Letter pubs.acs.org/NanoLett
Plasmonic Surface Lattice Resonances at the Strong Coupling Regime A. I. Vak̈ evaï nen, R. J. Moerland,† H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim,‡ and P. Törma*̈ COMP Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland S Supporting Information *
ABSTRACT: We show strong coupling involving three different types of resonances in plasmonic nanoarrays: surface lattice resonances (SLRs), localized surface plasmon resonances on single nanoparticles, and excitations of organic dye molecules. The measured transmission spectra show splittings that depend on the molecule concentration. The results are analyzed using finite-difference time-domain simulations, a coupled-dipole approximation, coupled-modes models, and Fano theory. The delocalized nature of the collective SLR modes suggests that in the strong coupling regime molecules near distant nanoparticles are coherently coupled. KEYWORDS: Strong coupling, plasmonics, surface lattice resonance, metal nanoparticle arrays, organic dye molecules
T
coupling in a system displaying collective modes, namely silver nanoparticle arrays, combined with organic molecules. The results pave the way for exploiting the combination of long lifetimes, and delocalized nature, of the collective modes and the strong coupling to quantum emitters provided by plasmonic nanoparticles. In this Letter, we explore the behavior of cylindrical silver nanoparticles arranged in a regular square lattice as shown in Figure 1, both with and without organic molecules, Rhodamine 6G in PMMA (R6G). The LSPR is given by the nanoparticle shape and size, and the DOs by the lattice periodicity. The nanoparticles are fabricated with electron-beam lithography on glass substrates. The LSPR is chosen to be close to the absorption maximum of the emitter (R6G) by tuning the diameter of the particle. Here, we go beyond the previous experimental and theoretical studies of SLRs19−21,23,25 by systematically varying the lattice spacing in approximately 10 nm steps, in order to scan the SLR frequency through the LSPR frequency, paying particular attention to the possibility of strong coupling phenomena near the crossing points of the LSPR, SLR, and R6G absorption frequencies. We first consider nanoparticle arrays without R6G. Then, we add an R6G layer on top of our nanoparticle arrays. The measurement method of the transmission spectra is described in Figure 1 and below. We explain our findings using finite-difference time-domain (FDTD) simulations, coupled-dipole approximation (CDA), and coupled-modes models.
he optics of metals, called plasmonics, takes an important place in providing the means of subwavelength confinement and control of light.1 The strong coupling regime of lightmatter interaction is the key for observing coherence phenomena such as Rabi oscillations and coherent energy transfer. The resonant character of plasmonic modes has enabled reaching the strong,2−9 even ultrastrong,10 coupling regime at room temperature and without cavities on planar and nanostructured metal surfaces. In order to reach strong coupling, the coupling, which in general is proportional to the square root of the density of emitters and the dipole moment of individual emitters, has to exceed the losses.11−13 Although losses are considerable in plasmonic structures, the high concentrations and large oscillator strengths of organic molecules have helped reaching the strong coupling regime. Metallic nanoparticles may display a resonant behavior of the electromagnetic field that can be tuned in frequency and space by careful choice of the geometry of the nanoparticle(s) and their respective location.14−17 Regular arrays of metallic nanoparticles can show extremely narrow extinction line shapes due to collective resonances14,15,18−23 (surface lattice resonances, SLRs). The SLRs are intricate combinations of localized surface plasmon resonances (LSPRs) on single nanoparticles and diffractive orders (DOs) present in periodic structures. Array structures can be realized also on the micrometer scale, with potential applications, for example, in infrared spectroscopy.24 The transmission and extinction spectra of such arrays can be partially described by a modified version of the Fano theory.26−30 A more microscopic description is given by the coupled-dipole approximation14,15 that incorporates the field scattered by all nanoparticles as an effective change of the polarizability. Here we show strong © XXXX American Chemical Society
Received: September 20, 2013 Revised: November 18, 2013
A
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
periodicities. The spectra show narrow resonances that resemble the asymmetric line shapes typical of Fanoresonances. Figure 2a is for a periodicity for which the frequency of the SLR is lower than the peak of the LSPR; in Figure 2b, the two frequencies are close. In contrast, in Figure 2c the SLR is higher in frequency than the LSPR and the narrow peak has transformed into a dip in the extinction spectrum. In Figure 2d, we plot the measured extinction spectra of Sample I in a dispersion diagram as a function of inverse lattice spacing (reciprocal lattice wave vector), k = 2π/h. Instead of varying the angle and thus the k-vector of the incident light, we vary the lattice spacing to study the effect of periodicity on the resonances of the system. Intriguingly, we observe a profound avoided crossing between the LSPR and the SLR extinction, indicating strong coupling. FDTD simulations of the systems corresponding to the experiments (for parameters see Supporting Information Section II) are carried out with commercially available software.31 Shown in Figure 2a−c,e are the calculated extinction spectra by nanoparticle arrays; these correspond excellently to the measured data. The narrow features in nanoparticle arrays are often referred to as Fano-type resonances, and indeed analysis of these plasmonic modes has been approached with a modified Fano description.29,30 The accuracy with which it describes particle arrays, however, depends strongly on the relative position of the SLR with respect to the LSPR.32 We analyze our data using an extended Fano description (Supporting Information Sections III and V) but find that it can only describe the observations for limited sets of lattice spacings for which the SLR frequency is below the LSPR. In the coupled-dipole approximation,15 each nanoparticle is considered to be a single dipole with a polarizability αi (i = 1...N) and the polarization Pi = αiEi of every particle is calculated, where Ei includes the incident field and the field generated by the other particles. Under plane-wave illumination at normal incidence, the extinction cross section can be obtained by calculating an effective polarizability, αeff = 1/(α−1 − S) that includes the single nanoparticle polarizability α and the lattice response S. In previous literature, usually the single nanoparticle polarizability has been based on a quasi-static approximation or Mie theory. Here, we use a multipole expansion33,34 applied to a single cylindrical nanoparticle illuminated by a plane wave. We thus obtain the polarizability of the single nanoparticle without any approximation. Furthermore, the strengths of the higher-order multipoles that we obtain confirm that a single dipole term is sufficient to describe the single nanoparticle, which excludes interference effects from within the same particle. Results of this approach are also displayed in Figure 2a−c and show a near-perfect match with the experiments and the FDTD results. In particular, the CDA also displays the bending of the dispersions (see Supporting Information Section IV). To characterize the magnitude of the bending, we fit a threecoupled-modes model to the measured data of Sample I, see Figure 2d. The three-coupled-modes model consists of a 3 × 3 matrix where the initial resonance frequencies of the LSPR and the two SLRs are on the diagonal and the coupling coefficients form the off-diagonal elements. The eigenvalues of this matrix give the resonance frequencies of the coupled system (e.g., the white curved lines in Figure 2d), which are fitted to the extinction maxima of all arrays. The maxima are extracted from the spectral data by fitting a single Gaussian to the local environment of each maximum separately. Coupling coef-
Figure 1. A schematic depiction of the samples and the measurement setup. Arrays of silver cylindrically shaped nanoparticles are fabricated on a glass substrate, in a square arrangement with lattice spacing h. A sample contains several arrays and each array has a different lattice spacing h. By restricting the transmission measurement to one array at a time, we are measuring a system with a certain reciprocal lattice wave vector k = 2π/h. Optionally, a layer of Rhodamine 6G in PMMA is spin-coated on top. The sample is immersed in index-matching oil and covered by an additional glass coverslip. A zoom-in on a fabricated nanoparticle array is shown as an inset. White light, incident from the top, is focused mildly onto the array. After passing through the sample, the light is collected with an objective and guided to a spectrometer.
