Abstract

Over the past 15 years there has been an ongoing debate regarding the influence of the photonic environment on Förster resonance energy transfer (FRET). Disparate results corresponding to enhancement, suppression and null effect of the photonic environment have led to a lack of consensus between the traditional theory of FRET and experiments. Here we show that the quantum electrodynamic theory (QED) of FRET near an engineered nanophotonic environment is exactly equivalent to an effective near-field model describing electrostatic dipole-dipole interactions. This leads to an intuitive and rigorously exact description of FRET, previously unavailable, bridging the gap between experimental observations and theoretical interpretations. Furthermore, we show that the widely used concept of Purcell factor variation is only important for understanding spontaneous emission and is an incorrect figure of merit (FOM) for analyzing FRET. To this end, we analyze the figures of merit which characterize FRET in a photonic environment 1) the FRET rate enhancement factor (FET), 2) FRET efficiency enhancement factor (Feff) and 3) Two-point spectral density (SEE) which is the photonic property of the environment governing FRET analogous to the local density of states that controls spontaneous emission. Counterintuitive to existing knowledge, we show that suppression of the Purcell factor is in fact necessary for enhancing the efficiency of the FRET process. We place fundamental bounds on the FRET figures of merit arising from material absorption in the photonic environment as well as key properties of emitters including intrinsic quantum efficiencies and orientational dependence. Finally, we use our approach to conclusively explain multiple recent experiments and predict regimes where the FRET rate is expected to be enhanced, suppressed or remain the same. Our work paves for a complete theory of FRET with predictive power for designing the ideal photonic environment to control FRET.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
  50. L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yee, “Electromagnetic dyadic green’s function in spherically multilayered media,” IEEE Trans. on Microw. Theory Tech. 42, 2302–2310 (1994).
    [Crossref]
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    [Crossref] [PubMed]

2017 (1)

C. L. Cortes and Z. Jacob, “Super-coulombic atom–atom interactions in hyperbolic media,” Nat. Commun.  8, 14144 (2017).
[Crossref]

2014 (4)

F. T. Rabouw, S. A. den Hartog, T. Senden, and A. Meijerink, “Photonic effects on the Förster resonance energy transfer efficiency,” Nat. Commun. 53610 (2014).
[Crossref]

F. Schleifenbaum, A. M. Kern, A. Konrad, and A. J. Meixner, “Dynamic control of Förster energy transfer in a photonic environment,” Phys. Chem. Chem. Phys.  16, 12812 (2014).
[Crossref] [PubMed]

P. Ghenuche, J. de Torres, S. B. Moparthi, V. Grigoriev, and J. Wenger, “Nanophotonic Enhancement of the Förster Resonance Energy-Transfer Rate with Single Nanoapertures,” Nano Lett. 14, 4707–4714 (2014).
[Crossref] [PubMed]

D. Lu, S. K. Cho, S. Ahn, L. Brun, C. J. Summers, and W. Park, “Plasmon Enhancement Mechanism for the Upconversion Processes in NaYF4: Yb3+, Er3+ Nanoparticles: Maxwell versus Förster,” ACS Nano 8, 7780–7792 (2014).
[Crossref] [PubMed]

2012 (4)

L. Zhao, T. Ming, L. Shao, H. Chen, and J. Wang, “Plasmon-Controlled Förster Resonance Energy Transfer,” Journ. Phys. Chem. C 116, 8287–8296 (2012).
[Crossref]

B. E. Hardin, H. J. Snaith, and M. D. McGehee, “The renaissance of dye-sensitized solar cells,” Nat. Photon. 6, 162–169 (2012).
[Crossref]

C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic Control of the Förster Resonance Energy Transfer Efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
[Crossref]

K.-S. Kim, J.-H. Kim, H. Kim, F. Laquai, E. Arifin, J.-K. Lee, S. I. Yoo, and B.-H. Sohn, “Switching off FRET in the hybrid assemblies of diblock copolymer micelles, quantum dots, and dyes by plasmonic nanoparticles,” ACS nano 6, 5051–5059 (2012).
[Crossref] [PubMed]

2011 (3)

M. L. Viger, D. Brouard, and D. Boudreau, “Plasmon-Enhanced Resonance Energy Transfer from a Conjugated Polymer to Fluorescent Multilayer Core- Shell Nanoparticles: A Photophysical Study,” Journ. Phys. Chem. C 115, 2974–2981 (2011).
[Crossref]

