Abstract

In this work, we present a systematic study of the plasmon modes in a system of vertically stacked pair of graphene discs. Quasistatic approximation is used to model the eigenmodes of the system. Eigen-response theory is employed to explain the spatial dependence of the coupling between the plasmon modes and a quantum emitter. These results show a good match between the semi-analytical calculation and full-wave simulations. Secondly, we have shown that it is possible to engineer the decay rates of a quantum emitter placed inside and near this cavity, using Fermi level tuning, via gate voltages and variation of emitter location and polarization. We highlighted that by coupling to the bright plasmon mode, the radiative efficiency of the emitter can be enhanced compared to the single graphene disc case, whereas the dark plasmon mode suppresses the radiative efficiency.

© 2014 Optical Society of America

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  30. C. Vandenbem, D. Brayer, L. S. Froufe-Pérez, R. Carminati, “Controlling the quantum yield of a dipole emitter with coupled plasmonic modes,” Phys. Rev. B 81, 085444 (2010).
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2014 (1)

K. H. Fung, A. Kumar, N. X. Fang, “Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory,” Phys. Rev. B 89, 045408 (2014).
[CrossRef]

2013 (2)

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, D. Zueco, “Weak and strong coupling regimes in plasmonic qed,” Phys. Rev. B 87, 115419 (2013).
[CrossRef]

M. Jablan, M. Soljacic, H. Buljan, “Plasmons in graphene: Fundamental properties and potential applications,” Proceedings of the IEEE 101, 1689–1704 (2013).
[CrossRef]

2012 (5)

H. Yan, F. Xia, Z. Li, P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[CrossRef]

J. B. Khurgin, A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bull. 37, 768–779 (2012).
[CrossRef]

W. Wang, S. P. Apell, J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[CrossRef]

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[CrossRef]

M. K. Schmidt, S. Mackowski, J. Aizpurua, “Control of single emitter radiation by polarization- and position-dependent activation of dark antenna modes,” Opt. Lett. 37, 1017–1019 (2012).
[CrossRef] [PubMed]

2011 (2)

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[CrossRef] [PubMed]

A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

2010 (3)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

C. Vandenbem, D. Brayer, L. S. Froufe-Pérez, R. Carminati, “Controlling the quantum yield of a dipole emitter with coupled plasmonic modes,” Phys. Rev. B 81, 085444 (2010).
[CrossRef]

E. Waks, D. Sridharan, “Cavity qed treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A 82, 043845 (2010).
[CrossRef]

2009 (3)

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

2008 (2)

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

E. Fort, S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D: Appl. Phys. 41, 013001 (2008).
[CrossRef]

2007 (2)

L. A. Falkovsky, A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

A. K. Geim, K. S. Novoselov, “The rise of graphene,” Nature Mat. 6, 183–191 (2007).
[CrossRef]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

1998 (1)

T. Ando, T. Nakanishi, “Impurity scattering in carbon nanotubes – absence of back scattering –,” J. Phys. Soc. Jpn 67, 1704–1713 (1998).
[CrossRef]

1986 (1)

A. L. Fetter, “Magnetoplasmons in a two-dimensional electron fluid: Disk geometry,” Phys. Rev. B 33, 5221–5227 (1986).
[CrossRef]

1982 (1)

J. I. Gersten, “Disk plasma oscillations,” J. Chem. Phys. 77, 6285–6288 (1982).
[CrossRef]

1975 (2)

R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (1975).
[CrossRef]

Ahn, C.-H.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Aizpurua, J.

Ando, T.

T. Ando, T. Nakanishi, “Impurity scattering in carbon nanotubes – absence of back scattering –,” J. Phys. Soc. Jpn 67, 1704–1713 (1998).
[CrossRef]

Apell, S. P.

W. Wang, S. P. Apell, J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[CrossRef]

Asano, T.

S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (1975).
[CrossRef]

Avouris, P.

H. Yan, F. Xia, Z. Li, P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[CrossRef]

Bolotin, K.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

Boltasseva, A.

J. B. Khurgin, A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bull. 37, 768–779 (2012).
[CrossRef]

Brayer, D.

C. Vandenbem, D. Brayer, L. S. Froufe-Pérez, R. Carminati, “Controlling the quantum yield of a dipole emitter with coupled plasmonic modes,” Phys. Rev. B 81, 085444 (2010).
[CrossRef]

Buljan, H.

