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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27411–27421
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Surface lattice resonances strongly coupled to Rhodamine 6G excitons: tuning the plasmon-exciton-polariton mass and composition

S.R.K. Rodriguez and J. Gómez Rivas  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 27411-27421 (2013)
http://dx.doi.org/10.1364/OE.21.027411


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Abstract

We demonstrate the strong coupling of surface lattice resonances (SLRs) — hybridized plasmonic/photonic modes in metallic nanoparticle arrays — to excitons in Rhodamine 6G molecules. We investigate experimentally angle-dependent extinction spectra of silver nanorod arrays with different lattice constants, with and without the Rhodamine 6G molecules. The properties of the coupled modes are elucidated with simple Hamiltonian models. At low momenta, plasmon-exciton-polaritons — the mixed SLR/exciton states — behave as free-quasiparticles with an effective mass, lifetime, and composition tunable via the periodicity of the array. The results are relevant for the design of plasmonic systems aimed at reaching the quantum degeneracy threshold, wherein a single quantum state becomes macroscopically populated.

© 2013 OSA

1. Introduction

Metallic nanostructures hold fascinating optical properties associated with the excitation of surface electromagnetic modes at the air-dielectric interface. These modes are known as surface plasmon polaritons (SPPs), and they exist in essentially two types: localized and propagating. Localized SPPs typically lead to a strong confinement of radiation in sub-wavelength volumes, making them ideal candidates for nanoscale optical antennas [1

1. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]

3

3. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef] [PubMed]

]. On the other hand, propagating SPPs typically display subwavelength confinement in 1 or 2 spatial dimensions only, while they transport energy in the other dimension(s) [4

4. P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24, 1011–1013 (1999). [CrossRef]

6

6. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008). [CrossRef] [PubMed]

]. Periodic arrays of metallic nanoparticles constitute an interesting system in which these two types of modes co-exist. Localized surface plasmon resonances (LSPRs) in the nanoparticles may couple to diffracted orders in the plane of the array, so-called Rayleigh anomalies, leading to mixed plasmonic/photonic states with variable degree of localization. These hybrid states are known as surface lattice resonances (SLRs).

In this paper we investigate the strong coupling of SLRs in arrays of silver nanorods to excitons in Rhodamine 6G (R6G) molecules. We present experimental results for three arrays having identical nanorods but varying lattice constants. Different SLR-exciton detunings are probed in each array by energy-momentum spectroscopy, as the steep dispersion band of the bare SLR crosses the flat dispersion band of the bare exciton. We focus on the low-energy band of the strongly coupled modes which anti-cross: “plasmon-exciton-polaritons” (PEPs). At low momenta PEPs effectively behave as free-quasiparticles, with mass, lifetime, and composition (the relative weights of SLR and exciton constituents in the admixture) tunable via the periodicity of the array. These results have implications for reaching the (yet unreported) quantum degeneracy threshold in plasmonic systems. For instance, as quantum condensation occurs when the de Broglie wavelength ( Λ1/mkBT with m the mass, kB Boltzmann’s constant, and T the temperature) exceeds the interparticle separation, a reduction in polariton mass is expected to increase the critical temperature for condensation at a given density of quasiparticles.

2. Sample preparation and experimental methods

Silver nanorod arrays were fabricated onto a fused silica substrate by substrate conformal imprint lithography: a technique enabling accurate reproduction of nanoscale features over large (>cm2) areas [35

35. M. A. Verschuuren, “Substrate conformal imprint lithography for nanophotonics,” PhD dissertation, Utrecht University (2010).

]. A 20 nm layer of Si3N4 was deposited on top of the arrays to prevent the silver from oxidizing. The Si3N4 also serves as a spacer layer between the nanorods and the organic molecules to avoid emission quenching [36

36. A. Wokaun, H.-P. Lutz, A. P. King, U. P. Wild, and R. R. Ernst, “Energy transfer in surface enhanced luminescence,” J. Chem. Phys. 79, 509 (1983). [CrossRef]

, 37

37. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef] [PubMed]