V. N. Pustovit and T. V. Shahbazyan, “Resonance energy transfer near metal nanostructures mediated by surface plasmons,” Phys. Rev. B 83, 085427 (2011).
[Crossref]

M. Lunz, V. A. Gerard, Y. K. Gun’ko, V. Lesnyak, N. Gaponik, A. S. Susha, A. L. Rogach, and A. L. Bradley, “Surface plasmon enhanced energy transfer between donor and acceptor CdTe nanocrystal quantum dot monolayers,” Nano Lett. 11, 3341–3345 (2011).
[Crossref] [PubMed]

2008 (5)

M. Durach, A. Rusina, V. I. Klimov, and M. I. Stockman, “Nanoplasmonic renormalization and enhancement of Coulomb interactions,” New J. Phys.  10, 105011 (2008).
[Crossref]

U. Hohenester and A. Trugler, “Interaction of Single Molecules With Metallic Nanoparticles,” IEEE J. Sel. Top. Quantum Electron. 14, 1430–1440 (2008).
[Crossref]

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-Type Resonant Energy Transfer Influenced by Metal Nanoparticles,” Nano Lett. 8, 4128–4133 (2008).
[Crossref]

V. K. Komarala, A. L. Bradley, Y. P. Rakovich, S. J. Byrne, Y. K. Gun’ko, and A. L. Rogach, “Surface plasmon enhanced Förster resonance energy transfer between the CdTe quantum dots,” Appl. Phys. Lett. 93, 123102 (2008).
[Crossref]

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452, 580–589 (2008).
[Crossref] [PubMed]

2007 (3)

J. Zhang, Y. Fu, and J. R. Lakowicz, “Enhanced Förster resonance energy transfer (FRET) on a single metal particle,” Journ. Phys. Chem. C 111, 50–56 (2007).
[Crossref]

A. O. Govorov, J. Lee, and N. A. Kotov, “Theory of plasmon-enhanced Förster energy transfer in optically excited semiconductor and metal nanoparticles,” Phys. Rev. B 76, 125308 (2007).
[Crossref]

H. Lee, Y.-C. Cheng, and G. R. Fleming, “Coherence dynamics in photosynthesis: protein protection of excitonic coherence,” Science. 316, 1462–1465 (2007).
[Crossref] [PubMed]

2005 (3)

H. Fujiwara, K. Sasaki, and H. Masuhara, “Enhancement of Förster energy transfer within a microspherical cavity,” Chem Phys Chem. 6, 2410–2416 (2005).
[Crossref]

H. Wallrabe and A. Periasamy, “Imaging protein molecules using fret and flim microscopy,” Curr. Opin. Biotech. 16, 19–27 (2005).
[Crossref] [PubMed]

M. J. A. De Dood, J. Knoester, A. Tip, and A. Polman, “Förster transfer and the local optical density of states in erbium-doped silica,” Phys. Rev. B 71, 115102 (2005).
[Crossref]

2003 (1)

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

2002 (2)

H. T. Dung, L. Knöll, and D.-G. Welsch, “Intermolecular energy transfer in the presence of dispersing and absorbing media,” Phys. Rev. A 65, 043813 (2002).
[Crossref]

J. R. Lakowicz, Y. Shen, S. D’Auria, J. Malicka, J. Fang, Z. Gryczynski, and I. Gryczynski, “Radiative decay engineering. 2. Effects of Silver Island films on fluorescence intensity, lifetimes, and resonance energy transfer,” Anal. Biochem. 301, 261–277 (2002).
[Crossref] [PubMed]

2001 (1)

C. E. Finlayson, D. S. Ginger, and N. C. Greenham, “Enhanced Förster energy transfer in organic/inorganic bilayer optical microcavities,” Chem. Phys. Lett. 338, 83–87 (2001).

2000 (2)

P. Andrew and W. L. Barnes, “Förster energy transfer in an optical microcavity,” Science. 290, 785–788 (2000).
[Crossref] [PubMed]

D. M. Basko, F. Bassani, G. C. La Rocca, and V. M. Agranovich, “Electronic energy transfer in a microcavity,” Phys. Rev. B 62, 15962 (2000).
[Crossref]

1999 (2)

M. Hopmeier, W. Guss, M. Deussen, E. O. Göbel, and R. F. Mahrt, “Enhanced dipole-dipole interaction in a polymer microcavity,” Phys. Rev. Lett. 82, 4118 (1999).
[Crossref]

P. I. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. 9, 48–52 (1999).
[Crossref] [PubMed]

1998 (2)

G. S. Agarwal and S. D. Gupta, “Microcavity-induced modification of the dipole-dipole interaction,” Phys. Rev. A 57, 667–670 (1998).

