Dynamics of Strongly Coupled Modes between Surface Plasmon

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Dynamics of strongly coupled modes between surface plasmon polaritons and photoactive molecules: the effect of the Stokes shift Svitlana Baieva, Ossi Hakamaa, Gerrit Groenhof, Tero T. Heikkila, and J. Jussi Toppari ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00482 • Publication Date (Web): 16 Dec 2016 Downloaded from http://pubs.acs.org on December 18, 2016

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Dynamics of strongly coupled modes between surface plasmon polaritons and photoactive molecules: the effect of the Stokes shift Svitlana Baieva*, Ossi Hakamaa, Gerrit Groenhof †, Tero T. Heikkilä and J. Jussi Toppari* University of Jyvaskyla, Department of Physics, Nanoscience Center, P.O. Box 35, FI-40014 University of Jyväskylä, Finland †University

of Jyvaskyla, Department of Chemistry, Nanoscience Center, P.O. Box 35, FI-40014 University of Jyväskylä, Finland

KEYWORDS surface plasmon polariton, strong coupling, polarization, Stokes shift, plexciton, dispersion relation.

ABSTRACT We have investigated the dynamics of strongly coupled modes of surface plasmon polaritons (SPP) and fluorescent molecules by analyzing their scattered emission polarization. While the scattered emission of SPP is purely transverse magnetic (TM) polarized, the strong coupling with molecules induces transverse electric (TE) polarized emission via the partial molecular nature of the formed SPP-molecule polariton mode. We observe that the TM/TE ratio

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of the polariton emission follows the contribution of the molecular excited states in this hybrid mode. By using several types of molecules, we observe that in addition to the coupling strength, which determines the contribution of the molecular excited states, also the Stokes shift of the molecule fluorescence influences the polarization of the emission - the larger the shift the lower the TE polarized emission. We argue that due to random orientation of the molecules, the emission of a fully coherent SPP-molecule polariton should be purely TM-polarized, like SPP. However, as a result of the unique micro-environments of the molecules in combination with thermal motion, this symmetry may break for individual excitations, providing a route to TE emission. The experimental results agree qualitatively with this model including the symmetry breaking. Furthermore, the relaxation rate of the polariton correlates with the Stokes shift, so that TE emission can only occur if the Stokes shift is small and consequently the lifetime is long. Our results suggest that taking into account microscopic details of the molecules in SPP-molecule polaritons is important for a thorough understanding of the molecular dynamics of molecules under strong coupling with light modes. Theoretical models that include these details will be essential to systematically exploit strong coupling for plasmonics or even controlling chemical reactions.

Since the pioneering work of Raether et al. [1] surface plasmon polaritons (SPP) have been under intense investigation because of their fascinating properties, such as the highly increased and confined electric field near the metal-dielectric interface [2, 3], which enhances interaction between optically active molecules and SPPs [4]. This enhancement can drive the SPP-molecule coupling into the strong-coupling limit, where new hybrid states between SPPs and molecules, i.e. SPP-molecule polaritons, are formed and the properties of the SPP and the molecule,


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sometimes even the chemical behavior of the latter, are affected [5, 6-8]. Because of the possibilities opened by these findings, the past decade has witnessed an increasing number of studies on strong coupling between molecules and systems supporting SPPs [5]. Already for some time the coupling between surface plasmons and molecules has been studied and utilized in plasmonics. Conversion from light to SPP and back is efficiently mediated via fluorescent molecules [9-12]. Many planar optical elements utilizing metal/fluorescent dye interfaces such as frequency converters [13], filters [14] and waveguides [12], as well as structures with amplification [15], stimulated emission [16, 17] or even lasing [18], are under development. Furthermore, surface plasmon coupled emission is used as an advanced (bio)analytical tool [19-22] together with the very widely utilized surface enhanced Raman spectroscopy [23]. The aforementioned applications all exploit weak coupling between SPPs and molecules. The regime of strong coupling was first achieved by Bellessa et al., who demonstrated strong coupling between SPP and J-aggregates [24]. Since then, strong coupling has been demonstrated for a variety of molecules and plasmonic systems [25-35] (For a review see Ref. 5). In these experiments, strong coupling is manifested by the appearance of an avoided crossing, i.e. Rabi splitting, at the degeneracy point of the SPP dispersion and molecule absorption maximum. The avoided crossing suggests the formation of strongly coupled SPP-molecule polariton states separated by the Rabi split. Rabi splittings with energies up to several hundreds of meV have been demonstrated [5] and the Rabi oscillations were observed also in time resolved measurements [36], providing further evidence for the existence of the new polariton states. Surface plasmons are not the only optical excitations with which to achieve strong lightmatter coupling. The first demonstration was realized already in 1987 with a Rydberg atom in a


