Abstract

We find the conditions for the existence of trapped modes in planar periodic particle arrays. Confined excitations of TE and TM symmetry are observed in symmetric environments, originating in lattice resonances that are signalled by the onset of new diffraction beams. This mechanism of mode formation is shown to be inhibited by the presence of a dielectric interface in an asymmetric configuration. Modes can still exist above a threshold finite distance from the interface. Both rigorous numerical simulation and analytical modeling are used to elucidate the origin and systematics of this unexpected difference in the behavior of trapped modes in self-standing and supported particle arrays.

© 2009 Optical Society of America

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  1. L. M. Liz-Marzán, "Tailoring surface plasmon through the morphology and assembly of metal nanoparticles," Langmuir 22, 32-41 (2006).
    [CrossRef]
  2. C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
    [CrossRef]
  3. P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, "Spectroscopic mode mapping of resonant plasmon nanoantennas," Phys. Rev. Lett. 101, 116,805 (2008).
    [CrossRef]
  4. M. Danckwerts and L. Novotny, "Optical frequency mixing at coupled gold nanoparticles," Phys. Rev. Lett. 98, 026,104 (2007).
    [CrossRef]
  5. L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
    [CrossRef] [PubMed]
  6. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
    [CrossRef]
  7. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
    [CrossRef] [PubMed]
  8. S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow Plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
    [CrossRef]
  9. E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
    [CrossRef] [PubMed]
  10. B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle Arrays," Phys. Rev. Lett. 101, 143,902 (2008).
    [CrossRef]
  11. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016,608 (2005).
    [CrossRef]
  12. F. J. García de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
    [CrossRef]
  13. S. A. Podosenov, A. A. Sokolov, and S. V. Al’betkov, "Method for determining the electric and magnetic polarizability of arbitrarily shaped conducting bodies," IEEE Trans. Electr. Compatibility 39, 1-10 (1997).
    [CrossRef]
  14. R. Gans, "The shape of ultra microscopic gold particles," Ann. Phys. (Leipzig) 37, 881-900 (1912).
  15. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  16. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  17. J. W. S. Rayleigh, "Note on the remarkable case of diffraction spectra described by Prof. Wood," Philos. Mag. 14, 60-65 (1907).
  18. We are concerned with the coefficient multiplying the zero-order reflected evanescent wave, normalized to the amplitude of an incident evanescent wave at the plane of the array.
  19. R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1973).
    [CrossRef]
  20. N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: Frequency bands and transmission coefficients," Comput. Phys. Commun. 113, 49-77 (1998).
    [CrossRef]
  21. N. Stefanou, V. Yannopapas, and A. Modinos, "MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals," Comput. Phys. Commun. 132, 189-196 (2000).
    [CrossRef]
  22. R. Zengerle, "Light propagation in singly and doubly periodic planar waveguides," J. Mod. Opt. 34, 1589-1617 (1987).
    [CrossRef]
  23. S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
    [CrossRef]
  24. S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045,102 (2002).
    [CrossRef]

2009 (1)

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
[CrossRef] [PubMed]

2008 (2)

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, "Spectroscopic mode mapping of resonant plasmon nanoantennas," Phys. Rev. Lett. 101, 116,805 (2008).
[CrossRef]

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle Arrays," Phys. Rev. Lett. 101, 143,902 (2008).
[CrossRef]

2007 (3)

F. J. García de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

M. Danckwerts and L. Novotny, "Optical frequency mixing at coupled gold nanoparticles," Phys. Rev. Lett. 98, 026,104 (2007).
[CrossRef]

C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
[CrossRef]

2006 (1)

L. M. Liz-Marzán, "Tailoring surface plasmon through the morphology and assembly of metal nanoparticles," Langmuir 22, 32-41 (2006).
[CrossRef]

2005 (2)

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016,608 (2005).
[CrossRef]

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow Plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

2003 (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

2002 (1)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045,102 (2002).
[CrossRef]

2000 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, "MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals," Comput. Phys. Commun. 132, 189-196 (2000).
[CrossRef]

1999 (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

1998 (2)

N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: Frequency bands and transmission coefficients," Comput. Phys. Commun. 113, 49-77 (1998).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
[CrossRef]

1997 (1)

S. A. Podosenov, A. A. Sokolov, and S. V. Al’betkov, "Method for determining the electric and magnetic polarizability of arbitrarily shaped conducting bodies," IEEE Trans. Electr. Compatibility 39, 1-10 (1997).
[CrossRef]

1988 (1)

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1987 (1)

R. Zengerle, "Light propagation in singly and doubly periodic planar waveguides," J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

1973 (1)

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1973).
[CrossRef]

1912 (1)

R. Gans, "The shape of ultra microscopic gold particles," Ann. Phys. (Leipzig) 37, 881-900 (1912).

1907 (1)

J. W. S. Rayleigh, "Note on the remarkable case of diffraction spectra described by Prof. Wood," Philos. Mag. 14, 60-65 (1907).