M. Jablan, M. Soljacic, H. Buljan, “Plasmons in graphene: Fundamental properties and potential applications,” Proceedings of the IEEE 101, 1689–1704 (2013).
[CrossRef]

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Carminati, R.

C. Vandenbem, D. Brayer, L. S. Froufe-Pérez, R. Carminati, “Controlling the quantum yield of a dipole emitter with coupled plasmonic modes,” Phys. Rev. B 81, 085444 (2010).
[CrossRef]

Chance, R. R.

R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[CrossRef] [PubMed]

Chen, X.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Choi, K.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Dean, C. R.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Engheta, N.

A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

Falkovsky, L. A.

L. A. Falkovsky, A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

Fang, N. X.

K. H. Fung, A. Kumar, N. X. Fang, “Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory,” Phys. Rev. B 89, 045408 (2014).
[CrossRef]

Fetter, A. L.

A. L. Fetter, “Magnetoplasmons in a two-dimensional electron fluid: Disk geometry,” Phys. Rev. B 33, 5221–5227 (1986).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Fort, E.

E. Fort, S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D: Appl. Phys. 41, 013001 (2008).
[CrossRef]

Froufe-Pérez, L. S.

C. Vandenbem, D. Brayer, L. S. Froufe-Pérez, R. Carminati, “Controlling the quantum yield of a dipole emitter with coupled plasmonic modes,” Phys. Rev. B 81, 085444 (2010).
[CrossRef]

Fudenberg, G.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

Fujita, M.

S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (1975).
[CrossRef]

Fung, K. H.

K. H. Fung, A. Kumar, N. X. Fang, “Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory,” Phys. Rev. B 89, 045408 (2014).
[CrossRef]

Garcia de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[CrossRef] [PubMed]

García-Vidal, F. J.

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, D. Zueco, “Weak and strong coupling regimes in plasmonic qed,” Phys. Rev. B 87, 115419 (2013).
[CrossRef]

Geim, A. K.

A. K. Geim, K. S. Novoselov, “The rise of graphene,” Nature Mat. 6, 183–191 (2007).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Gérard, J.-M.

J.-M. Gérard, “Solid-state cavity-quantum electrodynamics with self-assembled quantum dots,” in “Single Quantum Dots,”, vol. 90 of Topics in Applied Physics (SpringerBerlin Heidelberg, 2003), pp. 269–314.
[CrossRef]

Gersten, J. I.

J. I. Gersten, “Disk plasma oscillations,” J. Chem. Phys. 77, 6285–6288 (1982).
[CrossRef]

Gray, S. K.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

Grésillon, S.

E. Fort, S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D: Appl. Phys. 41, 013001 (2008).
[CrossRef]

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[CrossRef]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Guyot-Sionnest, P.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

Hecht, B.

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

Hone, J.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

Hümmer, T.

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, D. Zueco, “Weak and strong coupling regimes in plasmonic qed,” Phys. Rev. B 87, 115419 (2013).
[CrossRef]

Jablan, M.

M. Jablan, M. Soljacic, H. Buljan, “Plasmons in graphene: Fundamental properties and potential applications,” Proceedings of the IEEE 101, 1689–1704 (2013).
[CrossRef]

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Jiang, Z.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

Johnson, S. G.

M. T. H. Reid, S. G. Johnson, “Efficient computation of power, force, and torque in bem scattering calculations,” (2013), http://arxiv.org/abs/1307.2966 .

Khurgin, J. B.

J. B. Khurgin, A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bull. 37, 768–779 (2012).
[CrossRef]

Kim, K.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Kim, P.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

Kinaret, J. M.

W. Wang, S. P. Apell, J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[CrossRef]

Klima, M.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[CrossRef] [PubMed]

Kumar, A.

K. H. Fung, A. Kumar, N. X. Fang, “Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory,” Phys. Rev. B 89, 045408 (2014).
[CrossRef]

Kwon, I. C.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Lee, A.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Lee, C.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

Lee, S.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Lee, S.-Y.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

Lee, T.-W.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

Li, Z.

H. Yan, F. Xia, Z. Li, P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[CrossRef]

Liu, M.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

Mackowski, S.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Martín-Moreno, L.