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microwave cavity [37]. Later the strong coupling was also achieved with inorganic semiconductors integrated in microcavities [38, 39]. Furthermore, also for fluorescent (dye) molecules and J-aggregates that have been used with SPPs, strong coupling has been achieved in optical cavities [6, 40]. Because the mechanism by which molecules and confined light couple are likely to be similar, if not the same, our investigation into the effects of molecular properties on the dynamics of SPP-molecule polaritons may be generalized to other polaritons as well. What makes polaritons involving organic molecules particularly interesting is that there is substantial experimental evidence for unexpectedly long lifetimes [6], thermalization and even condensation among them [41]. Furthermore, the strong coupling has been shown to modify also photo chemical reactions [7]. Recently, a vast enhancement of the conductivity of an organic semiconductor layer was achieved via hybridization with SPPs [8]. These applications suggest that it may be possible to control chemistry with strong light-matter coupling. Despite recent progress in the theoretical description of molecules interacting with confined light [42-47], the effect of strong light-matter coupling on the dynamics and chemistry of the coupled molecules is still poorly understood [48]. To provide further insight in to the dynamics of molecule-SPP polaritons, we have analyzed the polarization of the emission, which may reveal important properties helping to realize the control of chemistry. Usually SPPs can be excited only with transverse magnetic (TM, p-polarized) light [1]. In an ideal case, the excited SPPs propagate up to hundreds of micrometers [3] before decaying due to losses in the metal induced by free-electron scattering and absorption via intra-band transitions [49]. However, in all experiments roughness of the metal surface causes scattering into freely propagating far-field photons of transverse electric (TE, s-polarized) polarization, in addition to the TM polarization [50-52]. However, the angular distributions of the scattered TE and TM


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polarized light differ significantly from each other [50]: TM polarized emission is mostly perpendicular to the interface while TE polarized emission is directed only onto higher angles almost parallel to the surface of the metal. Perpendicularly scattered TE polarized light is, however, possible in the case of diffraction gratings [53] or if the metal surface is covered with a thick layer of polymer that support also waveguide modes [54]. Both of these cases can be excluded in this study, since we do not use gratings and the polymer layers we use are too thin to support waveguide modes. In addition, it has been shown that the polarization of the scattered light can be altered via molecule-plasmon interaction [55], which is investigated further in this article. In this article we analyze the polarization of scattered emission from strongly coupled polaritons between SPPs and three fluorophores with different Stokes' shifts. Each of these fluorescent molecules is studied separately. We show that scattered emission from pure SPPs is solely TM polarized, when detected perpendicularly to the interface (as expected from Refs. 5052), while the strong coupling with the fluorescent molecules also induces TE polarization via the molecular contribution to the hybrid superposition state. This is a surprising result as it contradicts the earlier experiments showing only TM polarized polariton emission [56]. The measurements in this study clearly indicate that if emission of the SPP-molecule polariton includes TE polarization, it increases with the increasing molecular contribution to the polaritonic state as a function of the wave vector. Further, by comparing the emissions from the three different fluorescent molecules, we observe that in addition to the coupling strength, also the Stokes’ shift of the molecule's fluorescence has a major effect on the polarization of the polariton scattering: we find that the larger the Stokes’ shift, the lower is the TE polarized


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scattered emission, with no TE polarized emission for the molecule with the largest Stokes’ shift [56]. Based on these findings we propose a new hypothesis that suggests that the scattered emission of a fully coherent SPP-molecule polariton is purely TM-polarized, like SPP. TE emission is absent because of the inversion symmetry of the orientations of the molecules in the moleculeSPP polariton with respect to the plasmon propagation direction on the sample surface, causing destructive interference of TE-polarized molecular emission. However, during the polariton lifetime, thermal motions, as well as variations in the local environment of the molecules, can induce fluctuations of the molecular contributions to the polaritonic state, and cause symmetry breaking canceling the destructive interference. We speculate that this symmetry breaking is essential for TE emission to appear. Assuming a situation where the interference of the molecular contributions has totally vanished, we can fit the measured TM/TE ratio of the emission as a function of the wave vector in the case of molecules with negligible Stokes’ shift. However, for the molecules with larger Stokes’ shifts, the agreement between the model and the experiments is worse. We therefore speculate that for these molecules, the molecular relaxation into the excited state minimum (fluorescent energy), leads to a loss of the polaritonic state. For molecules with a large Stokes’ shift, this relaxation process is faster than the thermal breakdown of the symmetry. This suggests that all the emission at the polariton energy originates from the initial fully coherent polaritonic state and is thus solely TM polarized. This work also demonstrates that polarization of the emission could be an efficient tool for studying the properties of polaritons.


