Abstract

With the perspective to achieve an in-depth understanding of metallic periodic surfaces, we study the surface plasmon polaritons that are locally excited on the ridges (between the indentations) of metallic lamellar gratings composed of slits or grooves. An approximate model and fully vectorial computational results show that the normalized excitation rate is rather small for slit arrays (10 at maximum) and is surprisingly weakly dependent on the metal permittivity. Additionally, the analysis is supported by an intuitive microscopic model that shines new light on the role of surface plasmons in the transmission and resonance anomalies of periodic metallic surfaces.

© 2010 Optical Society of America

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  34. 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).
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    [CrossRef]

2010 (2)

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

B. Wang and P. Lalanne, “How many surface plasmons are locally excited on the ridges of metallic lamellar gratings,” Appl. Phys. Lett. 96, 051115 (2010).
[CrossRef]

2009 (4)

P. Lalanne, J. Hugonin, H. 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. Liu, J. White, S. Fan, and M. Brongersma, “Side-coupled cavity model for surface plasmon-polariton transmission across a groove,” Opt. Express 17, 17837–17848 (2009).
[CrossRef] [PubMed]

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

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal–dielectric interface,” Phys. Rev. B 80, 155407 (2009).
[CrossRef]

2008 (8)

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

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

B. Sturman, E. Podivilov, and M. Gorkunov, “Theory of extraordinary light transmission through arrays of subwavelength slits,” Phys. Rev. B 77, 075106 (2008).
[CrossRef]

A. Vengurlekar, “Optical properties of metallo-dielectric deep trench gratings: role of surface plasmons and Wood–Rayleigh anomaly,” Opt. Lett. 33, 1669–1671 (2008).
[CrossRef] [PubMed]

D. Pacifici, H. Lezec, H. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[CrossRef]

A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J. L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008).
[CrossRef]

A. Drezet, C. Genet, J. Laluet, and T. Ebbesen, “Optical chirality without optical activity: How surface plasmons give a twist to light,” Opt. Express 16, 12559–12570 (2008).
[CrossRef] [PubMed]

2007 (4)

C. Genet and T. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (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, 490–495 (2007).
[CrossRef]

A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B 76, 235430 (2007).
[CrossRef]

2006 (4)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

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

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled Bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608–1615 (2006).
[CrossRef]

2003 (2)

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]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

2002 (2)

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

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

2000 (1)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

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, 2845–2848 (1999).
[CrossRef]

1998 (3)

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

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

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795–4801 (1994).
[CrossRef]

1993 (1)

1991 (1)

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

1985 (1)

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

1979 (1)

J. L. Adams and L. C. Botten, “Double gratings and their applications as Fabry–Perot interferometers,” J. Opt. 10, 109–117 (1979).
[CrossRef]

1965 (1)

Adams, J. L.

J. L. Adams and L. C. Botten, “Double gratings and their applications as Fabry–Perot interferometers,” J. Opt. 10, 109–117 (1979).
[CrossRef]

Atwater, H.

D. Pacifici, H. Lezec, H. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

Barbara, A.

Bardou, N.

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Botten, L. C.

J. L. Adams and L. C. Botten, “Double gratings and their applications as Fabry–Perot interferometers,” J. Opt. 10, 109–117 (1979).
[CrossRef]

Brongersma, M.

Cao, Q.

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

Chavel, P.

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled Bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
[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]

Chen, Y.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Coe, J. V.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

Collin, S.

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J. L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008).
[CrossRef]

Dai, W.

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal–dielectric interface,” Phys. Rev. B 80, 155407 (2009).
[CrossRef]

Depine, R.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Doumuki, T.

Drezet, A.

Ebbesen, T.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Enoch, S.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

Fan, S.

Feng, L.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Fernandez-Dominguez, A. I.

A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B 76, 235430 (2007).
[CrossRef]

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, 490–495 (2007).
[CrossRef]

Garcia-Vidal, F. J.

A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B 76, 235430 (2007).
[CrossRef]

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

Gaylord, T. K.

Genet, C.

Ghaemi, H. F.

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Gorkunov, M.

B. Sturman, E. Podivilov, and M. Gorkunov, “Theory of extraordinary light transmission through arrays of subwavelength slits,” Phys. Rev. B 77, 075106 (2008).
[CrossRef]

Grann, E. B.

Grupp, D. E.

