Abstract

We develop an analytical approach to study the fundamentals of the resonant light emission of plasmonic crystals composed of lattices of plasmonic nanoparticles fed by coherent dipole emitters. Our theoretical approach leads to simple analytical expressions that elucidate the resonant mechanisms responsible for emission enhancement. We demonstrate that the emission can be efficiently controlled with localized plasmons, lattice surface modes, and Rayleigh anomalies, and discuss the interactions between these different contributions.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  38. B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
    [CrossRef]
  39. S. R. K. Rodriguez, M. C. Schaafsma, A. Berrier, and J. Gómez Rivas, “Collective resonances in plasmonic crystals: size matters,” Physica B 407, 4081–4085 (2012).
    [CrossRef]

2012 (5)

T. V. Teperik and A. Degiron, “Superradiant optical emitters coupled to an array of nanosize metallic antennas,” Phys. Rev. Lett. 108, 147401 (2012).
[CrossRef]

T. V. Teperik and A. Degiron, “Design strategies to tailor the narrow plasmon-photonic resonances in arrays of metallic nanoparticles,” Phys. Rev. B 86, 245425 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole–quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

S. R. K. Rodriguez, M. C. Schaafsma, A. Berrier, and J. Gómez Rivas, “Collective resonances in plasmonic crystals: size matters,” Physica B 407, 4081–4085 (2012).
[CrossRef]

2011 (2)

S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

2010 (3)

V. N. Pustovit and T. V. Shahbazyan, “Plasmon-mediated superradiance near metal nanostructures,” Phys. Rev. B 82, 075429 (2010).
[CrossRef]

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[CrossRef]

2009 (3)

I. Friedler, C. Sauvan, J. P. Hugonin, P. Lalanne, J. Claudon, and J. M. Gérard, “Solid-state single photon sources: the nanowire antenna,” Opt. Express 17, 2095–2110 (2009).
[CrossRef]

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
[CrossRef]

N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
[CrossRef]

2008 (4)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

2007 (3)

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
[CrossRef]

2006 (1)

R. Carminati, J.-J. Greffet, C. Henkel, and J. M. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368–375 (2006).
[CrossRef]

2005 (2)

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129–1179 (2005).
[CrossRef]

2004 (5)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3, 601–605 (2004).
[CrossRef]

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69, 205414 (2004).
[CrossRef]

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

S. Hughes, “Enhanced single-photon emission from quantum dots in photonic crystal waveguides and nanocavities,” Opt. Lett. 29, 2659–2661 (2004).
[CrossRef]

2003 (2)

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef]

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

2002 (2)

A. Neogi, C.-W. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonovitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66, 153305 (2002).
[CrossRef]

F. J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[CrossRef]

2001 (1)

G. S. Solomon, M. Pelton, and Y. Yamamoto, “Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity,” Phys. Rev. Lett. 86, 3903–3906 (2001).
[CrossRef]

1998 (1)

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

1986 (1)

1980 (1)

A. V. Andreev, V. I. Emel’yanov, and Y. A. ll’inskir, “Collective spontaneous emission (Dicke superradiance),” Sov. Phys. Usp. 23, 493–514 (1980).
[CrossRef]

Abass, A.

S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

Aizpurua, J.

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef]

Andreev, A. V.

A. V. Andreev, V. I. Emel’yanov, and Y. A. ll’inskir, “Collective spontaneous emission (Dicke superradiance),” Sov. Phys. Usp. 23, 493–514 (1980).
[CrossRef]

Auguié, B.

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
[CrossRef]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

Barnes, W. L.

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
[CrossRef]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

Ben Bakir, B.

N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
[CrossRef]

Benisty, H.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

Berrier, A.

S. R. K. Rodriguez, M. C. Schaafsma, A. Berrier, and J. Gómez Rivas, “Collective resonances in plasmonic crystals: size matters,” Physica B 407, 4081–4085 (2012).
[CrossRef]

Blanco, L.

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
[CrossRef]

Blanco, L. A.

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69, 205414 (2004).
[CrossRef]

Bohren, C.

C. Bohren and D. Hufmann, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Bouhelier, A.

A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
[CrossRef]

Brongersma, S. H.

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

Bryant, G. W.

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef]

Carminati, R.

R. Carminati, J.-J. Greffet, C. Henkel, and J. M. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368–375 (2006).
[CrossRef]

Carron, K. T.

Chauvin, N.

