Abstract

We study the dipole–dipole coupling between two fluorescent molecules in the presence of a chain of metallic nanoparticles. We analyze the spectral behavior of the coupling strength and its dependence on the molecular orientation. Our results show that for certain resonant wavelengths the coupling strength between the molecules is greatly enhanced and is strongly polarization sensitive. We also demonstrate how metallic nanoparticles can be utilized in implementing a polarization-sensitive coupler.

© 2007 Optical Society of America

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References

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  1. R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp. 1-65.
    [CrossRef]
  2. W. L. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661-699 (1998).
    [CrossRef]
  3. P. Anger, P. Bharadwaj, and L. Novotny, "Enhancement and quenching of single-molecule fluorescence," Phys. Rev. Lett. 96, 113002 (2006).
    [CrossRef] [PubMed]
  4. 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]
  5. G. Colas des Francs, C. Girard, and O. J. F. Martin, "Fluorescence resonant energy transfer in the optical near field," Phys. Rev. A 67, 053805 (2003).
    [CrossRef]
  6. G. S. Agarwal and S. D. Gupta, "Microcavity-induced modification of the dipole-dipole interaction," Phys. Rev. A 57, 667-670 (1998).
    [CrossRef]
  7. P. Andrew and W. L. Barnes, "Förster energy transfer in an optical microcavity," Science 290, 785-788 (2000).
    [CrossRef] [PubMed]
  8. R. L. Hartman and P. T. Leung, "Dynamical theory for modeling dipole-dipole interactions in a microcavity: the Green dyadic approach," Phys. Rev. B 64, 193308 (2001).
    [CrossRef]
  9. X. M. Hua and J. I. Gersten, "Enhanced energy transfer between donor and acceptor molecules near a long wire or fiber," J. Chem. Phys. 91, 1279-1286 (1989).
    [CrossRef]
  10. F. Le Kien, S. D. Gupta, K. P. Nayak, and K. Hakuta, "Nanofiber-mediated radiative transfer betweeen two distant atoms," Phys. Rev. A 72, 063815 (2006).
    [CrossRef]
  11. M. Cho and R. J. Silbey, "Suppression and enhancement of van der Waals interactions," J. Chem. Phys. 104, 8730-8741 (1996).
    [CrossRef]
  12. V. V. Klimov and V. S. Letokhov, "Resonance interaction between two atomic dipoles separated by the surface of a dielectric nanosphere," Phys. Rev. A 58, 3235-3247 (1998).
    [CrossRef]
  13. C. Girard, O. J. F. Martin, G. Lévèque, G. Colas des Francs, and A. Dereux, "Generalized Bloch equations for optical interactions in confined geometries," Chem. Phys. Lett. 404, 44-48 (2005).
    [CrossRef]
  14. P. Andrew and W. L. Barnes, "Energy transfer across a metal film mediated by surface plasmon polaritons," Science 306, 1002-1005 (2004).
    [CrossRef] [PubMed]
  15. L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. Al Wahsh, P. Zielinski, and J. P. Vigneron, "Simple nanometric plasmon multiplexer," Phys. Rev. E 69, 035601R (2004).
    [CrossRef]
  16. M. Sukharev and T. Seideman, "Phase and polarization control as a route to plasmonic nanodevices," Nano Lett. 6, 715-719 (2006).
    [CrossRef] [PubMed]
  17. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
    [CrossRef]
  18. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-R16359 (2000).
    [CrossRef]
  19. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
    [CrossRef] [PubMed]
  20. W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
    [CrossRef]
  21. C. Girard and R. Quidant, "Near-field optical transmittance of metal particle chain waveguides," Opt. Express 12, 6141-6146 (2004).
    [CrossRef] [PubMed]
  22. G. Colas des Francs, C. Girard, J.-C. Weeber, and A. Dereux, "Near field optical adressing of single molecules in coplanar geometry: a theoretical study," J. Microsc. 202, 307-312 (2001).
    [CrossRef]
  23. W. Nomura, T. Yatsui, and M. Ohtsu, "Efficient optical near-field energy transfer along an Au nanodot coupler with size-dependent resonance," Appl. Phys. B 84, 257-259 (2006).
    [CrossRef]
  24. L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
    [CrossRef]
  25. P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]

2006 (5)

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

F. Le Kien, S. D. Gupta, K. P. Nayak, and K. Hakuta, "Nanofiber-mediated radiative transfer betweeen two distant atoms," Phys. Rev. A 72, 063815 (2006).
[CrossRef]

M. Sukharev and T. Seideman, "Phase and polarization control as a route to plasmonic nanodevices," Nano Lett. 6, 715-719 (2006).
[CrossRef] [PubMed]