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, D. Zueco, “Weak and strong coupling regimes in plasmonic qed,” Phys. Rev. B 87, 115419 (2013).
[CrossRef]

Meric, I.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

Moon, D. H.

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

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S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
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T. Ando, T. Nakanishi, “Impurity scattering in carbon nanotubes – absence of back scattering –,” J. Phys. Soc. Jpn 67, 1704–1713 (1998).
[CrossRef]

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S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (1975).
[CrossRef]

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A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[CrossRef]

A. K. Geim, K. S. Novoselov, “The rise of graphene,” Nature Mat. 6, 183–191 (2007).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

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

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S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

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M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

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A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[CrossRef]

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R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

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M. T. H. Reid, S. G. Johnson, “Efficient computation of power, force, and torque in bem scattering calculations,” (2013), http://arxiv.org/abs/1307.2966 .

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S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

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Shepard, K. L.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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[CrossRef]

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R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

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M. Jablan, M. Soljacic, H. Buljan, “Plasmons in graphene: Fundamental properties and potential applications,” Proceedings of the IEEE 101, 1689–1704 (2013).
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M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Sorgenfrei, S.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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E. Waks, D. Sridharan, “Cavity qed treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A 82, 043845 (2010).
[CrossRef]

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K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

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C. Vandenbem, D. Brayer, L. S. Froufe-Pérez, R. Carminati, “Controlling the quantum yield of a dipole emitter with coupled plasmonic modes,” Phys. Rev. B 81, 085444 (2010).
[CrossRef]

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L. A. Falkovsky, A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

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E. Waks, D. Sridharan, “Cavity qed treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A 82, 043845 (2010).
[CrossRef]

Wang, L.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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W. Wang, S. P. Apell, J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[CrossRef]

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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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H. Yan, F. Xia, Z. Li, P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[CrossRef]

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H. Yan, F. Xia, Z. Li, P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[CrossRef]

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S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

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S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
[CrossRef] [PubMed]

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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

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T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, D. Zueco, “Weak and strong coupling regimes in plasmonic qed,” Phys. Rev. B 87, 115419 (2013).
[CrossRef]

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T. Ando, T. Nakanishi, “Impurity scattering in carbon nanotubes – absence of back scattering –,” J. Phys. Soc. Jpn 67, 1704–1713 (1998).
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Nano Lett. (2)

S. Lee, J. H. Ryu, K. Park, A. Lee, S.-Y. Lee, I.-C. Youn, C.-H. Ahn, S. M. Yoon, S.-J. Myung, D. H. Moon, X. Chen, K. Choi, I. C. Kwon, K. Kim, “Polymeric nanoparticle-based activatable near-infrared nanosensor for protease determination in vivo,” Nano Lett. 9, 4412–4416 (2009). PMID: .
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Nat. Photonics (2)

S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (1975).
[CrossRef]

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[CrossRef]

Nature Mat. (1)

A. K. Geim, K. S. Novoselov, “The rise of graphene,” Nature Mat. 6, 183–191 (2007).
[CrossRef]

Nature Nanotech. (1)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, J. Hone, “Boron nitride substrates for high-quality graphene electronic,” Nature Nanotech. 5, 722–726 (2010).
[CrossRef]

New J. Phys. (1)

H. Yan, F. Xia, Z. Li, P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

E. Waks, D. Sridharan, “Cavity qed treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A 82, 043845 (2010).
[CrossRef]

Phys. Rev. B (6)

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, D. Zueco, “Weak and strong coupling regimes in plasmonic qed,” Phys. Rev. B 87, 115419 (2013).
[CrossRef]

K. H. Fung, A. Kumar, N. X. Fang, “Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory,” Phys. Rev. B 89, 045408 (2014).
[CrossRef]

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[CrossRef]

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef] [PubMed]

Proceedings of the IEEE (1)

M. Jablan, M. Soljacic, H. Buljan, “Plasmons in graphene: Fundamental properties and potential applications,” Proceedings of the IEEE 101, 1689–1704 (2013).
[CrossRef]

Science (2)

A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

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K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[CrossRef]

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H. Reid, scuff-em suite version 0.95, http://homerreid.com/scuff-em .

M. T. H. Reid, S. G. Johnson, “Efficient computation of power, force, and torque in bem scattering calculations,” (2013), http://arxiv.org/abs/1307.2966 .

