Plasmon-exciton strong coupling in an organic material

Abstract

We report on strong coupling between surface plasmons and excitons in an optically nonmetallic excitonic dye-polymer material of different thicknesses. We carried experiments of angular scans of reflectivity from silver and dye-polymer layers in a Kretshmann-Raether configuration, and we obtained the dispersive dielectric constant of the dye solutions for different dye concentrations using Lorentz model. The data obtained from our experiments, i.e. from reflectometry and absorption and dielectric dispersion, was used to perform rigorous electromagnetic calculations and finite difference time domaine numerical simulations of reflectivity and electric field distribution at the layers. Reflectometry calculations yielded dispersion relations of hybrid modes of propagating surface plasmons and excitons. The latter exhibit anticrossing which is the signature of strong coupling. The energy of Rabi splitting, $\:{E}_{Rabi}$, is sample dependent, and is in the $\:173-215\:meV$ range, consistent with previously published experimental values of $\:{E}_{Rabi}$ of the dye-polymer studied. The theoretical calculations and simulations support the experimental findings and demonstrate enhancement and subwavelength confinement of the optical field in the bulk of the dye-polymer film as well as at its surface. Strong coupling between surface plasmons and excitons is due to the field localization and enhancement as well as the sharp transition in the absorption spectrum of the excitonic material.

Strong coupling between excitons and photons has been the subject of intensive studies, during the past decades, using microcavity modes and surface plasmon polaritons (SPPs)^1,2,3,4,5,6. By analogy with strong coupling of atomic states with cavity photon modes, strong coupling was first demonstrated in solid state physics in a semiconductor quantum cavity, i.e. GaAs quantum wells in a Fabry-Pérot microcavity by Weisbuch et al.⁷. In such cavities, strong coupling generates cavity polaritons which are characterized by a duet of dispersion curves which have a minimum of separation equal to the energy of Rabi splitting. The latter was in the order of 5–10 meV for Wannier-Mott excitons in inorganic semiconductors^1,3,4, and 100 meV large for organic semiconductors, i.e.; J-aggregates of dye molecules which support Frenkel excitons^5,8,9.

Organic semiconductors, i.e. organic materials which can hold excitons (electron-hole pairs), have received considerable attention in the past few years because they support strong and sharp excitonic transitions, i.e. large oscillator strength, which allows for operation at ambient temperature, and ease of fabrications of structures and integration in nanophotonic devices^{10,11,12,13,14}. Such materials are studied for light-matter coupling and creation of hybrid states seen by anti-crossing between organic excitons and optical resonances. The first demonstration of exciton-photon hybrid states in organic semiconductors was reported using reflectometry experiments on a porphyrin dye introduced as a guest into a polystyrene matrix in a microcavity by Lidzey et al.⁸, and strong coupling was demonstrated using J-aggregates of Cyanine dyes also in a microcavity a year later⁹. Strong coupling was reported between propagating surface plasmons and organic excitons of J-aggregates of Cyanine dyes in a polymer few year later by Bellessa et al.¹⁵; and we studied exciton-photon coupling in metal-insulator-metal (MIM) microcavities, using J-aggregates of Cyanine dyes¹⁶, and anticrossing of surface plasmon polaritons supported by MIM structures^17,18. Strong coupling and giant Rabi splitting was reported for localized surface plasmons at metallic nanogrooves and propagating surface plasmons¹⁹, and for bowtie plasmonic cavities filled with semiconductor quantum dots^20,21, and large Rabi splitting is observed in wide-band gap semiconductor cavities²². Recent reviews summarizing the field can be found in^23,24. While strong coupling between different photonic and material systems is described in detail in for example²³, any given photonic structure having a sufficiently sharp resonance can be used for strong coupling studies and applications, and for molecular materials having large transition dipole moments, strong coupling is readily observed, especially for small photonic mode-volume. Harnessing plasmonics for strong coupling offers the possibility of controlling light fields down to the nanoscale trough confinement and light field enhancement. We emphasize strong coupling using propagating surface plasmons because of the ease of structure preparation compared to demanding nanofabrication techniques required for the fabrication of plasmonic nanostructures, and the open structure of surface plasmons, versus cavities for example, allows for additional material functionality and characterization. For the material system, we choose an organic semiconductor, also for its ease of preparation and room temperature processing and for its strong and sharp excitonic transition.