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 (1998).
[Crossref]

1997 (1)

S. Bay, P. Lambropoulos, and K. Mølmer, “Atom-atom interaction in strongly modified reservoirs,” Phys. Rev. A 55, 1485–1496 (1997).

1995 (1)

T. Kobayashi, Q. Zheng, and T. Sekiguchi, “Resonant dipole-dipole interaction in a cavity,” Phys. Rev. A 52, 2835–2846 (1995).

1994 (1)

L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yee, “Electromagnetic dyadic green’s function in spherically multilayered media,” IEEE Trans. on Microw. Theory Tech. 42, 2302–2310 (1994).
[Crossref]

1991 (1)

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).

1988 (2)

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269 (1988).
[Crossref] [PubMed]

A. Leitner and H. Reinisch, “Reduced intermolecular energy transfer on silver island films,” Chem. Phys. Lett. 146, 320–324 (1988).

1985 (1)

X. M. Hua, J. I. Gersten, and A. Nitzan, “Theory of energy transfer between molecules near solid state particles,” The J. Chem. Phys. 83, 3650–3659 (1985).
[Crossref]

1984 (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Reports 113, 195–287 (1984).
[Crossref]

1978 (1)

R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys 37, 65 (1978).

1975 (1)

R. R. Chance, A. Prock, and R. Silbey, “Comments on the classical theory of energy transfer,” Journ. Chem. Phys. 62, 2245–2253 (1975).
[Crossref]

1948 (1)

T. Förster, “Zwischenmolekulare energiewanderung und fluoreszenz,” Annalen der physik 437, 55–75 (1948).
[Crossref]

1946 (1)

T. Förster, “Energiewanderung und fluoreszenz,” Naturwissenschaften 33, 166–175 (1946).
[Crossref]

Agarwal, G. S.

G. S. Agarwal and S. D. Gupta, “Microcavity-induced modification of the dipole-dipole interaction,” Phys. Rev. A 57, 667–670 (1998).

Agranovich, V.

V. Agranovich and M. Galanin, “Electron-excitation energy transfer in condensed media,” Mosc. IzdatelNauka1 (1978).

Agranovich, V. M.

D. M. Basko, F. Bassani, G. C. La Rocca, and V. M. Agranovich, “Electronic energy transfer in a microcavity,” Phys. Rev. B 62, 15962 (2000).
[Crossref]

Ahn, S.

D. Lu, S. K. Cho, S. Ahn, L. Brun, C. J. Summers, and W. Park, “Plasmon Enhancement Mechanism for the Upconversion Processes in NaYF4: Yb3+, Er3+ Nanoparticles: Maxwell versus Förster,” ACS Nano 8, 7780–7792 (2014).
[Crossref] [PubMed]

Andrew, P.

P. Andrew and W. L. Barnes, “Förster energy transfer in an optical microcavity,” Science. 290, 785–788 (2000).
[Crossref] [PubMed]

Andrews, D. L.

D. L. Andrews and A. A. Demidov, Resonance energy transfer(WileyNew York, 1999).

Arifin, E.

K.-S. Kim, J.-H. Kim, H. Kim, F. Laquai, E. Arifin, J.-K. Lee, S. I. Yoo, and B.-H. Sohn, “Switching off FRET in the hybrid assemblies of diblock copolymer micelles, quantum dots, and dyes by plasmonic nanoparticles,” ACS nano 6, 5051–5059 (2012).
[Crossref] [PubMed]

Barnes, W. L.

P. Andrew and W. L. Barnes, “Förster energy transfer in an optical microcavity,” Science. 290, 785–788 (2000).
[Crossref] [PubMed]

Basko, D. M.

D. M. Basko, F. Bassani, G. C. La Rocca, and V. M. Agranovich, “Electronic energy transfer in a microcavity,” Phys. Rev. B 62, 15962 (2000).
[Crossref]

Bassani, F.

D. M. Basko, F. Bassani, G. C. La Rocca, and V. M. Agranovich, “Electronic energy transfer in a microcavity,” Phys. Rev. B 62, 15962 (2000).
[Crossref]

Bastiaens, P. I.