We fabricate arrays formed of equally sized cylindrical silver nanoparticles in a square lattice (Figure 1). Sample I consists of 21 nanoparticle arrays, where each individual array is 40 × 40 μm large. In Sample I, the particle diameter is 89 nm on average, and the lattice period is varied from 297 to 495 nm. Therefore, the number of nanoparticles in one array is typically on the order of 100 × 100. Sample II consists of 23 arrays of nanoparticles, arranged similarly as in Sample I. In Sample II, the particle diameter is 65 nm on average, and the lattice period is varied from 275 to 491 nm. The diameter of a nanoparticle and the lattice period are measured with a scanning electron microscope. We consider nanoparticle arrays in a symmetrical index environment. The symmetrical index environment is crucial to obtain sharp SLRs,21 and this environment is created by immersing the nanoparticle arrays in index matching oil and placing a glass coverslip on top (see Figure 1). The transmission spectra of the samples are measured with an inverted optical microscope. The sample is illuminated from above with a white-light halogen source, and to ensure nearplane-wave excitation, the effective NA is restricted with a lensand-diaphragm system (NA ≈ 0.04). The transmitted light is collected below the sample with a 0.25 NA objective and is guided to a spectrometer. A spectrum taken through bare glass serves as a reference with which the transmission by the array is calculated. For the samples without R6G, typical extinction spectra are presented in Figures 2a−c for three different lattice B
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
Figure 2. Measured and calculated extinction spectra of the nanoparticle arrays on Sample I. Here, we define the extinction as (1 − T)h2 with T being the transmission by the array and h as the lattice spacing. (a−c) The measurements, FDTD simulations, and the CDA calculations are shown at lattice periods that lead the SLR to be below, at, and above the LSPR frequency, respectively. The match between the experiments, simulations and CDA calculations is nearly perfect. (d,e) The spectra as a dispersion diagram where k is the inverse lattice spacing, k = 2π/h. (d) The measurements of Sample I. The diagonal black lines display the expected SLR positions as given by the DOs. The black horizontal line indicates the LSPR frequency. In addition, the peak positions of the spectra are shown with black dots and a fit with a three-coupled-modes model is presented with the white curved lines. Some typical values for the errors in our measurements are indicated with error bars for a few selected data points in (d). Others are omitted for clarity. The vertical error bars are based on the error due to the peak position fitting and a possible error in spectrometer calibration. The horizontal error bars are based on the scanning electron microscope measurement accuracy when defining the lattice spacing. (e) The corresponding FDTD simulations. The k-values that the spectra in (a−c) correspond to are marked in (e) with vertical lines.
Figure 3. Measured extinction spectra of the nanoparticle arrays on Sample II (k is the inverse lattice spacing, k = 2π/h). (a) The measurement results without R6G and (b) the results for the same sample but now with a 50 nm layer of R6G (200 mM concentration) on top. The black straight solid lines are the DOs and the LSPR, and in (b) the dashed line is the measured R6G main absorption peak position and the dash-dotted line the measured R6G absorption shoulder. The LSPR and the R6G absorption shoulder are almost overlapping. Also presented are fits with the coupledmodes models (the gray curved lines).
ficients between the LSPR and both SLRs are obtained, while the coupling coefficient between the SLRs is kept zero. Also the LSPR is a fitting parameter in our three-coupled-modes fits. This fit gives a splitting of 107 ± 1 meV between the LSPR and the first-order SLR, and 142 ± 49 meV between the LSPR and
the second-order (higher frequency) SLR. The two SLRs correspond to two DOs. Such strong coupling-type behavior between the LSPR and the SLRs has not been paid much attention to in previous literature, possibly due to the complex dependence of the phenomenon on the system parameters. We C
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
find that it is related to singularities in αeff = [(αr/|α|2 − Sr)2 − i(αi/|α|2 + Si)]−1, where α is the single particle polarizability and S the geometrical lattice factor in CDA, and indices r and i correspond to real and imaginary parts, respectively. Splittings when single nanoring and SLR frequencies cross were theoretically suggested in ref 35 but there the focus was mainly on the term αr/|α|2 − Sr, however, we find that the imaginary part of the denominator is essential to describe the observed results. In Section V of the Supporting Information, we compare αeff and a corresponding quantity in the two coupled, lossy oscillators theory: the strong coupling in our case is similar although not identical to strong coupling of two lossy oscillators, with large Sr and Si (relative to 1/α) corresponding to large coupling. For the nanoparticle samples with R6G, a 50 nm thick PMMA layer with Rhodamine 6G molecules is formed on top of the substrate by spin-coating the solution of R6G in ethanol mixed with PMMA in anisole. The effective concentrations of R6G in the layer are calculated from the ratio between R6G and PMMA in the solution. The effective R6G concentrations in Sample II are 25, 50, and 200 mM. The experimental procedure is the same as above except that the following two reference spectra are taken: one through the R6G layer and one through bare glass. The extinction spectrum is obtained by subtracting the measured spectra from the transmission by the sample through a volume without the nanoparticles but with the R6G layer (for justification and details of the subtraction see Supporting Information Section VII). Figure 3 shows dispersion curves obtained by measurements performed on exactly the same sample (Sample II), but first without and then with R6G. Far away from the point where the LSPR and SLR frequencies are similar, we observe that the LSPR shows a clear down shift in frequency when R6G is included. We confirm that this is due to strong coupling of the LSPR and R6G (see Supporting Information Section VIII), the features now corresponding to a hybrid of the LSPR and R6G. Other shifts and bendings are observed as well, and at the crossing point of LSPR, R6G, and SLR frequencies the results have to be analyzed taking into account couplings between all modes. The experimental data of Sample II is repeated in Figure 4, which for clarity only contains the measured peak positions. The results for both types of measurement, that is, with or without R6G, are overlaid onto the same axes. We find that to characterize the system, we have to effectively describe it as five coupled oscillators: the LSPR, the two SLRs, the R6G main absorption peak, and the R6G absorption shoulder. The coupled-modes model that we fit the data with consists of a 5 × 5 matrix, with on the diagonal the original resonance frequencies of the five oscillators; the R6G absorption frequencies are determined from the extinction spectrum of the bare R6G film on the glass substrate and the LSPR is taken from the three-coupled-modes fit of the same sample. The extinction maxima of the arrays are determined as before by fitting a single Gaussian to the local environment of each maximum separately. Furthermore, the coupling coefficients between the SLRs, and between the R6G main absorption peak and shoulder are kept zero while performing the fit. The fit with this model is shown in Figures 3b and 4 for a concentration of R6G of 200 mM. Avoided crossings between the various modes are observed. For instance, at the crossing point of the LSPR, and the first-order SLR where they are strongly coupled with each other, both of these modes are expected to be strongly coupled to R6G, forming a novel hybrid
Figure 4. Dispersions of measured extinction spectra of the nanoparticle arrays on Sample II. The maxima of the measured extinction spectra of Sample II without R6G are shown with blue dots and the maxima for the same sample but now with a 200 mM R6G film are shown with red dots. The blue and red dots correspond directly to the black dots in Figure 3a,b, respectively. The corresponding fits with the coupled-modes models are now represented by the blue and red curved lines. The insets show the LSPR-R6G couplings obtained from the coupled-modes fits for four different concentrations (0, 25, 50, and 200 mM), displaying the expected square root dependence of the couplings on the absorbance peak value of the R6G film. Here Ω1 denotes the coupling between the LSPR and the R6G main absorption peak and Ω2 denotes the coupling between the LSPR and the R6G absorption shoulder, respectively.