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
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Figures (8)

Fig. 1
Fig. 1

Geometry for studying decay rate engineering: A) In this geometry, the emitter can excite only one of the two modes, depending on its location and polarization B) In this geometry, the emitter can excite both the dark as well as the bright modes. Hence it is suited to studying comparatively, the effect of these modes on the the decay rate of the quantum emitter. The numerical values of the disc separation D and the radius R, which were used for the BEM simulation are shown here.

Fig. 2
Fig. 2

A) Resonant frequencies of the modes calculated using the quasistatic solution Normalized resonant frequencies of the modes of different symmetry, where ω R 2 = e 2 E F / ( 2 π h ¯ 2 ε 0 ε R ). For each L, only the lowest two modes are shown. The dashed line is only a guide to the eye. B) Comparison of the resonant frequencies calculated using quasistatic approximation versus the full wave boundary element simulation Resonant frequencies of the L = 1, n = 1 modes as a function of Fermi level EF. Squares represent the BEM calculation and lines represent the quasistatic result. Note that in BEM we chose finite absorption whereas in the quasistatic approach we used a lossless graphene conductivity.

Fig. 3
Fig. 3

Semi-analytically calculated overlap terms for a Single Disc: The emitter is located at a vertical distance of 15nm above the disc and moves along Yd = 0. The colors correspond to different polarizations of the emitter: (oe-22-6-6400-i001), ŷ(oe-22-6-6400-i002) and (oe-22-6-6400-i003)

Fig. 4
Fig. 4

Semi-analytically calculated overlap terms for the disc dimer bright mode: The emitter is located on the inversion plane parallel to the discs and moves along Yd = 0. The colors correspond to different polarizations of the emitter: ( oe-22-6-6400-i004) and ŷ( oe-22-6-6400-i005). The -polarization has a zero overlap at these resonances.

Fig. 5
Fig. 5

Semi-analytically calculated overlap terms for the disc dimer dark mode: The emitter is located on the inversion plane parallel to the discs and moves along Yd = 0. The color ( oe-22-6-6400-i006) corresponds to the -polarization of the emitter. The and ŷ-polarizations produce zero overlap at these resonances.

Fig. 6
Fig. 6

Total decay rate as a function of emitter position and polarization: Using BEM, we calculate the total decay rate of an emitter placed at (Xd, 0, 0), at the bright (left) and dark (right) mode frequencies for (L = 1, n = 1) mode. (EF = 0.5 eV and τ = 0.05 ps)

Fig. 7
Fig. 7

a) Simulated (BEM) Spectrum of Decay Rates An example spectrum of the two decay rates into the radiative (ΓRAD0) and plasmon (≈ΓNR0) modes. The dipole moment of the emitter is aligned in the x-direction and it is located at Xd = 0 nm and Zd = 30 nm, fixed such that the emitter is located 15 nm above the closest disc. b) Comparison of Radiative Efficiency: The quantum emitter positioned at Xd = 0 nm at a vertical distance of 15 nm above the cavity. Depending on it’s resonant frequency, it can couple to both the dark as well as bright modes. It can be seen here that the dark mode suppresses radiative emission, whereas the bright mode enhances it, compared to the single disc case. (τ = 0.05 ps)

Fig. 8
Fig. 8

a) Simulated (BEM) Radiative efficiency as a function of emitter position and polarization: An x-polarized emitter is located at (Xd, 0, Zd). Zd is fixed such that the emitter is located 15 nm above the closest disc. The bright mode is found to enhance radiative decay rate, but the dark mode does not. b) Vacuum Rabi splitting versus Fermi level: Normalized vacuum Rabi splitting for the dark and bright modes when an x-polarized emitter is located at (0, 0, Zd) outside the cavity. Zd is fixed such that the emitter is located 15 nm above the closest disc. The dashed line represents g/κ = 1/2 below which splitting will not be observed. (κ ≈10 meV).

