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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 15847–15858
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Optical transport and sensing in plexcitonic nanocavities

Olalla Pérez-González, Javier Aizpurua, and Nerea Zabala  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15847-15858 (2013)
http://dx.doi.org/10.1364/OE.21.015847


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Abstract

We present a theoretical study of the optical properties of a strongly coupled metallic dimer when an ensemble of molecules is placed in the inter-particle cavity. The linking molecules are characterized by an excitonic transition which couples to the Bonding Dimer Plasmon (BDP) and the Bonding Quadrupolar Plasmon (BQP) resonances, arising from the hybridization of the dipolar and quadrupolar modes of the individual nanoparticles, respectively. As a consequence, both modes split into two coupled plasmon-exciton modes, so called plexcitons. The Charge Transfer Plasmon (CTP) resonance, involving plasmonic oscillations of the dimer as a whole, arises when the conductance of the excitonic junction is above a threshold value. The possibility of exploiting plexcitonic resonances for sensing is explored in detail. We find high sensitivity to the environment when different dielectric embedding media are considered. Contrary to standard methods, we propose a new framework for effective sensing based on the relative intensity of plexcitonic peaks.

© 2013 OSA

1. Introduction

During the last decade, the study of the interaction between light and nanometer-sized metallic particles has turned into a central and multidisciplinary area of research in nanoscience [1

1. M. Pelton, J. Aizpurua, and G. W. Bryant, “Metal-nanoparticle plasmonics,” Laser & Photon. Rev. 2, 136–159 (2008) [CrossRef] .

3

3. N.J. Halas, S. Lal, W.S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011) [CrossRef] [PubMed] .

]. This emerging field, called plasmonics, has been mainly boosted by the convergence of excellent computational tools and improved fabrication and optical characterization methods, which have led to extremely interesting potential applications in biosensing, surface-enhanced spectroscopies, cancer therapies, renewable energies and active devices [4

4. A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with Zeptomole sensitivity,” Nano Lett. 3, 1057–1062, (2003) [CrossRef] .

8

8. Y. B. Zheng, Y. Yang, L. Jensen, L. Fang, B. K. Juluri, A. H. Flood, P. S. Weiss, J. F. Stoddart, and T. J. Huang, “Active molecular plasmonics: controlling plasmon resonances with molecular switches,” Nano Lett. 9, 819–825 (2009) [CrossRef] [PubMed] .

]. A key property of metallic nanoparticles is the dependence of the energies of their Localised Surface Plasmon Resonances (LSPRs) on the geometry of the structure, as well as the sensitivity of the energy of these resonances to the dielectric environment. In order to tailor the resulting optical properties, a huge variety of nanostructures has been engineered showing different shapes, materials or geometric distributions [9

9. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003) [CrossRef] [PubMed] .

11

11. C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Nano Lett. 6, 683–688 (2006) [CrossRef] [PubMed] .

].

Among different designs, dimers have emerged as a useful canonical nanostructure to understand many basic processes in plasmonics [12

12. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004) [CrossRef] .

16

16. M. Schnell, A. García-Etxarri, A. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoatennas,” Nat. Photonics 3, 287–291 (2009) [CrossRef] .

]. In a dimer, two nanoparticles are placed close to each other giving rise to new resonant modes which are a result of the coupling between particles [12

12. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004) [CrossRef] .

]. For nearly touching particles, the optical response is mainly governed by a Bonding Dimer Plasmon (BDP) resonance, which arises from the hybridization of the dipolar modes of the individual nanoparticles [13

13. T. Atay, J. H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime,” Nano Lett. 4, 1627–1631 (2004) [CrossRef] .

, 14

14. I. Romero, J. Aizpurua, F. J. García de Abajo, and G. W. Bryant, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006) [CrossRef] [PubMed] .

]. This BDP mode presents strongly localised charge densities of opposite sign and enormously enhanced local electromagnetic fields at the cavity. In contrast, when a conductive path is established between both particles of the dimer, a Charge Transfer Plasmon (CTP) mode is allowed, with current density crossing through the cavity, involving an oscillating distribution of net charge at every individual nanoparticle [13

13. T. Atay, J. H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime,” Nano Lett. 4, 1627–1631 (2004) [CrossRef] .

, 14

14. I. Romero, J. Aizpurua, F. J. García de Abajo, and G. W. Bryant, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006) [CrossRef] [PubMed] .

, 17

17. O. Pérez-González, N. Zabala, A. Borisov, N.J. Halas, P. Nordlander, and J. Aizpurua, “Optical spectroscopy of conductive junctions in plasmonic cavities,” Nano Lett. 10, 3090–3095 (2010) [CrossRef] [PubMed] .

, 18

18. O. Pérez-González, N. Zabala, and J. Aizpurua, “Optical characterization of charge transfer (CTP) and bonding dimer (BDP) plasmons in linked interparticle gaps,” New J. Phys. 13, 083013 (2011) [CrossRef] .

]. In most of the studies dealing with these effects, classical electrodynamical approaches have been applied. However, recent works incorporating quantum effects have shown that special care must be taken in sub-nanometer wide gaps, because electron tunneling through the junction gives rise to redistribution and modification of optical modes [19

19. R. Esteban, A.G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nature Communications 3, 825 (2012) [CrossRef] [PubMed] .

, 20

20. D.C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339 (2012) [CrossRef] [PubMed] .

]. This regime has been recently revealed experimentally, opening up new prospects in the field of quantum plasmonics [21

21. K. J. Savage, M. M. Hawkeye, R. Esteban, A.G. Borisov, J. Aizpurua, and J.J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012) [CrossRef] [PubMed] .

