Abstract

We analyze both experimentally and theoretically the physical mechanisms that determine the optical transmission through deep sub-wavelength bull’s eye structures (concentric annular grooves surrounding a circular hole). Our analysis focus on the transmission resonance as a function of the distance between the central hole and its nearest groove. We find that, for that resonance, each groove behaves almost independently, acting as an optical cavity that couples to incident radiation, and reflecting the surface plasmons radiated by the other side of the same cavity. It is the constructive contribution at the central hole of these standing waves emitted by independent grooves which ends up enhancing transmission. Also for each groove the coupling and reflection coefficients for surface plasmons are incorporated into a phenomenological Huygens-Fresnel model that gathers the main mechanisms to enhance transmission. Additionally, it is shown that the system presents a collective resonance in the electric field that does not lead to resonant transmission, because the fields radiated by the grooves do not interfere constructively at the central hole.

© 2011 OSA

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2010 (6)

2009 (3)

Y. Cui and S. He, “A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves,” Opt. Express 17, 13995–14000 (2009).
[PubMed]

J. H. M. Consonni and G. Lérondel, “Fabry-Perot type enhancement in plasmonic visible nanosource,” Appl. Phys. Lett. 94, 051105-1-051105-3 (2009).

L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

2008 (2)

F. de León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys.: Condens. Matter 20, 304214 (2008).

2007 (4)

2006 (2)

2005 (4)

A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwave-length aperture,” Opt. Express 13, 3535–3542 (2005).
[PubMed]

Z.-B. Li, J.-G. Tian, Z.-B. Liu, W.-Y. Zhou, and C.-P. Zhang, “Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectrice,” Opt. Express 13, 9071–9077 (2005).
[PubMed]

T. Ishi, J. Fujikata, and K. Ohashi, “Large Optical Transmission through a Single Subwavelength Hole Associated with a Sharp-Apex Grating,” Jpn. J. Appl. Phys. 44, L170–L172 (2005).

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B (R) 72, 161405(R)–161408 (2005).

2004 (1)

2003 (3)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901–213904 (2003).
[PubMed]

F. I. Baida, D. V. Labeke, and B. Guizal, “Enhanced Confined Light Transmission by Single Subwavelength Apertures in Metallic Films,” Appl. Opt. 42, 68116815 (2003).
[PubMed]

2002 (2)

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

1998 (1)

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

1991 (1)

E. D. Palik, Handbook of optical constants of solids II (Boston: Academic Press, 1991, edited by Edward D. Palik, 1991).

1988 (1)

A. Roberts and R. McPhedran, “Bandpass grids with annular apertures,” IEEE Trans. Antennas Propag. 36, 607–611 (1988).

1960 (1)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continous Media (Pergamon Press, New York, 1960).

Agrawal, A.

Baida, F. I.

F. I. Baida, D. V. Labeke, and B. Guizal, “Enhanced Confined Light Transmission by Single Subwavelength Apertures in Metallic Films,” Appl. Opt. 42, 68116815 (2003).
[PubMed]

Brucoli, G.

F. de León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).

Cai, L.

Cao, H.

Cao, J.-X.

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

Chang, C. K.

Chang, Y. C.

Cheng, M.

Collins, R. T.

Consonni, J. H. M.

J. H. M. Consonni and G. Lérondel, “Fabry-Perot type enhancement in plasmonic visible nanosource,” Appl. Phys. Lett. 94, 051105-1-051105-3 (2009).

Cui, Y.

de León-Pérez, F.

F. de León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).

Degiron, A.

A. Degiron and T. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694–3700 (2004).
[PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

Dereux, A.

Devaux, E.

J.-Y. Laluet, E. Devaux, C. Genet, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Optimization of surface plasmons launching from subwavelength hole arrays: modelling and experiments,” Opt. Express 15, 3488–3495 (2007).
[PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

Du, Y.-C.

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

Ebbesen, T.

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. K. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729787 (2010).

O. Mahboub, S. C. Palacios, C. Genet, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and T. W. Ebbesen, “Optimization of bull’s eye structures for transmission enhancement,” Opt. Express 18, 11292–11299 (2010).
[PubMed]

J.-Y. Laluet, E. Devaux, C. Genet, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Optimization of surface plasmons launching from subwavelength hole arrays: modelling and experiments,” Opt. Express 15, 3488–3495 (2007).
[PubMed]

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

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901–213904 (2003).
[PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

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

Flammer, P. D.

