Abstract

Study of photon decay rate is essential to various optical devices, where graphene is an emerging building block due to its electrical tunability. In this paper, we study photon decay rate of a quantum emitter near a metallic split-ring resonator, which is embedded in a multilayered substrate incorporating a graphene layer. Analyzing photon decay rate in such a complex multilayered system is not only computationally challenging but also highly important to experimentally realizable devices. First, the dispersion relation of graphene plasmonics supported at a dieletric/graphene/dielectric structure is investigated systematically. Meanwhile, the dispersion relation of metallic plasmonics supported at a dielectric/metal structure is studied comparatively. According to our investigation, graphene offers several flexible tuning routes for manipulating photon decay rate, including tunable chemical potential and the emitter’s position and polarization. Next, considering plasmonic waves in a graphene sheet occur in the infrared regime, we carefully design a metallic split ring resonating around the same frequency range. Consequently, this design enables a mutual interaction between graphene plasmonics and metallic plasmonics. The boundary element method with a multilayered medium Green’s function is adopted in the numerical simulation. Blue-shifted and splitting resonance peaks are theoretically observed, which suggests a strong mode coupling. Moreover, the mode coupling has a switch on-off feature via electrostatically doping the graphene sheet. This work is helpful to dynamically manipulate photon decay rate in complex optical devices.

© 2015 Optical Society of America

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References

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2014 (3)

F. J. de Abajo García, “Graphene plasmonics: challenges and opportunities,” ACS Photo. 1(3), 135–152 (2014).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

A. Kumar, K. H. Fung, M. T. H. Reid, and N. X. Fang, “Photon emission rate engineering using graphene nanodisc cavities, Opt. Express 22(6), 6400–6415 (2014).
[Crossref] [PubMed]

2013 (3)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

E. Simsek, “Graphene in layered medium applications,” Micro. Opt. Tech. Lett. 55(10), 2293–2296 (2013).
[Crossref]

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

2012 (7)

X. W. Chen, M. Agio, and V. Sandoghdar, “Metallodielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett. 108(23), 233001 (2012).
[Crossref] [PubMed]

Y. P. Chen, W. C. Chew, and L. Jiang, “A new Green’s function formulation for modeling homogeneous objects in layered medium,” IEEE Trans. Antennas Propag. 60(10), 4766–4776 (2012).
[Crossref]

Y. P. Chen, W. E. I. Sha, W. C. H. Choy, L. Jiang, and W. C. Chew, “Study on spontaneous emission in complex multilayered plasmonic system via surface integral equation approach with layered medium Green’s function,” Opt. Express 20(18), 20210–20221 (2012).
[Crossref] [PubMed]

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photo. 6, 459–462 (2012).
[Crossref]

A. Mock, “Padé approximant spectral fit for FDTD simulation of graphene in the near infrared,” Opt. Mater. Express 2(6), 771–781 (2012).
[Crossref]

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

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

2011 (2)

F. H. L. Koppens, D. E. Chang, and F. J. de Abajo García, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

2010 (1)

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

2009 (3)

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

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, (4)732–740 (2009).
[Crossref]

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

2008 (1)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

2007 (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

2006 (2)

Ekmel Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green’s functions for multilayer media,” IEEE Trans. Micro. Theory Tech. 54(1), 216–225 (2006).
[Crossref]

2000 (2)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

J. Vučković, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

1998 (1)

Agio, M.

X. W. Chen, M. Agio, and V. Sandoghdar, “Metallodielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett. 108(23), 233001 (2012).
[Crossref] [PubMed]

Amanti, M. I.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

Avlasevich, Y.

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

Avouris, P.

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

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

Baudrion, A.-L.

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Beck, M.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

Buljan, H.

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

Capasso, F.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. de Abajo García, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chen, X. W.

X. W. Chen, M. Agio, and V. Sandoghdar, “Metallodielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett. 108(23), 233001 (2012).
[Crossref] [PubMed]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Chen, Y. P.

Chew, W. C.

Y. P. Chen, W. E. I. Sha, W. C. H. Choy, L. Jiang, and W. C. Chew, “Study on spontaneous emission in complex multilayered plasmonic system via surface integral equation approach with layered medium Green’s function,” Opt. Express 20(18), 20210–20221 (2012).
[Crossref] [PubMed]

Y. P. Chen, W. C. Chew, and L. Jiang, “A new Green’s function formulation for modeling homogeneous objects in layered medium,” IEEE Trans. Antennas Propag. 60(10), 4766–4776 (2012).
[Crossref]

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).

