Abstract

We present a detailed formalism allowing analytical calculations of the radiative properties of nanoantennas. This formalism does not rely on dipole approximations and utilizes multipolar multiple-scattering theory. The improvement in both accuracy and calculation speeds offered by this formulation provides significant advantages that are used in this work to study Yagi-Uda-type nanoantennas. We provide a study that questions the necessity of the reflector particle in nanoantennas.

© 2011 Optical Society of America

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    [CrossRef]
  3. M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
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  4. J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
    [CrossRef] [PubMed]
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  6. R. Carminati, J.-J. Greffet, C. Henkel, and J. Vigoureux, “Radiative and non-radiative decay of single molecule close to a metallic nanoparticle,” Opt. Commun. 261, 368–375 (2006).
    [CrossRef]
  7. H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
    [CrossRef]
  8. L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar, “Design of plasmonic nanoantennae for enhancing spontaneous emission,” Opt. Lett. 32, 1623–1625 (2007).
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  9. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. H. F. Hofman, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi-Uda antenna,” New J. Phys. 9, 217(2007).
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  15. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007).
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    [CrossRef] [PubMed]
  21. N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
    [CrossRef]
  22. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photon. 4, 312–315 (2010).
    [CrossRef]
  23. A. Curto, G. Volpe, T. Taminiau, M. Kreuzer, R. Quidant, and N. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
    [CrossRef] [PubMed]
  24. M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19, 4159–4174 (1980).
    [CrossRef] [PubMed]
  25. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76, 1681–1684 (1982).
    [CrossRef]
  26. Y. Kim, P. Leung, and T. George, “Classical decay rates for molecules in the presence of a spherical surface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
    [CrossRef]
  27. G. C. des Francs, A. Bouhelier, E. Finot, J. Weeber, A. Dereux, and E. Dujardin, “Fluorescence relaxation in the near-field of a mesoscopic metallic particle: distance dependence and role of plasmon modes,” Opt. Express 16, 17654–17666 (2008).
    [CrossRef]
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    [CrossRef]
  30. B. Stout, J. Auger, and A. Devilez, “Recursive T matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations,” J. Opt. Soc. Am. A 25, 2549–2557 (2008).
    [CrossRef]
  31. J.-C. Auger, V. Martinez, and B. Stout, “Absorption and scattering properties of dense ensembles of non-spherical particles,” J. Opt. Soc. Am. A 24, 3508–3516 (2007).
    [CrossRef]
  32. L. Novotny and B. Hecht, “Light emission and optical interactions in nanoscale environments,” in Principles of Nano-Optics (Cambridge University, 2006), pp. 250–303.
  33. L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
    [CrossRef]
  34. M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
    [CrossRef]
  35. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).
  36. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  37. Y. P. Pellegrini, B. Stout, and P. Thibaudeau, “Off-shell mean-field electromagnetic T-matrix of finite size spheres and fuzzy scatterers,” J. Phys. Condens. Matter 9, 177–191 (1997).
    [CrossRef]
  38. P. de Vries, D. V. van Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466(1998).
    [CrossRef]
  39. A. Lagendijk and B. Tiggelin, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
    [CrossRef]
  40. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1960).
  41. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons & Atoms: Introduction to Quantum Electrodynamics(Wiley, 1997).
  42. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

2011 (1)

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

2010 (5)

J. W. Liaw, C. S. Chen, and J. H. Chen, “Enhancement or quenching effect of metallic nanodimer on spontaneous emission,” J. Quant. Spectrosc. Radiat. Transfer 111, 454–465 (2010).
[CrossRef]

A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano. 4, 3390–3396 (2010).
[CrossRef] [PubMed]

N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
[CrossRef]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photon. 4, 312–315 (2010).
[CrossRef]

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

2009 (4)

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

A. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228–4233 (2009).
[CrossRef] [PubMed]

T. Pakizeh and M. Kall, “Unidirectional ultracompact optical antennas,” Nano Lett. 9, 2343–2349 (2009).
[CrossRef] [PubMed]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

2008 (4)

2007 (5)

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

H. F. Hofman, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi-Uda antenna,” New J. Phys. 9, 217(2007).
[CrossRef]

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007).
[CrossRef]

L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar, “Design of plasmonic nanoantennae for enhancing spontaneous emission,” Opt. Lett. 32, 1623–1625 (2007).
[CrossRef] [PubMed]