P. I. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. 9, 48–52 (1999).
[Crossref] [PubMed]

Bay, S.

S. Bay, P. Lambropoulos, and K. Mølmer, “Atom-atom interaction in strongly modified reservoirs,” Phys. Rev. A 55, 1485–1496 (1997).

Blum, C.

C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic Control of the Förster Resonance Energy Transfer Efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
[Crossref]

Bonner, C. E.

T. U. Tumkur, J. K. Kitur, C. E. Bonner, A. N. Poddubny, E. E. Narimanov, and M. A. Noginov, “Control of forster energy transfer in the vicinity of metallic surfaces and hyperbolic metamaterials,” Faraday Discuss. pp. 178, 395–412 (2015).

Boudreau, D.

M. L. Viger, D. Brouard, and D. Boudreau, “Plasmon-Enhanced Resonance Energy Transfer from a Conjugated Polymer to Fluorescent Multilayer Core- Shell Nanoparticles: A Photophysical Study,” Journ. Phys. Chem. C 115, 2974–2981 (2011).
[Crossref]

Bradley, A. L.

M. Lunz, V. A. Gerard, Y. K. Gun’ko, V. Lesnyak, N. Gaponik, A. S. Susha, A. L. Rogach, and A. L. Bradley, “Surface plasmon enhanced energy transfer between donor and acceptor CdTe nanocrystal quantum dot monolayers,” Nano Lett. 11, 3341–3345 (2011).
[Crossref] [PubMed]

V. K. Komarala, A. L. Bradley, Y. P. Rakovich, S. J. Byrne, Y. K. Gun’ko, and A. L. Rogach, “Surface plasmon enhanced Förster resonance energy transfer between the CdTe quantum dots,” Appl. Phys. Lett. 93, 123102 (2008).
[Crossref]

C. A. Marocico, X. Zhang, and A. L. Bradley, “Spectral overlap dependence of enhanced energy transfer near small Au nanoparticles,” in Transparent Optical Networks (ICTON), 2014 16th International Conference on, (IEEE, 2014), pp. 1–4.

Brouard, D.

M. L. Viger, D. Brouard, and D. Boudreau, “Plasmon-Enhanced Resonance Energy Transfer from a Conjugated Polymer to Fluorescent Multilayer Core- Shell Nanoparticles: A Photophysical Study,” Journ. Phys. Chem. C 115, 2974–2981 (2011).
[Crossref]

Brun, L.

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F. T. Rabouw, S. A. den Hartog, T. Senden, and A. Meijerink, “Photonic effects on the Förster resonance energy transfer efficiency,” Nat. Commun. 53610 (2014).
[Crossref]

Raether, H.

H. Raether, “Surface plasmons on smooth surfaces,” in Surface plasmons on smooth and rough surfaces and on gratings, (Springer, 1988), pp. 4–39.
[Crossref]

Rakovich, Y. P.

V. K. Komarala, A. L. Bradley, Y. P. Rakovich, S. J. Byrne, Y. K. Gun’ko, and A. L. Rogach, “Surface plasmon enhanced Förster resonance energy transfer between the CdTe quantum dots,” Appl. Phys. Lett. 93, 123102 (2008).
[Crossref]

Reil, F.

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-Type Resonant Energy Transfer Influenced by Metal Nanoparticles,” Nano Lett. 8, 4128–4133 (2008).
[Crossref]

Reinisch, H.

A. Leitner and H. Reinisch, “Reduced intermolecular energy transfer on silver island films,” Chem. Phys. Lett. 146, 320–324 (1988).

Rocca, G. C. La

D. M. Basko, F. Bassani, G. C. La Rocca, and V. M. Agranovich, “Electronic energy transfer in a microcavity,” Phys. Rev. B 62, 15962 (2000).
[Crossref]

Rogach, A. L.

M. Lunz, V. A. Gerard, Y. K. Gun’ko, V. Lesnyak, N. Gaponik, A. S. Susha, A. L. Rogach, and A. L. Bradley, “Surface plasmon enhanced energy transfer between donor and acceptor CdTe nanocrystal quantum dot monolayers,” Nano Lett. 11, 3341–3345 (2011).
[Crossref] [PubMed]

V. K. Komarala, A. L. Bradley, Y. P. Rakovich, S. J. Byrne, Y. K. Gun’ko, and A. L. Rogach, “Surface plasmon enhanced Förster resonance energy transfer between the CdTe quantum dots,” Appl. Phys. Lett. 93, 123102 (2008).
[Crossref]

Rusina, A.