Choy, W. C. H.

Cui, S.

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photo. 6, 459–462 (2012).
[Crossref]

de Abajo García, F. J.

F. J. de Abajo García, “Graphene plasmonics: challenges and opportunities,” ACS Photo. 1(3), 135–152 (2014).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. de Abajo García, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Deturche, R.

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Djurisic, A. B.

Eghlidi, H.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Elazar, J. M.

Engel, M.

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Faist, J.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

Fan, S.

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

Fang, N. X.

Ferrari, A. C.

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Fung, K. H.

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Genevet, P.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Gérard, D.

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Goffard, J.

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Götzinger, S.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Hanson, G. W.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nanooptics (Cambridge University, 2006).

Hu, E. L.

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photo. 6, 459–462 (2012).
[Crossref]

Jablan, M.

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

Jiang, L.

Kats, M. A.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Kern, A. M.

Kinkhabwala, A.

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

Kong, J.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. de Abajo García, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Krupke, R.

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Kukura, P.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Kumar, A.

Lee, K. G.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Lettow, R.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Li, Z.

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

Liu, Q. H.

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green’s functions for multilayer media,” IEEE Trans. Micro. Theory Tech. 54(1), 216–225 (2006).
[Crossref]

Liu, T.-L.

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photo. 6, 459–462 (2012).
[Crossref]

Löhneysen, H. v.

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Lombardo, A.

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Loncar, M.

J. Vučković, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

Low, T.

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Science+Business Media LLC, 2007).

Majewski, M. L.

Martin, O. J. F.

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, (4)732–740 (2009).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Miska, P.

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Mock, A.

Moerner, W. E.

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

Müllen, K.

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

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nanooptics (Cambridge University, 2006).

Ozbay, Ekmel

Ekmel Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Plain, J.

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Rakic, A. D.

Reid, M. T. H.

Renn, A.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Russell, K. J.

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photo. 6, 459–462 (2012).
[Crossref]

Sandoghdar, V.

X. W. Chen, M. Agio, and V. Sandoghdar, “Metallodielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett. 108(23), 233001 (2012).
[Crossref] [PubMed]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

Scalari, G.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

Scherer, A.

J. Vučković, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

Sha, W. E. I.

Simsek, E.

E. Simsek, “Graphene in layered medium applications,” Micro. Opt. Tech. Lett. 55(10), 2293–2296 (2013).
[Crossref]

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green’s functions for multilayer media,” IEEE Trans. Micro. Theory Tech. 54(1), 216–225 (2006).
[Crossref]

Soljacic, M.

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

Song, Y.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Steiner, M.

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Vuckovic, J.

J. Vučković, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

Walther, C.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

Wei, B.

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green’s functions for multilayer media,” IEEE Trans. Micro. Theory Tech. 54(1), 216–225 (2006).
[Crossref]

Xia, F.

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

Yan, H.

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

Yao, Y.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Yu, N.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Yu, Z.

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

ACS Nano (1)

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

ACS Photo. (1)

F. J. de Abajo García, “Graphene plasmonics: challenges and opportunities,” ACS Photo. 1(3), 135–152 (2014).
[Crossref]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

J. Vučković, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

IEEE Trans. Antennas Propag. (1)

Y. P. Chen, W. C. Chew, and L. Jiang, “A new Green’s function formulation for modeling homogeneous objects in layered medium,” IEEE Trans. Antennas Propag. 60(10), 4766–4776 (2012).
[Crossref]

IEEE Trans. Micro. Theory Tech. (1)

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green’s functions for multilayer media,” IEEE Trans. Micro. Theory Tech. 54(1), 216–225 (2006).
[Crossref]

J. Appl. Phys. (1)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

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

Micro. Opt. Tech. Lett. (1)

E. Simsek, “Graphene in layered medium applications,” Micro. Opt. Tech. Lett. 55(10), 2293–2296 (2013).
[Crossref]

Nano Lett. (2)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. de Abajo García, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Nat. Comm. (1)