consisting of an emitter, a collective mode, and a local plasmonic mode. The couplings in Sample II obtained from the three-coupled-modes model in the case without R6G are 108 ± 11 and 59 ± 8 meV between the LSPR and the first-order SLR, and between the LSPR and the second-order SLR, respectively. The couplings obtained from the five-coupled-modes model, in the case with R6G and with a full model including all eight couplings, are of the order 100 meV for the LSPR-R6G (main and shoulder) and for the LSPR-(first- and second-order) SLR. For the direct couplings between the SLR and R6G modes they are smaller, of the order 10 meV. We find that if direct couplings between the R6G and SLR modes are ignored, we can still fit the data fairly well and the system is a strongly coupled mixture of the R6G, SLR, and LSPR modes. The resulting model has four parameters, two for couplings between R6G main/shoulder and the LSPR and two for couplings between the two SLRs and the LSPR. As we demonstrate in the Supporting Information Section IX, all of these parameters must be included in order to reproduce our results qualitatively. The couplings obtained for this truncated five-coupled-modes model in Sample II with a 200 mM R6G layer are 150 ± 12 meV (LSPR and R6G main peak), 121 ± 12 meV (LSPR and R6G shoulder), 95 ± 6 meV (LSPR and first-order SLR), and 79 ± 7 meV (LSPR and second-order SLR). The truncated model is used for fitting in Figures 3b and 4 and in the following. Importantly, all four parameters have roughly the same magnitude so, similarly to quantum-mechanical threelevel Λ-configurations,36 there is a strong coupling between R6G and the SLRs that is mediated by the LSPR coupling strongly to both R6G and the SLRs. This corresponds to hybrids consisting of three types of modes: the LSPR, R6G, and D
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
Figure 5. Examples of the measured extinction spectra of the nanoparticle arrays on Sample II without and with R6G. (a−c) Correspond to 403, 354, and 305 nm lattice spacing, respectively. (a) The SLR is on the lower energy side of the LSPR and the R6G absorption maxima. (b) The SLR is in between the R6G main peak and the LSPR. (c) The SLR is on the higher energy side of the LSPR and the R6G resonances. The bottom spectra are measured without emitters and the spectra above correspond to the measurements with the R6G films of 25, 50, and 200 mM concentration, respectively. Peak positions are indicated with symbols on top of the curves and they correspond to the fitted extinction maxima as shown in Figure 4. Triangles, squares, and diamonds on the blue (no R6G) and the red (200 mM R6G layer) curves correspond to the data points marked with the same symbols in Figure 4. The spectra show a clear evolution as a function of concentration such that the extinction peaks of the strongly coupled hybrid modes emerge and become more prominent as they separate further away from each other.
calculations with the FDTD method on the single silver nanoparticle, centered inside a PMMA disk, doped with 200 mM R6G. The size of the PMMA disk is increased in a stepwise manner from a 32 nm radius and a 32 nm thickness to a 50 nm radius and a 50 nm thickness. The PMMA disk with the embedded silver particle is placed in a homogeneous dielectric environment with a refractive index of 1.51. The inset in Figure 6 shows the geometry used for the calculations, whereas the
SLR ones. The collective nature of the SLRs involved in this three-mode hybridization indicates that molecules near distant nanoparticles are coherently coupled. The size of the mode splitting due to strong coupling is expected to be proportional to the square root of the number of emitters, in our case the square root of the molecular concentration (absorbance of the film).2−8,10 The splitting is also proportional to the dipole moment. These dependences can be derived by considering a set of emitters interacting with a field, see, for example, ref 12. Recently, such a situation has been theoretically analyzed in the context of plasmonic modes,13 and the dependence of the splitting on the square root of the concentration times the dipole moment is also predicted in this case. The analysis of ref 13 gives information about the role of the orientation of the dipole on strong coupling, a feature especially relevant for the 2D planar surface plasmon polariton (SPP) modes. In the insets of Figure 4, we demonstrate this square root dependence by showing the LSPR-R6G couplings obtained from the five-oscillator model fits of the experimental data for different concentrations; for details see Supporting Information Section X. Example spectra for different lattice spacings and molecular concentrations are given in Figure 5, showing how the maxima of the spectra evolve for increasing concentration. The FDTD simulations describe the experiments excellently also in the case of samples with R6G, see Supporting Information Section XI. The CDA method in its standard form, however, is not valid for an absorbing medium. Therefore, we approximate a nanoparticle in the R6G film as a nanoparticle enveloped by a disk of R6G molecules in PMMA with a diameter of 100 and 50 nm thickness and extract the polarizability of the combination using the multipole expansion.33,34 We then use this polarizability within the CDA. The correspondence of these CDA results with the FDTD simulations and the measurements is excellent, which also confirms the validity of the subtraction procedure used for the measurements and simulations of the R6G samples (see Supporting Information Section XI). In order to estimate the number of molecules involved in the strong-coupling phenomenon, we perform a series of extinction
Figure 6. A silver disk, 60 nm in diameter and 30 nm high, placed on a 2 nm thick titanium adhesion layer, is concentrically enveloped by a PMMA disk doped with R6G molecules at a concentration of 200 mM. The radius of the PMMA disk is equal to the height of the disk, and is stepped from 32 to 50 nm. See the inset for a drawing of the geometry. The extinction cross section of the two concentric disks is calculated with the FDTD method and displayed as solid and dashed curves. Initially, the resonance frequency of the particle splits and shifts relatively rapidly but becomes more or less stationary at larger PMMA disk thicknesses.
main panel displays the results of the calculations. Initially, the extinction maximum shifts with an increase in PMMA disk size relatively quickly, but remains more or less stationary after a certain disk thickness. This indicates that the additional molecules present in the larger disks do not contribute to the strong coupling. E
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter ‡
We subsequently track the location of the extinction maximum as a function of PMMA disk size and fit a single exponential curve to this data. We find that a disk radius of 43 nm corresponds to the 1/e2-value of the peak shift. From the volume of the PMMA disk (not including the volume occupied by the silver particle) and the concentration of R6G molecules in the PMMA, we estimate a number of molecules on the order of 3 × 104 to be involved in the strong coupling per one metallic nanoparticle. In summary, we measure nanoparticle array systems with and without organic molecules and obtain spectra that display bendings and anticrossings typical for the strong coupling regime. We analyze the findings with four complementary approaches of different levels of approximation: FDTD simulations, coupled-dipole approximation, coupled-modes models, and Fano theory. In the case without the emitters, we observe strong coupling behavior and identify it to be connected to a delicate matching of the single nanoparticle polarizability with the geometrical lattice factor. In the case with R6G emitters, we observe strong coupling between the emitters and the various modes of the nanoparticle array, also collective ones. Because the SLR modes are collective, the strong coupling regime observed here implies that emitters near distant nanoparticles are coherently coupled. Strong coupling of an SPP mode with many emitters in general couples distant emitters, for example, on a planar metal surface the molecules within the coherence length of the SPP mode. The present system offers the possibility to design the dispersions and the geometrical arrangement of the molecules that couple strongly, as well as the nanoparticle shapes. It combines long coherence lengths and times with locally high field intensities (small mode volumes). The SLRs can have long lifetimes (high Q-factors) as shown by the sharpness of the peaks, whereas the LSPRs are broad but the high local field enhancement that they provide may be the key to achieving strong coupling with emitters; systems such as we consider here can combine the best features of both to display interesting coherence, quantum, and collective phenomena. This collective-mode plasmonic strongcoupling regime has the potential for the creation of light emission where collective effects are utilized. It is expected to provide interesting phenomena especially if one can place single quantum emitters on the nanoparticles. By tailoring the shape of the nanoparticles, extremely strong field enhancements are possible. Single-emitter strong coupling for such specially shaped nanoparticles has been predicted37,38 and combining that with collective effects in array structures is likely to be a fruitful direction of future research.