M. Durach, A. Rusina, V. I. Klimov, and M. I. Stockman, “Nanoplasmonic renormalization and enhancement of Coulomb interactions,” New J. Phys.  10, 105011 (2008).
[Crossref]

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H. Fujiwara, K. Sasaki, and H. Masuhara, “Enhancement of Förster energy transfer within a microspherical cavity,” Chem Phys Chem. 6, 2410–2416 (2005).
[Crossref]

Schleifenbaum, F.

F. Schleifenbaum, A. M. Kern, A. Konrad, and A. J. Meixner, “Dynamic control of Förster energy transfer in a photonic environment,” Phys. Chem. Chem. Phys.  16, 12812 (2014).
[Crossref] [PubMed]

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T. Kobayashi, Q. Zheng, and T. Sekiguchi, “Resonant dipole-dipole interaction in a cavity,” Phys. Rev. A 52, 2835–2846 (1995).

Senden, T.

F. T. Rabouw, S. A. den Hartog, T. Senden, and A. Meijerink, “Photonic effects on the Förster resonance energy transfer efficiency,” Nat. Commun. 53610 (2014).
[Crossref]

Shahbazyan, T. V.

V. N. Pustovit and T. V. Shahbazyan, “Resonance energy transfer near metal nanostructures mediated by surface plasmons,” Phys. Rev. B 83, 085427 (2011).
[Crossref]

Shao, L.

L. Zhao, T. Ming, L. Shao, H. Chen, and J. Wang, “Plasmon-Controlled Förster Resonance Energy Transfer,” Journ. Phys. Chem. C 116, 8287–8296 (2012).
[Crossref]

Shen, Y.

J. R. Lakowicz, Y. Shen, S. D’Auria, J. Malicka, J. Fang, Z. Gryczynski, and I. Gryczynski, “Radiative decay engineering. 2. Effects of Silver Island films on fluorescence intensity, lifetimes, and resonance energy transfer,” Anal. Biochem. 301, 261–277 (2002).
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B. E. Hardin, H. J. Snaith, and M. D. McGehee, “The renaissance of dye-sensitized solar cells,” Nat. Photon. 6, 162–169 (2012).
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Sohn, B.-H.

K.-S. Kim, J.-H. Kim, H. Kim, F. Laquai, E. Arifin, J.-K. Lee, S. I. Yoo, and B.-H. Sohn, “Switching off FRET in the hybrid assemblies of diblock copolymer micelles, quantum dots, and dyes by plasmonic nanoparticles,” ACS nano 6, 5051–5059 (2012).
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M. Durach, A. Rusina, V. I. Klimov, and M. I. Stockman, “Nanoplasmonic renormalization and enhancement of Coulomb interactions,” New J. Phys.  10, 105011 (2008).
[Crossref]

Subramaniam, V.

C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic Control of the Förster Resonance Energy Transfer Efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
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Summers, C. J.

D. Lu, S. K. Cho, S. Ahn, L. Brun, C. J. Summers, and W. Park, “Plasmon Enhancement Mechanism for the Upconversion Processes in NaYF4: Yb3+, Er3+ Nanoparticles: Maxwell versus Förster,” ACS Nano 8, 7780–7792 (2014).
[Crossref] [PubMed]

Susha, A. S.

M. Lunz, V. A. Gerard, Y. K. Gun’ko, V. Lesnyak, N. Gaponik, A. S. Susha, A. L. Rogach, and A. L. Bradley, “Surface plasmon enhanced energy transfer between donor and acceptor CdTe nanocrystal quantum dot monolayers,” Nano Lett. 11, 3341–3345 (2011).
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M. L. Viger, D. Brouard, and D. Boudreau, “Plasmon-Enhanced Resonance Energy Transfer from a Conjugated Polymer to Fluorescent Multilayer Core- Shell Nanoparticles: A Photophysical Study,” Journ. Phys. Chem. C 115, 2974–2981 (2011).
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L. Zhao, T. Ming, L. Shao, H. Chen, and J. Wang, “Plasmon-Controlled Förster Resonance Energy Transfer,” Journ. Phys. Chem. C 116, 8287–8296 (2012).
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ACS Nano (1)