Fujikata, J.

T. Ishi, J. Fujikata, and K. Ohashi, “Large Optical Transmission through a Single Subwavelength Hole Associated with a Sharp-Apex Grating,” Jpn. J. Appl. Phys. 44, L170–L172 (2005).

Garcia-Vidal, F. J.

O. Mahboub, S. C. Palacios, C. Genet, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and T. W. Ebbesen, “Optimization of bull’s eye structures for transmission enhancement,” Opt. Express 18, 11292–11299 (2010).
[PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. K. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729787 (2010).

García-Vidal, F. J.

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys.: Condens. Matter 20, 304214 (2008).

F. de León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B (R) 72, 161405(R)–161408 (2005).

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901–213904 (2003).
[PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

Genet, C.

Ghaemi, H. F.

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

Guizal, B.

F. I. Baida, D. V. Labeke, and B. Guizal, “Enhanced Confined Light Transmission by Single Subwavelength Apertures in Metallic Films,” Appl. Opt. 42, 68116815 (2003).
[PubMed]

Guo, G.-C.

L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

Guo, G.-P.

L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

He, S.

Hollingsworth, R. E.

Hugonin, J. P.

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

Ishi, T.

T. Ishi, J. Fujikata, and K. Ohashi, “Large Optical Transmission through a Single Subwavelength Hole Associated with a Sharp-Apex Grating,” Jpn. J. Appl. Phys. 44, L170–L172 (2005).

Janssen, O. T. A.

O. T. A. Janssen, H. P. Urbach, and G. W. t’ Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902–043905 (2007).
[PubMed]

Kim, H. C.

Ko, H.

Kuipers, L. K.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. K. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729787 (2010).

Labeke, D. V.

F. I. Baida, D. V. Labeke, and B. Guizal, “Enhanced Confined Light Transmission by Single Subwavelength Apertures in Metallic Films,” Appl. Opt. 42, 68116815 (2003).
[PubMed]

Lalanne, P.

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

Laluet, J.-Y.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continous Media (Pergamon Press, New York, 1960).

Lee, C. K.

Lérondel, G.

J. H. M. Consonni and G. Lérondel, “Fabry-Perot type enhancement in plasmonic visible nanosource,” Appl. Phys. Lett. 94, 051105-1-051105-3 (2009).

Lewen, G. D.

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

Lezec, H. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901–213904 (2003).
[PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

Lezec, H. L.

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

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

Li, G.

Li, Z.-B.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continous Media (Pergamon Press, New York, 1960).

Lin, D. Z.

Lin, M. W.

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

Liu, J. M.

Liu, L.

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

Liu, Z.-B.

López-Tejeira, F.

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B (R) 72, 161405(R)–161408 (2005).

Lv, Y.

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

Mahboub, O.

Martin-Moreno, L.

O. Mahboub, S. C. Palacios, C. Genet, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and T. W. Ebbesen, “Optimization of bull’s eye structures for transmission enhancement,” Opt. Express 18, 11292–11299 (2010).
[PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. K. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729787 (2010).

Martín-Moreno, L.

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys.: Condens. Matter 20, 304214 (2008).

F. de León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B (R) 72, 161405(R)–161408 (2005).

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901–213904 (2003).
[PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

McPhedran, R.

A. Roberts and R. McPhedran, “Bandpass grids with annular apertures,” IEEE Trans. Antennas Propag. 36, 607–611 (1988).

Nahata, A.

A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwave-length aperture,” Opt. Express 13, 3535–3542 (2005).
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T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

Niu, T.-Y.

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

Ohashi, K.

T. Ishi, J. Fujikata, and K. Ohashi, “Large Optical Transmission through a Single Subwavelength Hole Associated with a Sharp-Apex Grating,” Jpn. J. Appl. Phys. 44, L170–L172 (2005).

Palacios, S. C.

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids II (Boston: Academic Press, 1991, edited by Edward D. Palik, 1991).

Pellerin, K. M.

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continous Media (Pergamon Press, New York, 1960).

Ren, X.-F.

L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

Roberts, A.

A. Roberts and R. McPhedran, “Bandpass grids with annular apertures,” IEEE Trans. Antennas Propag. 36, 607–611 (1988).

Rodrigo, S. G.

Schick, I. C.

t’ Hooft, G. W.

