Abstract

We analytically and numerically analyze the fluorescence decay rate of a quantum emitter placed in the vicinity of a spherical metallic particle of mesoscopic size (i.e with dimensions comparable to the emission wavelength). We discuss the efficiency of the radiative decay rate and non-radiative coupling to the particle as well as their distance dependence. The electromagnetic coupling mechanisms between the emitter and the particle are investigated by analyzing the role of the plasmon modes and their nature (dipole, multipole or interface mode). We demonstrate that near-field coupling can be expressed in a simple form verifying the optical theorem for each particle modes.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  7. P. Anger, P. Bharadwaj, and L. Novotny, "Enhancement and quenching of single molecule fluorescence," Phys. Rev. Lett. 96, 113002 (2006).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  23. R. Carminati, J. Greffet, C. Henkel, and J. Vigoureux, "Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle," Opt. Commun. 261, 368-375 (2006).
    [CrossRef]
  24. R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
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    [CrossRef]
  28. W. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
    [CrossRef]
  29. C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
    [CrossRef] [PubMed]

2008

A. Trugler and U. Hohenester, "Strong coupling between a metallic nanoparticle and a single molecule," Phys. Rev. B 77, 115403 (2008).
[CrossRef]

2007

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "λ /4 resonance of an optical monopole antenna probed by single molecule fluorescence," Nano Lett. 7, 28-33 (2007).
[CrossRef] [PubMed]

H. Mertens, A. 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]

L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar, "Design of nanoantennae for the enhancement of spontaneous emission," Opt. Lett. 32, 1623-1625 (2007).
[CrossRef] [PubMed]

T. Hartling, P. Reichenbach, and L. M. Eng, "Near-field coupling of a single fluorescent molecule and a spherical gold nanoparticle," Opt. Express 15, 12806-12817 (2007).
[CrossRef] [PubMed]

P. Bharadwaj and L. Novotny, "Spectral dependence of single molecule fluorescence enhancement," Opt. Express 15, 14266-14274 (2007).
[CrossRef] [PubMed]

2006

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

D. Chang, A. S¨orensen, P. Hemmer, and M. Lukin, "Quantum Optics with Surface Plasmons," Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

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

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, "Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna," Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

2005

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

G. Colas des Francs, C. Girard, M. Juan, and A. Dereux, "Energy transfer in near-field optics," J. Chem. Phys. 123, 174709 (2005).
[CrossRef] [PubMed]

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

2004

R. P. Van Duyne, "Molecular plasmonics," Science 306, 985 (2004).

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

2002

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

1998

W. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
[CrossRef]

1996

V. Klimov, M. Ducloy, and V. S. Letokhov, "Radiative Frequency Shift and LineWidth of an Atom Dipole in the Vicinity of a Dielectric Microsphere," J. Mod. Opt. 43, 2251 (1996).
[CrossRef]

1990

P. T. Leung, "Decay of molecules at spherical surfaces: Nonlocal effects," Phys. Rev. B 42, 7622 (1990).
[CrossRef]

1989

C. Girard, S. Maghezzi, and F. Hache, "Multipolar propagators near a small metallic sphere : A self consistent calculation," J. Chem. Phys. 91, 5509-5517 (1989).
[CrossRef]

1988

Y. S. Kim, P. T. Leung, and T. F. George, "Classical Decay Rates for Molecules in the Presence of a Spherical Surface: a Complete Treatment," Surf. Sci. 195, 1-14 (1988).
[CrossRef]

1987

H. Chew, "Transitions rates of atoms near spherical surfaces," J. Chem. Phys. 87, 1355-1360 (1987).
[CrossRef]

1983

1978

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[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]

Baffou, G.

G. Baffou, C. Girard, E. Dujardin, G. Colas des Francs, and O. Martin, "Molecular quenching and relaxation in a plasmonic tunable nanogap," Phys. Rev. B 77, 121101(R) (2008).
[CrossRef]

Barnes, W.

W. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
[CrossRef]

Bharadwaj, P.

P. Bharadwaj and L. Novotny, "Spectral dependence of single molecule fluorescence enhancement," Opt. Express 15, 14266-14274 (2007).
[CrossRef] [PubMed]

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

Blanco, L. A.

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

Carminati, R.

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

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

Chang, D.

D. Chang, A. S¨orensen, P. Hemmer, and M. Lukin, "Quantum Optics with Surface Plasmons," Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Chew, H.

H. Chew, "Transitions rates of atoms near spherical surfaces," J. Chem. Phys. 87, 1355-1360 (1987).
[CrossRef]

de Abajo, F. J. G.

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

Ducloy, M.

V. Klimov, M. Ducloy, and V. S. Letokhov, "Radiative Frequency Shift and LineWidth of an Atom Dipole in the Vicinity of a Dielectric Microsphere," J. Mod. Opt. 43, 2251 (1996).
[CrossRef]

Dujardin, E.

G. Baffou, C. Girard, E. Dujardin, G. Colas des Francs, and O. Martin, "Molecular quenching and relaxation in a plasmonic tunable nanogap," Phys. Rev. B 77, 121101(R) (2008).
[CrossRef]

Dulkeith, E.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Eisler, H.-J.

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Eng, L. M.

Feldmann, J.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Fisher, M.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

George, T. F.

Y. S. Kim, P. T. Leung, and T. F. George, "Classical Decay Rates for Molecules in the Presence of a Spherical Surface: a Complete Treatment," Surf. Sci. 195, 1-14 (1988).
[CrossRef]

Girard, C.

C. Girard, S. Maghezzi, and F. Hache, "Multipolar propagators near a small metallic sphere : A self consistent calculation," J. Chem. Phys. 91, 5509-5517 (1989).
[CrossRef]

G. Baffou, C. Girard, E. Dujardin, G. Colas des Francs, and O. Martin, "Molecular quenching and relaxation in a plasmonic tunable nanogap," Phys. Rev. B 77, 121101(R) (2008).
[CrossRef]

Gittins, D. I.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Greffet, J.

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

Hache, F.

C. Girard, S. Maghezzi, and F. Hache, "Multipolar propagators near a small metallic sphere : A self consistent calculation," J. Chem. Phys. 91, 5509-5517 (1989).
[CrossRef]

Hakanson, U.

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, "Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna," Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Hartling, T.

Hecht, B.

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Hemmer, P.

D. Chang, A. S¨orensen, P. Hemmer, and M. Lukin, "Quantum Optics with Surface Plasmons," Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Henkel, C.

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

Hira, S.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

Hohenester, U.

A. Trugler and U. Hohenester, "Strong coupling between a metallic nanoparticle and a single molecule," Phys. Rev. B 77, 115403 (2008).
[CrossRef]

Hopkins, B.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

Javier, A.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

Jennings, T.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

Kaminski, F.

Kim, Y. S.

Y. S. Kim, P. T. Leung, and T. F. George, "Classical Decay Rates for Molecules in the Presence of a Spherical Surface: a Complete Treatment," Surf. Sci. 195, 1-14 (1988).
[CrossRef]

Klar, T. A.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Klimov, V.

V. Klimov, M. Ducloy, and V. S. Letokhov, "Radiative Frequency Shift and LineWidth of an Atom Dipole in the Vicinity of a Dielectric Microsphere," J. Mod. Opt. 43, 2251 (1996).
[CrossRef]

Koenderink, A.

H. Mertens, A. 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]

Kuhn, S.

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, "Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna," Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Kuipers, L.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "λ /4 resonance of an optical monopole antenna probed by single molecule fluorescence," Nano Lett. 7, 28-33 (2007).
[CrossRef] [PubMed]

Letokhov, V. S.

V. Klimov, M. Ducloy, and V. S. Letokhov, "Radiative Frequency Shift and LineWidth of an Atom Dipole in the Vicinity of a Dielectric Microsphere," J. Mod. Opt. 43, 2251 (1996).
[CrossRef]

Leung, P. T.