, 22

22. J.A. Scholl, A. García-Etxarri, A. L. Koh, and J.A. Dionne, “Observation of quantum tunneling between two plasmonic nanoparticles,” Nano Lett. 13(2), 564–569 (2013) [CrossRef] .

].

On the other hand, focusing on the field of molecular electronics, single molecules with well-defined molecular conductance [23

23. L. Venkataraman, J. E. Klare, I. W. Tam, C. Nuckolls, M. S. Hybertsen, and M. L. Steigerwald, “Single-molecule circuits with well-defined molecular conductance,” Nano Lett. 6, 458–462, (2006) [CrossRef] [PubMed] .

] are commonly used as interconnects in nanoelectronics and optoelectronics. Thus, we explore here the possibility of using different molecular linkers to establish conductive paths in plasmonic dimers and to understand their role in determining the optical properties of the entire molecule-plasmonic electrodes system. The interaction between plasmonic resonances and the excitonic states supported by molecules has become a problem of current interest [8

8. Y. B. Zheng, Y. Yang, L. Jensen, L. Fang, B. K. Juluri, A. H. Flood, P. S. Weiss, J. F. Stoddart, and T. J. Huang, “Active molecular plasmonics: controlling plasmon resonances with molecular switches,” Nano Lett. 9, 819–825 (2009) [CrossRef] [PubMed] .

, 24

24. J. Bellesa, C. Bonnand, J.C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93, 036404 (2004) [CrossRef] .

28

28. M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012) [CrossRef] [PubMed] .

]. Excitonic resonances in molecules or quantum dots, which consist of electron-hole pairs which can be created by the absorption of photons, couple to surface plasmon resonances creating plasmon-exciton states. These mixed states, so called plexcitons, are attractive due to their potential applications for optical devices but also because of the inherent interest of their physical properties. This problem has also been studied within a quantum mechanical approach to address the coupling between a metallic nanoparticle dimer and an excitonic quantum emitter placed in the gap [29

29. A. Manjavacas, F.J. García de Abajo, and P. Nordlander, “Quantum plexcitonics: strongly interacting plasmons and excitons,” Nano Lett. 11, 2318–2323 (2011) [CrossRef] [PubMed] .

], showing that the combined emitter-dimer structure undergoes dramatic changes when the excitation level of the emitter is tuned across the gap-plasmon resonance.

In this paper we present a theoretical study of the optical properties of a plasmonic cavity which consists of a strongly coupled nanoparticle dimer linked by a molecular junction characterized by the presence of an excitonic transition in its constituent molecules. We model the junction with a Drude-Lorentz dielectric function, which allows to tune in a simple way both the energy of the molecules and the corresponding dynamical conductance across the junction, and also to observe the consequences in the optical behaviour of the system.

One of the main interests of plasmonic nanostructures is their potential applications as sensors. Thus, structures with increasing asymmetry producing narrow spectral lines and Fano-resonances have been exploited during the last years to take advantage of the sensitivity of their plasmonic resonances to the dielectric environment [30

30. L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005) [CrossRef] [PubMed] .

34

34. F. López-Tejeira, R. Paniagua-Domínguez, and J. Sánchez-Gil, “High-performance nanosensors based on plasmonic Fano-like interference: probing refractive index with individual nanorice and nanobelts,” ACS Nano 6, 8989–8996 (2012) [CrossRef] [PubMed] .

]. The potential use of these systems for sensing is based on the shifts of their plasmonic resonances as the dielectric environment is changed. In this work, in addition to a study of the usual shift-based LSPR sensing, we propose an alternative concept for LSPR sensing based on the analysis of the relative intensities of the plexcitonic resonances as the dielectric function of the environment is tuned.

2. Dimer with a molecular linker

Fig. 1 (a) Schematic representation of a gold nanoparticle dimer connected by a molecular linker modelled as a cylinder of radius a and length d. The radius of the gold nanoparticles is R = 50 nm and the minimum separation distance between them is d = 1 nm (proportionality is not respected in this sketch). k is the wave vector of the incident electromagnetic plane wave with polarization of the electric field E along the vertical symmetry axis of the system. (b) Resonant behaviour of the conductance G for molecular linkers of radii a = 1 nm, 5 nm and 10 nm represented by the dielectric function of Eq. (1) with parameters Eex = ħωex = 1.51 eV, f = 1.5 and γex = 0.1 eV. (c) Calculated normalised optical extinction cross-section of a gold nanoparticle dimer bridged by a gold linker as a function of its radius a, and therefore as a function of conductance G as well. GCTP is the conductance threshold of the cavity load for the emergence of the CTP mode, as given by Eq. (3). (d) Analogous calculations as in (c), but with a molecular load described by a Drude-Lorentz dielectric function using the same parameters as in (b).

The resonant behavior of the dynamical conductance provided by the present model is shown in Fig. 1(b), where the conductance is expressed in units of the quantum of conductance G0 = 2e2/h = 7.7 × 10−5 S (e is the electron charge and h the Planck constant). We notice that the conductance through the molecule shows a lorentzian profile with a peak centred at energy E = Eex, and its maximum value increases when wider junctions are considered.

The conductance threshold value, which estimates the necessary conductance for the emergence of the CTP mode in conductive linkers, is found to be [17

17. O. Pérez-González, N. Zabala, A. Borisov, N.J. Halas, P. Nordlander, and J. Aizpurua, “Optical spectroscopy of conductive junctions in plasmonic cavities,” Nano Lett. 10, 3090–3095 (2010) [CrossRef] [PubMed] .

]:
GCTP=ωCTPR2/4πd.
(3)
We can observe in Fig. 1(c) that the CTP mode saturates at an energy around ECTP = 1.49 eV (λCTP = 835 nm) for very large conductance, yielding a threshold value of GCTP ≈ 656G0 according to Eq. (3). This GCTP value, marked in the figure by a dashed, white line, fits very well the full electrodynamic calculations.