In this paper, we focus on strong coupling between propagating surface plasmons and excitons in an optically nonmetallic J-aggregate of cyanine dye doped polymer using finite difference time domaine (FDTD) calculations. Strong coupling and Rabi splitting was reported for J-aggregates of cyanine dye in a large literature, albeit, without specifically addressing the metallic versus nonmetallic character of the material^15,25. In addition, studies and excitation of surface exciton polaritons were realized using optically metallic excitonic materials^26,27. We also present a detailed characterization of the excitonic material studied by absorption and surface plasmon expriments. In addition, we present an in-depth study of the electric field distribution at the plasmonic structures studied confirming the necessity of optical field confinement for the observation of strong coupling and Rabi splitting. We believe that the overall study is important to the polaritons community and to surface excitons and plasmons researchers.

To proceed, we comment on the choice of the material. Excitonic materials may exhibit negative permittivity for a spectral range near a strong narrow absorption; i.e. the excitonic layer appears as a metal from the optics point of view where the real part of its complex permittivity, $\:Re\left(\epsilon\:\right)$, is negative in a small energy range above the exciton resonance; a feature which allows for the excitation of exciton surface polaritons (ESP) at the excitonic material-air interface^28,29. ESPs have been observed in metallic J-aggregate of cyanine dye doped polymer^26,27, and few studies concerned properties and applications of positive $\:Re\left(\epsilon\:\right)$ of such materials. In this paper, we are interested in the nonmetallic character of our excitonic material, where $\:Re\left(\epsilon\:\right)$, is positive on the entire energy range of interest, to study coupling of exciton and plasmon polaritons when such a material overlays a metal surface. We perform experiments of angular scan of reflectivity on our excitonic material deposited on silver films, and we use rigorous electromagnetic (EM) and FDTD calculations of wavelength scans of Kretshman-Raether attenuated total reflection (KR-ATR) spectra for different incidence angles of light to discuss exciton-plasmon coupling. The excitonic material we used is the J-aggregate TDBC (5,6 - dichloro − 2 - [ [5,6 – dichloro − 1-ethyl – 3 - (4 - sulfobutyl)–benzimidazole-2-ylidene] propenyl] -1- ethyl- 3 - (4-sulfobutyl) – benzimidazolium - hydroxide, sodium salt, inner salt) molecule dissolved in polyvinyl alcohol (PVA) as a polymer host-matrix, referred hereto by TDBC-PVA. An advantageous aspect of employing this J-aggregate cyanine dye is its straightforward device preparation process, and in particular, the ease of layer deposition on substrates from aqueous solutions with different dye concentrations. The dye concentration plays a key role in the metallic versus nonmetallic optical appearance of TDBC J-aggregates. Large concentrations of TDBC lead to negative $\:Re\left(\epsilon\:\right)$ over a small energy range, and low concentrations lead to positive $\:Re\left(\epsilon\:\right)$ over the entire visible energy range^26,27.

The first part of the paper describes samples preparation and the experimental setup and material characterization, i.e. measurement of excitonic absorption and extraction of $\:Re\left(\epsilon\:\right)$ and $\:Im\left(\epsilon\:\right)$ of TDBC-PVA using Lorentz model^30,31. The second part is devoted to rigourous EM calculations and FDTD numerical simulations of reflectometry experiments and electric field enhancement at the film samples. The third part is devoted to reflectivity measurements and Fresnel theoretical fits to extract complex permittivities of the different layers of the structrures studied. The experimental results are discussed with the help of theoretical calculations of ATR spectra, electromagnetic field intensities, and dispersion curves.

Sample preparation is described in the supplemental material. The UV-vis absorption spectra, measured by using a spectrophotometer (Perkin Elmer-Lamda 1050), of the TDBC-PVA thin films, spun from aqueous solutions, as a monomer for the $\:1\times\:{10}^{-5}$ $\:M$ concentration, and for the three other concentrations, are shown in Fig. 1. The absorption spectra of TDBC molecules exhibit a sharp resonance for solutions exceeding $\:5\times\:{10}^{-5}\:M$ concentration due the formation of linear chains and J-aggregates of TDBC³². The monomer sample exhibits a resonance at 530 nm (2.34 eV), and the other, i.e. more concentrated samples have an absorption resonance centered at $\:2.104\:eV$ corresponding to a wavelength of $\:589\:nm$, and $\:67-92\:meV$ full width at half maximum (FWHM). The red-shifted and narrower absorption line at 589 nm, i.e. by the J-aggregate, is caused by the delocalization of excitation owing to interaction of the long one-dimensional chains of TDBC molecules, i.e. excitation of Frenkel excitons on the chains³².