]. Figure 1 shows a 3D inclined representation of the sample. The thin semi-transparent gray layer represents the Si3N4. The upper orange layer represents the polyvinyl alcohol (PVA) layer that can have R6G molecules embedded. The R6G excitons are represented by electron-hole pairs enclosed by a dashed ellipse. Figure 1(b) shows the normalized emission (gray line) and absorptance (black line) of a 300 ± 30 nm layer of R6G molecules. Figures 1(c)– 1(e) show scanning electron microscope images of the resist layers used in the fabrication of the arrays. Subsequent processing involved perpendicular evaporation of 20 nm silver and lift-off. All three arrays have nanorods with dimensions 230 × 70 × 20 nm3, and a lattice constant ay = 200 nm. The lattice constant along the long axis of the nanorods, ax, is 350 nm in Fig. 1(c), 360 nm in Fig. 1(d), and 370 nm in Fig. 1(e). The tolerances of the in plane dimensions are ±10 nm, while out of the plane it is ±2 nm.

Fig. 1 (a) Schematic representation of a silver nanorod array on an SiO2 substrate covered by a thin passivating Si3N4 layer (gray) and a Rhodamine 6G in PVA layer (orange). (b) Normalized photoluminescence (gray line) and absorptance of a 300 nm layer of Rhodamine 6G in PVA (black line) without the nanorod array. (c)–(e) Scanning electron microscope images of the resist layers used for the fabrication of the nanorod arrays. The scale bars denote the lattice constant which is tuned; other dimensions are fixed.

We measured the variable angle extinction spectra for all three arrays with and without the R6G molecules. The extinction is given by 1 − T0, with T0 the zeroth order transmittance of a white light beam from a halogen lamp. The incident beam was collimated (angular spread < 0.1°) and linearly polarized parallel to the short axis of the nanorods (y-axis). The sample was rotated about the y-axis by a computer controlled rotation stage with an angular resolution of 0.1°. Rotation by an angle θ changed the projection of the incident wave vector parallel to the long axis of the nanorods (x-axis). Namely, k||=ωcsin(θ)x^, with ω the incident frequency, c the vacuum speed of light, and a unit vector along the x-axis.

3. Extinction of nanoparticle arrays without R6G molecules

In Figure 2 we present extinction measurements of the three nanorod arrays previously discussed. All arrays are covered by a 300 nm layer of PVA without R6G molecules. The dispersive peaks in extinction underneath the black lines are SLRs. These are mixed states formed by the strong coupling of localized surface plasmons to Rayleigh anomalies. We illustrate this coupling mechanism with the following simplified 3 × 3 Hamiltonian,
H1=(ELiγLΩL+ΩLΩL+ER+iγR+Ω±ΩLΩ±ERiγR).
(1)

The diagonal terms in the Hamiltonian are the energies of the LSPR and Rayleigh anomalies associated with the (±1, 0) diffraction orders. Their real parts are shown as white lines in Figures 2(a)– 2(c), with the LSPR as a solid line, and the (±1, 0) Rayleigh anomalies as dashed lines. The Rayleigh anomalies are calculated from the conservation of the parallel component of the wave-vector: ER±(k||)=h¯cn|k||+mGx|. Here, m = ±1 is the order of diffraction, Gx=2πax is the x-component of the reciprocal lattice vector, and n = 1.47 is the effective refractive index of the medium in which the mode propagates. The value of n (intermediate between the refractive indices of SiO2 and PVA) is estimated from the measurements, which display a minimum in extinction at the Rayleigh anomaly condition [15

15. S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011). [CrossRef]

]. As the lattice constant is ax = 350 nm in Fig. 2(a), ax = 360 nm in Fig. 2(b), and ax = 370 nm in Fig. 2(c), the Rayleigh anomalies shift towards lower energies. The real part of the LSPR energy is set to EL = 2.5 eV based on the SLR dispersion, which asymptotically approaches the LSPR energy at large k|| (not shown here). This energy corresponds to the dipolar LSPR along the short axis of the nanorods, and it is in good agreement with the corresponding peak in the scattering spectra of single nanorods with dimensions similar to those herein considered [38

38. B. Wiley, Y. Sun, and Y. Xia, “Synthesis of silver nanostructures with controlled shapes and properties,” Acc. Chem. Res. 40, 1067–1076 (2007). [CrossRef] [PubMed]

]. We set equal LSPR energy for all arrays because the nanorod dimensions are the same.