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Results and Discussion

Measuring the dispersion relations. We performed attenuated total reflection (ATR) measurements for several samples containing Nile Red (NR), Rhodamine 6G (R6G) or J-aggregates of 5,6-Dichloro-2-[[5,6-dichloro-1-ethyl-3(4-sulfobutyl)-benzimidazol-2-ylidene]-propenyl]-1-ethyl-3-(4-sulfobutyl)-benzimidazolium hydroxide, inner salt (TDBC), embedded in a polymer (photoresist SU-8 or polyvinyl alcohol (PVA)) and deposited on top of a thin silver film. Figure 1 shows the schematics of our samples as well as the experimental setup employing the Kretschmann configuration [1, 24]. Details of the setup and experiments are reported in our earlier work [26, 40], and details of the sample preparation can be found in the Materials and methods section. We measured three NR samples, three R6G samples and five TDBC samples with varying concentrations of molecules characterized by the molecule to polymer mass ratios. Most of the experimental data for NR have already been presented also in our previous study [56] but are repeated here for the clarity of interpretations. Absorption and fluorescence spectra of each sample are shown in Figure S1 in supporting information.

Figure 1. Schematic representation of the experimental setup and the sample structure. α is the excitation as well as the detection angle. Sample consists of 30-50 nm thick layer of polymer, with the molecules embedded, on top of a ~50 nm thick silver film.


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The dispersion relations measured with the detection 1 geometry (reflection, D1, see Fig. 1) are shown in Figure 2. Examples of bare reflectance data are shown in the supplementary information Fig. S2. All the dispersions exhibit one or two avoided crossings, i.e. Rabi splits, at the molecule’s absorption maxima shown by the horizontal lines. This indicates that the strong coupling regime between SPP and the molecules has been achieved. Both NR and R6G have a minor absorption peak at a different energy in addition to the main absorption maximum (see Figures 2 and S1). At low molecule concentrations only the main absorption transition undergoes Rabi splitting but increasing the concentration brings also the minor absorption peak into the strong coupling regime and we can see two separate Rabi splits, as shown in Figure 1a and also for R6G in our earlier work [29, 56].

Figure 2. Measured dispersion relations of samples containing varying concentrations of (a) NR, (b) R6G and (c) TDBC embedded within a polymer layer on top of a ~50 nm thick silver film. In the reference samples no molecules are embedded into the polymer layer. The legends list the sample index and their molecule/polymer mass ratio. Absorption of the molecule/polymer film (without silver) is shown as a black solid line on the vertical axis (arbitrary units). The dashed horizontal lines show the main absorption maximum of the molecules while the dotted lines indicate the absorption shoulder in the cases of NR and R6G. The coordinates have been chosen such that SPPs propagate in the x-direction with a wave vector kx along the metal surface. Since the thickness of the polymer layer increases with molecular concentration due to fabrication issues, the uncoupled SPP-dispersion changes also from the shown reference. For the illustrative purposes the measured data are scaled to match the shown SPP-dispersion. The scaling method is explained in supporting information, where the original plots are shown as well (Figure S3).


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Modeling of the dispersions. To interpret the experimental results, we first use a simplified model of the full coupled oscillator model that would individually include all the molecular excitations within the system and their couplings to SPPs [29-35, 56-59]. In the simplified model all molecules with the same excitation energy are coupled collectively to the SPP band, and thus treated as a single strong oscillator [29-35, 56, 57]. The collective SPP-molecule coupling strengths are then used as fitting parameters. This simplified model yields the same energies for the hybrid polariton modes as the more elaborated model of many interacting molecules [42-44, 58, 59]. In the basis of energy eigenstates of isolated SPP and the relevant (one or two) molecular excitations that can couple to the SPP, the equations can be written in a matrix form as

0 = ,

0

(1)

where and , are the energies of isolated SPP and the molecular excitations, and

are the coupling strength between the molecular excitations and SPP, is the energy of an

eigenstate of the coupled system, and , and are the coefficients of SPP and molecular excitations in the coupled eigenstates, respectively. The coupling strength between SPP and a single molecular excitation can be written in the form [57]: =