M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. v. Löhneysen, P. Avouris, and R. Krupke, “Light-matter interaction in a microcavity-controlled graphene transistor,” Nat. Comm. 3, 906 (2012).
[Crossref]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Nat. Photo. (1)

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photo. 6, 459–462 (2012).
[Crossref]

Nat. Photon. (2)

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

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. 5(3), 166–169 (2011).
[Crossref]

New J. Phys. (1)

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

Opt. Express (2)

Opt. Mater. Express (1)

Phys. Rev. B (1)

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

Phys. Rev. E (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Phys. Rev. Lett. (1)

X. W. Chen, M. Agio, and V. Sandoghdar, “Metallodielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett. 108(23), 233001 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

J. Goffard, D. Gérard, P. Miska, A.-L. Baudrion, R. Deturche, and J. Plain, “Plasmonic engineering of spontaneous emission from silicon nanocrystals,” Sci. Rep. 3, 2672 (2013).
[Crossref] [PubMed]

Science (2)

Ekmel Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327, 1495–1497 (2010).
[Crossref] [PubMed]

Other (3)

L. Novotny and B. Hecht, Principles of Nanooptics (Cambridge University, 2006).

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Science+Business Media LLC, 2007).

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Figures (5)

Fig. 1
Fig. 1 The schematic configuration of a complicated electromagnetic system for manipulating photon decay rates. A rectangular gold (Au) split-ring resonator is embedded in the layer of ZnO with thickness d1 = 60 nm and dielectric constant (relative permittivity) ε1r = 3.61. The ZnO layer is attached to a graphene layer, which is backed by a SiO2 substrate with d2 = 100 nm and ε2r = 2.25. The mesh of the resonator is shown in the figure with a = 150 nm, b = 30 nm, g = 20 nm, and w = 25 nm. The emitter is put inside the gap of this resonator. The effective thickness of the graphene layer is set to be a typical value of d0 = 0.5 nm.
Fig. 2
Fig. 2 (a) A dielectric/graphene/dielectric structure. (b) A dielectric/metal (gold) structure. (c) The dispersion curves of the graphene structure in the infrared and visible light regime. (d) The dispersion curves of the metal structure in the visible light regime. (e) The photon decay rate of the graphene structure with a z-oriented dipole 10 nm above the interface. (f) The photon decay rate of the metal structure with a z-oriented dipole 10 nm above the interface.
Fig. 3
Fig. 3 (a) Polarization effect of a dipole 10 nm above the graphene layer. (b) Position effect of a z-oriented dipole above the graphene layer. (c) Position effect of a z-oriented dipole above a metal substrate. (d) Chemical potential effect of a z-oriented dipole 10 nm above the graphene layer.
Fig. 4
Fig. 4 (a) Polarization effect of a dipole at the center of the resonator gap without a graphene layer. (b) Position effect of a x-oriented dipole inside the resonator gap without a graphene layer. (c) Position effect of a x-oriented dipole with and without a graphene layer. (d) Chemical potential effect of a x-oriented dipole in the hybrid system.
Fig. 5
Fig. 5 (a) Near field distribution at wavelength 1 of Fig. 4(d) (shorter-wavelength peak). (b) Near field distribution at wavelength 2 of Fig. 4(d) (dip). (c) Near field distribution at wavelength 3 of Fig. 4(d) (longer-wavelength peak). (d) Near field distribution at wavelength 4 of Fig. 4(d).

Equations (6)

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γ γ 0 = Im [ G α α ( r , r , ω ) ] Im [ G 0 α α ( r , r , ω ) ]
E α ( r ) = j ω μ V G α α ( r , r ) δ ( r r ) d r
σ ( ω , μ c , Γ , T ) = j e 2 ( ω j 2 Γ ) π h ¯ 2 [ 1 ( ω j 2 Γ ) 2 0 ε ( f d ( ε ) ε f d ( ε ) ε ) d ε 0 f d ( ε ) f d ( ε ) ( ω j 2 Γ ) 2 4 ( ε / h ¯ ) 2 d ε ] .
ω ε 1 k 2 z ( ω ε 2 σ k 2 z ) k 1 z + 1 = 0.
k ρ = k 2 ( 2 ω ε σ ) 2 .
k ρ = ω c ε 1 r ε 2 r ε 1 r + ε 2 r .

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