■
(D.-H.K.) Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 500− 712, Korea.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the Academy of Finland through its Centres of Excellence Programme (Project Nos. 251748, 263347, 135000, and 141039). Part of the research was performed at the Micronova Nanofabrication Centre, supported by Aalto University.
■
ASSOCIATED CONTENT
S Supporting Information *
Additional experimental data and details of the experimental and theoretical methods. This material is available free of charge via the Internet at http://pubs.acs.org.
■
REFERENCES
(1) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 2003, 424, 824−830. (2) Pockrand, I.; Swalen, J. D.; Santo, R.; Brillante, A.; Philpott, M. R. Optical-properties of organic-dye monolayers by surface-plasmon spectroscopy. J. Chem. Phys. 1978, 69, 4001−4011. (3) Bellessa, J.; Bonnand, C.; Plenet, J. C.; Mugnier, J. Strong coupling between surface plasmons and excitons in an organic semiconductor. Phys. Rev. Lett. 2004, 93, 036404. (4) Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W. Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays. Phys. Rev. B 2005, 71, 035424. (5) Sugawara, Y.; Jelf, T. A.; Baumberg, J. J.; Abdelsalam, M. E.; Bartlett, P. N. Strong coupling between localized plasmons and organic excitons in metal nanovoids. Phys. Rev. Lett. 2006, 97, 266808. (6) Hakala, T. K.; Toppari, J. J.; Kuzyk, A.; Pettersson, M.; Tikkanen, H.; Kunttu, H.; Törmä, P. Vacuum Rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and Rhodamine 6G molecules. Phys. Rev. Lett. 2009, 103, 053602. (7) Gomez, D. E.; Vernon, K. C.; Mulvaney, P.; Davis, T. J. Surface Plasmon Mediated Strong Exciton-Photon Coupling in Semiconductor Nanocrystals. Nano Lett. 2010, 10, 274−278. (8) Vasa, P.; Wang, W.; Pomraenke, R.; Lammers, M.; Maiuri, M.; Manzoni, C.; Cerullo, G.; Lienau, C. Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with j-aggregates. Nat. Photonics 2013, 7, 128−132. (9) Schlather, A. E.; Large, N.; Urban, A. S.; Nordlander, P.; Halas, N. J. Near-Field Mediated Plexcitonic Coupling and Giant Rabi Splitting in Individual Metallic Dimers. Nano Lett. 2013, 13, 3281− 3286. (10) Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W. Reversible switching of ultrastrong light-molecule coupling. Phys. Rev. Lett. 2011, 106, 196405. (11) Houdré, R.; Stanley, R. P.; Ilegems, M. Vacuum-field Rabi splitting in the presence of inhomogeneous broadening: Resolution of a homogeneous linewidth in an inhomogeneously broadened system. Phys. Rev. A 1996, 53, 2711−2715. (12) Agranovich, V. M.; Litinskaia, M.; Lidzey, D. G. Phys. Rev. B 2003, 67, 085311. (13) González-Tudela, A.; Huidobro, P. A.; Martín-Moreno, L.; Tejedor, C.; García-Vidal, F. J. Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons. Phys. Rev. Lett. 2013, 110, 126801. (14) Markel, V. Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure. J. Modern Opt. 1993, 40, 2281−2291. (15) Zou, S.; Janel, N.; Schatz, G. C. Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes. J. Chem. Phys. 2004, 120, 10871−10875. (16) Mühlschlegel, P.; Eisler, H.-J.; Martin, O. J. F.; Hecht, B.; Pohl, D. W. Resonant optical antennas. Science 2005, 308, 1607−1609. (17) de Waele, R.; Koenderink, A. F.; Polman, A. Tunable Nanoscale Localization of Energy on Plasmon Particle Arrays. Nano Lett. 2007, 7, 2004−2008.
AUTHOR INFORMATION
Corresponding Author
*E-mail: paivi.torma@aalto.fi. Phone: +358 50 3826770. Present Addresses †
(R.J.M.) Department of Imaging Physics, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, NL2628 CJ, Delft, The Netherlands. F
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
(18) Carron, K. T.; Fluhr, W.; Meier, M.; Wokaun, A.; Lehmann, H. W. Resonances of two-dimensional particle gratings in surfaceenhanced raman scattering. J. Opt. Soc. Am. B 1986, 3, 430−440. (19) García de Abajo, F. J. Colloquium: Light scattering by particle and hole arrays. Rev. Mod. Phys. 2007, 79, 1267. (20) Kravets, V. G.; Schedin, F.; Grigorenko, A. N. Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles. Phys. Rev. Lett. 2008, 101, 087403. (21) Auguié, B.; Barnes, W. L. Collective resonances in gold nanoparticle arrays. Phys. Rev. Lett. 2008, 101, 143902. (22) Chu, Y.; Schonbrun, E.; Yang, T.; Crozier, K. B. Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays. Appl. Phys. Lett. 2008, 93, 181108. (23) Rodriguez, S. R. K.; Abass, A.; Maes, B.; Janssen, O. T. A.; Vecchi, G.; Gómez Rivas, J. Coupling bright and dark plasmonic lattice resonances. Phys. Rev. X 2011, 1, 021019. (24) Adato, R.; Yanik, A. A.; Amsden, J. J.; Kaplan, D. L.; Omenetto, F. G.; Hong, M. K.; Erramilli, S.; Altug, H. Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 19227−19232. (25) Farhang, A.; Ramakrishna, A.; Martin, O. J. F. Compound resonance-induced coupling effects in composite plasmonic metamaterials. Opt. Express 2012, 20, 29447−29456. (26) Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 1961, 124, 1866−1878. (27) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 2010, 9, 707−715. (28) Miroshnichenko, A. E.; Flach, S.; Kivshar, Y. S. Fano resonances in nanoscale structures. Rev. Mod. Phys. 2010, 82, 2257−2298. (29) Giannini, V.; Francescato, Y.; Amrania, H.; Phillips, C. C.; Maier, S. A. Fano Resonances in Nanoscale Plasmonic Systems: A Parameter-Free Modeling Approach. Nano Lett. 2011, 11, 2835−2840. (30) Gallinet, B.; Martin, O. J. F. Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials. Phys. Rev. B 2011, 83, 235427. (31) Lumerical Solutions, Inc., v 7.5, www.lumerical.com, date accessed 1/9/2012. (32) Francescato, Y.; Giannini, V.; Maier, S. A. Plasmonic Systems Unveiled by Fano Resonances. ACS Nano 2012, 6, 1830−1838. (33) Grahn, P.; Shevchenko, A.; Kaivola, M. Electromagnetic multipole theory for optical nanomaterials. New J. Phys. 2012, 14, 093033. (34) Grahn, P.; Shevchenko, A.; Kaivola, M. Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles. Phys. Rev. B 2012, 86, 035419. (35) Teperik, T. V.; Degiron, A. Design strategies to tailor the narrow plasmon-photonic resonances in arrays of metallic nanoparticles. Phys. Rev. B 2012, 86, 245425. (36) Scully, M. O.; Zubairy, S. M. Quantum Optics; Cambridge University Press: New York, 1997. (37) Trügler, A.; Hohenester, U. Strong coupling between a metallic nanoparticle and a single molecule. Phys. Rev. B 2008, 77, 115403. (38) Savasta, S.; Saija, R.; Ridolfo, A.; Di Stefano, O.; Denti, P.; Borghese, F. Nanopolaritons: Vacuum Rabi Splitting with a Single Quantum Dot in the Center of a Dimer Nanoantenna. ACS Nano 2010, 4, 6369−6376.