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

σ R P A ( ω ) = 2 e 2 k T π h ¯ 2 i ω + i / τ ln | 2 cosh ( μ 2 k T ) | + e 2 4 h ¯ [ H ( ω / 2 , T ) + 4 i ω π 0 d ζ H ( ζ , T ) H ( ω / 2 , T ) ω 2 4 ζ 2 ]
ε ( ω ) = 1 + i σ 2 D ( ω ) ω ε 0 Δ .
Γ tot Γ = 1 + 6 π ε 0 | μ ^ | 2 k 3 { μ ^ * E s ( x 0 ) } .
H = h ¯ ω 0 σ + σ + h ¯ ω ( a a + 1 2 ) + h ¯ g 2 ( a σ + a σ + )
d ρ d t = i h ¯ [ H , ρ ] κ 2 ( a a ρ 2 a ρ a + ρ a a ) Γ 2 ( σ + σ ρ 2 σ ρ σ + + ρ σ + σ )
Γ tot = Γ 0 + g 2 ( κ Γ ) 4 Δ 2 + ( κ Γ ) 2
2 Φ ( r , z ) = σ b Θ ( R r ) ε 0 ( δ ( z D / 2 ) + δ ( z + D / 2 ) )
2 [ Φ ( r , z ) e ι L ϕ ] = 0
ε u Φ ( r , z ) z | ( D 2 ) + ε m Φ ( r , z ) z | ( D 2 ) = σ b , u Θ ( R r ) ε 0
ε m Φ ( r , z ) z | ( D 2 ) + ε d Φ ( r , z ) z | ( D 2 ) = σ b , l Θ ( R r ) ε 0
Φ ( r , z ) e ι L ϕ = 0 d p p Φ ¯ ( p , z ) J L ( p r ) e ι L ϕ
0 d p p [ ( 2 z 2 p 2 ) Φ ¯ ( p , z ) ] J L ( p r ) e ι L ϕ = 0
Φ ¯ ( p , z ) = { A u e p ( z D / 2 ) if z D / 2 A m + e p ( z D / 2 ) + A m e p ( z + D / 2 ) , if | z | D / 2 A d e p ( z + D / 2 ) , if z D / 2
[ Φ ¯ u ( p ) Φ ¯ d ( p ) ] = 1 2 p ε 0 ε [ 1 e p D e p D 1 ] [ σ ¯ b , u ( p ) σ ¯ b , d ( p ) ]
[ Φ u ( r ) Φ d ( r ) ] = 1 ε 0 ε [ 0 R d r r K L o ( r , r ) 0 R d r r K L i ( r , r ) 0 R d r r K L i ( r , r ) 0 R d r r K L o ( r , r ) ] [ σ b , u ( r ) σ b , d ( r ) ]
| | J s + σ b t = 0
J s = σ ( ω ) E | |
[ σ b , u ( r ) σ b , d ( r ) ] = σ ( ω ) ι ω [ Θ ( R r ) | | 2 δ ( r R ) r 0 0 Θ ( R r ) | | 2 δ ( r R ) r ] [ Φ u ( r ) Φ d ( r ) ]
[ Φ u ( r ) Φ d ( r ) ] = σ ( ω ) ι ω ε 0 ω [ 0 R d r r K L o ( r , r ) 0 R d r r K L i ( r , r ) 0 R d r r K L i ( r , r ) 0 R d r r K L o ( r , r ) ] [ Θ ( R r ) | | 2 + δ ( r R ) r 0 0 Θ ( R r ) | | 2 + δ ( r R ) r ] [ Φ u ( r ) Φ d ( r ) ]
[ ϕ u ( x ) ϕ d ( x ) ] = η [ ^ L u u ( x ; x ) ^ L u d ( x ; x ) ^ L d u ( x ; x ) ^ L d d ( x ; x ) ] [ ϕ u ( x ) ϕ d ( x ) ]
| P = L = 0 α A , L | P A , L P A , L | E exc + α S , L | P S , L P S , L | E exc
Γ tot / Γ 0 = 1 + 6 π k i | μ ( r 0 ) | G ^ ( r , r 0 ) | i | 2 [ α i ( ω ) ]
J s = P s t = ι ω P s
J s = [ σ ( ω ) Θ ( R r ) ] E | | = [ σ ( ω ) Θ ( R r ) ] | | Φ
P s = [ σ ( ω ) Θ ( R r ) ι ω ] | | Φ
G ^ ( r , r 0 ) = k 4 π ( A ( k | r r 0 | ) + B ( k | r r 0 | ) | r r 0 r r 0 | | r r 0 | 2 )

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