Abstract

We theoretically investigate the coupling between molecular excitons and dipolar Fano-like cavity plasmon resonance in two-layered core-shell resonators consisting of a dielectric core with high refractive index and a thin metal outer shell gapped by a low refractive index thin dielectric layer containing molecules. We demonstrate that associated with the excitation of the dipolar Fano-like cavity plasmon, the electric fields can be highly localized within the dielectric gap shell, leading to very small mode volumes. By using the three-oscillator temporal coupled model to describe the proposed plasmon-exciton system, we are able to demonstrate that the coupling between molecular excitons and cavity plasmon resonance can reach the strong coupling regime. Furthermore, we also demonstrate that reducing the thickness or the refractive index of the dielectric gap shell layer can result in further compression of the mode volumes, and consequently decrease the minimum number of the coupled excitons that are required to fulfill the criteria for strong coupling.

© 2017 Optical Society of America

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2016 (3)

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

K. Santhosh, O. Bitton, L. Chuntonov, and G. Haran, “Vacuum Rabi splitting in a plasmonic cavity at the single quantum emitter limit,” Nat. Commun. 7, s11823 (2016).
[Crossref] [PubMed]

P. Gu, M. Wan, W. Wu, Z. Chen, and Z. Wang, “Excitation and tuning of Fano-like cavity plasmon resonances in dielectric-metal core-shell resonators,” Nanoscale 8(19), 10358–10363 (2016).
[Crossref] [PubMed]

2015 (4)

P. Gu, M. J. Wan, Q. Shen, X. D. He, Z. Chen, P. Zhan, and Z. L. Wang, “Experimental observation of sharp cavity plasmon resonances in dielectric-metal coreshell resonators,” Appl. Phys. Lett. 107(14), 141908 (2015).
[Crossref]

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref] [PubMed]

A. Shalabney, J. George, J. Hutchison, G. Pupillo, C. Genet, and T. W. Ebbesen, “Coherent coupling of molecular resonators with a microcavity mode,” Nat. Commun. 6, 5981 (2015).
[Crossref] [PubMed]

G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing Strong Light-Matter Interactions between Single-Nanoparticle Plasmons and Molecular Excitons at Ambient Conditions,” Phys. Rev. Lett. 114(15), 157401 (2015).
[Crossref] [PubMed]

2014 (6)

L. Shi, T. K. Hakala, H. T. Rekola, J.-P. Martikainen, R. J. Moerland, and P. Törmä, “Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes,” Phys. Rev. Lett. 112(15), 153002 (2014).
[Crossref] [PubMed]

J. M. Ménard, C. Poellmann, M. Porer, U. Leierseder, E. Galopin, A. Lemaître, A. Amo, J. Bloch, and R. Huber, “Revealing the dark side of a bright exciton-polariton condensate,” Nat. Commun. 5, 4648 (2014).
[Crossref] [PubMed]

P. Bhattacharya, T. Frost, S. Deshpande, M. Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112(23), 236802 (2014).
[Crossref] [PubMed]

X. Z. Liu, T. Galfsky, Zh. Sun, F. N. Xia, E. C. Lin, Y. H. Lee, S. K. Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2014).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508(7495), 241–244 (2014).
[Crossref] [PubMed]

T. J. Antosiewicz, S. P. Apell, and T. Shegai, “Plasmon−Exciton Interactions in a Core−Shell Geometry: From Enhanced Absorption to Strong Coupling,” ACS Photonics 1(5), 454–463 (2014).
[Crossref]

2013 (9)

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, “Monodisperse silicon nanocavities and photonic crystals with magnetic response in the optical region,” Nat. Commun. 4, 1904 (2013).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

T. Espinosa-Ortega and T. C. H. Liew, “Complete architecture of integrated photonic circuits based on and and not logic gates of exciton polaritons in semiconductor microcavities,” Phys. Rev. B 87(19), 195305 (2013).
[Crossref]

G. Y. Chen, Y. C. Yu, X. L. Zhuo, Y. G. Huang, H. X. Jiang, J. F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B 87(19), 195138 (2013).
[Crossref]

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13(7), 3281–3286 (2013).
[Crossref] [PubMed]

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton-polaritons in a polymer,” Nat. Mater. 13(3), 247–252 (2013).
[Crossref] [PubMed]

S. R. Rodriguez, J. Feist, M. A. Verschuuren, F. J. Garcia Vidal, and J. Gómez Rivas, “Thermalization and cooling of plasmon-exciton polaritons: towards quantum condensation,” Phys. Rev. Lett. 111(16), 166802 (2013).
[Crossref] [PubMed]

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110(20), 206403 (2013).
[Crossref] [PubMed]

P. Vasa, W. Wang, R. Pomraenke, M. Lammers, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates,” Nat. Photonics 7, 128–132 (2013).