J.-C. Auger, V. Martinez, and B. Stout, “Absorption and scattering properties of dense ensembles of non-spherical particles,” J. Opt. Soc. Am. A 24, 3508–3516 (2007).
[CrossRef]

2006 (3)

L. Novotny and B. Hecht, “Light emission and optical interactions in nanoscale environments,” in Principles of Nano-Optics (Cambridge University, 2006), pp. 250–303.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

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

2005 (1)

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

2004 (1)

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
[CrossRef]

2002 (2)

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, “Resonant light scattering from individual Ag nanoparticles and particle pairs,” Appl. Phys. Lett. 80, 1826–1828 (2002).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

2000 (1)

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

1999 (1)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

1998 (1)

P. de Vries, D. V. van Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466(1998).
[CrossRef]

1997 (2)

Y. P. Pellegrini, B. Stout, and P. Thibaudeau, “Off-shell mean-field electromagnetic T-matrix of finite size spheres and fuzzy scatterers,” J. Phys. Condens. Matter 9, 177–191 (1997).
[CrossRef]

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons & Atoms: Introduction to Quantum Electrodynamics(Wiley, 1997).

1996 (1)

A. Lagendijk and B. Tiggelin, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

1990 (1)

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1990).

1988 (1)

Y. Kim, P. Leung, and T. George, “Classical decay rates for molecules in the presence of a spherical surface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

1985 (1)

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

1984 (1)

H. Metiu, “Surface enhanced spectroscopy,” Prog. Surf. Sci. 17, 153–320 (1984).
[CrossRef]

1983 (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

1982 (1)

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76, 1681–1684 (1982).
[CrossRef]

1980 (2)

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19, 4159–4174 (1980).
[CrossRef] [PubMed]

1960 (1)

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1960).

1951 (1)

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Agio, M.

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Aouani, H.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

Arias-Gonzalez, J. R.

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
[CrossRef]

Auger, J.

Auger, J.-C.

J.-C. Auger, V. Martinez, and B. Stout, “Absorption and scattering properties of dense ensembles of non-spherical particles,” J. Opt. Soc. Am. A 24, 3508–3516 (2007).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

Avlasevich, Y.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Bidault, S.

N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bonod, N.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano. 4, 3390–3396 (2010).
[CrossRef] [PubMed]

N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
[CrossRef]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

Bouhelier, A.

Carminati, R.

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

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
[CrossRef]

Chen, C. S.

J. W. Liaw, C. S. Chen, and J. H. Chen, “Enhancement or quenching effect of metallic nanodimer on spontaneous emission,” J. Quant. Spectrosc. Radiat. Transfer 111, 454–465 (2010).
[CrossRef]

Chen, J. H.

J. W. Liaw, C. S. Chen, and J. H. Chen, “Enhancement or quenching effect of metallic nanodimer on spontaneous emission,” J. Quant. Spectrosc. Radiat. Transfer 111, 454–465 (2010).
[CrossRef]

Chew, H.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1990).

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons & Atoms: Introduction to Quantum Electrodynamics(Wiley, 1997).

Curto, A.

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

de Vries, P.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466(1998).
[CrossRef]

Dereux, A.

des Francs, G. C.

Devaux, E.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Devilez, A.

Dujardin, E.

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons & Atoms: Introduction to Quantum Electrodynamics(Wiley, 1997).

Ebbesen, T. W.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1960).

Eisler, H.-J.

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Engheta, N.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Fan, S.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

Farahani, J. N.

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Finot, E.

Garcia-Parajo, M. F.

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

George, T.

Y. Kim, P. Leung, and T. George, “Classical decay rates for molecules in the presence of a spherical surface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

Gérard, D.

Gersen, H.

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

Greffet, J.-J.

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

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons & Atoms: Introduction to Quantum Electrodynamics(Wiley, 1997).

Hecht, B.

L. Novotny and B. Hecht, “Light emission and optical interactions in nanoscale environments,” in Principles of Nano-Optics (Cambridge University, 2006), pp. 250–303.

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Henkel, C.

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

Hofman, H. F.

H. F. Hofman, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi-Uda antenna,” New J. Phys. 9, 217(2007).
[CrossRef]

Hofmann, H. F.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photon. 4, 312–315 (2010).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Kadoya, Y.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photon. 4, 312–315 (2010).
[CrossRef]

H. F. Hofman, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi-Uda antenna,” New J. Phys. 9, 217(2007).
[CrossRef]

Kall, M.

