetier, “Localized surface plasmons in lamellar metallic gratings,” J. Lightwave Technol. 17, 2191–2195 (1999).
[CrossRef]

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

Sauvan, C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Shah, N. C.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Silberstein, E.

Stiles, P. L.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Stokes, D.

M. Culha, D. Stokes, Leonardo R. Allain, and T. Vo-Dinh, “Surface-enhanced Raman scattering substrate based on a self-assembled monolayer for use in gene diagnostics,” Anal. Chem. 75, 6196–6201 (2003).
[CrossRef] [PubMed]

Tobías, I.

Tsai, Y. C.

Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
[CrossRef]

Van Duyne, R. P.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

Vo-Dinh, T.

M. Culha, D. Stokes, Leonardo R. Allain, and T. Vo-Dinh, “Surface-enhanced Raman scattering substrate based on a self-assembled monolayer for use in gene diagnostics,” Anal. Chem. 75, 6196–6201 (2003).
[CrossRef] [PubMed]

Voges, E.

M. Kahl and E. Voges, “Analysis of plasmon resonance and surface-enhanced Raman scattering on periodic silver structures,” Phys. Rev. B 61, 14078–14088 (2000).
[CrossRef]

Wallace, P. M.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

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, 453–469 (2009).
[CrossRef]

Wirgin, A.

A. Wirgin and A. A. Maradudin, “Resonant response of a bare metallic grating to S-polarized light,” Prog. Surf. Sci. 22, 1–99(1986).
[CrossRef]

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[CrossRef]

T. López-Ríos and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[CrossRef]

Wu, T. M.

Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
[CrossRef]

Xu, H. X.

H. X. Xu, J. Aizpirua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Yu, Q.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

Zhang, S. W.

Anal. Chem. (1)

M. Culha, D. Stokes, Leonardo R. Allain, and T. Vo-Dinh, “Surface-enhanced Raman scattering substrate based on a self-assembled monolayer for use in gene diagnostics,” Anal. Chem. 75, 6196–6201 (2003).
[CrossRef] [PubMed]

Annu. Rev. Anal. Chem. (1)

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

H. T. Miyazaki and Y. Kurokawa, “Controlled plasmon resonance in closed metal insulator metal nanocavities,” Appl. Phys. Lett. 89, 211126 (2006).
[CrossRef]

Appl. Surf. Sci. (1)

D. Lau and S. Furman, “Fabrication of nanoparticle micro-arrays patterned using direct write laser photo reduction,” Appl. Surf. Sci. 255, 2159–2161 (2008).
[CrossRef]

Electrochem. Commun. (1)

Y. C. Tsai, P. C. Hsu, Y. W. Lin, and T. M. Wu, “Electrochemical deposition of silver nanoparticles in multiwalled carbon nanotube-alumina-coated silica for surface-enhanced Raman scattering active substrates,” Electrochem. Commun. 11, 542–545(2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude?” IEEE J. Sel. Top. Quantum Electron. 14, 1565–1576 (2008).
[CrossRef]

J. Lightwave Technol. (1)

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

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

J. Opt. Soc. Am. A (4)

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

Nano Lett. (2)

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8, 1923–1928 (2008).
[CrossRef] [PubMed]

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4, 2015–2018 (2004).
[CrossRef]

Nature (1)

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (5)

M. Kahl and E. Voges, “Analysis of plasmon resonance and surface-enhanced Raman scattering on periodic silver structures,” Phys. Rev. B 61, 14078–14088 (2000).
[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]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82, 115418(2010).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[CrossRef]

Phys. Rev. E (1)

H. X. Xu, J. Aizpirua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166(1996).
[CrossRef] [PubMed]

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

T. López-Ríos, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Prog. Surf. Sci. (1)

A. Wirgin and A. A. Maradudin, “Resonant response of a bare metallic grating to S-polarized light,” Prog. Surf. Sci. 22, 1–99(1986).
[CrossRef]

Science (1)

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Solid State Commun. (1)