O. T. A. Janssen, H. P. Urbach, and G. W. t’ Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902–043905 (2007).
[PubMed]

Thio, T.

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

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

Tian, J.-G.

Urbach, H. P.

O. T. A. Janssen, H. P. Urbach, and G. W. t’ Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902–043905 (2007).
[PubMed]

Wang, L.

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

Wang, L.-L.

L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

Wang, Z.

Weeber, J.-C.

Wolff, P. A.

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

Xu, A.

Yang, C.

X. C. G. Zheng and C. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” PNAS 107, 9043–9048 (2010).
[PubMed]

G. Zheng and C. Yang, “Improving weak-signal identification via predetection background suppression by a pixel-level, surface-wave-enabled dark-field aperture,” Opt. Lett. 35, 2636–26348 (2010).
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L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

Yeh, C. S.

Yeh, J. T.

Zhang, C.-P.

Zheng, G.

Zheng, X. C. G.

X. C. G. Zheng and C. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” PNAS 107, 9043–9048 (2010).
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Zhou, W.-Y.

Appl. Opt. (2)

F. I. Baida, D. V. Labeke, and B. Guizal, “Enhanced Confined Light Transmission by Single Subwavelength Apertures in Metallic Films,” Appl. Opt. 42, 68116815 (2003).
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H. Ko, H. C. Kim, and M. Cheng, “Light focusing at metallic annular slit structure coated with dielectric layers,” Appl. Opt. 49, 950–954 (2010).
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Appl. Phys. Lett (1)

L.-L. Wang, X.-F. Ren, R. Yang, G.-C. Guo, and G.-P. Guo, “Transmission of doughnut light through a bulls eye structure,” Appl. Phys. Lett 95, 111111–111113 (2009).

Appl. Phys. Lett. (1)

J. H. M. Consonni and G. Lérondel, “Fabry-Perot type enhancement in plasmonic visible nanosource,” Appl. Phys. Lett. 94, 051105-1-051105-3 (2009).

IEEE Trans. Antennas Propag. (1)

A. Roberts and R. McPhedran, “Bandpass grids with annular apertures,” IEEE Trans. Antennas Propag. 36, 607–611 (1988).

J. Appl. Phys. (1)

L. Wang, J.-X. Cao, Y. Lv, L. Liu, T.-Y. Niu, and Y.-C. Du, “Experimental study of surface-wave-assisted microwave transmission through a single subwavelength slit,” J. Appl. Phys. 105, 093115-093115-6 (2009b).

J. Phys.: Condens. Matter (1)

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys.: Condens. Matter 20, 304214 (2008).

Jpn. J. Appl. Phys. (1)

T. Ishi, J. Fujikata, and K. Ohashi, “Large Optical Transmission through a Single Subwavelength Hole Associated with a Sharp-Apex Grating,” Jpn. J. Appl. Phys. 44, L170–L172 (2005).

Nanotechnology (1)

T. Thio, H. L. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of subwavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002).

Nature (2)

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

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

Nature Phys. (1)

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

New J. Phys. (1)

F. de León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. B (R) (1)

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B (R) 72, 161405(R)–161408 (2005).

Phys. Rev. Lett. (3)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of Highly Directional Emission from a Single Subwavelength Aperture Surrounded by Surface Corrugations,” Phys. Rev. Lett. 90, 167401–167404 (2003).
[PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901–213904 (2003).
[PubMed]

O. T. A. Janssen, H. P. Urbach, and G. W. t’ Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99, 043902–043905 (2007).
[PubMed]

PNAS (1)

X. C. G. Zheng and C. Yang, “Surface-wave-enabled darkfield aperture for background suppression during weak signal detection,” PNAS 107, 9043–9048 (2010).
[PubMed]

Rev. Mod. Phys. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. K. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729787 (2010).

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[PubMed]

Other (2)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continous Media (Pergamon Press, New York, 1960).

E. D. Palik, Handbook of optical constants of solids II (Boston: Academic Press, 1991, edited by Edward D. Palik, 1991).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic representation of a BE structure, consisting of a metal film of thickness h deposited on a glass substrate, perforated by a central hole with radius rc and N concentrical circular grooves (all with the same width wg and depth hg ) separated by a period p. The variable distance between the hole the nearest groove is a 1. (b) SEM image of a experimental structure milled by FIB lithography. The scale bar corresponds to 2 μm. (c) Sketch of the re-illumination SP component as implemented in the phenomenological model described in the text.

