Abstract

Commensurate gratings of deep-metallic grooves have highly localized cavity resonances which do not exist for purely periodic gratings. In this paper we present the experimental dispersion diagram of the resonances of a commensurate grating with three sub-wavelength cavities per period. We observe selective light localization within the cavities, transition from a localized to a delocalized mode and modifications of the coupling of modes with the external plane-wave that may lead to the generation of black modes. This unexpected complexity is analyzed via a theoretical study in full agreement with the experiments. These results open a way to the control of wavelength-dependent hot spot predicted in more complex commensurate gratings.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. A. Wirgin, “Resonance scattering of electromagnetic waves from a rectangular groove on a metallic mirror,” Opt. Commun. 7(1), 70 (1973).
    [CrossRef]
  4. A. Wirgin and A. A. Maradudin, “Resonant response of a bare metallic grating to s-polarized light,” Prog. Surf. Sci. 22, 1 (1986)
    [CrossRef]
  5. A. Wirgin, and T. López-Ríos, “Can surface enhanced raman scattering be caused by waveguide resonances,” Opt. Commun. 48, 416 (1984); ibid. “Errata”, Opt. Commun. 49, 455 (1984).
    [CrossRef]
  6. E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
    [CrossRef]
  7. 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]
  8. S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
    [CrossRef]
  9. M. I. Stockman, S. V. Faleev, and D. J. Bergam, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?,” Phys. Rev. Lett. 87, 167401 (2001).
    [CrossRef] [PubMed]
  10. A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
    [CrossRef]
  11. T. A. Leskova, A. A. Maradudin, and J. Munoz-Lopez, “Coherence of light scattered from a randomly rough surface,” Phys. Rev. E 71, 036606 (2005).
    [CrossRef]
  12. M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
    [CrossRef] [PubMed]
  13. E. L. Albuquerque, and M. G. Cottamb, “Theory of elementary excitations in quasiperiodic structures,” Phys. Reports 376, 225 (2003).
    [CrossRef]
  14. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
    [CrossRef] [PubMed]
  15. 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 (2008).
    [CrossRef]
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    [CrossRef]
  18. P. Quémerais, “Model of growth for long-range chemically ordered structures: application to quasicrystals,” J. Phys. I France 4, 1669 (1994).
    [CrossRef]
  19. F. Ducastelle and P. Quémerais, “Chemical self-organization during crystal growth,” Phys. Rev. Lett. 78, 102 (1997).
    [CrossRef]
  20. J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
    [CrossRef] [PubMed]
  21. M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
    [CrossRef]
  22. C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J-L Pelouard, “Angle-resolved transmission measurements through anisotropic 2D plasmonic crystals,” Opt. Lett. 33, 165 (2008).
    [CrossRef] [PubMed]
  23. 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 (1998).
    [CrossRef]
  24. A. Barbara, P. Quémerais, E. Bustarret, T. López-Ríos, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D. 23, 143-154 (2003).
    [CrossRef]
  25. D. Skigin and R. Depine, “Transmission resonances of metallic compound gratings with subwavelength slits,” Phys. Rev. lett. 95, 217402 (2005) and references therein.
    [CrossRef] [PubMed]
  26. E. D. Palik, Handbook of optical constants of solids, Academic Press.
  27. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 033107 (2001).
    [CrossRef]

2009 (1)

M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

2008 (3)

2007 (1)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
[CrossRef] [PubMed]

2005 (2)

D. Skigin and R. Depine, “Transmission resonances of metallic compound gratings with subwavelength slits,” Phys. Rev. lett. 95, 217402 (2005) and references therein.
[CrossRef] [PubMed]

T. A. Leskova, A. A. Maradudin, and J. Munoz-Lopez, “Coherence of light scattered from a randomly rough surface,” Phys. Rev. E 71, 036606 (2005).
[CrossRef]

2003 (2)

E. L. Albuquerque, and M. G. Cottamb, “Theory of elementary excitations in quasiperiodic structures,” Phys. Reports 376, 225 (2003).
[CrossRef]

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

2001 (2)

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 033107 (2001).
[CrossRef]

M. I. Stockman, S. V. Faleev, and D. J. Bergam, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?,” Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

1999 (1)

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

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 (1998).
[CrossRef]

1997 (1)

F. Ducastelle and P. Quémerais, “Chemical self-organization during crystal growth,” Phys. Rev. Lett. 78, 102 (1997).
[CrossRef]

1994 (2)

P. Quémerais, “Model of growth for long-range chemically ordered structures: application to quasicrystals,” J. Phys. I France 4, 1669 (1994).
[CrossRef]

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

1993 (2)

C. Berger, E. Belin, and D. Mayou, “Electronic properties of quasicrystals,” Ann. Chim.-Sci. Mat. (Paris) 18, 485 (1993).