T. López-Ríos and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[CrossRef]

Surf. Sci. Rep. (1)

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, 453–469 (2009).
[CrossRef]

Other (4)

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

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

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

E. D. Palik, Handbook of Optical Constants of Solids Part II (Academic, 1985).

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Figures (8)

Fig. 1
Fig. 1

(a) Groove array in gold substrate illuminated by an obliquely incident TM-polarized plane wave. (b) Definitions of the transmission coefficient t A and of the reflected field ψ r ( x _ , z ) for an incident plane wave, which illuminates a periodic array of infinite-depth slits. (c) Definitions of the reflection and transmission coefficients r A and t A and of the transmitted field ψ t ( x _ , z ) for an incident fundamental mode that is sent from the slit array. (d) Definition of the reflection coefficient r m of the fundamental mode in the slit array etched in a full metal space.

Fig. 2
Fig. 2

(a) EF as a function of the groove depth h for a groove array with Λ = 0.8 λ and w = 0.1 λ . RCWA data and model predictions are shown by the circles and solid curves, respectively. The vertical dashed lines show the resonance depths h res ( m ) given by Eq. (5) with different m ( m = 0 , 1, 2, 3, from left to right). (b), (c) Spatial distribution of the normalized electric-field intensity | E x | 2 / | E inc | 2 for Λ = 0.8 λ , w = 0.1 λ and h = h res ( m = 0 ) = 0.11 λ , which are obtained with RCWA (b) and with the model (c). Here | E inc | 2 denotes the electric-field intensity of the incident plane wave. The superimposed white solid lines show the groove boundaries. All data in (a)–(c) are obtained for a normally incident plane wave ( λ = 1 μm , n m = 0.26 + 6.82 i for gold).

Fig. 3
Fig. 3

(a)  EF res of the groove array achieved for (b)  h = h res ( m = 0 ) , which are plotted as functions of array period Λ for several groove widths ( w = 0.01 λ , 0.05 λ , 0.1 λ , 0.2 λ ). The groove array is under illumination by a normally incident plane wave ( λ = 1 μm ). In (a), the RCWA data and model predictions are shown by discrete markers and continuous curves, respectively. The horizontal beelines show the fully vectorial values of EF res for a single groove with w = 0.01 λ (dotted), 0.05 λ (dashed), 0.1 λ (solid), 0.2 λ (dashed–dotted), which are achieved for h = h res ( m = 0 ) = 0.077 λ , 0.120 λ , 0.123 λ , and 0.112 λ , respectively.

Fig. 4
Fig. 4

(a)–(c)  | t A | , | r A | and N res as functions of period Λ for different groove widths, w = 0.01 λ (dotted), 0.05 λ (dashed), 0.1 λ (solid), and 0.2 λ (dashed–dotted). The data are calculated with RCWA for a normally incident plane wave ( λ = 1 μm ). The horizontal markers show the | t | in (a) and | r a | in (b) for a single groove with w = 0.01 λ (dots), 0.05 λ (pluses), 0.1 λ (circles), 0.2 λ (triangles), for which N res = 1.90 , 1.84, 1.75, 1.59, respectively. η and n eff are independent of Λ and their values are | η | = 2.44 , 1.40, 1.21, 1.11 and n eff = 2.44 + 0.44 i , 1.40 + 0.01 i , 1.21 + 0.008 i , 1.11 + 0.004 i for w = 0.01 λ , 0.05 λ , 0.1 λ , and 0.2 λ , respectively.

Fig. 5
Fig. 5

(a)–(d)  EF res , | t A | , | r A | and N res as functions of array period Λ for a normally incident plane wave. The data are obtained with RCWA for w = 0.05 λ and for various wavelengths, λ = 0.7 (dotted), 1 (dashed), 3 (solid), and 10 μm (dashed–dotted). For the four wavelengths, n m = 0.16 + 3.95 i , 0.26 + 6.82 i , 1.64 + 18.59 i , 12.39 + 55.04 i , | η | = 1.66 , 1.40, 1.16, 1.05, and n eff = 1.66 + 0.03 i , 1.40 + 0.001 i , 1.16 + 0.01 i , 1.05 + 0.01 i , respectively. For (a) and (d), the groove depth is h = h res ( m = 0 ) .