G
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Plasmonic Surface Lattice Resonances at the Strong Coupling Regime A. I. Vak̈ evaï nen, R. J. Moerland,† H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim,‡ and P. Törma*̈ COMP Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland S Supporting Information *
ABSTRACT: We show strong coupling involving three different types of resonances in plasmonic nanoarrays: surface lattice resonances (SLRs), localized surface plasmon resonances on single nanoparticles, and excitations of organic dye molecules. The measured transmission spectra show splittings that depend on the molecule concentration. The results are analyzed using finite-difference time-domain simulations, a coupled-dipole approximation, coupled-modes models, and Fano theory. The delocalized nature of the collective SLR modes suggests that in the strong coupling regime molecules near distant nanoparticles are coherently coupled. KEYWORDS: Strong coupling, plasmonics, surface lattice resonance, metal nanoparticle arrays, organic dye molecules
T
coupling in a system displaying collective modes, namely silver nanoparticle arrays, combined with organic molecules. The results pave the way for exploiting the combination of long lifetimes, and delocalized nature, of the collective modes and the strong coupling to quantum emitters provided by plasmonic nanoparticles. In this Letter, we explore the behavior of cylindrical silver nanoparticles arranged in a regular square lattice as shown in Figure 1, both with and without organic molecules, Rhodamine 6G in PMMA (R6G). The LSPR is given by the nanoparticle shape and size, and the DOs by the lattice periodicity. The nanoparticles are fabricated with electron-beam lithography on glass substrates. The LSPR is chosen to be close to the absorption maximum of the emitter (R6G) by tuning the diameter of the particle. Here, we go beyond the previous experimental and theoretical studies of SLRs19−21,23,25 by systematically varying the lattice spacing in approximately 10 nm steps, in order to scan the SLR frequency through the LSPR frequency, paying particular attention to the possibility of strong coupling phenomena near the crossing points of the LSPR, SLR, and R6G absorption frequencies. We first consider nanoparticle arrays without R6G. Then, we add an R6G layer on top of our nanoparticle arrays. The measurement method of the transmission spectra is described in Figure 1 and below. We explain our findings using finite-difference time-domain (FDTD) simulations, coupled-dipole approximation (CDA), and coupled-modes models.
he optics of metals, called plasmonics, takes an important place in providing the means of subwavelength confinement and control of light.1 The strong coupling regime of lightmatter interaction is the key for observing coherence phenomena such as Rabi oscillations and coherent energy transfer. The resonant character of plasmonic modes has enabled reaching the strong,2−9 even ultrastrong,10 coupling regime at room temperature and without cavities on planar and nanostructured metal surfaces. In order to reach strong coupling, the coupling, which in general is proportional to the square root of the density of emitters and the dipole moment of individual emitters, has to exceed the losses.11−13 Although losses are considerable in plasmonic structures, the high concentrations and large oscillator strengths of organic molecules have helped reaching the strong coupling regime. Metallic nanoparticles may display a resonant behavior of the electromagnetic field that can be tuned in frequency and space by careful choice of the geometry of the nanoparticle(s) and their respective location.14−17 Regular arrays of metallic nanoparticles can show extremely narrow extinction line shapes due to collective resonances14,15,18−23 (surface lattice resonances, SLRs). The SLRs are intricate combinations of localized surface plasmon resonances (LSPRs) on single nanoparticles and diffractive orders (DOs) present in periodic structures. Array structures can be realized also on the micrometer scale, with potential applications, for example, in infrared spectroscopy.24 The transmission and extinction spectra of such arrays can be partially described by a modified version of the Fano theory.26−30 A more microscopic description is given by the coupled-dipole approximation14,15 that incorporates the field scattered by all nanoparticles as an effective change of the polarizability. Here we show strong © XXXX American Chemical Society
Received: September 20, 2013 Revised: November 18, 2013
A
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
periodicities. The spectra show narrow resonances that resemble the asymmetric line shapes typical of Fanoresonances. Figure 2a is for a periodicity for which the frequency of the SLR is lower than the peak of the LSPR; in Figure 2b, the two frequencies are close. In contrast, in Figure 2c the SLR is higher in frequency than the LSPR and the narrow peak has transformed into a dip in the extinction spectrum. In Figure 2d, we plot the measured extinction spectra of Sample I in a dispersion diagram as a function of inverse lattice spacing (reciprocal lattice wave vector), k = 2π/h. Instead of varying the angle and thus the k-vector of the incident light, we vary the lattice spacing to study the effect of periodicity on the resonances of the system. Intriguingly, we observe a profound avoided crossing between the LSPR and the SLR extinction, indicating strong coupling. FDTD simulations of the systems corresponding to the experiments (for parameters see Supporting Information Section II) are carried out with commercially available software.31 Shown in Figure 2a−c,e are the calculated extinction spectra by nanoparticle arrays; these correspond excellently to the measured data. The narrow features in nanoparticle arrays are often referred to as Fano-type resonances, and indeed analysis of these plasmonic modes has been approached with a modified Fano description.29,30 The accuracy with which it describes particle arrays, however, depends strongly on the relative position of the SLR with respect to the LSPR.32 We analyze our data using an extended Fano description (Supporting Information Sections III and V) but find that it can only describe the observations for limited sets of lattice spacings for which the SLR frequency is below the LSPR. In the coupled-dipole approximation,15 each nanoparticle is considered to be a single dipole with a polarizability αi (i = 1...N) and the polarization Pi = αiEi of every particle is calculated, where Ei includes the incident field and the field generated by the other particles. Under plane-wave illumination at normal incidence, the extinction cross section can be obtained by calculating an effective polarizability, αeff = 1/(α−1 − S) that includes the single nanoparticle polarizability α and the lattice response S. In previous literature, usually the single nanoparticle polarizability has been based on a quasi-static approximation or Mie theory. Here, we use a multipole expansion33,34 applied to a single cylindrical nanoparticle illuminated by a plane wave. We thus obtain the polarizability of the single nanoparticle without any approximation. Furthermore, the strengths of the higher-order multipoles that we obtain confirm that a single dipole term is sufficient to describe the single nanoparticle, which excludes interference effects from within the same particle. Results of this approach are also displayed in Figure 2a−c and show a near-perfect match with the experiments and the FDTD results. In particular, the CDA also displays the bending of the dispersions (see Supporting Information Section IV). To characterize the magnitude of the bending, we fit a threecoupled-modes model to the measured data of Sample I, see Figure 2d. The three-coupled-modes model consists of a 3 × 3 matrix where the initial resonance frequencies of the LSPR and the two SLRs are on the diagonal and the coupling coefficients form the off-diagonal elements. The eigenvalues of this matrix give the resonance frequencies of the coupled system (e.g., the white curved lines in Figure 2d), which are fitted to the extinction maxima of all arrays. The maxima are extracted from the spectral data by fitting a single Gaussian to the local environment of each maximum separately. Coupling coef-
Figure 1. A schematic depiction of the samples and the measurement setup. Arrays of silver cylindrically shaped nanoparticles are fabricated on a glass substrate, in a square arrangement with lattice spacing h. A sample contains several arrays and each array has a different lattice spacing h. By restricting the transmission measurement to one array at a time, we are measuring a system with a certain reciprocal lattice wave vector k = 2π/h. Optionally, a layer of Rhodamine 6G in PMMA is spin-coated on top. The sample is immersed in index-matching oil and covered by an additional glass coverslip. A zoom-in on a fabricated nanoparticle array is shown as an inset. White light, incident from the top, is focused mildly onto the array. After passing through the sample, the light is collected with an objective and guided to a spectrometer.