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Haidar, R.

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

Heer, J. M.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

Hessel, A.

Huang, C.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Hugonin, J.

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

Hugonin, J. P.

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[CrossRef]

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled Bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608–1615 (2006).
[CrossRef]

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

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Lalanne, P.

B. Wang and P. Lalanne, “How many surface plasmons are locally excited on the ridges of metallic lamellar gratings,” Appl. Phys. Lett. 96, 051115 (2010).
[CrossRef]

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

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

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608–1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled Bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
[CrossRef]

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

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]

Laluet, J.

Le Perchec, J.

Lezec, H.

D. Pacifici, H. Lezec, H. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Li, J.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Liu, H.

P. Lalanne, J. Hugonin, H. 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. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[CrossRef]

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

Liu, H. T.

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

Liu, J.

Liu, X.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Lochbihler, H.

López-Ríos, T.

Lu, M.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Martin-Moreno, L.

A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B 76, 235430 (2007).
[CrossRef]

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

Matsumoto, S.

Ming, N.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Moharam, M. G.

Nevière, M.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

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, 490–495 (2007).
[CrossRef]

Oliner, A. A.

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Pacifici, D.

D. Pacifici, H. Lezec, H. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

Palik, E. D.

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

Pelouard, J. L.

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J. L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008).
[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]

Podivilov, E.

B. Sturman, E. Podivilov, and M. Gorkunov, “Theory of extraordinary light transmission through arrays of subwavelength slits,” Phys. Rev. B 77, 075106 (2008).
[CrossRef]

Pommet, D. A.

Popov, E.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[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.

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

Quémerais, P.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Reinisch, R.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608–1615 (2006).
[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]

Rodriguez, K. R.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

Rommeluere, S.

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

Sambles, J.

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

Sauvan, C.

A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J. L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008).
[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]

Sobnack, M.

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

Soukoulis, C. M.

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal–dielectric interface,” Phys. Rev. B 80, 155407 (2009).
[CrossRef]

Sturman, B.

B. Sturman, E. Podivilov, and M. Gorkunov, “Theory of extraordinary light transmission through arrays of subwavelength slits,” Phys. Rev. B 77, 075106 (2008).
[CrossRef]

Tamada, H.

Tan, W.

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

Teeters-Kennedy, S.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Tian, H.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

Vassallo, C.

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

Vengurlekar, A.

Vincent, G.

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

Wang, B.

B. Wang and P. Lalanne, “How many surface plasmons are locally excited on the ridges of metallic lamellar gratings,” Appl. Phys. Lett. 96, 051115 (2010).
[CrossRef]

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

Wanstall, N.

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

Weiner, J.

D. Pacifici, H. Lezec, H. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

White, J.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Yamaguchi, T.

Yang, X.

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[CrossRef]

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, 153903 (2009).
[CrossRef] [PubMed]

Zhu, S.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Zhu, Y.

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59, 179–202 (2008).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

B. Wang and P. Lalanne, “How many surface plasmons are locally excited on the ridges of metallic lamellar gratings,” Appl. Phys. Lett. 96, 051115 (2010).
[CrossRef]

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

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. (1)

J. L. Adams and L. C. Botten, “Double gratings and their applications as Fabry–Perot interferometers,” J. Opt. 10, 109–117 (1979).
[CrossRef]

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

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

J. Opt. Soc. Am. A (2)

Nat. Phys. (1)

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

Nature (4)

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

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. F. Ghaemi, T. Thio, D. E. Grupp, and H. J. Lezec, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

C. Genet and T. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (8)

D. Pacifici, H. Lezec, H. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B 76, 235430 (2007).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[CrossRef]

B. Sturman, E. Podivilov, and M. Gorkunov, “Theory of extraordinary light transmission through arrays of subwavelength slits,” Phys. Rev. B 77, 075106 (2008).
[CrossRef]

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795–4801 (1994).
[CrossRef]

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

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal–dielectric interface,” Phys. Rev. B 80, 155407 (2009).
[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]

Phys. Rev. Lett. (6)

S. Collin, G. Vincent, R. Haidar, N. Bardou, S. Rommeluere, and J. L. Pelouard, “Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane,” Phys. Rev. Lett. 104, 027401 (2010).
[CrossRef] [PubMed]