D. Lu, S. K. Cho, S. Ahn, L. Brun, C. J. Summers, and W. Park, “Plasmon Enhancement Mechanism for the Upconversion Processes in NaYF4: Yb3+, Er3+ Nanoparticles: Maxwell versus Förster,” ACS Nano 8, 7780–7792 (2014).
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M. L. Viger, D. Brouard, and D. Boudreau, “Plasmon-Enhanced Resonance Energy Transfer from a Conjugated Polymer to Fluorescent Multilayer Core- Shell Nanoparticles: A Photophysical Study,” Journ. Phys. Chem. C 115, 2974–2981 (2011).
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L. Zhao, T. Ming, L. Shao, H. Chen, and J. Wang, “Plasmon-Controlled Förster Resonance Energy Transfer,” Journ. Phys. Chem. C 116, 8287–8296 (2012).
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F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-Type Resonant Energy Transfer Influenced by Metal Nanoparticles,” Nano Lett. 8, 4128–4133 (2008).
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P. Ghenuche, J. de Torres, S. B. Moparthi, V. Grigoriev, and J. Wenger, “Nanophotonic Enhancement of the Förster Resonance Energy-Transfer Rate with Single Nanoapertures,” Nano Lett. 14, 4707–4714 (2014).
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B. E. Hardin, H. J. Snaith, and M. D. McGehee, “The renaissance of dye-sensitized solar cells,” Nat. Photon. 6, 162–169 (2012).
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F. Schleifenbaum, A. M. Kern, A. Konrad, and A. J. Meixner, “Dynamic control of Förster energy transfer in a photonic environment,” Phys. Chem. Chem. Phys.  16, 12812 (2014).
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Other (6)

C. A. Marocico, X. Zhang, and A. L. Bradley, “Spectral overlap dependence of enhanced energy transfer near small Au nanoparticles,” in Transparent Optical Networks (ICTON), 2014 16th International Conference on, (IEEE, 2014), pp. 1–4.

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Figures (6)

