Abstract

We present theory to describe the plasmonic resonances of a subwavelength annular aperture in a real metal plate. The theory provides the reflection, including the amplitude and phase, of radially polarized surface plasmon waves from the end faces of the aperture with a significant departure from the perfect electric conductor case due to plasmonic effects. Oscillations in the reflection amplitude and phase are observed. These oscillations arise from transverse resonances and depend on the geometry of the annulus. The theory is applied to the design of various aperture structures operating at the same resonance wavelength, and it is confirmed by comprehensive electromagnetic simulations. The results are contrasted to the perfect electric conductor case and they will be of significant interest to emerging applications in metamaterials, plasmonic sensors, and near-field optics.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
  4. F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. R. Gordon, “Reflection of cylindrical surface waves,” Opt. Express 17(21), 18621–18629 (2009).
    [CrossRef]
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    [CrossRef]
  8. J. Wang, W. Zhou, and E. P. Li, “Enhancing the light transmission of plasmonic metamaterials through polygonal aperture arrays,” Opt. Express 17(22), 20349–20354 (2009).
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    [CrossRef]
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    [CrossRef]
  28. M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  38. R. Gordon, “Near-field interference in a subwavelength double slit in a perfect conductor,” J. Opt. A 8, L1 (2006).
    [CrossRef]
  39. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
    [CrossRef] [PubMed]
  40. A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
    [CrossRef] [PubMed]

2011

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
[CrossRef] [PubMed]

2010

P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express 18(10), 10896–10904 (2010).
[CrossRef] [PubMed]

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18(12), 12770–12778 (2010).
[CrossRef] [PubMed]

D. Li and R. Gordon, “Electromagnetic transmission resonances for a single annular aperture in a metal plate,” Phys. Rev. A 82(4), 041801 (2010).
[CrossRef]

2009

R. Gordon, “Reflection of cylindrical surface waves,” Opt. Express 17(21), 18621–18629 (2009).
[CrossRef]

P. B. Catrysse and S. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

J. Wang, W. Zhou, and E. P. Li, “Enhancing the light transmission of plasmonic metamaterials through polygonal aperture arrays,” Opt. Express 17(22), 20349–20354 (2009).
[CrossRef] [PubMed]

F. I. Baida, Y. Poujet, J. Salvi, D. V. Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-λλ annular aperture arrays,” J. Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave–particle duality of single surface plasmon polaritons,” Nat. Phys. 5(7), 470–474 (2009).
[CrossRef]

2008

2007

2006

R. Gordon, “Vectorial method for calculating the Fresnel reflection of surface plasmon polaritons,” Phys. Rev. B 74(15), 153417 (2006).
[CrossRef]

R. Gordon, “Near-field interference in a subwavelength double slit in a perfect conductor,” J. Opt. A 8, L1 (2006).
[CrossRef]

S. M. Orbons and A. Roberts, “Resonance and extraordinary transmission in annular aperture arrays,” Opt. Express 14(26), 12623–12628 (2006).
[CrossRef] [PubMed]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006).
[CrossRef]

K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. 31(10), 1528–1530 (2006).
[CrossRef] [PubMed]

Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
[CrossRef]

2005

Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005).
[CrossRef] [PubMed]

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

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
[CrossRef] [PubMed]

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87(26), 261107 (2005).
[CrossRef]

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

H. Caglayan, I. Bulu, and E. Ozbay, “Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture,” Opt. Express 13(5), 1666–1671 (2005).
[CrossRef] [PubMed]

2004

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92(14), 147401 (2004).
[CrossRef] [PubMed]

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20(12), 4813–4815 (2004).
[CrossRef]

2001

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86(24), 5601–5603 (2001).
[CrossRef] [PubMed]

2000

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

1994

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994).
[CrossRef] [PubMed]

1989

1988

A. Roberts and R. C. McPhedran, “Bandpass grids with annular apertures,” IEEE Trans. Antenn. Propag. 36(5), 607–611 (1988).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Ashby, P.