We fabricate arrays formed of equally sized cylindrical silver nanoparticles in a square lattice (Figure 1). Sample I consists of 21 nanoparticle arrays, where each individual array is 40 × 40 μm large. In Sample I, the particle diameter is 89 nm on average, and the lattice period is varied from 297 to 495 nm. Therefore, the number of nanoparticles in one array is typically on the order of 100 × 100. Sample II consists of 23 arrays of nanoparticles, arranged similarly as in Sample I. In Sample II, the particle diameter is 65 nm on average, and the lattice period is varied from 275 to 491 nm. The diameter of a nanoparticle and the lattice period are measured with a scanning electron microscope. We consider nanoparticle arrays in a symmetrical index environment. The symmetrical index environment is crucial to obtain sharp SLRs,21 and this environment is created by immersing the nanoparticle arrays in index matching oil and placing a glass coverslip on top (see Figure 1). The transmission spectra of the samples are measured with an inverted optical microscope. The sample is illuminated from above with a white-light halogen source, and to ensure nearplane-wave excitation, the effective NA is restricted with a lensand-diaphragm system (NA ≈ 0.04). The transmitted light is collected below the sample with a 0.25 NA objective and is guided to a spectrometer. A spectrum taken through bare glass serves as a reference with which the transmission by the array is calculated. For the samples without R6G, typical extinction spectra are presented in Figures 2a−c for three different lattice B
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
Figure 2. Measured and calculated extinction spectra of the nanoparticle arrays on Sample I. Here, we define the extinction as (1 − T)h2 with T being the transmission by the array and h as the lattice spacing. (a−c) The measurements, FDTD simulations, and the CDA calculations are shown at lattice periods that lead the SLR to be below, at, and above the LSPR frequency, respectively. The match between the experiments, simulations and CDA calculations is nearly perfect. (d,e) The spectra as a dispersion diagram where k is the inverse lattice spacing, k = 2π/h. (d) The measurements of Sample I. The diagonal black lines display the expected SLR positions as given by the DOs. The black horizontal line indicates the LSPR frequency. In addition, the peak positions of the spectra are shown with black dots and a fit with a three-coupled-modes model is presented with the white curved lines. Some typical values for the errors in our measurements are indicated with error bars for a few selected data points in (d). Others are omitted for clarity. The vertical error bars are based on the error due to the peak position fitting and a possible error in spectrometer calibration. The horizontal error bars are based on the scanning electron microscope measurement accuracy when defining the lattice spacing. (e) The corresponding FDTD simulations. The k-values that the spectra in (a−c) correspond to are marked in (e) with vertical lines.
Figure 3. Measured extinction spectra of the nanoparticle arrays on Sample II (k is the inverse lattice spacing, k = 2π/h). (a) The measurement results without R6G and (b) the results for the same sample but now with a 50 nm layer of R6G (200 mM concentration) on top. The black straight solid lines are the DOs and the LSPR, and in (b) the dashed line is the measured R6G main absorption peak position and the dash-dotted line the measured R6G absorption shoulder. The LSPR and the R6G absorption shoulder are almost overlapping. Also presented are fits with the coupledmodes models (the gray curved lines).
ficients between the LSPR and both SLRs are obtained, while the coupling coefficient between the SLRs is kept zero. Also the LSPR is a fitting parameter in our three-coupled-modes fits. This fit gives a splitting of 107 ± 1 meV between the LSPR and the first-order SLR, and 142 ± 49 meV between the LSPR and
the second-order (higher frequency) SLR. The two SLRs correspond to two DOs. Such strong coupling-type behavior between the LSPR and the SLRs has not been paid much attention to in previous literature, possibly due to the complex dependence of the phenomenon on the system parameters. We C
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
find that it is related to singularities in αeff = [(αr/|α|2 − Sr)2 − i(αi/|α|2 + Si)]−1, where α is the single particle polarizability and S the geometrical lattice factor in CDA, and indices r and i correspond to real and imaginary parts, respectively. Splittings when single nanoring and SLR frequencies cross were theoretically suggested in ref 35 but there the focus was mainly on the term αr/|α|2 − Sr, however, we find that the imaginary part of the denominator is essential to describe the observed results. In Section V of the Supporting Information, we compare αeff and a corresponding quantity in the two coupled, lossy oscillators theory: the strong coupling in our case is similar although not identical to strong coupling of two lossy oscillators, with large Sr and Si (relative to 1/α) corresponding to large coupling. For the nanoparticle samples with R6G, a 50 nm thick PMMA layer with Rhodamine 6G molecules is formed on top of the substrate by spin-coating the solution of R6G in ethanol mixed with PMMA in anisole. The effective concentrations of R6G in the layer are calculated from the ratio between R6G and PMMA in the solution. The effective R6G concentrations in Sample II are 25, 50, and 200 mM. The experimental procedure is the same as above except that the following two reference spectra are taken: one through the R6G layer and one through bare glass. The extinction spectrum is obtained by subtracting the measured spectra from the transmission by the sample through a volume without the nanoparticles but with the R6G layer (for justification and details of the subtraction see Supporting Information Section VII). Figure 3 shows dispersion curves obtained by measurements performed on exactly the same sample (Sample II), but first without and then with R6G. Far away from the point where the LSPR and SLR frequencies are similar, we observe that the LSPR shows a clear down shift in frequency when R6G is included. We confirm that this is due to strong coupling of the LSPR and R6G (see Supporting Information Section VIII), the features now corresponding to a hybrid of the LSPR and R6G. Other shifts and bendings are observed as well, and at the crossing point of LSPR, R6G, and SLR frequencies the results have to be analyzed taking into account couplings between all modes. The experimental data of Sample II is repeated in Figure 4, which for clarity only contains the measured peak positions. The results for both types of measurement, that is, with or without R6G, are overlaid onto the same axes. We find that to characterize the system, we have to effectively describe it as five coupled oscillators: the LSPR, the two SLRs, the R6G main absorption peak, and the R6G absorption shoulder. The coupled-modes model that we fit the data with consists of a 5 × 5 matrix, with on the diagonal the original resonance frequencies of the five oscillators; the R6G absorption frequencies are determined from the extinction spectrum of the bare R6G film on the glass substrate and the LSPR is taken from the three-coupled-modes fit of the same sample. The extinction maxima of the arrays are determined as before by fitting a single Gaussian to the local environment of each maximum separately. Furthermore, the coupling coefficients between the SLRs, and between the R6G main absorption peak and shoulder are kept zero while performing the fit. The fit with this model is shown in Figures 3b and 4 for a concentration of R6G of 200 mM. Avoided crossings between the various modes are observed. For instance, at the crossing point of the LSPR, and the first-order SLR where they are strongly coupled with each other, both of these modes are expected to be strongly coupled to R6G, forming a novel hybrid
Figure 4. Dispersions of measured extinction spectra of the nanoparticle arrays on Sample II. The maxima of the measured extinction spectra of Sample II without R6G are shown with blue dots and the maxima for the same sample but now with a 200 mM R6G film are shown with red dots. The blue and red dots correspond directly to the black dots in Figure 3a,b, respectively. The corresponding fits with the coupled-modes models are now represented by the blue and red curved lines. The insets show the LSPR-R6G couplings obtained from the coupled-modes fits for four different concentrations (0, 25, 50, and 200 mM), displaying the expected square root dependence of the couplings on the absorbance peak value of the R6G film. Here Ω1 denotes the coupling between the LSPR and the R6G main absorption peak and Ω2 denotes the coupling between the LSPR and the R6G absorption shoulder, respectively.