W. Nomura, T. Yatsui, and M. Ohtsu, "Efficient optical near-field energy transfer along an Au nanodot coupler with size-dependent resonance," Appl. Phys. B 84, 257-259 (2006).
[CrossRef]

2005 (1)

C. Girard, O. J. F. Martin, G. Lévèque, G. Colas des Francs, and A. Dereux, "Generalized Bloch equations for optical interactions in confined geometries," Chem. Phys. Lett. 404, 44-48 (2005).
[CrossRef]

2004 (4)

P. Andrew and W. L. Barnes, "Energy transfer across a metal film mediated by surface plasmon polaritons," Science 306, 1002-1005 (2004).
[CrossRef] [PubMed]

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. Al Wahsh, P. Zielinski, and J. P. Vigneron, "Simple nanometric plasmon multiplexer," Phys. Rev. E 69, 035601R (2004).
[CrossRef]

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

C. Girard and R. Quidant, "Near-field optical transmittance of metal particle chain waveguides," Opt. Express 12, 6141-6146 (2004).
[CrossRef] [PubMed]

2003 (2)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

G. Colas des Francs, C. Girard, and O. J. F. Martin, "Fluorescence resonant energy transfer in the optical near field," Phys. Rev. A 67, 053805 (2003).
[CrossRef]

2001 (2)

R. L. Hartman and P. T. Leung, "Dynamical theory for modeling dipole-dipole interactions in a microcavity: the Green dyadic approach," Phys. Rev. B 64, 193308 (2001).
[CrossRef]

G. Colas des Francs, C. Girard, J.-C. Weeber, and A. Dereux, "Near field optical adressing of single molecules in coplanar geometry: a theoretical study," J. Microsc. 202, 307-312 (2001).
[CrossRef]

2000 (2)

P. Andrew and W. L. Barnes, "Förster energy transfer in an optical microcavity," Science 290, 785-788 (2000).
[CrossRef] [PubMed]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-R16359 (2000).
[CrossRef]

1998 (4)

V. V. Klimov and V. S. Letokhov, "Resonance interaction between two atomic dipoles separated by the surface of a dielectric nanosphere," Phys. Rev. A 58, 3235-3247 (1998).
[CrossRef]

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

G. S. Agarwal and S. D. Gupta, "Microcavity-induced modification of the dipole-dipole interaction," Phys. Rev. A 57, 667-670 (1998).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
[CrossRef]

1997 (1)

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

1996 (1)

M. Cho and R. J. Silbey, "Suppression and enhancement of van der Waals interactions," J. Chem. Phys. 104, 8730-8741 (1996).
[CrossRef]

1989 (1)

X. M. Hua and J. I. Gersten, "Enhanced energy transfer between donor and acceptor molecules near a long wire or fiber," J. Chem. Phys. 91, 1279-1286 (1989).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Appl. Phys. B (1)

W. Nomura, T. Yatsui, and M. Ohtsu, "Efficient optical near-field energy transfer along an Au nanodot coupler with size-dependent resonance," Appl. Phys. B 84, 257-259 (2006).
[CrossRef]

Chem. Phys. Lett. (1)

C. Girard, O. J. F. Martin, G. Lévèque, G. Colas des Francs, and A. Dereux, "Generalized Bloch equations for optical interactions in confined geometries," Chem. Phys. Lett. 404, 44-48 (2005).
[CrossRef]

J. Appl. Phys. (1)

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

J. Chem. Phys. (2)

X. M. Hua and J. I. Gersten, "Enhanced energy transfer between donor and acceptor molecules near a long wire or fiber," J. Chem. Phys. 91, 1279-1286 (1989).
[CrossRef]

M. Cho and R. J. Silbey, "Suppression and enhancement of van der Waals interactions," J. Chem. Phys. 104, 8730-8741 (1996).
[CrossRef]

J. Microsc. (1)

G. Colas des Francs, C. Girard, J.-C. Weeber, and A. Dereux, "Near field optical adressing of single molecules in coplanar geometry: a theoretical study," J. Microsc. 202, 307-312 (2001).
[CrossRef]

J. Mod. Opt. (1)

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

Nano Lett. (1)

M. Sukharev and T. Seideman, "Phase and polarization control as a route to plasmonic nanodevices," Nano Lett. 6, 715-719 (2006).
[CrossRef] [PubMed]

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Opt. Commun. (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]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (4)

V. V. Klimov and V. S. Letokhov, "Resonance interaction between two atomic dipoles separated by the surface of a dielectric nanosphere," Phys. Rev. A 58, 3235-3247 (1998).
[CrossRef]

F. Le Kien, S. D. Gupta, K. P. Nayak, and K. Hakuta, "Nanofiber-mediated radiative transfer betweeen two distant atoms," Phys. Rev. A 72, 063815 (2006).
[CrossRef]