Fig. 1
Fig. 1 (a) Energy-level diagram depicting spontaneous emission. γrad denotes the rate of radiative energy transfer to any location in the environment. The acceptor is not considered as part of the environment. (b) Energy-level diagram depicting FRET. FRET occurs when two neighboring atoms or molecules, denoted as donor and acceptor, have overlapping emission and absorption spectra and couple due to a Coulombic dipole-dipole interaction. The FRET rate ΓDA denotes the energy transfer to the acceptor location only.
Fig. 2
Fig. 2 Environment modified dipole-dipole interactions and FRET. QED theory of dipole-dipole interactions in the near-field is completely captured by an effective dipole model. FRET is governed by induced image dipoles in the metallic environment explaining a multitude of puzzling experimental observations. (a) Image dipole method for half-space structure. The magnitude of the image dipole moment is given by p i m a g e = ϵ 2 ϵ 1 ϵ 2 + ϵ 1 p D. (b) Visualization of normalized electric field plots for vertical donor dipole (above) and vertical image dipole (below) with |ϵ2| > |ϵ1|. Note that a non-trivial superposition of fields due to the vectorial nature of the electric field results in regimes of suppression, enhancement, and null effect on FRET. These regimes cannot be explained by the LDOS or Purcell factor alone. (c) FRET rate figure of merit for two dipoles 7 nm apart, and 7 nm above silver. Enhancement is seen when |ϵ2| < |ϵ1|, suppression is seen when |ϵ2| > |ϵ1|, while no effect is seen when |ϵ2| ≈ |ϵ1|. These regimes are determined by the orientation of the image dipole. Note also that the FRET rate enhancement has a non-trivial dependence on the wavelength (see also Table 1). Exact QED results are denoted by the solid lines which are in complete agreement with our analytical expressions (circles).
Fig. 3
Fig. 3 Effect of losses. (a) Purcell factor Fp. (b) FRET figure of merit FET. Bottom half-space is modelled as Drude metal with ωp = 6.3 × 1015s−1 and the Drude relaxation time of τ = 5 f s (black) and τ = 2.5 f s (red). Dashed lines correspond to the two terms, dispersive dipole-dipole interaction and dissipative dipole-dipole interaction, in Eq. (12). Note the FRET enhancement factor is in general much smaller than the Purcell factor in agreement with widely reported observations.
Fig. 4
Fig. 4 FRET near nanosphere. (a) FRET rate enhancement factor for spherical nanoparticle systems widely used in experiment. The donor and acceptor are both 8 nm away from an Ag nanosphere of 10 nm radius. Inset: Calculated Purcell factor for same system. The peaks are related to dipolar surface plasmon resonance and higher order multipolar non-radiative modes. We emphasize that FpFET for plasmonic systems near the LSP resonance implying the energy transfer to the sphere (environment) is larger than the energy transfer to the acceptor. (b) Distance dependence of FET and Fp at the 650 nm wavelength region (away from resonance). Note that a tangential dipole exhibits a suppression in the Purcell factor due to near-field interference effects. This effect can be used to boost the FRET efficiency (FeffFET/Fp). The enhancement, suppression and null effect features in the three curves of different colors corresponding to the orientations of the dipole moments of the acceptor and donor are in agreement with Table 1.
Fig. 5
Fig. 5 FRET efficiency. (a) FRET efficiency enhancement occurs when FET/Fp > 1. We show that this ratio can be optimized for particular distances away from the nanoparticle. Results are shown for same set-up as Fig. 4(b) but with R = 40 nm nanoparticle, where ϵ1 = (1.33)2 and ϵ2 = −19.5 + 0.47i. (b) Counter-intuitive to prevalent designs, here we provide an all-dielectric design to engineer FRET efficiency using a transparent nanosphere (ϵ2 = 6.25 > 0) and 40 nm radius. The efficiency enhancement in FRET implies a larger fraction of the donor energy is transferred to the acceptor in presence of the nanosphere. This effect arises from suppression of the Purcell factor which is necessary to avoid energy transfer to the environment.
Fig. 6
Fig. 6 Comparison to experiments. (a) Theoretical comparison to experiment in ref. [25]. The system configuration is shown in the inset. The FRET figure of merit is theoretically calculated to be FET ≈ 1 for a wide range of separation distances d from the mirror, in agreement with the experiment (plotted at the donor’s peak emission wavelength of 525 nm). Theoretical Purcell factor Fp shows excellent agreement with experimental results (lower inset). However, using our theoretical model, we predict a drastic change in the FRET FOM near the Ag SPP resonance in the limit d → 0 (top inset). This shows that FRET rate can be modified for the same experiment if the regime is modified. (b) Theoretical comparison to experiment in [26]. The donor-acceptor pair is embedded inside a nanocrystal (4 nm diameter) with assumed refractive index n = 1.7 (LaPO4). By varying the refractive index of the surrounding medium, we find that FET ≈ 1 in agreement with our analysis. Note that we also predict the linear dependence of the Purcell factor as measured in the experiment (inset). (c) However, we predict that a silver-coated nanocrystal would produce a drastic change in the FRET FOM as well as the Purcell factor. This result would require the donor-acceptor overlap spectrum to lie around the 400 nm wavelength range. Note that the above results clearly show that FRET can be engineered by the environment even though it is extremely difficult in comparison to modifying spontaneous emission. The dyadic Green function formalism and results from QED theory were used to calculate all results and parameters were obtained from the experiments.

Tables (3)

Tables Icon

Table 1 Experimental Results of FRET

Tables Icon

Table 2 Perfect reflector regimes for FET

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Table 3 Comparison to Lakowicz experiment for various orientations: FRET rate enhancement factor, Purcell factor, intrinsic quantum yield, FRET efficiency.

Equations (41)