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
[CrossRef] [PubMed]

Atwater, H. A.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18(12), 12770–12778 (2010).
[CrossRef] [PubMed]

Baida, F. I.

F. I. Baida, Y. Poujet, J. Salvi, D. V. Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-λλ annular aperture arrays,” J. Opt. Commun. 282(7), 1463–1466 (2009).
[CrossRef]

Y. Poujet, J. Salvi, and F. I. Baida, “90% Extraordinary optical transmission in the visible range through annular aperture metallic arrays,” Opt. Lett. 32(20), 2942–2944 (2007).
[CrossRef] [PubMed]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
[CrossRef]

Balasubramanian, G.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave–particle duality of single surface plasmon polaritons,” Nat. Phys. 5(7), 470–474 (2009).
[CrossRef]

Banzer, P.

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Bokor, J.

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
[CrossRef] [PubMed]

Brolo, A. G.

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[CrossRef] [PubMed]

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20(12), 4813–4815 (2004).
[CrossRef]

Brueck, S. R.

Brueck, S. R. J.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Bulu, I.

Burgos, S. P.

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18(12), 12770–12778 (2010).
[CrossRef] [PubMed]

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

Cabrini, S.

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
[CrossRef] [PubMed]

Caglayan, H.

Cao, Q.

Catrysse, P. B.

P. B. Catrysse and S. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Chu, H. V.

Cornaglia, M.

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
[CrossRef] [PubMed]

Davis, T. J.

Dawes, D. H.

de Waele, R.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18(12), 12770–12778 (2010).
[CrossRef] [PubMed]

Deckert, V.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

Fainman, Y.

Fan, S.

P. B. Catrysse and S. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009).
[CrossRef]

Fan, W.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Frauenglass, A.

Freeman, D.

S. M. Orbons, M. I. Haftel, C. Schlockermann, D. Freeman, M. Milicevic, T. J. Davis, B. Luther-Davies, D. N. Jamieson, and A. Roberts, “Dual resonance mechanisms facilitating enhanced optical transmission in coaxial waveguide arrays,” Opt. Lett. 33(8), 821–823 (2008).
[CrossRef] [PubMed]

S. M. Orbons, A. Roberts, D. Jamieson, M. I. Haftel, C. Schlockermann, D. Freeman, and B. Luther-Davies, “Extraordinary optical transmission with coaxial apertures,” Appl. Phys. Lett. 90(25), 251107 (2007).
[CrossRef]

Freeman, M. R.

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87(26), 261107 (2005).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Gordon, R.

A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
[CrossRef] [PubMed]

D. Li and R. Gordon, “Electromagnetic transmission resonances for a single annular aperture in a metal plate,” Phys. Rev. A 82(4), 041801 (2010).
[CrossRef]

R. Gordon, “Reflection of cylindrical surface waves,” Opt. Express 17(21), 18621–18629 (2009).
[CrossRef]

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[CrossRef] [PubMed]

R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006).
[CrossRef]

R. Gordon, “Vectorial method for calculating the Fresnel reflection of surface plasmon polaritons,” Phys. Rev. B 74(15), 153417 (2006).
[CrossRef]

R. Gordon, “Near-field interference in a subwavelength double slit in a perfect conductor,” J. Opt. A 8, L1 (2006).
[CrossRef]

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M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
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M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
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J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92(14), 147401 (2004).
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A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20(12), 4813–4815 (2004).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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Li, E. P.

Liu, Y.