Fig. 2 Extinction —in the same color scale for all plots— as a function of the incident photon energy and wave-vector component parallel to the long axis of the nanorods. The lattice constants are (a) ax = 350 nm, (b) ax = 360 nm, and (c) ax = 370 nm. The nanorod arrays are all covered by a 300 nm PVA layer without R6G molecules. The white lines indicate the energies of the bare states: LSPR as white solid line, and (±1, 0) Rayleigh anomalies as white dashed lines. The black lines indicate the energies of the coupled states: upper SLR as black dashed line and lower SLR as black dash-dotted line.

The imaginary parts of the LSPR and Rayleigh anomaly energies (the time-decay of the modes) are estimated from the linewidths in the measurements. We take these to be the half-width at half maximum at k|| = 0, where the energy detuning of the uncoupled states is largest and the coupled states resemble most the uncoupled ones. The off-diagonal terms in the Hamiltoninan are the coupling constants, which are fitted to match the dispersion measured for each array. Both decay and coupling constants are here assumed to be frequency-independent for simplicity. The values used in the calculations of Fig. 2 are reported in Table 1.

Table 1. Input parameters to the model Hamiltonian in Eq. (1) yielding the eigenenergies in Fig. 2. All quantities are in units of meV.

table-icon
View This Table

Diagonalization of the the Hamiltonian H1 in Eq. (1) leads to three new eigenstates. Only two of these states appear in the energy range of the measurements. These are the upper and lower SLRs, which are shown in Fig. 2 as black dashed and dash-dotted lines, respectively. The calculated eigenenergies are in good agreement with the measurements, indicating that the simplified model here employed describes reasonably well the experiments. In our analysis, we have ignored the resonances on the high-energy side of the measurements in Fig. 2 because they represent only a small perturbation to the upper SLR at large k||. Since we are interested in the small k|| regime for the upper SLR (near the ground state), these effects are mostly irrelevant for the purpose of this work.

The changes in the SLR group velocity (∂E/∂k||) and linewidth are associated with the energy detuning between the LSPR and Rayleigh anomalies. Besides k||, another important detuning parameter is the periodicity of the array, as it determines the relative weights of the LSPR and Rayleigh anomalies in the mixed SLR state at a particular wave vector. Considering the case at k|| = 0, we observe in Figs. 2(a)– 2(c) that the SLR linewidth decreases for increased lattice constants. This implies an increase in the lifetime of the excitation and a weaker confinement of the electromagnetic field. Thus, the SLR becomes more “photonic” and less “plasmonic” in character. Geometry and periodicity are the origin of these effects, as these determine the polarizability, and coupling conditions, of the particles constituting the array [12

12. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008). [CrossRef] [PubMed]

, 15

15. S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011). [CrossRef]

, 17

17. T. V. Teperik and A. Degiron, “Design strategies to tailor the narrow plasmon-photonic resonances in arrays of metallic nanoparticles,” Phys. Rev. B 86, 245425 (2012). [CrossRef]

].

4. Extinction of nanoparticle arrays with R6G molecules

We proceed with measurements of the same arrays but in the presence of R6G molecules. For this purpose we removed the PVA layer, and deposited a new PVA layer of the same thickness but doped with R6G molecules at 30 weight %. Figure 3 shows extinction measurements in this new system. The relevant bare states are now the upper SLR and the R6G exciton. The radiative coupling of these two states, which is determined by the spatial overlap of the associated electric fields, leads to the formation of two new states: the plasmon-exciton-polaritons (PEPs). We calculate the PEP eigenenergies in a similar manner as the SLR eigenenergies were calculated, using the following 2 × 2 Hamiltonian,
H2=(EXiγXΩXSΩXSESLRiγSLR).
(2)

Fig. 3 Extinction of the same arrays in Figure 2, but here covered by a 300 nm layer of PVA doped with R6G at 30 weight %. The solid black line indicates the bare exciton energy, while the dashed black line indicates the upper SLR as calculated in Figure 2; these are the bare states. The dash-dotted black lines are the energies of the plasmon-exciton-polaritons, i.e., the eigenenergies of the Hamiltonian in Eq. (2); these are the coupled states. The lattice constants are (a) ax = 350 nm, (b) ax = 360 nm, and (c) ax = 370 nm.