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γ D , r a d = 2 ω D 2 | p D | 2 ϵ 0 c 2 [ n D Im { G ¯ ¯ ( r D , r D ; ω D ) } n D ]
ρ E ( r D ; ω ) = 6 ω π c 2 n D Im { G ¯ ¯ ( r D , r D ; ω ) } n D
F p = γ D , r a d γ D , r a d o = ρ E ( r D ; ω ) ρ E o ( r D ; ω ) .
γ D γ D o = ( 1 Q D ) + Q D F p .
Γ D A = 2 π 2 d ω | V E E ( ω ) | 2 σ D ( ω ) σ A ( ω )
V E E ( r A , r D ; ω ) = ω 2 ϵ o c 2 p A G ¯ ¯ ( r A , r D ; ω ) p D
F E T = Γ D A Γ D A o
γ D A = F p γ D o + F E T Γ D A o
n A E ( r A ; ω D ) = p D 4 π n 1 2 κ r 3 + p i m a g e 4 π n 1 2 κ r 3
p i m a g e = ϵ 2 ϵ 1 ϵ 2 + ϵ 1 p D .
F E T = | κ r 3 + ϵ 2 ϵ 1 ϵ 2 + ϵ 1 κ r 3 | 2 .
F E T = [ ( ϵ 2 + ϵ 1 ) + q ] 2 | ϵ 2 + ϵ 1 | 2 + ϵ 2 2 ( 1 + Ω ) 2 | ϵ 2 + ϵ 1 | 2
F p = 1 + 3 16 ϵ 1 ϵ 2 | ϵ 1 + ϵ 2 | 2 κ ( k 1 z D ) 3
F E T = 4 κ 2 r 6 κ 2 r 6 ( ϵ 1 ϵ 2 ) 2 + ( 1 + κ r 3 κ r 3 ) 2 .
F p = 1 + 3 32 π 3 n 1 3 ( λ D z D ) 3 ( ϵ 1 ϵ 2 )
η = Γ D A γ D + Γ D A .
F e f f = η η o = F E T F E T η o + [ ( 1 Q D ) + Q D F p ] ( 1 η o )
F e f f > 1 F E T > F p
Q > 3 128 π 3 n 1 3 ( λ D z D ) 3 κ 2 r 6 κ 2 r 6 ..
P D A = ω o 2 Im { p A * E D ( r A ) } .
E D ( r A ) = ω o 2 ϵ 0 c 2 G ¯ ( r A , r D ; ω o ) p D
P D   A P o = 6 π ω o ϵ 0 c α A ( ω o ) | n A G ¯ ( r A , r D ; ω o ) n D | 2 .
| i = | D * , A | { 0 } | f = | D , A * | { 0 }
Γ i f = 2 π | M f i | 2 δ ( E f E i ) .
M f i = f | H i n t | i + k f | H i n t | k k | H i n t | i E i E k
H ^ i n t = p ^ D E ^ ( r D ) p ^ A E ^ ( r A )
E ^ ( r , ω ) = i ω ϵ o c 2 d 3 r G ¯ ( r , r , ω ) j ^ N ( r , ω ) .
j ^ N ( r , ω ) = ω ϵ o π ϵ ( r , ω ) f ^ ( r , ω )
E ^ ( r ) = 0 d ω E ^ ( r , ω ) + h . c .
Γ D A γ o = 6 π ω ϵ 0 c α A ( ω ) | n A G ¯ ( r A , r D ; ω ) n D | 2
α A ( ω ) = lim η 0 | p A | 2 1 ω ω A + i η
n D G ¯ ( r D , r D ) n D D = 1 3 Tr [ G ¯ ( r D , r D ) ] .
| n A G ¯ ( r A , r D ) n D | 2 D , A = 1 9 Tr [ G ¯ ( r A , r D ) G ¯ ( r A , r D ) ]
G r r = i k 1 4 π n = 1 n ( n + 1 ) ( 2 n + 1 ) h 1 a h 1 d ρ 1 a ρ 1 d P n ( cos θ ) R p f
G r θ = i k 1 4 π n = 1 ( 2 n + 1 ) h 1 a h 1 d ρ 1 a ρ 1 d P n ( cos θ ) sin θ R p f
G θ r = i k 1 4 π n = 1 ( 2 n + 1 ) h 1 a h 1 d ρ 1 a ρ 1 d P n ( cos θ ) sin θ R p f
G θ θ = i k 1 4 π n = 1 ( 2 n + 1 ) { h 1 a h 1 d n ( n + 1 ) P n ( cos θ ) R s f + h 1 a h 1 d ρ 1 a ρ 1 d ( P n ( cos θ ) P n ( cos θ ) cos θ n ( n + 1 ) ) R p f }
G ϕ ϕ = i k 1 4 π n = 1 ( 2 n + 1 ) { h 1 a h 1 d ρ 1 a ρ 1 d P n ( cos θ ) n ( n + 1 ) R p f + h 1 a h 1 d ( P n ( cos θ ) P n ( cos θ ) cos θ n ( n + 1 ) ) R s f }
F E T | 1 + r 3 κ n = 1 ( n + 1 ) 2 α ˜ n P n ( cos θ A ) r A n + 2 r D n + 2 | 2 .
α ˜ n = α n [ 1 i α n ( n + 1 ) k 1 2 n + 1 n ( 2 n 1 ) ! ! ( 2 n + 1 ) ! ! ] 1
α n = n ( ϵ 2 ϵ 1 ) n ϵ 2 + ( n + 1 ) ϵ 1 R ( 2 n + 1 ) .

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