!" #

$% ∙ '( + * '(# ,

"

(2)

where + is the SPP dispersion relation, , describes an effective length of the mode

[60], - is the vacuum permittivity, $% is a transition dipole moment of the molecular excitation j,


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'( and '(# are unit vectors in x, z directions, respectively. Here we have chosen the Cartesian coordinates such that the SPP propagates in the x-direction along the interface located in the x,yplane, and the inner product takes into account the molecule’s orientation. For the simplified

model we sum up the coupling strengths of all the molecular excitations with energy . to

obtain the effective total coupling strength . in Equation (1). If we assume a homogeneous

spatial distribution of the molecules with randomly oriented transition dipole moments with the same strength, i.e. /$% / = $. for all j, we can transform the sum into integrals over z and the

angle 0 between $% and '( , and write

. = 1. 2- 2- / / 40 45 , 6

3

(3)

where 7 is the thickness of the polymer layer and 1. is the density of the molecular excitations

with energy . and transition dipole strength $. . In case of a molecule with two different

excitation energies (i = 1,2), like NR or R6G, 1 = 1 = 1, but and can still differ if the

transition dipoles are not identical. In order to fit the model to the measured dispersion relations (Fig. 1) we use the SPPdispersion for a plain silver/polymer sample without molecules ( ) calculated by solving the Fresnel equations, and the absorption maxima of the molecules measured from a reference sample without the silver layer, as the non-coupled states. By varying D (see supporting

information) as well as the coupling parameters $ √1 , $ √1 accounting for different

transition dipole moments as well as for possible different densities if possible (see Eq. (3)), we obtain the best overlap with the experimental data. Note that due to the random orientation of the molecules within the polymer the fitted transition dipoles are effective values averaged over all orientations. This averaging results into a factor 1/3 multiplying the molecular densities. Examples of dispersion relations for samples containing R6G and TDBC together with the fitted


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curves are plotted in Figure 3 (for NR data see ref. [56]). The obtained fitting parameters for the samples can be found in Supporting Information Table S1. The relative weights (, and ) of

the lower branch are plotted in Figure 3 indicating the change of the hybrid state nature from a

pure SPP ( ~1) to the lower molecular excitation ( ~1) as the wave vector, kx, increases. The relative weights for the middle and upper branches can be found in supporting information (Figure S4). We determined the energy gap widths, i.e. Rabi splittings, from the fitted theoretical dispersion curves as the energy difference between the polariton branches at the crossing points of the SPP-

dispersion for the silver/polymer structure with the absorption maxima of the molecule. The R6G sample 1 (Fig. 3a) has the lower energy gap width of 170 meV and the upper gap width of 166 meV, while the NR sample 1 has an energy gap of 70 meV, and TDBC sample 4 of 167 meV (Fig. 3b). The splitting is linearly proportional to the square root of the total absorbance, as shown in Supporting Information Figure S5.

Figure 3. (a) Measured dispersion curve for R6G sample 1 (0.61) in D1 (black circles) and D2 (empty circles) geometry together with the fitted coupled oscillator model (red solid line). Absorption of the reference R6G sample (without silver) is shown as a black solid line on the left axis. Relative coefficients of the lower energy branch calculated from the fitted theoretical dispersions are shown in the lower panel. (b) The same for TDBC sample 3 (0.13).


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Emission measurements: TM/TE polarization ratio The emission measurements were performed in detection geometry 2 (D2, see Fig. 1 and [50]). We collected the emission perpendicular to the sample surface at two different polarizations with respect to the launched SPP (TM or TE polarized emission) while changing the excitation angle. As shown in figure 3, this yielded the same dispersions as D1. Samples containing only silver (50 nm) evaporated on top of the glass as well as those having a 30 nm thick polymer layer deposited on top of the silver film, were first measured as references. In both cases we observed only TM polarized signals as shown in Figures 4a and S6. Addition of NR molecules into the polymer layer induced the Rabi splitting(s) as shown above, but did not change the emission behavior, i.e., polariton modes still had purely TM polarized emission and the only TE emission we detected was from the unpolarized fluorescence of the NR molecules as shown in Fig. 4b. It should be stressed that we always observe the fluorescence of molecules together with the emission of scattered polaritons. The fluorescence spectrum is the same as for the uncoupled molecules and is independent of the excitation angle. However, its

intensity follows the molecular weights ( and ) of the excited SPP-molecule polariton modes as explained in detail in our previous study with NR [56]. This means that the fluorescence at least partially results from the excited SPP-molecule polaritons after the polariton state is lost via molecular relaxation into the minimum on the excited state potential energy surface of a single molecule before emission. The situation is different for samples with R6G molecules or TDBC J-aggregates embedded in the polymer layer. As can be seen in Figures 4c and 4d, both TM and TE polarizations are detected from the polariton modes (i.e. at the polaritonic energies), in particular from the lower one, in contrast to the samples with Nile Red or no molecules. The existence of TE polarized