Al’betkov, S. V.

S. A. Podosenov, A. A. Sokolov, and S. V. Al’betkov, "Method for determining the electric and magnetic polarizability of arbitrarily shaped conducting bodies," IEEE Trans. Electr. Compatibility 39, 1-10 (1997).
[CrossRef]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Auguie, B.

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle Arrays," Phys. Rev. Lett. 101, 143,902 (2008).
[CrossRef]

Aussenegg, F. R.

Barnes, W. L.

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle Arrays," Phys. Rev. Lett. 101, 143,902 (2008).
[CrossRef]

Cherukulappurath, S.

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, "Spectroscopic mode mapping of resonant plasmon nanoantennas," Phys. Rev. Lett. 101, 116,805 (2008).
[CrossRef]

Danckwerts, M.

M. Danckwerts and L. Novotny, "Optical frequency mixing at coupled gold nanoparticles," Phys. Rev. Lett. 98, 026,104 (2007).
[CrossRef]

Didiot, C.

C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
[CrossRef]

Draine, B. T.

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Fagot-Revurat, Y.

C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Gans, R.

R. Gans, "The shape of ultra microscopic gold particles," Ann. Phys. (Leipzig) 37, 881-900 (1912).

García de Abajo, F. J.

F. J. García de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016,608 (2005).
[CrossRef]

Ghenuche, P.

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, "Spectroscopic mode mapping of resonant plasmon nanoantennas," Phys. Rev. Lett. 101, 116,805 (2008).
[CrossRef]

Gippius, N. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045,102 (2002).
[CrossRef]

Gunnarsson, L.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Hicks, E. M.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Ishihara, T.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045,102 (2002).
[CrossRef]

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow Plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Käll, M.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Kasemo, B.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Kierren, B.

C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Krenn, J. R.

Leitner, A.

Liz-Marzán, L. M.

L. M. Liz-Marzán, "Tailoring surface plasmon through the morphology and assembly of metal nanoparticles," Langmuir 22, 32-41 (2006).
[CrossRef]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Malterre, D.

C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
[CrossRef]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, "MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals," Comput. Phys. Commun. 132, 189-196 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: Frequency bands and transmission coefficients," Comput. Phys. Commun. 113, 49-77 (1998).
[CrossRef]

Muljarov, E. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045,102 (2002).
[CrossRef]

Novotny, L.

M. Danckwerts and L. Novotny, "Optical frequency mixing at coupled gold nanoparticles," Phys. Rev. Lett. 98, 026,104 (2007).
[CrossRef]

Podosenov, S. A.

S. A. Podosenov, A. A. Sokolov, and S. V. Al’betkov, "Method for determining the electric and magnetic polarizability of arbitrarily shaped conducting bodies," IEEE Trans. Electr. Compatibility 39, 1-10 (1997).
[CrossRef]

Pons, S.

C. Didiot, S. Pons, B. Kierren, Y. Fagot-Revurat, and D. Malterre, "Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures," Nat. Nanotech. 2, 617-621 (2007).
[CrossRef]

Quidant, R.

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, "Spectroscopic mode mapping of resonant plasmon nanoantennas," Phys. Rev. Lett. 101, 116,805 (2008).
[CrossRef]

Quinten, M.

Rayleigh, J. W. S.

J. W. S. Rayleigh, "Note on the remarkable case of diffraction spectra described by Prof. Wood," Philos. Mag. 14, 60-65 (1907).

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Rindzevicius, T.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Rodríguez-Lorenzo, L.

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
[CrossRef] [PubMed]

Schatz, G. C.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow Plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

Sokolov, A. A.