2012 (2)

S. Hayashi, Y. Ishigaki, and M. Fujii, “Plasmonic effects on strong exciton-photon coupling in metal-insulator-metal microcavities,” Phys. Rev. B 86(4), 045408 (2012).
[Crossref]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

2011 (2)

G. Nardin, G. Grosso, Y. Léger, B. Pietka, F. Morier-Genoud, and B. Deveaud-Plédran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nat. Phys. 7(8), 635–641 (2011).
[Crossref]

N. T. Fofang, N. K. Grady, Z. Fan, A. O. Govorov, and N. J. Halas, “Plexciton dynamics: exciton-plasmon coupling in a J-aggregate-Au nanoshell complex provides a mechanism for nonlinearity,” Nano Lett. 11(4), 1556–1560 (2011).
[Crossref] [PubMed]

2010 (1)

P. Vasa, R. Pomraenke, G. Cirmi, E. De Re, W. Wang, S. Schwieger, D. Leipold, E. Runge, G. Cerullo, and C. Lienau, “Ultrafast Manipulation of Strong Coupling in Metal-Molecular Aggregate Hybrid Nanostructures,” ACS Nano 4(12), 7559–7565 (2010).
[Crossref] [PubMed]

2008 (2)

N. T. Fofang, T. H. Park, O. Neumann, N. A. Mirin, P. Nordlander, and N. J. Halas, “Plexcitonic Nanoparticles: Plasmon-Exciton Coupling in Nanoshell-J-Aggregate Complexes,” Nano Lett. 8(10), 3481–3487 (2008).
[Crossref] [PubMed]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett. 100(24), 240404 (2008).
[Crossref] [PubMed]

2007 (4)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 (2007).
[Crossref] [PubMed]

S. Christopoulos, G. B. von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J. F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

E. Iglesias-Silva, J. Rivas, L. M. León Isidro, and M. A. López-Quintela, “Synthesis of silver-coated magnetite nanoparticles,” J. Non-Cryst. Sol. 353(8), 829–831 (2007).

2006 (1)

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature 443(7110), 409–414 (2006).
[Crossref] [PubMed]

2005 (2)

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. At. Mol. Opt. Phys. 38(9), S551–S565 (2005).
[Crossref]

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
[Crossref]

2004 (2)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[Crossref] [PubMed]

I. Shelykh, G. Malpuech, K. Kavokin, A. Kavokin, and P. Bigenwald, “Spin dynamics of interacting exciton polaritons in microcavities,” Phys. Rev. B 70(11), 115301 (2004).
[Crossref]

2003 (4)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425(6955), 268–271 (2003).
[Crossref] [PubMed]

J. Zhang, Z. Chen, Z. Wang, W. Zhang, and N. Ming, “Preparation of monodisperse polystyrene spheres in aqueous alcohol system,” Mater. Lett. 57(28), 4466–4470 (2003).
[Crossref]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[Crossref] [PubMed]

1999 (1)

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref] [PubMed]

1998 (1)

S. J. Oldenburg, R. D. Averitt, S. L. Westcott, and N. J. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett. 288(2), 243–247 (1998).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of two-layered plasmonic core-shell resonator composed of a high refractive index (ncore) silicon core (radius: rin), a low refractive index dielectric layer (refractive index: nd; thickness: d) and an outer silver shell (thickness: t). (b) Extinction spectrum of the two-layered plasmonic CSR with the silver shell thickness of t = 14.5 nm, the LRI dielectric gap shell thickness of d = 6 nm and LRI dielectric gap shell refractive index of nd = 1.5. (c) Spatial distribution of electric field magnitude (|E|) in k-E plane at the Fano resonance in (b).
Fig. 2
Fig. 2 (a) Extinction spectra of the plasmonic CSRs without (top panel) and with molecules (middle panel), and absorption spectra of the CSRs with molecules (bottom panel). The dielectric shell thickness is fixed to d = 6 nm. Horizontal dashed line indicates the transition of molecular excitons. Vertical dashed line indicates the silver shell thickness of t = 14.5 nm where the CSR reaches the on-resonance condition. (b) Extinction and absorption spectra of the molecule-doped CSR with the particular parameters of d = 6 nm and t = 14.5 nm.
Fig. 3
Fig. 3 (a) Extinction spectrums of Fano line-shape plasmon resonance without molecules calculated by Mie theory (blue circles) and fitted by three-oscillator temporal coupled model (red solid line). (b) Extinction spectrums of plexciton mode in the molecule-doped CSR calculated by Mie theory (blue circles) and further fitted by three-oscillator temporal coupled model with the parameters obtained in (a) (red solid line). (c) Comparisons of resonant dispersion between Mie theory (blue circles) and temporal coupled model (red solid line) as a function of the silver shell thickness t. (d) Coupling strength κ1e obtained from temporal coupled model on dependence of silver shell thickness t. Dashed vertical line indicates the on-resonance condition.
Fig. 4
Fig. 4 The equi-energy plot of the Fano resonance for the case of nd = 1.5 as functions of d and t (a), and for the case of d = 6 nm as functions of nd and t (b). The dashed lines in (a) and (b) indicate the 1.79 eV contours. The mode volumes (red line with circles) and damping rates (blue line with squares) of the Fano resonances with the energy of 1.79 eV are plotted as a function of the LRI dielectric shell thickness of d (c) and as a function of the LRI dielectric shell refractive index of nd (d).
Fig. 5
Fig. 5 (a) and (b) The dependencies of the coupling strengths of the interactions between the excitons and the Fano-like cavity plasmon resonances having the same energy of 1.79 eV supported by the CSRs with the specified parameters located in the dashed lines shown in Figs. 4(a) and 4(b) on f , respectively. The dashed lines are linear fit. (c) and (d) Strong coupling criteria κ1e/κc on dependence of the numbers of coupled excitons N for different d and nd, respectively. The horizontal dashed lines indicate κ1e/κc = 1.

Equations (6)

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d P p1 dt =j ω p1 P p1 +j κ 1e P e +j κ 12 e jφ P p2 + γ 1s s + ,
d P e dt =j ω e P e γ e 2 P e +j κ 1e P p1 ,
d P p2 dt =j ω p2 P p2 γ p2 2 P p2 +j κ 12 e jφ P p1 j γ 2s s + ,
s = s + + γ 1s P p1 +j γ 2s P p2 ,
E inner = | s + | 2 | s | 2 .
κ 1e = N μ J | E vac |,

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