consisting of an emitter, a collective mode, and a local plasmonic mode. The couplings in Sample II obtained from the three-coupled-modes model in the case without R6G are 108 ± 11 and 59 ± 8 meV between the LSPR and the first-order SLR, and between the LSPR and the second-order SLR, respectively. The couplings obtained from the five-coupled-modes model, in the case with R6G and with a full model including all eight couplings, are of the order 100 meV for the LSPR-R6G (main and shoulder) and for the LSPR-(first- and second-order) SLR. For the direct couplings between the SLR and R6G modes they are smaller, of the order 10 meV. We find that if direct couplings between the R6G and SLR modes are ignored, we can still fit the data fairly well and the system is a strongly coupled mixture of the R6G, SLR, and LSPR modes. The resulting model has four parameters, two for couplings between R6G main/shoulder and the LSPR and two for couplings between the two SLRs and the LSPR. As we demonstrate in the Supporting Information Section IX, all of these parameters must be included in order to reproduce our results qualitatively. The couplings obtained for this truncated five-coupled-modes model in Sample II with a 200 mM R6G layer are 150 ± 12 meV (LSPR and R6G main peak), 121 ± 12 meV (LSPR and R6G shoulder), 95 ± 6 meV (LSPR and first-order SLR), and 79 ± 7 meV (LSPR and second-order SLR). The truncated model is used for fitting in Figures 3b and 4 and in the following. Importantly, all four parameters have roughly the same magnitude so, similarly to quantum-mechanical threelevel Λ-configurations,36 there is a strong coupling between R6G and the SLRs that is mediated by the LSPR coupling strongly to both R6G and the SLRs. This corresponds to hybrids consisting of three types of modes: the LSPR, R6G, and D
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
Figure 5. Examples of the measured extinction spectra of the nanoparticle arrays on Sample II without and with R6G. (a−c) Correspond to 403, 354, and 305 nm lattice spacing, respectively. (a) The SLR is on the lower energy side of the LSPR and the R6G absorption maxima. (b) The SLR is in between the R6G main peak and the LSPR. (c) The SLR is on the higher energy side of the LSPR and the R6G resonances. The bottom spectra are measured without emitters and the spectra above correspond to the measurements with the R6G films of 25, 50, and 200 mM concentration, respectively. Peak positions are indicated with symbols on top of the curves and they correspond to the fitted extinction maxima as shown in Figure 4. Triangles, squares, and diamonds on the blue (no R6G) and the red (200 mM R6G layer) curves correspond to the data points marked with the same symbols in Figure 4. The spectra show a clear evolution as a function of concentration such that the extinction peaks of the strongly coupled hybrid modes emerge and become more prominent as they separate further away from each other.
calculations with the FDTD method on the single silver nanoparticle, centered inside a PMMA disk, doped with 200 mM R6G. The size of the PMMA disk is increased in a stepwise manner from a 32 nm radius and a 32 nm thickness to a 50 nm radius and a 50 nm thickness. The PMMA disk with the embedded silver particle is placed in a homogeneous dielectric environment with a refractive index of 1.51. The inset in Figure 6 shows the geometry used for the calculations, whereas the
SLR ones. The collective nature of the SLRs involved in this three-mode hybridization indicates that molecules near distant nanoparticles are coherently coupled. The size of the mode splitting due to strong coupling is expected to be proportional to the square root of the number of emitters, in our case the square root of the molecular concentration (absorbance of the film).2−8,10 The splitting is also proportional to the dipole moment. These dependences can be derived by considering a set of emitters interacting with a field, see, for example, ref 12. Recently, such a situation has been theoretically analyzed in the context of plasmonic modes,13 and the dependence of the splitting on the square root of the concentration times the dipole moment is also predicted in this case. The analysis of ref 13 gives information about the role of the orientation of the dipole on strong coupling, a feature especially relevant for the 2D planar surface plasmon polariton (SPP) modes. In the insets of Figure 4, we demonstrate this square root dependence by showing the LSPR-R6G couplings obtained from the five-oscillator model fits of the experimental data for different concentrations; for details see Supporting Information Section X. Example spectra for different lattice spacings and molecular concentrations are given in Figure 5, showing how the maxima of the spectra evolve for increasing concentration. The FDTD simulations describe the experiments excellently also in the case of samples with R6G, see Supporting Information Section XI. The CDA method in its standard form, however, is not valid for an absorbing medium. Therefore, we approximate a nanoparticle in the R6G film as a nanoparticle enveloped by a disk of R6G molecules in PMMA with a diameter of 100 and 50 nm thickness and extract the polarizability of the combination using the multipole expansion.33,34 We then use this polarizability within the CDA. The correspondence of these CDA results with the FDTD simulations and the measurements is excellent, which also confirms the validity of the subtraction procedure used for the measurements and simulations of the R6G samples (see Supporting Information Section XI). In order to estimate the number of molecules involved in the strong-coupling phenomenon, we perform a series of extinction
Figure 6. A silver disk, 60 nm in diameter and 30 nm high, placed on a 2 nm thick titanium adhesion layer, is concentrically enveloped by a PMMA disk doped with R6G molecules at a concentration of 200 mM. The radius of the PMMA disk is equal to the height of the disk, and is stepped from 32 to 50 nm. See the inset for a drawing of the geometry. The extinction cross section of the two concentric disks is calculated with the FDTD method and displayed as solid and dashed curves. Initially, the resonance frequency of the particle splits and shifts relatively rapidly but becomes more or less stationary at larger PMMA disk thicknesses.
main panel displays the results of the calculations. Initially, the extinction maximum shifts with an increase in PMMA disk size relatively quickly, but remains more or less stationary after a certain disk thickness. This indicates that the additional molecules present in the larger disks do not contribute to the strong coupling. E
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter ‡
We subsequently track the location of the extinction maximum as a function of PMMA disk size and fit a single exponential curve to this data. We find that a disk radius of 43 nm corresponds to the 1/e2-value of the peak shift. From the volume of the PMMA disk (not including the volume occupied by the silver particle) and the concentration of R6G molecules in the PMMA, we estimate a number of molecules on the order of 3 × 104 to be involved in the strong coupling per one metallic nanoparticle. In summary, we measure nanoparticle array systems with and without organic molecules and obtain spectra that display bendings and anticrossings typical for the strong coupling regime. We analyze the findings with four complementary approaches of different levels of approximation: FDTD simulations, coupled-dipole approximation, coupled-modes models, and Fano theory. In the case without the emitters, we observe strong coupling behavior and identify it to be connected to a delicate matching of the single nanoparticle polarizability with the geometrical lattice factor. In the case with R6G emitters, we observe strong coupling between the emitters and the various modes of the nanoparticle array, also collective ones. Because the SLR modes are collective, the strong coupling regime observed here implies that emitters near distant nanoparticles are coherently coupled. Strong coupling of an SPP mode with many emitters in general couples distant emitters, for example, on a planar metal surface the molecules within the coherence length of the SPP mode. The present system offers the possibility to design the dispersions and the geometrical arrangement of the molecules that couple strongly, as well as the nanoparticle shapes. It combines long coherence lengths and times with locally high field intensities (small mode volumes). The SLRs can have long lifetimes (high Q-factors) as shown by the sharpness of the peaks, whereas the LSPRs are broad but the high local field enhancement that they provide may be the key to achieving strong coupling with emitters; systems such as we consider here can combine the best features of both to display interesting coherence, quantum, and collective phenomena. This collective-mode plasmonic strongcoupling regime has the potential for the creation of light emission where collective effects are utilized. It is expected to provide interesting phenomena especially if one can place single quantum emitters on the nanoparticles. By tailoring the shape of the nanoparticles, extremely strong field enhancements are possible. Single-emitter strong coupling for such specially shaped nanoparticles has been predicted37,38 and combining that with collective effects in array structures is likely to be a fruitful direction of future research.