In addition to the BDP and CTP modes, a Bonding Quadrupolar Plasmon (BQP) mode is also observed as a small spectral feature around EBQP = 2.30 eV (λBQP = 540 nm). This BQP mode, arising from the hybridization of the quadrupolar modes (l = 2) of the individual nanoparticles, loses intensity as the conductance of the plasmonic cavity increases [18

18. O. Pérez-González, N. Zabala, and J. Aizpurua, “Optical characterization of charge transfer (CTP) and bonding dimer (BDP) plasmons in linked interparticle gaps,” New J. Phys. 13, 083013 (2011) [CrossRef] .

].

We describe now the results shown in Fig. 1(d), where a molecular linker with an excitonc excitation is considered. In this case the plasmonic resonances of the cavity show a more complex optical response than in the case of the metallic load, since the plasmon-exciton coupling produces a splitting of the BDP mode, which also affects the CTP. We have checked the nature of each plasmon resonance and assigned their character by analysing the symmetry of the near-field modes calculated for each branch [40

40. N. Zabala, O. Pérez-González, P. Nordlander, and J. Aizpurua, “Coupling of nanoparticle plasmons with molecular linkers,” Proc. of SPIE 8096, 80961L (2011) [CrossRef] .

]. For the molecular linker, the BDP and BQP modes, initially found at EBDP = 1.85 eV (λBDP = 670 nm) and EBQP = 2.30 eV (λBQP = 540 nm), corresponding to the situation where there is no molecule in the gap, also blue-shift and lose intensity progressively as a, and thus conductance G, are increased. However, two resonant modes appear in the Near-InfraRed (NIR) range of the spectrum, in contrast to the only presence of the CTP resonance in the case of the metallic linker at long wavelength region in Fig. 1(c). From the near-field maps [40

40. N. Zabala, O. Pérez-González, P. Nordlander, and J. Aizpurua, “Coupling of nanoparticle plasmons with molecular linkers,” Proc. of SPIE 8096, 80961L (2011) [CrossRef] .

], we have checked that the most red-shifted resonance, around E ≈ 1.24 eV (λ ≈ 1000 nm), also has a BDP character, exactly as the blue-shifted BDP. In contrast, the resonance around E ≈ 1.55 eV (λ ≈ 800 nm) presents a clear CTP profile. Another remarkable difference between the response of metallic (Fig. 1(c)) and molecular (Fig. 1(d)) linkers is that, for the molecular case, the CTP mode does not emerge blue-shifting from the NIR range of the spectrum, as for the metallic linker, but it appears approximately at the transition energy Eex of the exciton. Consequently, these results show that a more complex description to characterize the optical response of the load strongly affects the behaviour of the plasmonic cavity modes. We have also performed additional calculations for larger values of the interparticle distance d, observing a completely analogous splitting of the modes and the same physical trends, thus establishing a robust pattern of spectral splittings in all cases.

3. Plexcitonic splitting

It is well known in the context of atomic physics that the presence of an atom or molecule produces the splitting of the resonances in an optical cavity [41

41. J. J. Sánchez-Mondragón, N. B. Naroznhy, and J. H. Eberly, “Theory of spontaneous-emission line shape in an ideal cavity,” Phys. Rev. Lett. 51, 550–553 (1983) [CrossRef] .

43

43. S. Rudin and T.L. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227–10233 (1999) [CrossRef] .

]. Similarly, in our system, the cavity BDP and BQP plasmon resonances can couple to the excitons of the molecular linker, giving rise to mixed plasmon-exciton modes so called plexcitons [24

24. J. Bellesa, C. Bonnand, J.C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93, 036404 (2004) [CrossRef] .

26

26. N.T. Fofang, T. Park, O. Neumann, N.A. Mirin, P. Nordlander, and N.J. Halas, “Plexciton nanoparticles: plasmon-exciton coupling in nanoshell-J-aggregates complexes,” Nano Lett. 8, 3481–3487 (2008) [CrossRef] [PubMed] .

]. This coupling of the plasmon modes to the excitons can be interpreted in terms of a simple model of two coupled oscillators [27

27. D. E. Gómez, K. C. Vernon, P. Mulvaney, and T. J. Davis, “Surface plasmon mediated strong exciton-photon coupling in semiconductor nanocrystals,” Nano Lett. 10, 274–278 (2010) [CrossRef] .

, 44

44. X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express 18, 23633–23645 (2010) [CrossRef] [PubMed] .

]. The resulting mixed BDP-exciton modes are called BDP+ and BDP modes, while the mixing of the BQP to the exciton produces the BQP+ and BQP modes, where + and − refer to higher and lower energies, respectively. According to this coupled-oscillator interpretation of plexcitons, their energies can be expressed as follows [27

27. D. E. Gómez, K. C. Vernon, P. Mulvaney, and T. J. Davis, “Surface plasmon mediated strong exciton-photon coupling in semiconductor nanocrystals,” Nano Lett. 10, 274–278 (2010) [CrossRef] .

, 39

39. O. Pérez-González, Optical properties and high-frequency electron transport in plasmonic cavities, PhD Thesis, (University of the Basque Country, UPV-EHU, 2011).

, 43

43. S. Rudin and T.L. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227–10233 (1999) [CrossRef] .

]:
E±=EP+Eex2±[(ΩR2)2+14(EPEex)2]1/2,
(4)
where EP and Eex are the energies of the plasmonic mode (BDP or BQP) and the exciton, respectively. The term ħΩR is the Rabi splitting, which is obtained from the full electrodynamical calculations when EP = Eex.