Based on the absorption measurements of the bare R6G layer in Fig. 1(b), we set EXX = (2.3 − i0.15) eV for the bare exciton energy. EX is shown as black solid lines in Fig. 3. The complex SLR energy, ESLRSLR, is calculated from the diagonalization of H1 in Eq. (1). ESLR is shown as black dashed lines in Fig. 3. The mixed states (plasmon-exiton-polaritons) are obtained from the diagonalization of the Hamiltonian H2 in Eq. (2), while the coupling constant ΩXS was fitted to match the experiments. The resultant PEP energies are shown as black dash-dotted lines in Fig. 3. The calculated PEP dispersion agrees reasonably well with the measurements. The small disagreements are likely due to the simplicity of the model. In particular, we have used a constant ΩXS, although this parameter is expected to vary with the wave vector because the field overlap between the modes changes. We note that González-Tudela and co-workers have recently demonstrated how to rigorously calculate the coupling between SPPs in a flat metallic layer and an ensemble of quantum emitters under the influence of decay and dephasing [34

34. A. González-Tudela, P. A. Huidobro, L. Martín-Moreno, C. Tejedor, and F. J. García-Vidal, “Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons,” Phys. Rev. Lett. 110, 126801 (2013). [CrossRef]

].

In what follows, we will concentrate on the lower PEP band. Let us analyze the composition of PEPs, which include SLR and exciton constituents depending on k||. We express the PEP eigenstates as |(k||)〉 = x(k||)|X〉 + s(k||)|S〉, with |X〉 and |S〉 the exciton and SLR states, respectively. The coefficients in the expansion of light-matter quasiparticles are often called the Hopfield coefficients [39

39. H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82, 1489–1537 (2010). [CrossRef]

], in honor to J.J. Hopfield, who: i) showed that excitons are approximate bosons (a key element enabling Bose condensates in excitonic systems), and ii) introduced the term “polariton” to describe the exciton-photon admixture [40

40. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958). [CrossRef]

]. Here, the Hopfield coefficients are the components of the eigenvector associated with the PEP’s eigenenergy. The magnitude squared of the Hopfield coefficients yields the eigenstate fractions, or composition, of the admixture. We plot these in Figs. 4(a)– 4(c) for the lower PEP band in Figs. 3(a)– 3(c), with the exciton fraction |x(k||)|2 as a black line and the SLR fraction |s(k||)|2 as a gray line.

Fig. 4 Eigenstate fractions for the lower plasmon-exciton-polariton bands in Fig. 3 as a function of the incident wave vector. The black line represents the exciton fraction |x|2, whereas the grey line represents the SLR fraction |s|2. The lattice constants are (a) ax = 350 nm, (b) ax = 360 nm, and (c) ax = 370 nm.

In Fig. 5 we analyze the dispersion and linewidth of the lower PEP bands in the three arrays. For this purpose, we approximate the PEP lineshape at each wave-vector as a Lorentzian resonance, which we fit by a least-squares method to the measurements. Figure 5(a) shows an example of such fitting at k|| = 0 to the lower PEP resonance of the three arrays. The data points are the measurements, and the black solid lines are the fits. The fits cover a limited energy range only (same range for all k||, different for each array) to exclude the influence of other resonances at k|| ≠ 0. We extract the central energy and full width at half maximum (FWHM = 2γ with γ the damping) of the fitted Lorentzians as a function of k||, and we plot these in Fig. 5(b) and Fig. 5(c), respectively. In Figs. 5(a)–(c), the blue squares correspond to the ax = 350 nm array, the gray circles to the ax = 360 nm array, and the red triangles to the ax = 370 nm array. The error bars in the central energy and FWHM represent a 2σ (95%) confidence interval in the fits.

Fig. 5 (a) Extinction spectra at k|| = 0, (b) dispersion relations, and (c) full width at half maximum (FWHM), of the lower plasmon-exciton-polariton in Figs. 3(a)–(c). The blue squares, grey circles, and red triangles in all figures correspond to the arrays in Figure 3(a), 3(b), and 3(c), respectively. Notice that the scales are different from Figure 2 and Figure 3. The error bars in (b) and (c) [smaller than the data points in (b)] represent a 2σ confidence interval in fitting the measured resonance with a Lorentzian lineshape at each k||. An example of such fitting procedure is shown in (a), where the fitted Lorentzians are shown as solid black lines. The dashed black lines in (b) are quadratic fits used to retrieve the plasmon-exciton-polariton effective mass.