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M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
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J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92(14), 147401 (2004).
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S. M. Orbons, A. Roberts, D. Jamieson, M. I. Haftel, C. Schlockermann, D. Freeman, and B. Luther-Davies, “Extraordinary optical transmission with coaxial apertures,” Appl. Phys. Lett. 90(25), 251107 (2007).
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Pohl, D. W.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
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Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
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S. M. Orbons, A. Roberts, D. Jamieson, M. I. Haftel, C. Schlockermann, D. Freeman, and B. Luther-Davies, “Extraordinary optical transmission with coaxial apertures,” Appl. Phys. Lett. 90(25), 251107 (2007).
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Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
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F. I. Baida, Y. Poujet, J. Salvi, D. V. Labeke, and B. Guizal, “Extraordinary transmission beyond the cut-off through sub-λλ annular aperture arrays,” J. Opt. Commun. 282(7), 1463–1466 (2009).
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Y. Poujet, J. Salvi, and F. I. Baida, “90% Extraordinary optical transmission in the visible range through annular aperture metallic arrays,” Opt. Lett. 32(20), 2942–2944 (2007).
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Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
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M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
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Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
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A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
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R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
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R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave–particle duality of single surface plasmon polaritons,” Nat. Phys. 5(7), 470–474 (2009).
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J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92(14), 147401 (2004).
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A. Weber-Bargioni, A. Schwartzberg, M. Cornaglia, A. Ismach, J. J. Urban, Y. Pang, R. Gordon, J. Bokor, M. B. Salmeron, D. F. Ogletree, P. Ashby, S. Cabrini, and P. J. Schuck, “Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes,” Nano Lett. 11(3), 1201–1207 (2011).
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F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
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Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: Spectral analysis and near-field optical images in the visible range,” Photon. Nanostructures 4(1), 47–53 (2006).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave–particle duality of single surface plasmon polaritons,” Nat. Phys. 5(7), 470–474 (2009).
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B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
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Figures (6)

Fig. 1
Fig. 1

Schematic view of an annular aperture in a metal film. The regions 1, 2, 3 and 4 have relative permittivity constants of ε1 , ε2 , ε3 and ε4 .

Fig. 2
Fig. 2

Evaluation of the theoretical reflection expression (Eq. (12)) for annular apertures in gold plate at 632.8 nm free-space wavelength. The results are contrasted with PEC case, using dashed lines. (a) The reflectivity and (b) the phase of reflection as function of inner radius, a, for slit widths (b-a) of 20 nm and 50 nm.

Fig. 3
Fig. 3

Comparison between reflection for the PEC case and the real metal case, both for annular aperture with slit size of 20 nm illuminated with 500 nm wavelength light. (a) Reflectivity and (b) phase.

Fig. 4
Fig. 4

(a) Transmission in arbitrary units for (b-a) value of 20 nm. Each curve relates to a different structure as specified in the legend and the dashed line is at 632.8 nm. In this figure a is the inner radius and l is the thickness of the plate (b) The (b-a) value is changed to 50 nm.

Fig. 5
Fig. 5

Variations of resonance wavelength with plate thickness l. The annular aperture inner radius is kept fixed at a = 50 nm.

Fig. 6
Fig. 6

2D electric field intensity plot in logarithmic scale (base 10) calculated by FDTD showing cross section of the annular aperture with a = 50 nm, b = 100 nm and l = 124 nm. (a) On resonance at the wavelength 632.8 nm. (b) Off resonance at 500 nm wavelength.

Tables (1)

Tables Icon

Table 1 The Effective Refractive Indexes and Peak Wavelength for Geometries in Fig. 4, for Annular Aperture Structures in Gold Designed to Have Peak at 632.8 nm

Equations (14)