E. Belin and D. Mayou, “Electronic properties of quasicrystals,” Phys. Scr. T49, 356 (1993).
[CrossRef]

1990 (1)

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
[CrossRef]

1986 (2)

A. Hessel and A. A. Oliner, “Wood’s anomaly effects on gratings of large amplitude,” Opt. Commun. 59, 327 (1986).
[CrossRef]

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

1984 (1)

A. Wirgin, and T. López-Ríos, “Can surface enhanced raman scattering be caused by waveguide resonances,” Opt. Commun. 48, 416 (1984); ibid. “Errata”, Opt. Commun. 49, 455 (1984).
[CrossRef]

1983 (1)

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[CrossRef]

1973 (1)

A. Wirgin, “Resonance scattering of electromagnetic waves from a rectangular groove on a metallic mirror,” Opt. Commun. 7(1), 70 (1973).
[CrossRef]

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
[CrossRef] [PubMed]

Aigouy, L.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

Albano, E.

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[CrossRef]

Albuquerque, E. L.

E. L. Albuquerque, and M. G. Cottamb, “Theory of elementary excitations in quasiperiodic structures,” Phys. Reports 376, 225 (2003).
[CrossRef]

Barbara, A.

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 (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]

J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
[CrossRef] [PubMed]

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

Bardou, N.

Belin, E.

C. Berger, E. Belin, and D. Mayou, “Electronic properties of quasicrystals,” Ann. Chim.-Sci. Mat. (Paris) 18, 485 (1993).

E. Belin and D. Mayou, “Electronic properties of quasicrystals,” Phys. Scr. T49, 356 (1993).
[CrossRef]

Bergam, D. J.

M. I. Stockman, S. V. Faleev, and D. J. Bergam, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?,” Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

Berger, C.

C. Berger, E. Belin, and D. Mayou, “Electronic properties of quasicrystals,” Ann. Chim.-Sci. Mat. (Paris) 18, 485 (1993).

Beruete, M.

M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Billaudeau, C.

Boccara, A.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

Bustarret, E.

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

Collin, S.

Cottamb, M. G.

E. L. Albuquerque, and M. G. Cottamb, “Theory of elementary excitations in quasiperiodic structures,” Phys. Reports 376, 225 (2003).
[CrossRef]

Daiser, S.

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[CrossRef]

Depine, R.

D. Skigin and R. Depine, “Transmission resonances of metallic compound gratings with subwavelength slits,” Phys. Rev. lett. 95, 217402 (2005) and references therein.
[CrossRef] [PubMed]

Desmarest, C.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

Ducastelle, F.

F. Ducastelle and P. Quémerais, “Chemical self-organization during crystal growth,” Phys. Rev. Lett. 78, 102 (1997).
[CrossRef]

Ertl, G.

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[CrossRef]

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergam, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?,” Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

Fournier, T.

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

Gadenne, P.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

Garcia, N.

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[CrossRef]

García-Vidal, F. J.

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 (1998).
[CrossRef]

George, T. F.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

Grésillon, S.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

Hessel, A.

A. Hessel and A. A. Oliner, “Wood’s anomaly effects on gratings of large amplitude,” Opt. Commun. 59, 327 (1986).
[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]

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 (2008).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
[CrossRef] [PubMed]

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, and J. Munoz-Lopez, “Coherence of light scattered from a randomly rough surface,” Phys. Rev. E 71, 036606 (2005).
[CrossRef]

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]

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 (2008).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
[CrossRef] [PubMed]

A. Barbara, P. Quémerais, E. Bustarret, T. López-Ríos, and T. Fournier, “Electromagnetic resonances of subwavelength rectangular metallic gratings,” Eur. Phys. J. D. 23, 143-154 (2003).
[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 (1998).
[CrossRef]

A. Wirgin, and T. López-Ríos, “Can surface enhanced raman scattering be caused by waveguide resonances,” Opt. Commun. 48, 416 (1984); ibid. “Errata”, Opt. Commun. 49, 455 (1984).
[CrossRef]

Maradudin, A. A.

T. A. Leskova, A. A. Maradudin, and J. Munoz-Lopez, “Coherence of light scattered from a randomly rough surface,” Phys. Rev. E 71, 036606 (2005).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
[CrossRef]

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

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
[CrossRef] [PubMed]

Mayou, D.

E. Belin and D. Mayou, “Electronic properties of quasicrystals,” Phys. Scr. T49, 356 (1993).
[CrossRef]

C. Berger, E. Belin, and D. Mayou, “Electronic properties of quasicrystals,” Ann. Chim.-Sci. Mat. (Paris) 18, 485 (1993).

McGurn, A. R.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
[CrossRef]

Mendez, E. R.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
[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 (1998).
[CrossRef]

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
[CrossRef]

Miranda, R.