P. T. Leung, "Decay of molecules at spherical surfaces: Nonlocal effects," Phys. Rev. B 42, 7622 (1990).
[CrossRef]

Y. S. Kim, P. T. Leung, and T. F. George, "Classical Decay Rates for Molecules in the Presence of a Spherical Surface: a Complete Treatment," Surf. Sci. 195, 1-14 (1988).
[CrossRef]

Levi, S. A.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Lukin, M.

D. Chang, A. S¨orensen, P. Hemmer, and M. Lukin, "Quantum Optics with Surface Plasmons," Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Maghezzi, S.

C. Girard, S. Maghezzi, and F. Hache, "Multipolar propagators near a small metallic sphere : A self consistent calculation," J. Chem. Phys. 91, 5509-5517 (1989).
[CrossRef]

Martin, O. J. F.

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Meier, M.

Mertens, H.

H. Mertens, A. 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]

Moerland, R. J.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "λ /4 resonance of an optical monopole antenna probed by single molecule fluorescence," Nano Lett. 7, 28-33 (2007).
[CrossRef] [PubMed]

Moller, M.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Morteani, A. C.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Muhlschlegel, P.

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Niedereichholz, T.

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C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
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C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
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Reinhoudt, D. N.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
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[CrossRef] [PubMed]

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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "λ /4 resonance of an optical monopole antenna probed by single molecule fluorescence," Nano Lett. 7, 28-33 (2007).
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R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "λ /4 resonance of an optical monopole antenna probed by single molecule fluorescence," Nano Lett. 7, 28-33 (2007).
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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "λ /4 resonance of an optical monopole antenna probed by single molecule fluorescence," Nano Lett. 7, 28-33 (2007).
[CrossRef] [PubMed]

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E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J.M. van Veggel, D. N. Reinhoudt and M. Moller, and D. I. Gittins, "Fluorescence Quenching of Dye Molecules near Gold Nanoparticles: Radiative and Nonradiative Effects," Phys. Rev. Lett. 89, 203002 (2002).
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R. Carminati, J. Greffet, C. Henkel, and J. 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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C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
[CrossRef] [PubMed]

Adv. Chem. Phys.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

J. Am. Chem. Soc.

C. S. Yun, A. Javier, T. Jennings, M. Fisher, S. Hira, S. Peterson, B. Hopkins, N. O. Reich, G. F. Strouse Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier, J. Am. Chem. Soc. 127, 3115-3119 (2005) .
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[CrossRef] [PubMed]

Opt. Commun.

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

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[CrossRef]

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[CrossRef] [PubMed]

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, "Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna," Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

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

D. Chang, A. S¨orensen, P. Hemmer, and M. Lukin, "Quantum Optics with Surface Plasmons," Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Science

R. P. Van Duyne, "Molecular plasmonics," Science 306, 985 (2004).

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005).
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Figures (8)

Fig. 1.
Fig. 1.

Model used to study the molecule-particle coupling.

Fig. 2.
Fig. 2.

Error done on the non radiative decay rate when approximated by Eq. (9) or (10) for a perpendicular or parallel orientation, respectively. The molecule is located 1 nm from a gold particle in air. The emission wavelength is λ 0=580 nm.

Fig. 3.
Fig. 3.

Non radiative decay rate dependence for an emitter placed 5 nm above a gold nanoparticle (80 nm diameter) embedded in a PMMA matrix (solid line) or above a flat gold/PMMA interface film (dashed line, quasi-static approximation). (a) Dipole parallel to the surface. (b) Dipole perpendicular to the surface. Vertical lines indicate the Au/PMMA interface plasmon mode resonance.

Fig. 4.
Fig. 4.