T. Pakizeh and M. Kall, “Unidirectional ultracompact optical antennas,” Nano Lett. 9, 2343–2349 (2009).
[CrossRef] [PubMed]

Kaminski, F.

Kerker, M.

Kim, Y.

Y. Kim, P. Leung, and T. George, “Classical decay rates for molecules in the presence of a spherical surface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

Kinkhabwala, A.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

Koenderink, A.

A. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228–4233 (2009).
[CrossRef] [PubMed]

Koenderink, A. F.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

Kosako, T.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photon. 4, 312–315 (2010).
[CrossRef]

H. F. Hofman, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi-Uda antenna,” New J. Phys. 9, 217(2007).
[CrossRef]

Kreuzer, M.

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

Kuipers, L.

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

Kuwata, H.

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, “Resonant light scattering from individual Ag nanoparticles and particle pairs,” Appl. Phys. Lett. 80, 1826–1828 (2002).
[CrossRef]

Lafait, J.

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

Lagendijk, A.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466(1998).
[CrossRef]

A. Lagendijk and B. Tiggelin, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Lax, M.

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Leung, P.

Y. Kim, P. Leung, and T. George, “Classical decay rates for molecules in the presence of a spherical surface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

Li, J.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Liaw, J. W.

J. W. Liaw, C. S. Chen, and J. H. Chen, “Enhancement or quenching effect of metallic nanodimer on spontaneous emission,” J. Quant. Spectrosc. Radiat. Transfer 111, 454–465 (2010).
[CrossRef]

Mahboud, O.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Martinez, V.

Mertens, H.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Metiu, H.

H. Metiu, “Surface enhanced spectroscopy,” Prog. Surf. Sci. 17, 153–320 (1984).
[CrossRef]

Miyano, K.

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, “Resonant light scattering from individual Ag nanoparticles and particle pairs,” Appl. Phys. Lett. 80, 1826–1828 (2002).
[CrossRef]

Miyazaki, H. T.

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, “Resonant light scattering from individual Ag nanoparticles and particle pairs,” Appl. Phys. Lett. 80, 1826–1828 (2002).
[CrossRef]

Moerner, W. E.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

Mullen, K.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, “Light emission and optical interactions in nanoscale environments,” in Principles of Nano-Optics (Cambridge University, 2006), pp. 250–303.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

Pakizeh, T.

T. Pakizeh and M. Kall, “Unidirectional ultracompact optical antennas,” Nano Lett. 9, 2343–2349 (2009).
[CrossRef] [PubMed]

Pellegrini, Y. P.

Y. P. Pellegrini, B. Stout, and P. Thibaudeau, “Off-shell mean-field electromagnetic T-matrix of finite size spheres and fuzzy scatterers,” J. Phys. Condens. Matter 9, 177–191 (1997).
[CrossRef]

Pohl, D. W.

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Polman, A.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Popov, E.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

Quidant, R.

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

Rigneault, H.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

Rogobete, L.

Rolly, B.

N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
[CrossRef]

Ruppin, R.

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76, 1681–1684 (1982).
[CrossRef]

Salandrino, A.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Sandoghdar, V.

Segerink, F. B.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photon. 2, 234–237 (2008).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Stefani, F. D.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photon. 2, 234–237 (2008).
[CrossRef]

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16, 10858–10866(2008).
[CrossRef] [PubMed]

Stout, B.

N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
[CrossRef]

A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano. 4, 3390–3396 (2010).
[CrossRef] [PubMed]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

B. Stout, J. Auger, and A. Devilez, “Recursive T matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations,” J. Opt. Soc. Am. A 25, 2549–2557 (2008).
[CrossRef]

J.-C. Auger, V. Martinez, and B. Stout, “Absorption and scattering properties of dense ensembles of non-spherical particles,” J. Opt. Soc. Am. A 24, 3508–3516 (2007).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

Y. P. Pellegrini, B. Stout, and P. Thibaudeau, “Off-shell mean-field electromagnetic T-matrix of finite size spheres and fuzzy scatterers,” J. Phys. Condens. Matter 9, 177–191 (1997).
[CrossRef]

Tamaru, H.