In order to explore the mixed modes in dimer cavities, we have tuned the energy of the excitonic resonance of the ensemble of molecules connecting both nanoparticles. We have changed the energy of the exciton Eex so that the product fωex2 in Eq. (1) is kept constant. We are thus varying at the same time the frequency ωex of the excitonic transition of the molecules and the reduced oscillator strength f describing them, while we keep constant the damping factor γex = 0.1eV in Eq. (1). In this manner, the conductivity and the maximum conductance for a given volume of the molecular load is fixed, i.e, the centre of the lorentzian function describing the conductance in the cavity G (see Fig. 1(b)) shifts while the intensity of its maximum does not vary.

Figure 2 shows the calculated normalised optical extinction cross-section of a gold nanoparticle dimer bridged by a molecular linker as the energy is tuned as described above, for a given material load volume (a fixed). In this case, four different radii have been considered, a = 1 nm, 5 nm, 10 nm and 15 nm, describing different volumes of molecular loads in the gap. Even for the thinnest linker, we observe that both the BDP and the BQP resonances split into two branches, showing an anti-crossing behaviour centred at the point of intersection of the exciton energy and the BDP and BQP energy lines, indicated by white, solid lines in Fig. 2. The situation is much more evident in the case of the BDP than in the BQP due to the difference in spectral weight between both resonances (BQP is a minor spectral feature in comparison to BDP). In the splitting of the BDP mode into the BDP and the BDP+ modes in Fig. 2, the energy of one of the branches, EBDP, is below the energy of the plasmon cavity mode, while the energy of the other one, EBDP+, is above the corresponding plasmon energy. An analogous behaviour is observed in the splitting of the BQP mode into the BQP and the BQP+ modes.

Fig. 2 Calculated normalised optical extinction cross-section of a gold nanoparticle dimer bridged by a molecular linker filling the interparticle separation of d = 1 nm with fixed size characterized by a molecular load radius a, as the energy and the oscillator strength of the excitonic transition in the cavity is varied. (a) a = 1 nm, (b) a = 5 nm, (c) a = 10 nm and (d) a = 15 nm. The white, solid lines included indicate the following: Ex the exciton energy line, BDP and BQP the energy lines of the dipolar and quadrupolar bonding plasmon modes when there is no linker. Finally, the white, dashed lines EBDP+, EBDP, EBQP+ and EBQP indicate the energies of the coupled modes derived from Eq. (4).

Figure 2 also shows that, as the linker becomes wider (from (a) to (d), a = 1 nm – a = 15 nm), the energy splitting between the coupled modes EBDP and EBDP+ increases. As already mentioned, the magnitude of the Rabi splitting ħΩR in Eq. (4) is estimated from the full electrodynamic simulations when EP = Eex and, for the cases under consideration in this study, it is of the order of hundreds of meV. From our calculations, we have also observed that the Rabi splitting increases rapidly as the radius of the molecular load grows, but presents a saturation trend for a > 10 nm.

The results of the approximation derived from Eq. (4) to obtain the energy lines of the coupled modes are shown in Fig. 2 as white dashed lines superimposed to the full electrodynamical calculation ( EBDP, EBDP+, EBQP and EBQP+), showing a good agreement with the simulations. This agreement is slightly affected by the intense interaction between the coupled modes of the BDP and the BQP resonances, which increases as the linker becomes wider, and by the presence of the CTP mode as well. We would like to notice that this coupled oscillator model considers the coupling of each plasmon mode with the exciton individually, as if each plasmon mode was the only resonance in the cavity, whereas in practise both plasmon modes are present, and we therefore observe the interaction between the BDP+, BDP, BQP+, BQP and CTP modes.

It is also remarkable that in Figs. 2(c) and 2(d) (a = 10 nm and 15 nm), where big cavity loads of molecules are considered, we observe the emergence of the CTP mode, in contrast to the cases with small loads in Figs. 2(a) and 2(b) (a = 1 nm and 5 nm), where the CTP does not appear. This effect is again interpreted with the help of the concept of threshold of conductance GCTP expressed by Eq. (3) [17

17. O. Pérez-González, N. Zabala, A. Borisov, N.J. Halas, P. Nordlander, and J. Aizpurua, “Optical spectroscopy of conductive junctions in plasmonic cavities,” Nano Lett. 10, 3090–3095 (2010) [CrossRef] [PubMed] .

, 18

18. O. Pérez-González, N. Zabala, and J. Aizpurua, “Optical characterization of charge transfer (CTP) and bonding dimer (BDP) plasmons in linked interparticle gaps,” New J. Phys. 13, 083013 (2011) [CrossRef] .

]. We have described how for very large conductance, the CTP mode saturates at energy ECTP = 1.52 eV, leading to a threshold value of the conductance GCTP ≈ 672 G0. For the small molecular loads in Figs. 2(a) and 2(b) the conductance of the linker is below the threshold value, thus, the CTP does not emerge. In contrast, for the big loads in Figs. 2(c) and 2(d), the conductance of the linker at the exciton energy is above the threshold value, G(a = 10 nm) ≈ 1000 G0 > GCTP and G(a = 15 nm) ≈ 1500 G0 > GCTP. Consequently, in these cases the CTP mode is active.

We have performed additional calculations keeping fixed f = 0.5 and changing only the excitonic energy Eex[39

39. O. Pérez-González, Optical properties and high-frequency electron transport in plasmonic cavities, PhD Thesis, (University of the Basque Country, UPV-EHU, 2011).

]. The plexciton splitting obtained in this way is similar to that of Fig. 2, but the CTP mode is not activated in such a case, because the conductance is smaller for the same load volume and the conductance threshold value is not reached at the range of energies considered. The concept of conductance threshold is thus a very useful tool to identify and predict the emergence of the CTP mode and, therefore, to analyse high-frequency transport in coupled cavities filled with optically active molecules.