■
(D.-H.K.) Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 500− 712, Korea.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the Academy of Finland through its Centres of Excellence Programme (Project Nos. 251748, 263347, 135000, and 141039). Part of the research was performed at the Micronova Nanofabrication Centre, supported by Aalto University.
■
ASSOCIATED CONTENT
S Supporting Information *
Additional experimental data and details of the experimental and theoretical methods. This material is available free of charge via the Internet at http://pubs.acs.org.
■
REFERENCES
(1) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 2003, 424, 824−830. (2) Pockrand, I.; Swalen, J. D.; Santo, R.; Brillante, A.; Philpott, M. R. Optical-properties of organic-dye monolayers by surface-plasmon spectroscopy. J. Chem. Phys. 1978, 69, 4001−4011. (3) Bellessa, J.; Bonnand, C.; Plenet, J. C.; Mugnier, J. Strong coupling between surface plasmons and excitons in an organic semiconductor. Phys. Rev. Lett. 2004, 93, 036404. (4) Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W. Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays. Phys. Rev. B 2005, 71, 035424. (5) Sugawara, Y.; Jelf, T. A.; Baumberg, J. J.; Abdelsalam, M. E.; Bartlett, P. N. Strong coupling between localized plasmons and organic excitons in metal nanovoids. Phys. Rev. Lett. 2006, 97, 266808. (6) Hakala, T. K.; Toppari, J. J.; Kuzyk, A.; Pettersson, M.; Tikkanen, H.; Kunttu, H.; Törmä, P. Vacuum Rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and Rhodamine 6G molecules. Phys. Rev. Lett. 2009, 103, 053602. (7) Gomez, D. E.; Vernon, K. C.; Mulvaney, P.; Davis, T. J. Surface Plasmon Mediated Strong Exciton-Photon Coupling in Semiconductor Nanocrystals. Nano Lett. 2010, 10, 274−278. (8) Vasa, P.; Wang, W.; Pomraenke, R.; Lammers, M.; Maiuri, M.; Manzoni, C.; Cerullo, G.; Lienau, C. Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with j-aggregates. Nat. Photonics 2013, 7, 128−132. (9) Schlather, A. E.; Large, N.; Urban, A. S.; Nordlander, P.; Halas, N. J. Near-Field Mediated Plexcitonic Coupling and Giant Rabi Splitting in Individual Metallic Dimers. Nano Lett. 2013, 13, 3281− 3286. (10) Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W. Reversible switching of ultrastrong light-molecule coupling. Phys. Rev. Lett. 2011, 106, 196405. (11) Houdré, R.; Stanley, R. P.; Ilegems, M. Vacuum-field Rabi splitting in the presence of inhomogeneous broadening: Resolution of a homogeneous linewidth in an inhomogeneously broadened system. Phys. Rev. A 1996, 53, 2711−2715. (12) Agranovich, V. M.; Litinskaia, M.; Lidzey, D. G. Phys. Rev. B 2003, 67, 085311. (13) González-Tudela, A.; Huidobro, P. A.; Martín-Moreno, L.; Tejedor, C.; García-Vidal, F. J. Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons. Phys. Rev. Lett. 2013, 110, 126801. (14) Markel, V. Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure. J. Modern Opt. 1993, 40, 2281−2291. (15) Zou, S.; Janel, N.; Schatz, G. C. Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes. J. Chem. Phys. 2004, 120, 10871−10875. (16) Mühlschlegel, P.; Eisler, H.-J.; Martin, O. J. F.; Hecht, B.; Pohl, D. W. Resonant optical antennas. Science 2005, 308, 1607−1609. (17) de Waele, R.; Koenderink, A. F.; Polman, A. Tunable Nanoscale Localization of Energy on Plasmon Particle Arrays. Nano Lett. 2007, 7, 2004−2008.
AUTHOR INFORMATION
Corresponding Author
*E-mail: paivi.torma@aalto.fi. Phone: +358 50 3826770. Present Addresses †
(R.J.M.) Department of Imaging Physics, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, NL2628 CJ, Delft, The Netherlands. F
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
Nano Letters
Letter
(18) Carron, K. T.; Fluhr, W.; Meier, M.; Wokaun, A.; Lehmann, H. W. Resonances of two-dimensional particle gratings in surfaceenhanced raman scattering. J. Opt. Soc. Am. B 1986, 3, 430−440. (19) García de Abajo, F. J. Colloquium: Light scattering by particle and hole arrays. Rev. Mod. Phys. 2007, 79, 1267. (20) Kravets, V. G.; Schedin, F.; Grigorenko, A. N. Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles. Phys. Rev. Lett. 2008, 101, 087403. (21) Auguié, B.; Barnes, W. L. Collective resonances in gold nanoparticle arrays. Phys. Rev. Lett. 2008, 101, 143902. (22) Chu, Y.; Schonbrun, E.; Yang, T.; Crozier, K. B. Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays. Appl. Phys. Lett. 2008, 93, 181108. (23) Rodriguez, S. R. K.; Abass, A.; Maes, B.; Janssen, O. T. A.; Vecchi, G.; Gómez Rivas, J. Coupling bright and dark plasmonic lattice resonances. Phys. Rev. X 2011, 1, 021019. (24) Adato, R.; Yanik, A. A.; Amsden, J. J.; Kaplan, D. L.; Omenetto, F. G.; Hong, M. K.; Erramilli, S.; Altug, H. Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 19227−19232. (25) Farhang, A.; Ramakrishna, A.; Martin, O. J. F. Compound resonance-induced coupling effects in composite plasmonic metamaterials. Opt. Express 2012, 20, 29447−29456. (26) Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 1961, 124, 1866−1878. (27) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 2010, 9, 707−715. (28) Miroshnichenko, A. E.; Flach, S.; Kivshar, Y. S. Fano resonances in nanoscale structures. Rev. Mod. Phys. 2010, 82, 2257−2298. (29) Giannini, V.; Francescato, Y.; Amrania, H.; Phillips, C. C.; Maier, S. A. Fano Resonances in Nanoscale Plasmonic Systems: A Parameter-Free Modeling Approach. Nano Lett. 2011, 11, 2835−2840. (30) Gallinet, B.; Martin, O. J. F. Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials. Phys. Rev. B 2011, 83, 235427. (31) Lumerical Solutions, Inc., v 7.5, www.lumerical.com, date accessed 1/9/2012. (32) Francescato, Y.; Giannini, V.; Maier, S. A. Plasmonic Systems Unveiled by Fano Resonances. ACS Nano 2012, 6, 1830−1838. (33) Grahn, P.; Shevchenko, A.; Kaivola, M. Electromagnetic multipole theory for optical nanomaterials. New J. Phys. 2012, 14, 093033. (34) Grahn, P.; Shevchenko, A.; Kaivola, M. Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles. Phys. Rev. B 2012, 86, 035419. (35) Teperik, T. V.; Degiron, A. Design strategies to tailor the narrow plasmon-photonic resonances in arrays of metallic nanoparticles. Phys. Rev. B 2012, 86, 245425. (36) Scully, M. O.; Zubairy, S. M. Quantum Optics; Cambridge University Press: New York, 1997. (37) Trügler, A.; Hohenester, U. Strong coupling between a metallic nanoparticle and a single molecule. Phys. Rev. B 2008, 77, 115403. (38) Savasta, S.; Saija, R.; Ridolfo, A.; Di Stefano, O.; Denti, P.; Borghese, F. Nanopolaritons: Vacuum Rabi Splitting with a Single Quantum Dot in the Center of a Dimer Nanoantenna. ACS Nano 2010, 4, 6369−6376.
G
dx.doi.org/10.1021/nl4035219 | Nano Lett. XXXX, XXX, XXX−XXX