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, “Resonant light scattering from individual Ag nanoparticles and particle pairs,” Appl. Phys. Lett. 80, 1826–1828 (2002).
[CrossRef]

Taminiau, T.

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

Taminiau, T. H.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16, 10858–10866(2008).
[CrossRef] [PubMed]

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photon. 2, 234–237 (2008).
[CrossRef]

Thibaudeau, P.

Y. P. Pellegrini, B. Stout, and P. Thibaudeau, “Off-shell mean-field electromagnetic T-matrix of finite size spheres and fuzzy scatterers,” J. Phys. Condens. Matter 9, 177–191 (1997).
[CrossRef]

Thomas, M.

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
[CrossRef]

Tiggelin, B.

A. Lagendijk and B. Tiggelin, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Tsang, L.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

van Coevorden, D. V.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466(1998).
[CrossRef]

van Hulst, N.

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

van Hulst, N. F.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16, 10858–10866(2008).
[CrossRef] [PubMed]

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photon. 2, 234–237 (2008).
[CrossRef]

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

Veerman, J. A.

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

Vigoureux, J.

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

Volpe, G.

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

Wang, D.-S.

Weeber, J.

Wenger, J.

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B 26, 1473–1478 (2009).
[CrossRef]

Yu, Z.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

ACS Nano. (1)

A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” ACS Nano. 4, 3390–3396 (2010).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, “Resonant light scattering from individual Ag nanoparticles and particle pairs,” Appl. Phys. Lett. 80, 1826–1828 (2002).
[CrossRef]

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, “Single-molecule spontaneous emission close to absorbing nanostructures,” Appl. Phys. Lett. 85, 3863–3865 (2004).
[CrossRef]

J. Appl. Phys. (1)

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

J. Chem. Phys. (1)

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76, 1681–1684 (1982).
[CrossRef]

J. Mod. Opt. (1)

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

J. Phys. Condens. Matter (1)

Y. P. Pellegrini, B. Stout, and P. Thibaudeau, “Off-shell mean-field electromagnetic T-matrix of finite size spheres and fuzzy scatterers,” J. Phys. Condens. Matter 9, 177–191 (1997).
[CrossRef]

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

J. W. Liaw, C. S. Chen, and J. H. Chen, “Enhancement or quenching effect of metallic nanodimer on spontaneous emission,” J. Quant. Spectrosc. Radiat. Transfer 111, 454–465 (2010).
[CrossRef]

Nano Lett. (3)

H. Aouani, O. Mahboud, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

A. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228–4233 (2009).
[CrossRef] [PubMed]

T. Pakizeh and M. Kall, “Unidirectional ultracompact optical antennas,” Nano Lett. 9, 2343–2349 (2009).
[CrossRef] [PubMed]

Nat. Photon. (3)

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657(2009).
[CrossRef]

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photon. 2, 234–237 (2008).
[CrossRef]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photon. 4, 312–315 (2010).
[CrossRef]

New J. Phys. (1)

H. F. Hofman, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical Yagi-Uda antenna,” New J. Phys. 9, 217(2007).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rep. (1)

A. Lagendijk and B. Tiggelin, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Phys. Rev. B (3)

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76, 115123 (2007).
[CrossRef]

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 245403 (2007).
[CrossRef]

N. Bonod, A. Devilez, B. Rolly, S. Bidault, and B. Stout, “Ultracompact and unidirectional metallic antennas,” Phys. Rev. B 82, 115429 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[CrossRef]

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Prog. Surf. Sci. (1)

H. Metiu, “Surface enhanced spectroscopy,” Prog. Surf. Sci. 17, 153–320 (1984).
[CrossRef]

Rev. Mod. Phys. (2)

P. de Vries, D. V. van Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466(1998).
[CrossRef]

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Science (1)

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

Surf. Sci. (1)

Y. Kim, P. Leung, and T. George, “Classical decay rates for molecules in the presence of a spherical surface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

Other (7)

L. Novotny and B. Hecht, “Light emission and optical interactions in nanoscale environments,” in Principles of Nano-Optics (Cambridge University, 2006), pp. 250–303.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1960).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons & Atoms: Introduction to Quantum Electrodynamics(Wiley, 1997).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1990).