Fig. 2
Fig. 2

(a) Optical transmittance for the considered bull’s eye with N = 6 annular grooves, h = 280nm, hg = 90nm, wg = 220nm and rc = 125nm. The spectra are acquired as a function of both distance between the hole and the first groove, a 1, and incident wavelength λ. The color scale is linear and in arbitrary units. (b) Experimental transmittance collected at λ≃ 660 nm as a function of a 1, normalized to the transmission maximum. The continuous line is a fit from the phenomenological model of Eq.(1) with fitting parameters discussed in the text. (c) Zoom of the results in panel (b) over a smaller region of a 1 values, in logarithmic scale. (d) CMM calculations for the transmission of light normalized to hole area.

Fig. 3
Fig. 3

For the geometrical parameters in Fig. 2, computed re-illumination from the grooves in the central hole (panel (a)) and amplitude of the electric field at the entrance of the fourth annular groove |E 4| (panel (b)), as a function of a 1 and λ. Panels (c) and (d) show the same as panels (a) and (b), respectively, but for a system of “disconnected” grooves, i.e. by setting Gnm = 0 for nm. Grey lines depict the condition 2an = mnλ SP for each annular groove. The white line in panel (a) renders the spectral dependence for the transmittance through a single hole (×1000).

Fig. 4
Fig. 4

Transmission spectra measured through BE structures with N = 5, h = 280nm, hg = 90nm, wg = 330nm, rc = 170nm, and different periods (see label) being a 1 = p. For each period, the predicted location of λR is indicated. These wavelengths follow Eq. (3), so that Re[ksp [λR ]] = 2π/(p/l), being l = 2, and Eq.(4) with m = 4.

Fig. 5
Fig. 5

For the geometrical parameters in Fig. 2 and λR = 630nm, comparison between the exact values for |G 0|, |G| obtained directly from Eq. (2), and those fitted using Eq. (5), as a function of a. The inset shows |σ(a)|, |β(a)|, and |Γ(a)| values as a function of a.

Fig. 6
Fig. 6

Reillumination of a single groove, |Ig |, as a function of a. The black curve represents the exact calculations obtained directly from Eq. (2). The blue and red curves show the result after fitting α(a) and r(a) and truncating the sum in Eq. (9) to jmax = 1 and 2 terms, respectively. Geometrical parameters as in Fig. 3 and λR = 630nm.

Fig. 7
Fig. 7

Calculation (within the CMM model) for α(a) (panel (a)) and r(a) (panel (b)) for different set of parameters. The black curve is for the system considered in Fig. 2, which is taken as the reference. For the other cases, the labels give the parameters that are different from those in the reference.

Fig. 8
Fig. 8

Calculation (within the CMM model) in logarithmic scale for αarray as a function of a 1 for the same geometrical parameters as in Fig. 2 at λR = 630nm. The black curve represents calculations from Eq. (12) and the red one, the fitting curve where |αarray | ∼ a 1 x with x = 0.45. The inset shows the corresponding calculations for |rarray |.

Equations (12)

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F array 1 + γ a 1 e ( i k s p a 1 ) + r γ a 1 e ( 3 i k s p a 1 )
{ n E n + m G n m E m = I n + G n ν E n n E n + m G n m E n = G n ν E n
λ SP p l
a 1 m λ SP 2
G 0 n ( a n ) = σ ( a n ) e i k s p a n G n n ( a n ) = β ( a n ) + Γ ( a n ) e 2 i k s p a n
E ( a ) = I ( a ) G ( a ) + ( a ) I ( a ) β ( a ) + ( a ) · 1 1 r ( a ) e 2 i k s p a
r ( a ) Γ ( a ) β ( a ) + ( a )
E ( a ) = I ( a ) β ( a ) + ( a ) j = 0 [ r ( a ) e 2 i k s p a ] j
I g ( a ) = α ( a ) e i k s p a j = 0 [ r ( a ) e 2 i k s p a ] j
α ( a ) σ ( a ) I ( a ) β ( a ) + ( a )
I G = α array e i k s p a 1 ( 1 + r a r r a y e 2 i k s p a 1 )
α array = n α ( a n ) e i k s p ( n 1 ) p r array = r · n α ( a n ) e 3 i k s p ( n 1 ) p n α ( a n ) e i k s p ( n 1 ) p

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