M. Lu, X. Liu, L. Feng, J. Li, C. Huang, Y. Chen, Y. Zhu, S. Zhu, and N. Ming, “Extraordinary acoustic transmission through a 1D grating with very narrow apertures,” Phys. Rev. Lett. 99, 174301 (2007).
[CrossRef] [PubMed]

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

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]

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

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Surf. Sci. Rep. (1)

P. Lalanne, J. Hugonin, H. 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 (2)

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

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

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Figures (8)

Fig. 1
Fig. 1

Local excitation of SPPs on the individual ridges of periodic metallic surfaces. (a) Example of an interface between a homogeneous medium (permittivity ε d ) and a periodic medium composed of an array of semi-infinite slits. r n , t n , r , and t are scattering coefficients used in the analytical model of Section 3. e SP + and e SP represent the normalized excitation rate of SPPs propagating along positive and negative x directions. (b) An example of SPP-excitation rates [ e SP + : lighter (red online) curve, and e SP : darker (blue online) curve] calculated for gold ( ε m = 9.04 + 1.06 i ) , a = 0.7 μ m , w = 100 nm , f = w a = 0.143 , λ = 637 nm and θ = 0 . The black circles show the SPP damping on flat metal surfaces, exp ( 2 Im ( k SP ) x ) .

Fig. 2
Fig. 2

Efficiencies of SPPs locally excited on the ridges of an 11-groove SPP-coupler in a gold substrate illuminated by a normally incident Gaussian beam. The efficiencies are normalized by the power of the Gaussian beam. The optimization is performed for λ = 800 nm ( n m = 0.18 + 5.13 i ) . The coupler is symmetric, and starting from the center ( x = 0 ) , the width w, height h, and central location of the five outer grooves are w = 0.32 , 0.40, 0.42, 0.40, 0.41 μ m ; h = 0.07 , 0.07, 0.07, 0.05, 0.015 μ m ; and x = 0.35 , 1.12, 1.84, 2.63, 3.38 μ m . The width and depth of the central groove are w = 0.37 μ m and h = 0.08 μ m , respectively.

Fig. 3
Fig. 3

Normalized SPP-excitation rate in the ( ω - k ) diagram at visible frequencies. (a) Fully vectorial [Eqs. (2a, 2b)] result showing e SP + + e SP as a function of the parallel wave vector k = k 0 n d sin ( θ ) and the normalized frequency a λ . The results hold for the gold geometry of Fig. 1a and for a = 0.7 μ m . The dimmer (red online) and brighter (blue online) dashed curves represent the Rayleigh anomalies and the folded dispersion relation of SPPs on flat metal surfaces. (b) and (c) are enlarged views of (a) obtained, respectively, with the RCWA and the approximate model [Eqs. (5a, 5b)]. Quantitative agreement is achieved.

Fig. 4
Fig. 4

Normalized SPP-excitation rate spectrum for fixed angles of incidence. (a) θ = 10 ° and (b) θ = 0 ° . Solid (red online), dashed (blue online), and dotted–dashed (black online) curves refer to the data obtained with the RCWA, the approximate model, and the pure SPP model, respectively. Note that e SP + and e SP merge for normal incidence because of the symmetry. Other parameters used for the computation are a = 0.7 μ m and w = 0.143 a . The vertical dashed lines (red online) represent the Raleigh wavelengths, λ R a = 1 ± sin ( θ ) . The vertical dashed lines (blue online) represent the SPP wavelengths, λ SP a = [ ε m ε d ( ε m + ε d ) ] 1 2 ± sin ( θ ) .

Fig. 5
Fig. 5

Influence of metal conductivity on the normalized SPP-excitation rate spectrum. (a) and (b) Spectra are calculated as a function of the wavelength of the incident illumination for various grating periods, so that the front and rear curves correspond to visible and infra red frequencies, respectively. (a) θ = 10 ° and (b) θ = 0 ° . The dashed (red online) lines under the peaks denote the Rayleigh wavelengths. (c) Maxima of the excitation rate at normal incidence. The circles are fully vectorial data obtained with RCWA. The solid (red online) and dashed (blue online) curves, respectively, refer to the predictions of the analytical and pure SPP models. (d) Dependence of | β | 2 , | 1 - τ | 2 on the metal conductivity. The variation of | ε m | 1 is also shown as a reference. The insets show the definition of β, τ, and ρ.