N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
[CrossRef]

Chichkov, B. N.

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole–quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

Chu, Y.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Claudon, J.

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Crego-Calama, M.

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

Crozier, K. B.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Curto, A. G.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[CrossRef]

Degiron, A.

T. V. Teperik and A. Degiron, “Superradiant optical emitters coupled to an array of nanosize metallic antennas,” Phys. Rev. Lett. 108, 147401 (2012).
[CrossRef]

T. V. Teperik and A. Degiron, “Design strategies to tailor the narrow plasmon-photonic resonances in arrays of metallic nanoparticles,” Phys. Rev. B 86, 245425 (2012).
[CrossRef]

Dereux, A.

A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
[CrossRef]

Emel’yanov, V. I.

A. V. Andreev, V. I. Emel’yanov, and Y. A. ll’inskir, “Collective spontaneous emission (Dicke superradiance),” Sov. Phys. Usp. 23, 493–514 (1980).
[CrossRef]

Esteban, R.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

Everitt, H. O.

A. Neogi, C.-W. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonovitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Evlyukhin, A. B.

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole–quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Fiore, A.

N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
[CrossRef]

Fluhr, W.

Friedler, I.

García de Abajo, F. J.

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[CrossRef]

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
[CrossRef]

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69, 205414 (2004).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef]

F. J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[CrossRef]

Gayral, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

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S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

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P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
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S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

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S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

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R. Carminati, J.-J. Greffet, C. Henkel, and J. M. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368–375 (2006).
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S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

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L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

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R. Carminati, J.-J. Greffet, C. Henkel, and J. M. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368–375 (2006).
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S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

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J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
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J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
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V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
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A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
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A. Neogi, C.-W. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonovitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66, 153305 (2002).
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N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
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Maes, B.

S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

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A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3, 601–605 (2004).
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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3, 601–605 (2004).
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E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
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B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129–1179 (2005).
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G. S. Solomon, M. Pelton, and Y. Yamamoto, “Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity,” Phys. Rev. Lett. 86, 3903–3906 (2001).
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V. N. Pustovit and T. V. Shahbazyan, “Plasmon-mediated superradiance near metal nanostructures,” Phys. Rev. B 82, 075429 (2010).
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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
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E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

Rodriguez, S. R. K.

S. R. K. Rodriguez, M. C. Schaafsma, A. Berrier, and J. Gómez Rivas, “Collective resonances in plasmonic crystals: size matters,” Physica B 407, 4081–4085 (2012).
[CrossRef]

S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

Sauvan, C.

Schaafsma, M. C.

S. R. K. Rodriguez, M. C. Schaafsma, A. Berrier, and J. Gómez Rivas, “Collective resonances in plasmonic crystals: size matters,” Physica B 407, 4081–4085 (2012).
[CrossRef]

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

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S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3, 601–605 (2004).
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[CrossRef]

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J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

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V. N. Pustovit and T. V. Shahbazyan, “Plasmon-mediated superradiance near metal nanostructures,” Phys. Rev. B 82, 075429 (2010).
[CrossRef]

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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3, 601–605 (2004).
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E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

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G. S. Solomon, M. Pelton, and Y. Yamamoto, “Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity,” Phys. Rev. Lett. 86, 3903–3906 (2001).
[CrossRef]

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J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef]

Tackeuchi, A.

A. Neogi, C.-W. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonovitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66, 153305 (2002).
[CrossRef]

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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
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R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[CrossRef]

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J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[CrossRef]

Van Thourhout, D.

S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

Varoutsis, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

Vecchi, G.

S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

Verschuuren, M. A.

S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

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E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

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R. Carminati, J.-J. Greffet, C. Henkel, and J. M. Vigoureux, “Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368–375 (2006).
[CrossRef]

Viktorovitch, P.

N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
[CrossRef]

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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[CrossRef]

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E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement of quantum dots in a photonic crystal wire,” Phys. Rev. Lett. 95, 183901 (2005).
[CrossRef]

Wokaun, A.

Yablonovitch, E.

A. Neogi, C.-W. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonovitch, “Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling,” Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Yamamoto, Y.

G. S. Solomon, M. Pelton, and Y. Yamamoto, “Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity,” Phys. Rev. Lett. 86, 3903–3906 (2001).
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Zhang, Y.