Radiative decay rate for an emitter placed 5 nm above a gold nanoparticle (80 nm in diameter). (a) Dipole parallel to the surface. (b) Dipole perpendicular to the surface. The solid curves are calculated from Mie formalism (Eq. 3,4). The dashed curves assume a dipolar response of the particle, including finite size effects [Eq. 28) and (29) in appendix (6.2)]. Vertical lines indicate the sphere dipolar resonance.

Fig. 5.
Fig. 5.

Non radiative decay rates as a function of the distance d=(z 0-a) to the particle surface (solid lines) or gold flat film(dashed lines, quasi-static approximation) for a parallel (a) and perpendicular (b) dipole. The emission wavelength is λ 0=580 nm.

Fig. 6.
Fig. 6.

Radiative decay rate dependence with respect to the distance d between the particle and the molecule: for a dipole (a) parallel or (b) perpendicular to the particle surface. ‘Exact’ curves refers to Mie formalism (Eq. 3,4), ‘dipolar’ corresponds to a dipolar model, including finite size effects [Eq. 28) and (29) in appendix (6.2)] and ‘dipolar (point-like)’ assumes a point-like dipolar response of the particle to an external field [(Eq. 28) and (29) where α e f f is approximated by α 1]. The insets show far-field behaviours. The emission wavelength is λ 0=580 nm.

Fig. 7.
Fig. 7.

Normalized electric-field intensity (a), decay rate (b) and non-radiative rate (c) calculated 10 nm away the particle surface as a function of both wavelength and particle radius. The system is shown in the inset of Fig. 7(a). The molecule is oriented perpendicularly to the sphere surface.

Fig. 8.
Fig. 8.

Fluorescent enhancement for ‘DiD-gold particle’ coupled system embedded in PMMA.

Equations (35)