S. A. Podosenov, A. A. Sokolov, and S. V. Al’betkov, "Method for determining the electric and magnetic polarizability of arbitrarily shaped conducting bodies," IEEE Trans. Electr. Compatibility 39, 1-10 (1997).
[CrossRef]

Spears, K. G.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, "MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals," Comput. Phys. Commun. 132, 189-196 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: Frequency bands and transmission coefficients," Comput. Phys. Commun. 113, 49-77 (1998).
[CrossRef]

Tacke, M.

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1973).
[CrossRef]

Taminiau, T. H.

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, "Spectroscopic mode mapping of resonant plasmon nanoantennas," Phys. Rev. Lett. 101, 116,805 (2008).
[CrossRef]

Tikhodeev, S. G.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 045,102 (2002).
[CrossRef]

Ulrich, R.

R. Ulrich and M. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1973).
[CrossRef]

Van Duyne, R. P.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, "Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

van Hulst, N. F.

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Other (2)

We are concerned with the coefficient multiplying the zero-order reflected evanescent wave, normalized to the amplitude of an incident evanescent wave at the plane of the array.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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Figures (3)

Fig. 1.
Fig. 1.

Surface modes in planar arrays of perfect-conductor ellipsoidal particles. The coefficient Γ, which enters the dispersion relation of Eq. (4), is represented here as a function of the ellipsoid aspect ratio AR=L/D (see right inset) for modes of TE and TM symmetry. The plot inset shows the electrostatic polarizability along directions parallel and perpendicular to the plane of the array.

Fig. 2.
Fig. 2.

Surface modes of a planar particle array in an asymmetric environment. (a) Geometrical and dielectric parameters of the structure under consideration. The array has square symmetry with period a and we consider TM polarized light. The particles are spheres of diameter D=0.4a and permittivity εp =6ε 1 relative to the permittivity of medium 1. (b) Dispersion diagram of the particle array for t →∞ (symmetric ε1 environment). The color scale gives the modulus of the specular reflection coefficient [18]. (c) Parallel-wavevector dependence of the reflection coefficient ra for k 1a =π/2 [see arrow in (b)] and ε 2=0.5ε 1. Three different values of the separation t between the array and the planar interface are considered (see labels). Dotted and dashed curves are calculated by adding an imaginary part to εp equal to 0.25ε 1i and 0.5ε 1i, respectively. (d) Evolution of the surface-mode peak reflectivity (ra max) and parallel wavevector (ka ) as a function of t under the same conditions as in (c). The solid circles and the arrow correspond to the maxima of the curves in (c). Full numerical calculations for k a (solid curve) are compared to analytical results (dashed curve, see text). The parallel wavevector is normalized to the light wavevector in the medium surrounding the particles in each case (k 1 for t>0 and k 2 for t<0). (e) Same as (d), as a function of ε 2/ε 1 for t=2a. All dielectric functions used in this figure are real, except for the addition of an imaginary part only in the broken curves of (c), as noted above.

Fig. 3.
Fig. 3.

Surface modes of a planar particle array near a plasmon-supporting surface. (a) Geometrical and dielectric parameters of the structure under consideration. We take εp =6 and εh =2. The particle diameter is D=200nm and the spacing is a=1000nm. (b) Dependence of the TM reflection coefficient [18] on separation t and parallel wavevector k for a free-space wavelength λ=1550nm. At large t, the silver SPP and array mode are well separated. The two modes converge to a single one at t ~2µm, below which no well-defined mode is observed.

Tables (1)

Tables Icon

Table 1. Surface excitations in different configurations of planar small-particle arrays. An array in a symmetric environment can sustain both TE and TM modes, provided the polarizabilities satisfy the conditions γE +γM >0 and γE +γM >0, respectively, where ‖ and ⊥ refer to directions relative to the plane of the array. Near a perfect-conductor substrate, TE modes are suppressed, while TM modes are more bound. Finally, no excitations are allowed near a dielectric substrate.

Equations (5)

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[ p m ] = 1 α 1 G · [ E ext H ext ] ,
G yy EE , G zz EE , G yz EM 2 π k 2 A κ Σ
r TE a = γ E Σ 1 ( γ E + γ M ) 2 α 0 E 2 Σ 1 α 0 E ,
r TM a = γ M Σ 1 ( γ E + γ M ) α 0 E 2 Σ 1 α 0 E ,
k 2 = k 2 + Γ S 3 k 4 A 2 ,

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