4. Plexcitonic sensing

Let us explore now the sensing capabilities of the plexcitonic resonances studied above. Fig. 3 shows the calculated normalised optical extinction cross-section of a gold nanoparticle dimer with a gap between the particles of distance d = 1 nm, as the dielectric function of the embedding medium εd is modified. In Fig. 3(a) we consider, as a reference, the dimer with no load in the gap, while in Fig. 3(b) the particles are bridged by a molecular linker of radius a = 3 nm, characterized by an excitonic transition with energy Eex = 1.24 eV, corresponding to λex = 1000 nm. In the case of disconnected nanoparticles, the BDP mode, which is the plasmonic resonance governing the optical spectrum, red-shifts as the dielectric constant of the embedding medium is increased. The behaviour shown in Fig. 3(a) is similar to that of other nanostructures under similar conditions, and is the basis for conventional LSPR sensing [18

18. O. Pérez-González, N. Zabala, and J. Aizpurua, “Optical characterization of charge transfer (CTP) and bonding dimer (BDP) plasmons in linked interparticle gaps,” New J. Phys. 13, 083013 (2011) [CrossRef] .

, 30

30. L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005) [CrossRef] [PubMed] .

]. The BDP+ plexciton in Fig. 3(b) also presents a similar behaviour, red-shifting as the surrounding dielectric constant εd is increased. However, the BDP plexciton hardly red-shifts as εd is increased, indicating that this is not an adequate resonant mode for this type of sensing. This is also observed in Fig. 3(c), where we summarize the evolution of the shifts of the BDP (black), BDP+ (blue) and BDP (red) modes as a function of the dielectric constant of the embedding medium. The efficiency of plasmonic systems as sensors in shift-based LSPR sensing is usually estimated by its figure of merit (FOM), which is defined as [30

30. L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005) [CrossRef] [PubMed] .

]:
FOM=m(eV/RIU)/fwhm(eV).
(5)
In that expression m is the linear regression slope for the refractive index dependence, which indicates the ratio of the plasmon energy shift to the change in refractive index of the embedding medium, and fwhm is the full width at half maximum of the mode. From the results shown in Fig. 3(c) we obtain FOM = 1.0 for the BDP mode and FOM = 0.8 for the BDP+ plexciton.

Fig. 3 (a) Calculated normalised optical extinction cross-section of a gold nanoparticle dimer with a minimum separation distance between the particles d = 1 nm, as the dielectric embedding constant εd is varied. (b) Calculated normalised optical extinction cross-section of a gold nanoparticle dimer bridged by a molecular linker with length d = 1 nm, load radius a = 3 nm and excitation energy Eex = 1.24 eV (λex = 1000 nm), as the dielectric embedding constant εd is varied. (c) Shift of the BDP, BDP+ and BDP modes in Figs. 3 (a) and (b) as a function of the dielectric constant of the embedding medium. (d) Variation of the relative intensity of the BDP+ and BDP modes in (b) as a function of the dielectric constant of the embedding medium.

In the following, we focus our attention on the behaviour of the BDP mode, since this resonance shows a nonconventional behaviour. This plexciton, which is a minor spectral feature when the embedding medium is vacuum, hardly red-shifts as the surrounding dielectric constant εd is increased. However, by increasing εd the BDP mode becomes a spectral feature as strong as the the BDP+ mode in terms of intensity, as shown in Fig. 3(d), where the relative intensities of the BDP+ and BDP modes change as the embedding dielectric constant εd is varied. This figure shows that, for large values of the dielectric constant, the BDP mode gains enough spectral weight to become more intense than the BDP+, indicating that the balance of spectral weight of both plexcitons can be inverted by means of a change in the dielectric embedding medium. We believe that this dramatic variation of the relative intensity of the lower energy plexciton mode might be the key for a new strategy for LSPR sensing based on the variation of the intensity of the peaks rather than on their shift.

This different behaviour of the BDP+ and BDP plexciton modes can be understood with help of Fig. 2. The BDP+ mode at the considered excitation energy Eex = 1.24 eV presents a plasmon-like behaviour, thus red-shifting as the dielectric constant of the embedding medium is increased, as plasmon resonances do in standard localised plasmon sensing. In contrast, the BDP plexciton presents an excitonic-like character, thus keeping its energy constant as the medium is varied. This suggests that, depending on the desired purpose, plexciton modes can be tuned by means of the excitation energy Eex to exhibit a more or less pronounced exciton/plasmon-like behaviour.

Fig. 4 (a) Calculated normalised optical extinction cross-section of a gold nanoparticle dimer bridged by a molecular linker, with length d = 1 nm, load radius a = 10 nm and excitation energy Eex = 0.5 eV (λex = 2480 nm), as the dielectric embedding constant εd is varied. (b) Shift of the BDP and CTP modes in Fig. 3 (a) as a function of the dielectric constant of the embedding medium. (c) Linear plot of the CTP shifts vs. refractive index of the embedding medium.

5. Concluding remarks

In conclusion, we have studied theoretically the optical properties of a plasmonic cavity consisting of a strongly coupled metallic dimer when an ensemble of molecules, characterized by an excitonic transition, is placed in the cavity. The Bonding Dimer Plasmon (BDP) and the Bonding Quadrupolar Plasmon (BQP) resonances, arising respectively from the hybridization of the dipolar and quadrupolar modes of the individual nanoparticles, couple to the excitonic transition. As a consequence, these modes split into two coupled plasmon-exciton modes, called plexcitons. The Charge Transfer Plasmon (CTP) resonance, arising from the hydridization of the monopolar modes of the individual nanoparticles, is highly blue-shifted from its original spectral position and it depends strongly on the conductance of the molecular linker. The concept of conductance threshold for the emergence of the CTP mode previously introduced for metallic linkers is still valid, in spite of the complexity introduced in the linker with respect to a pure conductor.