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γ γ 0 = n B { 1 + 3 2 R e Σ n = 1 n ( n + 1 ) ( 2 n + 1 ) B n [ h n ( 1 ) ( u ) u ] 2 } ,
γ γ 0 = n B { 1 + 3 2 R e Σ n = 1 ( n + 1 2 ) [ B n [ ζ n ' ( u ) u ] 2 + A n [ h n ( 1 ) ( u ) ] 2 ] } ,
γ rad γ 0 = 3 n B 2 Σ n = 1 n ( n + 1 ) ( 2 n + 1 ) j n ( u ) + B n h n ( 1 ) ( u ) u 2 ,
γ rad γ 0 = 3 n B 4 Σ n = 1 ( 2 n + 1 ) [ j n ( u ) + A n h n ( 1 ) ( u ) 2 + ψ n ( u ) + B n ζ n ( u ) u 2 ] ,
γ rad γ 0 = n B + 3 n B 2 Σ n = 1 n ( n + 1 ) ( 2 n + 1 ) B n h n ( 1 ) ( u ) 2 + 2 j n ( u ) R e [ B n h n ( 1 ) ( u ) ] u 2 ,
γ rad γ 0 = n B + 3 n B 4 Σ n = 1 ( 2 n + 1 )
[ A n h n ( 1 ) ( u ) 2 + 2 j n ( u ) R e [ A n h n ( 1 ) ( u ) ] + B n ζ n ( 1 ) ( u ) 2 + 2 ψ n ' ( u ) R e [ B n ζ n ( 1 ) ( u ) ] u 2 ] .
γ NR γ 0 = γ γ 0 γ rad γ 0 = 3 n B 2 Σ n = 1 n ( n + 1 ) ( 2 n + 1 ) h n ( 1 ) ( u ) u 2 [ R e ( B n ) B n 2 ] ,
γ NR γ 0 = γ γ 0 γ rad γ 0
= 3 n B 2 Σ n = 1 ( n + 1 2 ) [ ζ n ( 1 ) ( u ) u 2 [ R e ( B n ) B n 2 ] + h n ( 1 ) ( u ) 2 [ R e ( A n ) A n 2 ] ] .
γ N R γ 0 u 0 ˜ 3 n B 2 u 3 Σ n = 1 ( n + 1 ) 2 u ( 2 n + 1 ) k B 2 n + 1
[ I m ( α n ) n + 1 n ( 2 n 1 ) ! ! ( 2 n + 1 ) ! ! k B 2 n + 1 α n 2 ] , and
γ N R γ 0 u 0 ˜ 3 n B 2 u 3 Σ n = 1 n ( n + 1 ) ( n + 1 2 ) ( 2 n + 1 ) u ( 2 n + 1 ) k B 2 n + 1
[ I m ( α n ) n + 1 n ( 2 n 1 ) ! ! ( 2 n + 1 ) ! ! k B 2 n + 1 α n 2 ] ,
α n = n ( ε S ε B ) ( n + 1 ) ε B + n ε S a ( 2 n + 1 ) .
γ N R γ 0 z 0 a ˜ 3 n B 2 u 3 a z 0 I m ( ε S ε B ε S + ε B ) Σ n > > 1 n 2 ( a z 0 ) 2 n ,
z 0 a ˜ 3 n B 8 k B 3 I m ( ε S ε B ε S + ε B ) 1 ( z 0 a ) 3
γ N R γ 0 z 0 a ˜ 3 n B 4 u 3 a z 0 I m ( ε S ε B ε S + ε B ) Σ n > > 1 n 2 ( a z 0 ) 2 n ,
z 0 a ˜ 3 n B 16 k B 3 I m ( ε S ε B ε S + ε B ) 1 ( z 0 a ) 3 .
γ rad γ 0 u 0 ˜ n B + 3 2 u 2 Σ n = 1 n ( n + 1 ) 2 ( 2 n + 1 ) { n + 1 [ ( 2 n + 1 ) ! ! ] 2 u 2 n + 2 k B 4 n + 2 α n 2
+ 2 [ ( 2 n + 1 ) ! ! ] 2 u k B 2 n + 1 R e ( α n )
2 ( 2 n 1 ) ! ! [ ( 2 n + 1 ) ! ! ] 3 u 2 n k B 2 n + 1 I m ( α n ) } .
γ rad γ 0 z 0 a ˜ n B { 1 + 4 z 0 3 R e ( α 1 ) + 4 z 0 6 α 1 2 }
γ rad γ 0 z 0 a ˜ n B { 1 2 z 0 3 R e ( α 1 ) + 1 z 0 6 α 1 2 } ,
α e f f = [ 1 M B α 1 a 3 ] 1 α 1
M B = 2 [ ( 1 i k B a ) e i k B a 1 ]
η f l u o ( r 0 ) = u · E ( λ e x c , r 0 ) 2 γ rad ( r 0 ) γ ( r 0 ) ,
A n = j n ( k B a ) ψ n ( k S a ) j n ( k S a ) ψ n ( k B a ) j n ( k S a ) ζ n ( k B a ) h n ( 1 ) ( k B a ) ψ n ( k S a ) ,
B n = ε B j n ( k B a ) ψ n ( k S a ) ε S j n ( k S a ) ψ n ( k B a ) ε S j n ( k S a ) ζ n ( k B a ) ε B h n ( 1 ) ( k B a ) ψ n ( k S a ) .
γ γ 0 = n B { 1 + 3 k B 3 2 I m [ α e f f e 2 i u ( 1 u + i u 2 1 u 3 ) 2 ] } ,
γ γ 0 = n B { 1 + 6 k B 3 I m [ α e f f e 2 i u ( 1 u 3 i u 3 ) 2 ] } ,
γ N R γ 0 = 3 n B 2 k B 3 [ I m ( α e f f ) 2 k B 3 3 α e f f 2 ] [ 1 u 2 1 u 4 + 1 u 6 ] ,
γ N R γ 0 = 6 k B 3 n B [ I m ( α e f f ) 2 k B 3 3 α e f f 2 ] [ 1 u 4 + 1 u 6 ] .
γ rad γ 0 = γ γ 0 γ N R γ 0
γ rad γ 0 = γ γ 0 γ N R γ 0 .

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