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
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A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole–quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

ACS Nano (1)

P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Appl. Rev. Lett. (1)

S. R. K. Rodriguez, G. Lozano, M. A. Verschuuren, R. Gomes, K. Lambert, B. D. Geyter, A. Hassinen, D. Van Thourhout, Z. Hens, and J. Gómez Rivas, “Quantum rod emission coupled to plasmonic lattice resonances: a collective directional source of polarized light,” Appl. Rev. Lett. 100, 111103 (2012).

J. Chem. Phys. (1)

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

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J. Phys. Chem. B (1)

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transfer 89, 11–16 (2004).
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Nat. Mater. (1)

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[CrossRef]

Nat. Photonics (2)

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[CrossRef]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
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N. Chauvin, P. Nedel, C. Seassal, B. Ben Bakir, X. Letartre, M. Gendry, A. Fiore, and P. Viktorovitch, “Control of the spontaneous emission from a single quantum dash using a slow-light mode in a two-dimensional photonic crystal on a Bragg reflector,” Phys. Rev. B 80, 045315 (2009).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the periodic system composed of nanoring antennas in a SiO2 matrix fed by an array of coherent emitters (represented as double arrows). (b) Geometry of the Au rings.

Fig. 2.
Fig. 2.

Polarizability α [(a) amplitude, (b) phase] and the dipole moment pd [(c) amplitude, (d) phase] as a function of the wavelength for a single ring with internal radius r=60nm (black curves) and r=90nm (red curves). Both rings have a width t=40nm and height h=20nm. Inset: Induced electric field distribution (in arbitrary units) visualized in the horizontal xy plane and the vertical xz planes. The red and blue correspond to positive and negative values of the fields.

Fig. 3.
Fig. 3.

(a), (e) Amplitude of the induced dipole p as a function of wavelength. (b), (f) Wavelength dependence of the real part of the lattice sum S (black line) and inverse polarizability 1/αε (green line). (c), (g) Representation of the sum appearing in Eq. (12). (d), (h) Normalized power η radiated upward (or downward) by a square lattice of rings fed by dipole emitters through the unit-cell area a2=1μm×1μm. Black curves: solutions of Eq. (12). Red curves: numerical simulations with commercial FEM code. The calculations have been performed for two geometries: (a)–(d) small rings with r=60nm and (e)–(h) large rings with r=90nm. Except for the ring radius, both structures have the same geometrical parameters: a=1000nm, h=20nm, and t=40nm. (b), (f) are normalized to 4πa3. 900 plane wave harmonics have been used in the calculations. Vertical dotted lines indicate the resonant wavelength of the localized plasmon resonance of a single ring (red line) and the plasmon resonance supported by a lattice of particles (black line).

Fig. 4.
Fig. 4.

Normalized power η radiated upward (or downward) through the unit-cell area a2 for a range of lattice constants a varying from 300 to 800 nm, accompanied by a schematic representation of the charge distribution for neighboring rings. Black curves: solutions of Eq. (12); red curves: numerical simulations with commercial FEM code. The curves are shifted by an increment of 10 for clarity. r=60nm, h=20, and t=40nm.

Fig. 5.
Fig. 5.

Normalized power η radiated upward (or downward) through the unit-cell area a2. (a) Spectra computed for different ring widths t: 20, 25, 30, and 40 nm (from right to left); (b) spectra computed for different ring heights h: 15, 20, 25, and 35 nm (from right to left). The other geometrical parameters are r=60nm, a=800nm. Red curves: numerical simulations with commercial FEM code.

Equations (13)

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pn=εε0αEloc(Rn),
pn=εε0αEinc+εαk02nnG(RnRn)pn,
p=ε0Exinc1/αεS,
S=k02nnGxx(RnRn)
Gxx(rr)=[1+1k22x2]g(rr)
S=i2εlimz0{1a2geiqz|z|(k2gx2)gz18π2dqxdqyeiqz|z|(k2qx2)qz}.
S=12εlimz0{ia2geiqz|z|(k2gx2)gzeik|z|2πz3[(kz)2+ikz1]}.
pn=pd+ε0αεEinc(nn)+αεk02nnG(RnRn)pn,
p=ε0Exinc(nn)+pd/αε1/αεS.
p=dS+pd/αε1/αεS.
E(x,y,z=0)=i(p+d)2ϵ0a2geig·Rqz[x^(k2gx2)y^gxgyz^gxqz].
η=ASzP0dA=3π|p+d|22k2d2a2gk2gx2kqze2Im(qz)z.
η=3π|p+d|22k2d2a2gk2gx2kqz.

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