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Figures (9)

Fig. 1
Fig. 1

(a) Yagi-Uda antenna design with a silver reflector element 120 nm in diameter and a collector array of eight silver spheres 100 nm in diameter. (b) Radiation pattern I ˜ ( θ , ϕ ) of this antenna in the far field for an emitter operating at a vacuum wavelength of λ v = 618 nm .

Fig. 2
Fig. 2

(a) Antenna schematic: four silver spheres D Ag = 100 nm in diameter with or without a D R = 120 nm reflector particle. (b) Directivity parameter 10 log 10 ( 4 π I axis / Γ r ) as a function of vacuum wavelength. (c) Radiative enhancement, Γ r / Γ 0 . (d) Quantum efficiency, η = Γ r / Γ tot .

Fig. 3
Fig. 3

(a) Antenna schematic: same characteristics as in Fig. 2, but with an eight-particle collector array. (b) Directivity parameter 10 log 10 ( 4 π I axis / Γ r ) as a function of vacuum wavelength. (c) Radiative enhancement, Γ r / Γ 0 . (d) Quantum efficiency, η = Γ r / Γ tot .

Fig. 4
Fig. 4

Power emitted along the collector axis for emitters 30 nm from the first collector particle in configurations with and without a reflector particle. Full squares, eight-particle collector without reflector; full circles, four-particle collector without reflector; open squares, eight-particle collector with reflector; open circles, four-particle collector with reflector.

Fig. 5
Fig. 5

(a) Quantum efficiency and (b) radiative enhancement as functions of the wavelength for a nine-particle Yagi- Uda with the same parameters as in Fig. 1 with varying reflector– collector separations (emitter equidistant from reflector and first collector particles: 2 d = 60 , 70 , 80 , 100 nm ).

Fig. 6
Fig. 6

(a), (b) Directivity, D . (c), (d) On-axis normalized radiative power enhancement as functions of wavelength and distance, d, of the emitter to the first collector. (a), (c) Four-particle collector, (b), (d) eight-particle collector.

Fig. 7
Fig. 7

Radiation diagrams at the optimal parameters obtained from Fig. 6. (Irradiance is normalized such that one corresponds to the intensity of maximum free-space radiation.) Optimal directivity for a (a) four-particle collector at λ = 617 nm and emitter–collector separation of d = 40 nm , (b) eight-particle collector at λ = 626 nm with d = 35 nm . Optimal on-axis irradiance for a (c) four-particle collector at λ = 630 nm with d = 90 nm , (d) eight-particle collector at λ = 638 nm with d = 85 nm .

Fig. 8
Fig. 8

Directivity, in decibels, plotted as a function of the angle of the emitter with the direction perpendicular to the collector chain for a four- and eight-particle collector chain (without reflector) and emitter–collector separations of d = 30 nm (respective operating wavelengths of λ = 615 nm and λ = 626 nm selected respectively for high directivities).

Fig. 9
Fig. 9

(a) Comparison between coupled electric dipole results and multipole calculations for an eight-particle collector array antenna. (b) Directivity parameter 10 log 10 ( 4 π I axis / Γ r ) . (c) Radiative enhancement, Γ r / Γ 0 . (d) Quantum efficiency, η = Γ r / Γ tot .

Equations (45)