In order to estimate the PEP effective mass, we approximate PEPs as free-quasiparticles in the low momentum regime. The black lines in Fig. 5(b) are fits of a quadratic function to the PEP dispersion near k|| = 0. The good agreement between these quadratic fits and the PEP dispersion for the 3 arrays confirms that PEPs effectively behave as free-quasiparticles, with an effective mass m*=h¯2(2E/k||2)1. This yields m* = 5.4 ± 0.3 × 10−37 kg for ax = 350 nm, m* = 3.1±0.1×10−37 kg for ax = 360 nm, and m* = 2.6±0.1×10−37 kg for ax = 370 nm. The error in the mass represents a 2σ (95%) confidence interval in the quadratic fits to the dispersion relation in the plotted range. The changes in effective mass here observed are a manifestation of the changing PEP composition. As the PEP ground state energy is increasingly detuned from the bare exciton energy (the most heavy amongst the SLR and exciton), the effective PEP mass is reduced. The lightest of the three PEPs here analyzed is roughly 7 orders of magnitude lighter than the electron rest mass.

To assess the total loss rates of the PEPs, we plot their FWHM in Fig. 5(c). The FWHM is influenced by the periodicity of the array and by k||. From the increase of the FWHM with the lattice constant at any k||, it follows that the loss rates are primarily dictated by the periodicity. The origin of this dependence can be traced to the dependence of the SLR FWHM on the periodicity, as observed in Fig. 2. For shorter lattice constants the SLR FWHM is broadened by the increasingly dominant LSPR fraction (the most lossy amongst the underlying SLR constituents). Thus, the PEP FWHM is broadened accordingly. The PEP FWHM has a secondary dependence on k||, which is also based on the properties of the underlying SLR. For small k||, the mutual coupling between SLRs leads to pronounced changes in linewidth and dispersion [15

15. S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011). [CrossRef]

]. Standing waves are formed in the upper SLR band, while subradiant damping sets in the lower SLR band. These k||-dependent changes in radiative damping are the origin of the variations in FWHM observed in Fig. 5(c). Certainly, Ohmic losses will set a lower limit on the FWHM, and this can drive the material of choice. Here we have used silver, which is well known for its low optical losses in the visible spectrum. However, we envisage that by fine tuning the geometry of the nanorods and the periodicity of the array, radiative losses can be minimized even further to yield PEPs with longer lifetimes.

The results in Fig. 4 and Fig. 5 demonstrate the opportunities and challenges that plasmon-exciton-polaritons may face in their way towards the quantum degeneracy threshold. For increasingly negative SLR-exciton detuning (larger lattice constant), the effective PEP mass is reduced and this is beneficial for increasing the critical temperature required for condensation. However, one should note that such an admixture has a reduced plasmonic and excitonic content at k|| = 0. Another important parameter is the FWHM of the resonance, which also decreases for increasingly negative SLR-exciton detuning as shown in Fig. 5(c). The lifetime of the excitations (inversely proportional to the FWHM) is a key element to consider in the pursuit of a quantum condensate, as it will influence the dynamics (e.g. equilibrium vs non-equilibrium) of the system. In summary, we reckon the simultaneous decrease in linewidth and plasmonic content as a manifestation of the well-known trade-off between localization and losses in plasmonic systems.

5. Conclusion

In conclusion, we have investigated the strong coupling of surface lattice resonances in periodic arrays of metallic particles to excitons in Rhodamine 6G molecules. The properties of plasmon-exciton-polaritons (PEPs), the quasiparticles emerging from this coupling, were analyzed. We showed how the PEP effective mass, composition, and lifetime, can be tuned by varying the lattice constant of the array. We envisage these results to aid in the design of plasmonic systems that could open a yet un-explored but potentially rich avenue for plasmonics research: quantum condensation.

Acknowledgments

We thank Marc Verschuuren for the fabrication of the nanorod arrays, and Johannes Feist and Fracisco J. Garcia Vidal for stimulating discussions. This work was supported by the Netherlands Foundation for Fundamental Research on Matter (FOM) and the Netherlands Organization for Scientific Research (NWO), and is part of an industrial partnership program between Philips and FOM.

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Y. Sugawara, T. A. Kelf, J. J. Baumberg, M. E. Abdelsalam, and P. N. Bartlett, “Strong coupling between localized plasmons and organic excitons in metal nanovoids,” Phys. Rev. Lett. 97, 266808 (2006). [CrossRef]

29.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures,” Phys. Rev. Lett. 101, 116801 (2008). [CrossRef] [PubMed]

30.