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E ρ ( ρ , ϕ , z = 0 ) { E ρ ( 1 ) = ( 1 + r ) j β p 1 A 1 I 1 ( p 1 ρ )                                                                           if               ρ < a E ρ ( 2 ) = ( 1 + r ) j β p 2 [ A 2 I 1 ( p 2 ρ ) A 3 K 1 ( p 2 ρ ) ]                   if     a < ρ < b E ρ ( 3 ) = ( 1 + r ) j β p 3 A 4 K 1 ( p 3 ρ )                                                                         if                   ρ > b
H ϕ ( ρ , ϕ , z = 0 ) { H ϕ ( 1 ) = ( 1 r ) j ω ε 1 p 1 A 1 I 1 ( p 1 ρ )                                                                               if               ρ < a H ϕ ( 2 ) = ( 1 r ) j ω ε 2 p 2 [ A 2 I 1 ( p 2 ρ ) A 3 K 1 ( p 2 ρ ) ]               if     a < ρ < b H ϕ ( 3 ) = ( 1 r ) j ω ε 3 p 3 A 4 K 1 ( p 3 ρ )                                                                   if             ρ > b
A B C D = 0
A = I 0 ( p 2 a ) I 0 ( p 1 a ) ε 2 p 1 ε 1 p 2 I 1 ( p 2 a ) I 1 ( p 1 a ) ,                   B = ε 2 p 3 ε 3 p 2 K 1 ( p 2 b ) K 1 ( p 1 b ) K 0 ( p 2 b ) K 0 ( p 1 b ) , C = K 0 ( p 2 a ) I 0 ( p 1 a ) + ε 2 p 1 ε 1 p 2 K 1 ( p 2 a ) I 1 ( p 1 a ) ,           D = ε 2 p 3 ε 3 p 2 I 1 ( p 2 b ) K 1 ( p 3 b ) I 0 ( p 2 b ) K 0 ( p 3 b ) .
E ρ ( ρ , ϕ , z = 0 + ) = 0 t ( k ) ω 2 μ 0 ε 4 k 2 ω ε 4 J 1 ( k ρ ) d k ,
H ϕ ( ρ , ϕ , z = 0 + ) = 0 t ( k ) J 1 ( k ρ ) d k .
t ( k ) = ( 1 + r ) ω k β ε 4 ω 2 μ 0 ε 4 k 2 [ D 1 ( k ) + D 2 ( k ) + D 3 ( k ) + D 4 ( k ) ]
D 1 ( k ) = j A 1 p 1 ( p 1 2 + k 2 ) a ( p 1 J 1 ( k a ) I 2 ( p 1 a ) + k J 2 ( k a ) I 1 ( p 1 a ) )
D 2 ( k ) = j A 2 p 2 ( p 2 2 + k 2 ) [ b ( p 2 J 1 ( k b ) I 2 ( p 2 b ) + k J 2 ( k b ) I 1 ( p 2 b ) )                                                                                             a ( p 2 J 1 ( k a ) I 2 ( p 2 a ) + k J 2 ( k a ) I 1 ( p 1 a ) ) ]
D 3 ( k ) = j A 3 p 2 ( p 2 2 + k 2 ) [ b ( k J 2 ( k b ) K 1 ( p 2 b ) p 2 J 1 ( k b ) K 2 ( p 2 b ) )                                                                                             a ( k J 2 ( k a ) K 1 ( p 2 a ) p 2 J 1 ( k a ) K 2 ( p 2 a ) ) ]
D 4 ( k ) = j A 4 p 3 ( p 3 2 + k 2 ) b ( k J 2 ( k b ) K 1 ( p 3 b ) p 3 J 1 ( k a ) K 2 ( p 3 b ) )
r = 1 G 1 + G
G = 0 k β ε 4 ω 2 μ 0 ε 4 k 2 [ D 1 ( k ) + D 2 ( k ) + D 3 ( k ) + D 4 ( k ) ] 2 d k ε 1 A 1 2 p 1 2 0 a I 1 2 ( p 1 ρ ) ρ d ρ + ε 2 p 2 2 a b [ A 2 I 1 ( p 2 ρ ) A 3 K 1 ( p 2 ρ ) ] 2 ρ d ρ ε 3 A 4 2 p 3 2 b K 1 2 ( p 3 ρ ) ρ d ρ .
l = m π ϕ β ,

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