We have explored the efficiency of the new mixed states for LSPR sensing, showing that the CTP mode is a good candidate for shift-based sensing, with a FOM value around 12. Furthermore, for the BDP-exciton mixed states, we have observed an interesting behavior for sensing based on the change of the relative intensity of the resonances, thus introducing a new framework for sensing based on the evolution of plexcitonic intensities rather than on spectral shifts.

We believe that the study of this kind of structures may contribute to improve the knowledge of plasmonic nanostructures for their use as active devices.

Acknowledgments

This project was supported by the Etortek project nanoiker from the Basque Government (BG), project FIS2010-19609-C02-01 from the Spanish Ministry of Science and Innovation and grant IT-366-07 from BG-UPV/EHU. O.P.G. acknowledges financial support from Vicerrectorado de Investigación of the University of the Basque Country (Ayudas Especialización Doctores). Computational resources were provided by DIPC (UPV/EHU, MICINN, BG, ESF).

References and links

1.

M. Pelton, J. Aizpurua, and G. W. Bryant, “Metal-nanoparticle plasmonics,” Laser & Photon. Rev. 2, 136–159 (2008) [CrossRef] .

2.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007) [CrossRef] .

3.

N.J. Halas, S. Lal, W.S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011) [CrossRef] [PubMed] .

4.

A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with Zeptomole sensitivity,” Nano Lett. 3, 1057–1062, (2003) [CrossRef] .

5.

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000) [CrossRef] .

6.

M. R. Choi, K. J. Stanton-Maxey, J. K. Stanley, C. S. Levin, R. Bardhan, D. Akin, S. Badve, J. Sturgis, J. P. Robinson, R. Bashir, N. J. Halas, and S.E. Clare, “A cellular Trojan horse for delivery of therapeutic nanoparticles into tumors,” Nano Lett. 7, 3759–3765 (2007) [CrossRef] [PubMed] .

7.

H. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Materials 9, 205–213 (2010) [CrossRef] .

8.

Y. B. Zheng, Y. Yang, L. Jensen, L. Fang, B. K. Juluri, A. H. Flood, P. S. Weiss, J. F. Stoddart, and T. J. Huang, “Active molecular plasmonics: controlling plasmon resonances with molecular switches,” Nano Lett. 9, 819–825 (2009) [CrossRef] [PubMed] .

9.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003) [CrossRef] [PubMed] .

10.

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano 4, 2649–2654 (2010) [CrossRef] [PubMed] .

11.

C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Nano Lett. 6, 683–688 (2006) [CrossRef] [PubMed] .

12.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004) [CrossRef] .

13.

T. Atay, J. H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime,” Nano Lett. 4, 1627–1631 (2004) [CrossRef] .

14.

I. Romero, J. Aizpurua, F. J. García de Abajo, and G. W. Bryant, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006) [CrossRef] [PubMed] .

15.

J. B. Lassiter, J. Aizpurua, L. I. Hernández, D. W. Brandl, I. Romero, S. Lal, J. H. Hafner, P. Nordlander, and N. J. Halas, “Close encounters between two nanoshells,” Nano Lett. 8, 1212–1218 (2008) [CrossRef] [PubMed] .

16.

M. Schnell, A. García-Etxarri, A. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoatennas,” Nat. Photonics 3, 287–291 (2009) [CrossRef] .

17.

O. Pérez-González, N. Zabala, A. Borisov, N.J. Halas, P. Nordlander, and J. Aizpurua, “Optical spectroscopy of conductive junctions in plasmonic cavities,” Nano Lett. 10, 3090–3095 (2010) [CrossRef] [PubMed] .

18.

O. Pérez-González, N. Zabala, and J. Aizpurua, “Optical characterization of charge transfer (CTP) and bonding dimer (BDP) plasmons in linked interparticle gaps,” New J. Phys. 13, 083013 (2011) [CrossRef] .

19.

R. Esteban, A.G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nature Communications 3, 825 (2012) [CrossRef] [PubMed] .

20.

D.C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339 (2012) [CrossRef] [PubMed] .

21.

K. J. Savage, M. M. Hawkeye, R. Esteban, A.G. Borisov, J. Aizpurua, and J.J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012) [CrossRef] [PubMed] .

22.

J.A. Scholl, A. García-Etxarri, A. L. Koh, and J.A. Dionne, “Observation of quantum tunneling between two plasmonic nanoparticles,” Nano Lett. 13(2), 564–569 (2013) [CrossRef] .

23.

L. Venkataraman, J. E. Klare, I. W. Tam, C. Nuckolls, M. S. Hybertsen, and M. L. Steigerwald, “Single-molecule circuits with well-defined molecular conductance,” Nano Lett. 6, 458–462, (2006) [CrossRef] [PubMed] .

24.

J. Bellesa, C. Bonnand, J.C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93, 036404 (2004) [CrossRef] .

25.

G.A. Wurtz, P.R. Evans, W. Hendren, R. Atkinson, W. Dyckson, R.J. Pollard, and A. V. Zayats, “Molecular plasmonics with tunable exciton-plasmon coupling strength in J-aggregate hybridized Au nanorod assemblies,” Nano Lett. 7, 1297–1303 (2007) [CrossRef] [PubMed] .

26.

N.T. Fofang, T. Park, O. Neumann, N.A. Mirin, P. Nordlander, and N.J. Halas, “Plexciton nanoparticles: plasmon-exciton coupling in nanoshell-J-aggregates complexes,” Nano Lett. 8, 3481–3487 (2008) [CrossRef] [PubMed] .