T. K. Hakala, J. J. Toppari, A. Kuzyk, M. Pettersson, H. Tikkanen, H. Kunttu, and P. Törmä, “Vacuum rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and rhodamine 6g molecules,” Phys. Rev. Lett. 103, 053602 (2009). [CrossRef] [PubMed]

31.

N. I. Cade, T. Ritman-Meer, and D. Richards, “Strong coupling of localized plasmons and molecular excitons in nanostructured silver films,” Phys. Rev. B 79, 241404 (2009). [CrossRef]

32.

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

33.

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett. 106, 196405 (2011). [CrossRef] [PubMed]

34.

A. González-Tudela, P. A. Huidobro, L. Martín-Moreno, C. Tejedor, and F. J. García-Vidal, “Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons,” Phys. Rev. Lett. 110, 126801 (2013). [CrossRef]

35.

M. A. Verschuuren, “Substrate conformal imprint lithography for nanophotonics,” PhD dissertation, Utrecht University (2010).

36.

A. Wokaun, H.-P. Lutz, A. P. King, U. P. Wild, and R. R. Ernst, “Energy transfer in surface enhanced luminescence,” J. Chem. Phys. 79, 509 (1983). [CrossRef]

37.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef] [PubMed]

38.

B. Wiley, Y. Sun, and Y. Xia, “Synthesis of silver nanostructures with controlled shapes and properties,” Acc. Chem. Res. 40, 1067–1076 (2007). [CrossRef] [PubMed]

39.

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82, 1489–1537 (2010). [CrossRef]

40.

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958). [CrossRef]

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(230.4555) Optical devices : Coupled resonators

ToC Category:
Plasmonics

History
Original Manuscript: July 31, 2013
Revised Manuscript: September 23, 2013
Manuscript Accepted: September 24, 2013
Published: November 4, 2013

Virtual Issues
Surface Plasmon Photonics (2013) Optics Express

Citation
S.R.K. Rodriguez and J. Gómez Rivas, "Surface lattice resonances strongly coupled to Rhodamine 6G excitons: tuning the plasmon-exciton-polariton mass and composition," Opt. Express 21, 27411-27421 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-27411


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References

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  29. P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures,” Phys. Rev. Lett.101, 116801 (2008). [CrossRef] [PubMed]
  30. T. K. Hakala, J. J. Toppari, A. Kuzyk, M. Pettersson, H. Tikkanen, H. Kunttu, and P. Törmä, “Vacuum rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and rhodamine 6g molecules,” Phys. Rev. Lett.103, 053602 (2009). [CrossRef] [PubMed]
  31. N. I. Cade, T. Ritman-Meer, and D. Richards, “Strong coupling of localized plasmons and molecular excitons in nanostructured silver films,” Phys. Rev. B79, 241404 (2009). [CrossRef]
  32. A. Manjavacas, F. Garcia de Abajo, and P. Nordlander, “Quantum plexcitonics: Strongly interacting plasmons and excitons,” Nano Lett.11, 2318–2323 (2011). [CrossRef] [PubMed]
  33. T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett.106, 196405 (2011). [CrossRef] [PubMed]
  34. A. González-Tudela, P. A. Huidobro, L. Martín-Moreno, C. Tejedor, and F. J. García-Vidal, “Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons,” Phys. Rev. Lett.110, 126801 (2013). [CrossRef]
  35. M. A. Verschuuren, “Substrate conformal imprint lithography for nanophotonics,” PhD dissertation, Utrecht University (2010).
  36. A. Wokaun, H.-P. Lutz, A. P. King, U. P. Wild, and R. R. Ernst, “Energy transfer in surface enhanced luminescence,” J. Chem. Phys.79, 509 (1983). [CrossRef]
  37. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett.96, 113002 (2006). [CrossRef] [PubMed]
  38. B. Wiley, Y. Sun, and Y. Xia, “Synthesis of silver nanostructures with controlled shapes and properties,” Acc. Chem. Res.40, 1067–1076 (2007). [CrossRef] [PubMed]
  39. H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys.82, 1489–1537 (2010). [CrossRef]
  40. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev.112, 1555–1567 (1958). [CrossRef]

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