Fig. 6
Fig. 6

Influence of the slit width. (a) Normalized SPP-excitation rate as a function of the wavelength for a = 3.5 μ m and for various slit widths w ( f = w a ) . The results are obtained with the RCWA for normal incidence ( e SP + = e SP = e SP ) . (b) Peak value of e SP . (c) Peak width Δ λ . In (b) and (c), the RCWA data and analytical data are shown with solid curves and circles, respectively.

Fig. 7
Fig. 7

Normalized SPP-excitation rate on the ridges of a grating composed of a periodic array of grooves in gold. (a) RCWA data obtained for groove depths h = 0.3 a and 0.6 a , a = 0.7 μ m , w = 100 nm . (b) Corresponding results obtained with the approximate model.

Fig. 8
Fig. 8

Normalized SPP-excitation rate for periodic groove arrays in gold at normal incidence. (a) and (b): Spectra obtained for h = 0.3 a (a) and h = 0.6 a (b). The RCWA data and analytical results are denoted by solid (red online) and dotted (blue online) curves, respectively. (c) Excitation rate as a function of the wavelength and of the groove depth for a = 0.7 μ m . The circles indicate the location of the groove resonances according to Eq. (10). (d) Excitation rate as a function of the wavelength (horizontal axis) and of the grating period (vertical axis) for h = 0.6 a . As for slits, the peak width narrows and the peak value remains constant as the metal permittivity increases.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

H y ( x , z ) = [ β SP + ( x ) + β SP ( x ) ] H SP ( z ) + Σ σ a σ H y ( σ ) ( x , z ) ,
E z ( x , z ) = [ β SP + ( x ) β SP ( x ) ] E SP ( z ) + Σ σ a σ E z ( σ ) ( x , z ) ,
e SP + ( x ) = | β SP + ( x ) | 2 = ( 4 N SP ) 2 | [ E SP ( z ) H y ( x , z ) + E z ( x , z ) H SP ( z ) ] d z | 2 ,
e SP ( x ) = | β SP ( x ) | 2 = ( 4 N SP ) 2 | [ E SP ( z ) H y ( x , z ) E z ( x , z ) H SP ( z ) ] d z | 2 ,
e SP + ( x ) = Σ n 0 | r n | 2 ( 4 | N SP | ) 2 | [ E SP ( z ) H y ( n ) ( x , z ) + E z ( n ) ( x , z ) H SP ( z ) ] d z | 2 ,
e SP ( x ) = Σ n 0 | r n | 2 ( 4 | N SP | ) 2 | [ E SP ( z ) H y ( n ) ( x , z ) E z ( n ) ( x , z ) H SP ( z ) ] d z | 2 ,
r n = δ n , 0 γ n Z s γ n + Z s + 2 ( Z s n eff ) f g 0 g n γ 0 ( γ 0 + Z s ) ( γ n + Z s ) ( 1 I ) .
e SP + = R 1 Q 1 = | r 1 | 2 | γ SP ( α 1 + k SP ) k SP ( γ 1 k 0 + γ SP ) | 2 ,
e SP = R 1 Q 1 = | r 1 | 2 | γ SP ( α 1 k SP ) k SP ( γ 1 k 0 + γ SP ) | 2 ,
Q ± 1 4 | 1 + [ 2 ϵ m ( λ ± 1 λ ) a ] 1 2 | 2 ,
e SP ( max ) | 4 f n m sinc ( π f ) ( 1 + 2 f n m sinc 2 ( π f ) ) | 2 ,
Δ λ a ( 2 2 ) | Z s | 2 ,
e SP + = R 1 Q 1 = | r 1 + t t 1 r b u 2 1 u 2 r b r | 2 | ( α 1 + k SP ) k d ( γ 1 k 0 + k d ) k SP | 2 ,
e SP = R 1 Q 1 = | r 1 + t t 1 r b u 2 1 u 2 r b r | 2 | ( α 1 k SP ) k d ( γ 1 k 0 + k d ) k SP | 2 ,
t 1 = f g 1 [ Z s + n eff + ( Z s n eff ) r ] γ 1 + Z s ,
t 1 = f g 1 [ Z s + n eff + ( Z s n eff ) r ] γ 1 + Z s ,
2 Re ( n eff ) k 0 h + arg ( r b ) + arg ( r ) 2 Re ( n eff ) k 0 h + arg ( r ) = 0 ( modulo 2 π ) ,

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