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E ( x ) = i ω μ 0 d x G ( x x ) j e ( x ) .
G ( x , x ) = G 0 ( x , x ) + G s ( x , x ) .
× × G 0 ( x x ) k b 2 G 0 ( x x ) = I δ 3 ( x x ) ,
G 0 ( r ) = e i k b r 4 π k b 2 r 3 P . V . { ( 1 i k b r ) ( 3 r ^ r ^ I ) + k b 2 r 2 ( I r ^ r ^ ) } I 3 k b 2 δ 3 ( r ) ,
E 0 ( x ) = e i k b r 4 π ε b ϵ 0 r 3 { ( 1 i k b r ) [ 3 r ^ ( r ^ · p e ) p e ] + k b 2 r 2 [ p e r ^ ( r ^ · p e ) ] } p e 3 ε b ϵ 0 δ 3 ( r ) .
G s = G 0 ( i = 1 , j = 1 N T ( i , j ) ) G 0 ,
T ( i , j ) = q = 1 , q = 1 2 n = 1 ; n = 1 m = n m = n m = n m = n | Ψ q , n , m T q , n , m ; q , n , m ( i , j ) Ψ q n , m | ,
[ T N ( 1 , 1 ) T N ( 1 , 2 ) T N ( 1 , N ) T N ( 2 , 1 ) T N ( 2 , 2 ) T N ( 2 , N ) T N ( N , 1 ) T N ( N , 2 ) T N ( N , N ) ] = [ [ t ( 1 ) ] 1 H ( 1 , 2 ) H ( 1 , N ) H ( 2 , 1 ) [ t ( 2 ) ] 1 H ( 2 , N ) H ( N , 1 ) H ( N , 2 ) [ t ( N ) ] 1 ] 1 ,
Γ t 1 T 0 T d t d xE t ( x , t ) · j e ( x , t ) = ω 3 2 μ 0 Im { p e * ( x j ) · G ( x j , x j ) · p e ( x j ) } .
lim r H t ( r ) = k b μ 0 ω r ^ × E t .
r lim r S = lim r 1 2 Re { E t * × H t } = 1 2 k b ω μ 0 r ^ E t 2 .
I r ( θ , ϕ ) lim r r 2 S · r ^ and Γ r d Ω I r ( θ , ϕ ) .
Γ t , 0 = ω 3 2 μ 0 Im { p e * ( x j ) · G 0 ( x j , x j ) · p e ( x j ) } = | p e | 2 ω 3 12 π ϵ 0 c 2 Re { k b } .
I r , 0 ( r ^ ) = ω 3 k b 32 π 2 ϵ 0 c 2 ( 1 ( r ^ · p ^ e ) 2 ) | p e | 2 , Γ 0 d Ω I r , 0 ( θ , ϕ ) = | p e | 2 ω 3 k b 12 π ϵ 0 c 2 .
G 0 ( r , 0 ) = i k b m = 1 1 N 1 m ( k b , r ) R g { N ˜ 1 m ( 0 ) } r ^ r ^ k b 2 δ ( r ) ,
E 0 ( x ) = ω 2 μ 0 d x G 0 ( x , x ) · p e δ 3 ( x ) = i k b ω 2 p e ϵ 0 c 2 m = 1 1 N 1 m ( k b x ) f 2 , 1 , m ,
f 2 , 1 , m R g { N ˜ 1 m ( 0 ) } · n ^ = Ψ 2 , n , m | 0 · n ^ ,
f q , n , 0 = δ q , 2 δ n , 1 1 6 π z ^ · n ^ , f q , n , 1 = δ q , 2 δ n , 1 2 3 π ( x ^ + i y ^ ) · n ^ , f q , n , 1 = δ q , 2 δ n , 1 2 3 π ( x ^ + i y ^ ) · n ^ .
E t ( r ) = E 0 + E s = i p e k b ω 2 ϵ 0 c 2 [ N ( r ) f + j , l = 1 N [ M ( k r j ) , N ( k r j ) ] T ( j , l ) H ( l , e ) f ] i p e k b ω 2 ϵ 0 c 2 E ˜ t ( r ) ,
I ˜ r 4 π I r ( θ , ϕ ) Γ 0 = 24 π 2 lim r ( k b r ) 2 E ˜ t ( r ) 2 .
Γ t ˜ Γ t Γ t , 0 = 1 + Re { 6 π k b j , l = 1 N f H ( e , j ) T ( j , l ) H ( l , e ) f } Re { k b } .
Γ r ˜ Γ r Γ 0 = 1 + 6 π i , j , k , l = 1 N [ T ( j , i ) H ( i , e ) f ] J ( j , k ) T ( k , l ) H ( l , e ) f + 12 π Re [ j , l = 1 N f J ( e , j ) T ( j , l ) H ( l , e ) f ] ,
Γ t ˜ = 1 + Re { 6 π k b f H ( e , j ) t H ( j , e ) f } Re { k b } ,