G. Colas des Francs, C. Girard, and O. J. F. Martin, "Fluorescence resonant energy transfer in the optical near field," Phys. Rev. A 67, 053805 (2003).
[CrossRef]

G. S. Agarwal and S. D. Gupta, "Microcavity-induced modification of the dipole-dipole interaction," Phys. Rev. A 57, 667-670 (1998).
[CrossRef]

Phys. Rev. B (4)

R. L. Hartman and P. T. Leung, "Dynamical theory for modeling dipole-dipole interactions in a microcavity: the Green dyadic approach," Phys. Rev. B 64, 193308 (2001).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-R16359 (2000).
[CrossRef]

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Rev. E (1)

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. Al Wahsh, P. Zielinski, and J. P. Vigneron, "Simple nanometric plasmon multiplexer," Phys. Rev. E 69, 035601R (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (2)

P. Andrew and W. L. Barnes, "Förster energy transfer in an optical microcavity," Science 290, 785-788 (2000).
[CrossRef] [PubMed]

P. Andrew and W. L. Barnes, "Energy transfer across a metal film mediated by surface plasmon polaritons," Science 306, 1002-1005 (2004).
[CrossRef] [PubMed]

Other (1)

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," in Advances in Chemical Physics, I.Prigogine and S.A.Rice, eds. (Wiley, 1978), Vol. 37, pp. 1-65.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Energy-level diagram of the donor and acceptor molecules. The states e 1 and v 2 are coupled by the dipole–dipole interaction characterized by the coupling factor J 12 . The parameters Γ v 1 , v 2 and Γ e 1 , e 2 denote the radiative decay rates from the excited states v 1 , 2 and e 1 , 2 to the ground states g 1 , 2 , whereas K denotes the nonradiative vibrational relaxation rate. Furthermore, the energy associated with the transitions e 1 g 1 and v 2 g 2 is ω , and ω 1 is the angular frequency of the exciting light.

Fig. 2
Fig. 2

The coupling strength Ω 12 as a function of wavelength λ for different number of particles N in the chain. The center-to-center distance between the particles is 30 nm , and the molecules are at a distance of 20 nm from the outermost particles. Chains with N = 2 (solid curve), 4 (dashed curve), 10 (dotted curve) particles respectively correspond to a distance of 70, 130, and 310 nm between the acceptor and the donor molecules. The dipole moments of the donor and acceptor are oriented parallel to the chain.

Fig. 3
Fig. 3

Nanoparticle chain geometries: (a) straight chain, (b) right-angle corner, (c) arc ( 1 4 circle), and (d) coupler. The positions of the donor and acceptor are marked with (+) and (×), respectively. The center-to-center distance in (a), (b), and (d) is 30 nm , and in (c) 29.4 nm .

Fig. 4
Fig. 4

Coupling strength Ω 12 , x x (solid curve) and Ω 12 , y y (dashed curve) as a function of the wavelength λ for the straight particle chain of Fig. 3a.

Fig. 5
Fig. 5

Coupling strengths Ω 12 , x x (solid curve) and Ω 12 , y x (dashed curve) in the geometry of Fig. 3b (right-angle corner), and Ω 12 , y x (dotted curve) in the geometry of Fig. 3c (arc) as a function of the wavelength λ.

Fig. 6
Fig. 6

Coupling strengths Ω 12 , y y ( 1 ) and Ω 12 , x x ( 2 ) (solid curve), Ω 12 , y x ( 1 ) and Ω 12 , x y ( 2 ) (dashed curve), Ω 12 , x x ( 1 ) and Ω 12 , y y ( 2 ) (dotted curve), and Ω 12 , x y ( 1 ) and Ω 12 , y x ( 2 ) (dashed–dotted curve) as a function of the wavelength λ in the geometry of Fig. 3d.

Equations (8)

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J 12 = μ 2 G ( r 2 , r 1 , ω ) μ 1 ,
J 12 = ( Ω 12 i γ 12 ) ,
E ( r , ω ) = G ( r , r , ω ) p ( r , ω ) .
E ( r , ω ) = E 0 ( r , ω ) + n = 1 N G 0 ( r , r n , ω ) p n ,
p n = ϵ 0 α n ( ω ) E exc ( r n , ω ) ,
α n ( ω ) = α 0 ( ω ) 1 i k 3 α 0 ( ω ) ( 6 π ) ,
α 0 ( ω ) = 4 π a 3 ϵ ( ω ) 1 ϵ ( ω ) + 2 ,
p k = ϵ 0 α k ( ω ) E 0 ( r k , ω ) + n = 1 n k N ϵ 0 α k ( ω ) G 0 ( r k , r n , ω ) p n ,

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