Fig. 6
Fig. 6

(a), (b)  EF res as a function of array period ( Λ = 0.2 λ 2 λ ) and of the x component k x of the wave vector of the obliquely incident plane wave ( k x = 2 π λ 1 sin θ , θ being the incident angle, θ = 0 ° 60 ° for the data). EF res are calculated with RCWA (a) and with the model (b) for h = h res ( m = 0 ) . The superimposed dashed lines show the air light lines at which a diffraction order propagates parallel to the surface. (c), (d)  | t A | and | r A | as functions of array period Λ and of k x obtained with RCWA. All the data are calculated for w = 0.05 λ and λ = 1 μm .

Fig. 7
Fig. 7

(a), (b)  EF ( 0 , 0 ) at the mouth center of the central groove as a function of the groove number N of a finite groove array. (a)  EF ( 0 , 0 ) for Λ = 0.8 λ and for several groove widths, w = 0.01 λ (dots), 0.05 λ (pluses), 0.1 λ (circles), and 0.2 λ (triangles). (b)  EF ( 0 , 0 ) for w = 0.05 λ and for several periods, Λ = 0.4 λ (dots), 0.6 λ (pluses) and 0.8 λ (circles). (c)–(d)  EF ( x , 0 ) at z = 0 as a function of x for N = 31 , Λ = 0.8 λ and w = 0.05 λ . In (a)–(d), the horizontal beelines show the EF res achieved by an infinite array of grooves ( N ). All the data are obtained with a-FMM for a normally incident plane wave ( λ = 1 μm ) and for h = h res ( m = 0 ) .

Fig. 8
Fig. 8

(a), (b)  EF ( 0 , 0 , 0 ) at the center of the groove mouth as a function of groove length L in the y direction. (a)  EF ( 0 , 0 , 0 ) for Λ = 0.8 λ and for several groove widths, w = 0.01 λ (dots), 0.05 λ (pluses), 0.1 λ (circles) and 0.2 λ (triangles). (b)  EF ( 0 , 0 , 0 ) for w = 0.05 λ and for several periods, Λ = 0.4 λ (dots), 0.6 λ (pluses) and 0.8 λ (circles). (c)  EF ( 0 , y , 0 ) along the central line of the groove mouth ( x = z = 0 ) as a function of y, which is calculated for L = 25 λ , Λ = 0.8 λ , and w = 0.05 λ . In (a)–(c), the horizontal beelines show the EF res achieved by an array of infinite-length grooves ( L ). All the data are obtained with a-FMM for a normally incident plane wave ( λ = 1 μm ) and for h = h res ( m = 0 ) .

Equations (8)

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ψ i n ( x , z ) = a ψ 0 ( x ) exp ( i k 0 n eff z ) + b ψ 0 + ( x ) exp [ i k 0 n eff ( z + h ) ] ,
a = t A + r A exp ( i k 0 n eff h ) b , b = r m exp ( i k 0 n eff h ) a .
ψ out ( x , z ) = ψ PW ( x , z ) + ψ r ( x , z ) + b exp ( i k 0 n eff h ) ψ t ( x , z ) ,
EF = | η t A 1 r m exp ( i 2 k 0 n eff h ) 1 r A r m exp ( i 2 k 0 n eff h ) | 2 ,
2 k 0 Re ( n eff ) h + arg ( r A ) + arg ( r m ) = 2 m π ,
EF res = | η t A | 2 N res 2 | 1 | r A | | r m | exp [ 2 k 0 Im ( n eff ) h res ] | 2 ,
Λ λ = m Re ( k SP / k 0 ) ,
Λ λ = ± k x / ( 2 π / Λ ) + m Re ( k SP / k 0 ) ,

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