Γ r ˜ = 1 + 6 π [ H ( j , e ) f ] t t H ( j , e ) f + 12 π Re [ f J ( e , j ) t H ( j , e ) f ] ,
p ( ω ) = ϵ 0 ε b α ( ω ) E exc ( ω ) ,
E exc , j = E inc , j l j e i k b d j , l a l 3 d j , l 3 ( 1 i k b d j , l k b 2 d j , l 2 ) α ˜ l ( ω ) E exc , l = E inc , j + l j γ j , l α ˜ l ( ω ) E exc , l ,
α ˜ j ( ω ) α j ( ω ) 4 π a j 3
γ j , l e i k b d j , l ( a l d j , l ) 3 ( 1 i k b d j , l k b 2 d j , l 2 ) γ j , e e i k b d j , e ( a j d j , e ) 3 ( 1 i k b d j , e k b 2 d j , e 2 )
p ˜ j α ˜ j ( ω ) E exc , j ,
[ p ˜ 1 p ˜ N ] = [ α ˜ 1 1 γ 1 , 2 γ 1 , N γ 2 , 1 α ˜ 2 1 γ 2 , N γ N , 1 γ N , 2 α ˜ N 1 ] 1 [ E inc , 1 E inc , N ] .
α ˜ j eff ( ω ) p ˜ j E inc , j .
E inc , j = e i k b d j , e ( 1 d j , e ) 3 ( 1 i k b d j , e k b 2 d j , e 2 ) p e 4 π ϵ 0 ε b .
E t ( r ) = 1 4 π ϵ 0 ε b j = 0 N e i k b r j r j 3 { ( 1 i k b r j ) [ 3 r ^ j ( r ^ j · p j ) p j ] + k b 2 r j 2 ( p j r ^ j ( r ^ j · p j ) ) } ,
lim r E ˜ t ( r , θ , ϕ ) = e i k b r 4 π i k b r sin θ θ ^ [ 1 + j = 1 N γ j , e α ˜ j eff e i k b d j , e sin θ cos ϕ ] I ˜ r ( θ , ϕ ) 4 π I r ( θ , ϕ ) Γ 0 = 3 2 sin 2 θ | 1 + j = 1 N γ j , e α ˜ j eff e i k b d j , e sin θ cos ϕ | 2 ,
Γ t ˜ Γ t Γ t , 0 = 1 + 3 2 j = 1 N Im { ( γ j , e k b a j ) 2 α ˜ j eff } Re { k b a j } ,
Γ r ˜ Γ r Γ 0 = 1 + j = 1 N | α ˜ j eff γ j , e | 2 + j = 1 N 3 Re [ α ˜ j eff γ j , e ] [ ( k b d j , e ) 2 1 ( k b d j , e ) 3 sin ( k b d j , e ) + cos ( k b d j , e ) ( k b d j , e ) 2 ] + l > j N 3 Re [ γ l , e * α ˜ l eff , * α ˜ j eff γ j , e ] [ ( k b d l , j ) 2 1 ( k b d l , j ) 3 sin ( k b d l , j ) + cos ( k b d l , j ) ( k b d l , j ) 2 ] ,
α ( ω ) = 6 π i k b 3 t 2 , 1 ( ω ) ,
α ˜ ( ω ) = α ( ω ) 4 π a 3 = 3 2 i ( a k b ) 3 j 1 ( a k b ) h 1 ( a k b ) ε s φ 1 ( a k b ) ε b φ 1 ( a k s ) ε b φ 1 ( a k s ) ε s φ 1 ( 3 ) ( a k b ) ,
φ 1 ( z ) [ z j 1 ( z ) ] j 1 ( z ) , φ 1 ( 3 ) ( x ) [ z h 1 ( z ) ] h 1 ( z ) .
Y n m ( θ , ϕ ) r ^ Y n m ( θ , ϕ ) ,
Z n m ( θ , ϕ ) r Y n m ( θ , ϕ ) n ( n + 1 ) ,
X n m ( θ , ϕ ) Z n m ( θ , ϕ ) × r ^ .
W n m ( i ) W ν μ ( j ) ( ) m 0 4 π W n , m ( i ) · W ν μ ( j ) d Ω = δ i j δ n ν δ m μ .
Ψ 1 , n , m | r R g { M ˜ n , m ( k r ) } ( ) m j n ( k r ) X n , m ( r ^ ) Ψ 2 , n , m | r R g { N ˜ n m ( k r ) } , n = 1 , 2 , ... , m = n , ... , n ( ) m k r { n ( n + 1 ) j n ( k r ) r ^ Y n , m ( r ^ ) + [ k r j n ( k r ) ] Z n , m ( r ^ ) } .
N n m ( k r ) 1 k r { n ( n + 1 ) h n ( k r ) r ^ Y n m ( r ^ ) + [ k r h n ( k r ) ] Z n m ( r ^ ) } , M n m ( k r ) h n ( k r ) X n m ( r ^ ) .

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