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[CrossRef]

Munoz-Lopez, J.

T. A. Leskova, A. A. Maradudin, and J. Munoz-Lopez, “Coherence of light scattered from a randomly rough surface,” Phys. Rev. E 71, 036606 (2005).
[CrossRef]

Muratov, L. S.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

Nahata, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
[CrossRef] [PubMed]

Navarro-Cía, M.

M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Oliner, A. A.

A. Hessel and A. A. Oliner, “Wood’s anomaly effects on gratings of large amplitude,” Opt. Commun. 59, 327 (1986).
[CrossRef]

Pandey, L. N.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

Pannetier, B.

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 (1998).
[CrossRef]

Pardo, F.

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J-L Pelouard, “Angle-resolved transmission measurements through anisotropic 2D plasmonic crystals,” Opt. Lett. 33, 165 (2008).
[CrossRef] [PubMed]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 033107 (2001).
[CrossRef]

Pelouard, J.-L.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 033107 (2001).
[CrossRef]

Pelouard, J-L

Pelouard, J-L.

Quelin, X.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

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]

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 (2008).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
[CrossRef] [PubMed]

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

F. Ducastelle and P. Quémerais, “Chemical self-organization during crystal growth,” Phys. Rev. Lett. 78, 102 (1997).
[CrossRef]

P. Quémerais, “Model of growth for long-range chemically ordered structures: application to quasicrystals,” J. Phys. I France 4, 1669 (1994).
[CrossRef]

Rivoal, J. C.

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

Sánchez-Dehesa, J.

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 (1998).
[CrossRef]

Sauvan, C.

Skigin, D.

M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

D. Skigin and R. Depine, “Transmission resonances of metallic compound gratings with subwavelength slits,” Phys. Rev. lett. 95, 217402 (2005) and references therein.
[CrossRef] [PubMed]

Sorolla, M.

M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Stockman, M. I.

M. I. Stockman, S. V. Faleev, and D. J. Bergam, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?,” Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

Teissier, R.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 033107 (2001).
[CrossRef]

Vardeny, Z. V.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
[CrossRef] [PubMed]

Wandelt, K.

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[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 (1986)
[CrossRef]

A. Wirgin, and T. López-Ríos, “Can surface enhanced raman scattering be caused by waveguide resonances,” Opt. Commun. 48, 416 (1984); ibid. “Errata”, Opt. Commun. 49, 455 (1984).
[CrossRef]

A. Wirgin, “Resonance scattering of electromagnetic waves from a rectangular groove on a metallic mirror,” Opt. Commun. 7(1), 70 (1973).
[CrossRef]

. Phys. I France (1)

P. Quémerais, “Model of growth for long-range chemically ordered structures: application to quasicrystals,” J. Phys. I France 4, 1669 (1994).
[CrossRef]

Ann. Chim.-Sci. Mat. (Paris) (1)

C. Berger, E. Belin, and D. Mayou, “Electronic properties of quasicrystals,” Ann. Chim.-Sci. Mat. (Paris) 18, 485 (1993).

Ann. Phys. (NY) (1)

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (NY) 203, 255 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

M. Navarro-Cía, D. Skigin, M. Beruete, and M. Sorolla, “Experimental observation of phase resonances in metallic compound gratings with subwavelength slits in the millimiter wave regime,” Appl. Phys. Lett. 94, 091107 (2009).
[CrossRef]

Eur. Phys. J. D. (1)

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

Nature (1)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517 (2007).
[CrossRef] [PubMed]

Opt. Commun. (3)

A. Hessel and A. A. Oliner, “Wood’s anomaly effects on gratings of large amplitude,” Opt. Commun. 59, 327 (1986).
[CrossRef]

A. Wirgin, “Resonance scattering of electromagnetic waves from a rectangular groove on a metallic mirror,” Opt. Commun. 7(1), 70 (1973).
[CrossRef]

A. Wirgin, and T. López-Ríos, “Can surface enhanced raman scattering be caused by waveguide resonances,” Opt. Commun. 48, 416 (1984); ibid. “Errata”, Opt. Commun. 49, 455 (1984).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Reports (1)

E. L. Albuquerque, and M. G. Cottamb, “Theory of elementary excitations in quasiperiodic structures,” Phys. Reports 376, 225 (2003).
[CrossRef]

Phys. Rev. B (1)

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 033107 (2001).
[CrossRef]

Phys. Rev. E (1)

T. A. Leskova, A. A. Maradudin, and J. Munoz-Lopez, “Coherence of light scattered from a randomly rough surface,” Phys. Rev. E 71, 036606 (2005).
[CrossRef]

Phys. Rev. Lett. (8)

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

E. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, and N. Garcia, “Nature of surface-enhanced-Ramanscattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314-2317 (1983).
[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]