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emission is more pronounced in the case of TDBC, which has the smallest Stokes’ shift. As in earlier measurements, we also note that the integrated intensities of reflectance dips and scattered peaks do not behave in a similar way [29, 35, 56]. The higher branches seem to lose intensity in D2 compared to the lowest one, which suggests that complex processes occur before polaritons are scattered.

Figure 4. TM polarized (black) and TE polarized (red) detection 2 spectra of (a) silver/SU-8, (b) NR sample 2, (c) R6G sample 1 (TE polarized signal is multiplied by 10) and (d) TDBC sample 3 at different excitation angles. The curves with different excitation angles are shifted vertically for clarity. Dashed line indicates the maximum of the fluorescence peak of the molecules. Note that in NR (b) the TE polarized signal is present only around the fluorescence peak, whereas in R6G (c) and TDBC (d) show it also elsewhere, i.e., at the polariton energies, which vary with angle along the dispersion (see Fig. 1).

To further analyze the polarization of the scattered polariton emission, we determine the ratio between the TM and TE emission signals and plot it in Figure 5, except for the NR in which case the TE signal was always vanishing for polaritons and only appearing at the fluorescence wavelength. We calculated the ratios by integrating the full intensity of the corresponding peak separately for the measured TE and TM polarized spectra, and taking the ratio between those numbers. As expected, for the lower polariton branch the ratio is higher in the region of small wave vectors, where SPP-molecule hybrid state is mostly plasmonic and thus scatters only with TM emission (Figure 3). Similarly, the ratio decreases towards the gap region where the polariton has more molecular state properties thus yielding unpolarized emission (TM/TE ~ 1).


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All the R6G and TDBC samples clearly show this behavior (see Figure 5). One could expect that for the upper branch the behavior would be the same – the growth of the ratio with an increasing wave vector. However, surprisingly the experimental data show the absence of such dependence for the upper branch of R6G samples, and for the TDBC samples the expected behavior was just faintly visible (see Figure 6). The data of the lower polariton branch show an interesting tendency for the molecules: the TE emission is fully absent in the case of NR, with the highest Stokes shift (≥300 meV), while the highest TE emission is detected for TDBC, with practically no Stokes shift, and R6G (Stokes shift of ~90 meV) is in between (see Fig. 5). The amount of TE-polarized emission thus correlates with the Stokes shift, i.e., the larger the Stokes shift, the smaller the TE emission. The Stokes shift is proportional to the energy difference between the Franck-Condon region and the minimum of the electronic excited state potential energy surface. The larger this difference, the higher the steepness of the surface, and the rate at which the molecule reaches the excited state minimum, from where the Stokes-shifted emission, i.e. fluorescence, can occur. This suggests that the higher Stokes shift leads to a faster relaxation of the molecule and thus also to a faster decay of the SPP-molecule polariton into an excited state localized on a single molecule, which is has a lower energy than coupled absorption state. Emission from this localized excited state is thus the same as the molecular fluorescence.

Figure 5. Ratios of TM to TE signal intensities of lower polariton branch of R6G and TDBC samples.


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Possible origin of TM/TE polarization ratio To explain the observed ratio of TM to TE polarization and the trend that this TM/TE ratio increases with the Stokes' shift, we propose a hypothesis that takes into account (i) the heterogeneity of the molecules, including their orientation and local environment, and (ii) the shape of the excited-state potential energy surface of the molecules, which determine their Stokes shift. First, we extend the simplified coupled oscillator model that we used previously to fit the polariton dispersions, to many molecules with different orientations, following both Agranovich and co-workers [59] and González-Tudela et al. [58]. We furthermore use Fermi's golden rule to estimate the ratio between TM and TE emission: ?@ ; ?A ;

=

BCD>?@ /E?A BE

Dynamics of Strongly Coupled Modes between Surface Plasmon

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