27.

D. E. Gómez, K. C. Vernon, P. Mulvaney, and T. J. Davis, “Surface plasmon mediated strong exciton-photon coupling in semiconductor nanocrystals,” Nano Lett. 10, 274–278 (2010) [CrossRef] .

28.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012) [CrossRef] [PubMed] .

29.

A. Manjavacas, F.J. García de Abajo, and P. Nordlander, “Quantum plexcitonics: strongly interacting plasmons and excitons,” Nano Lett. 11, 2318–2323 (2011) [CrossRef] [PubMed] .

30.

L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005) [CrossRef] [PubMed] .

31.

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124, 10596–10604 (2002) [CrossRef] [PubMed] .

32.

J.M. Nam, C. S. Thaxton, and C. A. Mirkin, “Nanoparticle-based bio-bar codes for the ultrasensitive detection of proteins,” Science 301, 1884–1886 (2003) [CrossRef] [PubMed] .

33.

E. Galopin, J. Niedziólka-Jönsson, A. Akjouj, Y. Pennec, B. Djafari-Rouhani, A. Noual, R. Boukherroub, and S. Szunerits, “Sensitivity of plasmonic nanostructures coated with thin oxide films for refractive index sensing: experimental and theoretical investigations,” J. Phys. Chem. C , 11411769–11775 (2010) [CrossRef] .

34.

F. López-Tejeira, R. Paniagua-Domínguez, and J. Sánchez-Gil, “High-performance nanosensors based on plasmonic Fano-like interference: probing refractive index with individual nanorice and nanobelts,” ACS Nano 6, 8989–8996 (2012) [CrossRef] [PubMed] .

35.

F.J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002) [CrossRef] .

36.

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

37.

M. Dressel and G. Grüner, Electrodynamics of solids (Cambridge University Press, U.K., 2002) [CrossRef] .

38.

K.E. Oughstun and N.A. Cartwright, “On the Lorentz-Lorentz formula and the Lorentz model of dielectric dispersion,” Optics Express 11, 1541–1546 (2003) [CrossRef] .

39.

O. Pérez-González, Optical properties and high-frequency electron transport in plasmonic cavities, PhD Thesis, (University of the Basque Country, UPV-EHU, 2011).

40.

N. Zabala, O. Pérez-González, P. Nordlander, and J. Aizpurua, “Coupling of nanoparticle plasmons with molecular linkers,” Proc. of SPIE 8096, 80961L (2011) [CrossRef] .

41.

J. J. Sánchez-Mondragón, N. B. Naroznhy, and J. H. Eberly, “Theory of spontaneous-emission line shape in an ideal cavity,” Phys. Rev. Lett. 51, 550–553 (1983) [CrossRef] .

42.

G.S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett. 53, 1732–1734 (1984) [CrossRef] .

43.

S. Rudin and T.L. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227–10233 (1999) [CrossRef] .

44.

X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express 18, 23633–23645 (2010) [CrossRef] [PubMed] .

OCIS Codes
(250.0250) Optoelectronics : Optoelectronics
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Sensors

History
Original Manuscript: March 28, 2013
Revised Manuscript: May 15, 2013
Manuscript Accepted: May 30, 2013
Published: June 25, 2013

Citation
Olalla Pérez-González, Javier Aizpurua, and Nerea Zabala, "Optical transport and sensing in plexcitonic nanocavities," Opt. Express 21, 15847-15858 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15847