S. Grésillon, L. Aigouy, A. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, and P. Gadenne, “Experimental observation of localized excitations in Random metal-dielectric films,” Phys. Rev. Lett. 82, 4520 (1999).
[CrossRef]

M. I. Stockman, S. V. Faleev, and D. J. Bergam, “Localization versus delocalization of surface plasmons in nanosystems: can one state have both characteristics?,” Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

F. Ducastelle and P. Quémerais, “Chemical self-organization during crystal growth,” Phys. Rev. Lett. 78, 102 (1997).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97, 036405 (2006).
[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 (1998).
[CrossRef]

D. Skigin and R. Depine, “Transmission resonances of metallic compound gratings with subwavelength slits,” Phys. Rev. lett. 95, 217402 (2005) and references therein.
[CrossRef] [PubMed]

Phys. Scr. (1)

E. Belin and D. Mayou, “Electronic properties of quasicrystals,” Phys. Scr. T49, 356 (1993).
[CrossRef]

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 (1986)
[CrossRef]

Other (2)

K. Kneipp, M. Moskovits, and H. Kneipp, ed., Surface-Enhanced Raman Scattering, Topics in Applied Physics, 103, (Springer, 2006).
[CrossRef]

E. D. Palik, Handbook of optical constants of solids, Academic Press.

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Figures (4)

Fig. 1.
Fig. 1.

(a) SEM image of the gold grating and (b) experimental set-up as described in [22]. The sample is mounted in the center of the motorized stage. For each θ/2θ position of the sample/detector, specular reflectivity as a function of the incident wavelength is measured. (c) shows the spectrum measured at θ = 20.5° corresponding to a scan along the blue line added in the experimental dispersion maps displayed in (d). The dispersion diagram is obtained from the normalized intensity of the specular reflectivity plotted as a function of the in-plane wave vector k// and the wave number 1/λ. The excited modes appear as dips in the specular reflectivity dips and as dark lines in the dispersion diagram. The hatched peak is due to the infra-red absorption of residual water in the experiment set-up.

Fig. 2.
Fig. 2.

Experimental (a) and calculated (b) dispersion diagram of the two thin cavity modes of the grating. The dashed line indicates the theoretical dispersion of the plasmon branch n = −1. (c) to (f): experimental (black) and calculated (gray) spectra measured at an incidence angle θ = 2.5° showing the weak excitation of the anti-symmetrical mode (→ 0 ←) (c), θ = 36° where the pseudo-symmetrical mode (→←→) is extinguished (d), θ = 18° where the pseudo-symmetrical mode should cross the horizontal surface branch (e) and θ = 70° where the anti-symmetrical mode couples with the surface plasmon branch (f). The hatched dip is due to water pollution in the experiment.

Fig. 3.
Fig. 3.

(a) Projection as a function of the incidence angle of the eigenvectors U1 (squares) and U2 (dots) on the excitation vector V. (b–e) Intensity maps of the magnetic near-field intensity for the anti-symmetrical mode calculated at θ = 36°, 1/λ = 0.215µm−1 (b) and at θ =0°, 1/λ = 0.255µm−1 (c) and for the pseudo-symmetrical mode calculated at θ = 36°,1/λ = 0.296µm−1 (d) and θ = 0°,1/λ = 0.283µm−1 (e). The color bar gives the scale of the normalized magnetic field intensities.

Fig. 4.
Fig. 4.

Intensity maps of the magnetic field of the anti-symmetrical mode when excited at θ = 10°, 1/λ = 0.249µm−1 (a) and at θ = 66°, 1/λ = 0.188µm−1 (c). (b) shows the magnetic field intensity along the solid black line in (a) and the dotted line in (b). At θ = 10° the mode (→0←) is strongly confined inside the cavities. Its expansion outside the cavities increases at larger incident angles due to its coupling with the horizontal surface plasmon. (d) Intensity maps of the magnetic field of the pseudo-symmetrical mode (→←→) when excited at θ = 18°, 1/λ = 0:29µm−1.

Equations (5)

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H z ( I ) ( x , y ) = e ik ( γ 0 x β 0 y ) + Σ m = m = + R m e ik ( γ m x + β m y ) ,
H z , p ( II ) ( x , y ) = Σ = 0 + A , p cos [ π w ( x x p + w 2 ) ] ( e i μ ( y + 2 h ) + r e i μ y ) .
R m = β 0 η β 0 + η δ m , 0 + w D Σ p = 1 Q Σ = 0 + A p S m e ik γ m x p ( e 2 i μ h 1 ) ( μ k + η β m + η ) ,
A , p = ( 2 1 + δ , 0 ) 1 e 2 i μ h + r Σ m = + S m + e ik γ m x p ( δ m , 0 + R m ) .
V , p = ( 2 1 + δ , 0 ) 2 β 0 β 0 + η S 0 + e ik γ 0 x p .

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