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References

  1. M. Pelton, J. Aizpurua, and G. W. Bryant, “Metal-nanoparticle plasmonics,” Laser & Photon. Rev.2, 136–159 (2008). [CrossRef]
  2. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1, 641–648 (2007). [CrossRef]
  3. N.J. Halas, S. Lal, W.S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111, 3913–3961 (2011). [CrossRef] [PubMed]
  4. A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with Zeptomole sensitivity,” Nano Lett.3, 1057–1062, (2003). [CrossRef]
  5. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E62, 4318–4324 (2000). [CrossRef]
  6. M. R. Choi, K. J. Stanton-Maxey, J. K. Stanley, C. S. Levin, R. Bardhan, D. Akin, S. Badve, J. Sturgis, J. P. Robinson, R. Bashir, N. J. Halas, and S.E. Clare, “A cellular Trojan horse for delivery of therapeutic nanoparticles into tumors,” Nano Lett.7, 3759–3765 (2007). [CrossRef] [PubMed]
  7. H. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Materials9, 205–213 (2010). [CrossRef]
  8. Y. B. Zheng, Y. Yang, L. Jensen, L. Fang, B. K. Juluri, A. H. Flood, P. S. Weiss, J. F. Stoddart, and T. J. Huang, “Active molecular plasmonics: controlling plasmon resonances with molecular switches,” Nano Lett.9, 819–825 (2009). [CrossRef] [PubMed]
  9. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett.90, 057401 (2003). [CrossRef] [PubMed]
  10. H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano4, 2649–2654 (2010). [CrossRef] [PubMed]
  11. C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Nano Lett.6, 683–688 (2006). [CrossRef] [PubMed]
  12. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett.4, 899–903 (2004). [CrossRef]
  13. T. Atay, J. H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime,” Nano Lett.4, 1627–1631 (2004). [CrossRef]
  14. I. Romero, J. Aizpurua, F. J. García de Abajo, and G. W. Bryant, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express14, 9988–9999 (2006). [CrossRef] [PubMed]
  15. J. B. Lassiter, J. Aizpurua, L. I. Hernández, D. W. Brandl, I. Romero, S. Lal, J. H. Hafner, P. Nordlander, and N. J. Halas, “Close encounters between two nanoshells,” Nano Lett.8, 1212–1218 (2008). [CrossRef] [PubMed]
  16. M. Schnell, A. García-Etxarri, A. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoatennas,” Nat. Photonics3, 287–291 (2009). [CrossRef]
  17. O. Pérez-González, N. Zabala, A. Borisov, N.J. Halas, P. Nordlander, and J. Aizpurua, “Optical spectroscopy of conductive junctions in plasmonic cavities,” Nano Lett.10, 3090–3095 (2010). [CrossRef] [PubMed]
  18. O. Pérez-González, N. Zabala, and J. Aizpurua, “Optical characterization of charge transfer (CTP) and bonding dimer (BDP) plasmons in linked interparticle gaps,” New J. Phys.13, 083013 (2011). [CrossRef]
  19. R. Esteban, A.G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nature Communications3, 825 (2012). [CrossRef] [PubMed]
  20. D.C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12, 1333–1339 (2012). [CrossRef] [PubMed]
  21. K. J. Savage, M. M. Hawkeye, R. Esteban, A.G. Borisov, J. Aizpurua, and J.J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature491, 574–577 (2012). [CrossRef] [PubMed]
  22. J.A. Scholl, A. García-Etxarri, A. L. Koh, and J.A. Dionne, “Observation of quantum tunneling between two plasmonic nanoparticles,” Nano Lett.13(2), 564–569 (2013). [CrossRef]
  23. L. Venkataraman, J. E. Klare, I. W. Tam, C. Nuckolls, M. S. Hybertsen, and M. L. Steigerwald, “Single-molecule circuits with well-defined molecular conductance,” Nano Lett.6, 458–462, (2006). [CrossRef] [PubMed]
  24. J. Bellesa, C. Bonnand, J.C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett.93, 036404 (2004). [CrossRef]
  25. G.A. Wurtz, P.R. Evans, W. Hendren, R. Atkinson, W. Dyckson, R.J. Pollard, and A. V. Zayats, “Molecular plasmonics with tunable exciton-plasmon coupling strength in J-aggregate hybridized Au nanorod assemblies,” Nano Lett.7, 1297–1303 (2007). [CrossRef] [PubMed]
  26. N.T. Fofang, T. Park, O. Neumann, N.A. Mirin, P. Nordlander, and N.J. Halas, “Plexciton nanoparticles: plasmon-exciton coupling in nanoshell-J-aggregates complexes,” Nano Lett.8, 3481–3487 (2008). [CrossRef] [PubMed]
  27. D. E. Gómez, K. C. Vernon, P. Mulvaney, and T. J. Davis, “Surface plasmon mediated strong exciton-photon coupling in semiconductor nanocrystals,” Nano Lett.10, 274–278 (2010). [CrossRef]
  28. M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett.108, 106402 (2012). [CrossRef] [PubMed]
  29. A. Manjavacas, F.J. García de Abajo, and P. Nordlander, “Quantum plexcitonics: strongly interacting plasmons and excitons,” Nano Lett.11, 2318–2323 (2011). [CrossRef] [PubMed]
  30. L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5, 2034–2038 (2005). [CrossRef] [PubMed]
  31. A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc.124, 10596–10604 (2002). [CrossRef] [PubMed]
  32. J.M. Nam, C. S. Thaxton, and C. A. Mirkin, “Nanoparticle-based bio-bar codes for the ultrasensitive detection of proteins,” Science301, 1884–1886 (2003). [CrossRef] [PubMed]
  33. E. Galopin, J. Niedziólka-Jönsson, A. Akjouj, Y. Pennec, B. Djafari-Rouhani, A. Noual, R. Boukherroub, and S. Szunerits, “Sensitivity of plasmonic nanostructures coated with thin oxide films for refractive index sensing: experimental and theoretical investigations,” J. Phys. Chem. C, 11411769–11775 (2010). [CrossRef]
  34. F. López-Tejeira, R. Paniagua-Domínguez, and J. Sánchez-Gil, “High-performance nanosensors based on plasmonic Fano-like interference: probing refractive index with individual nanorice and nanobelts,” ACS Nano6, 8989–8996 (2012). [CrossRef] [PubMed]
  35. F.J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B65, 115418 (2002). [CrossRef]
  36. P.B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370 (1972). [CrossRef]
  37. M. Dressel and G. Grüner, Electrodynamics of solids (Cambridge University Press, U.K., 2002). [CrossRef]
  38. K.E. Oughstun and N.A. Cartwright, “On the Lorentz-Lorentz formula and the Lorentz model of dielectric dispersion,” Optics Express11, 1541–1546 (2003). [CrossRef]
  39. O. Pérez-González, Optical properties and high-frequency electron transport in plasmonic cavities, PhD Thesis, (University of the Basque Country, UPV-EHU, 2011).
  40. N. Zabala, O. Pérez-González, P. Nordlander, and J. Aizpurua, “Coupling of nanoparticle plasmons with molecular linkers,” Proc. of SPIE8096, 80961L (2011). [CrossRef]
  41. J. J. Sánchez-Mondragón, N. B. Naroznhy, and J. H. Eberly, “Theory of spontaneous-emission line shape in an ideal cavity,” Phys. Rev. Lett.51, 550–553 (1983). [CrossRef]
  42. G.S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett.53, 1732–1734 (1984). [CrossRef]
  43. S. Rudin and T.L. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B59, 10227–10233 (1999). [CrossRef]
  44. X. Wu, S. K. Gray, and M. Pelton, “Quantum-dot-induced transparency in a nanoscale plasmonic resonator,” Opt. Express18, 23633–23645 (2010). [CrossRef] [PubMed]

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