Fig. 1

(a) Absorption spectra of PVA, undoped (0), and doped with TDBC dye in monomer phase (1) and J-aggregate phases (2–4), and its dependence on the TDBC concentration. 1, 2, 3 and 4 correspond, in weight% (wt%), to 0.006, 0.15, 0.3, and 0.8% w/w; respectively. Absorption increases with the increased concentration. The structure of TDBC is shown as an inset to the left figure. (b) Normalized spectra of the monomer and J-aggregate phases. (c) Complex dielectric constant, i.e. real and imaginary parts, i.e. $\:{\epsilon\:}^{{\prime\:}}\left(\omega\:\right)$ and $\:{\epsilon\:}^{{\prime\:}{\prime\:}}\left(\omega\:\right)$, of TDBC-PVA samples having three different concentrations. Subscripts 1, 2, 3 in this figure correspond to subscripts 2, 3, 4 of Fig. (a), i.e. they correspond to the 3 different solutions of J-aggregate TDBC. The samples thicknesses are indicated as an inset to the figure.

In order to discuss the experimental results, the dispersive values of $\:\epsilon\:\left(\omega\:\right)$ are needed. A material relative permittivity involving multiple resonances $\:i$ can be described by the Lorentz model, with a resonance energy $\:{e}_{i}$, and a corresponding oscillator strength $\:{f}_{i}$ and a damping rate $\:{\gamma\:}_{i}$, and when one resonance dominates, $\:i=0$, which is often the case, the energy dependent form of the dielectric constant $\:\epsilon\:\left(e\right)$ can be expressed as follows^30,31

$$\:\epsilon\:\left(e\right)={\epsilon\:}_{b}-\frac{{f}_{0}{e}_{0}^{2}}{{e}^{2}-{e}_{0}^{2}+ie{\gamma\:}_{0}}$$

$\:{\epsilon\:}_{b}$ is the background dielectric constant which takes into account nonresonant transitions far from resonance. The permittivity of TDBC-PVA can be described by the above function where $\:{f}_{0}$ plays a major role in the description of the metal-like optical character of the excitonic material. When $\:{f}_{0}$ is large $\:Re\left(\epsilon\:\right)$ becomes negative, over a given, albeit, small spectral range, and the material becomes optically metallic. For $\:{f}_{0}=0.1$, or smaller, TDBC-PVA is nonmetallic. Lorentz model fits to our experimental data, i.e. Absorbance $\:\propto\:$ $\:Im\left(\epsilon\:\right)$, yield $\:{e}_{0}=2.1\:eV$, $\:0.068<{\gamma\:}_{0}<0.09$, and $\:0.04<{f}_{0}<0.08$. $\:{\gamma\:}_{0}$ and $\:{f}_{0}$ depend on the concentration of the TDBC solutions, and increase with the increased concentration of TDBC. We took $\:{\epsilon\:}_{b}=2.31$²⁷, and we calculated $\:Re\left(\epsilon\:\right)$ for the three solutions which we prepared (Fig. 1(c)). We study TDBC-PVA, and when pure TDBC is considered, $\:{\epsilon\:}_{b}=0$ is used²⁶. The data we found are realistic and are comparable to those of the published litterature²⁶, and positive $\:Re\left(\epsilon\:\right)$ over the visible spectrum range confirms that our TDBC-PVA is nonmetallic. Metallic TDBC-PVA is obtained for higher concentrations of TDBC. For example Gentile et al.²⁷ used a $\:2.6\times\:{10}^{-2}M$ solution of TDBC and $\:\sim\:0.97\:\text{\%}\:w/w$ TDBC-PVA to prepare metallic films of TDBC-PVA.

Next, we discuss reflectivity scans measured for the $\:0.15\:\%\:w/w$ TDBC-PVA films, having different thicknesses, prepared by $\:2.13\times\:{10}^{-3}M\:$solution of TDBC. All the experiments discussed in the following sections correspond this concentration. For the KR-ATR configuration, we used a custom made optical set up which is described in detail in our previous papers^17,33,34 and briefly in the supplemental material.

We performed ATR-scans measurements using 3 types of samples. 1: glass/Ag/air; 2: glass/PVA-TDBC/air; and 3: glass/Ag/PVA-TDBC/air. In a first series of experiments, we recorded SPPs at thin Ag layers with $\:48;54;57;60\:nm$ thicknesses (samples 0); then these layers were coated by films of TDBC-PVA having the same dye loading of the polymer, i.e. $\:0.15\:\%\:w/w$, and different thicknesses, i.e. $\:35\:\sim\:48\:nm$ (samples 1 to 3). Reflectivity scans are shown in Fig. 2. The incident laser light with a wave vector $\:k$ couples to a SP when the projection of $\:k$ on the plane of the Ag film, in the direction of propagation of the SP, matches the wavevector $\:{k}_{x}$ of SP at the Ag/PVA-TDBC interface, and a dip, i.e. resonance, is observed in the reflectivity, corresponding to SP coupling. The SP resonance is shifted to larger resonance angles for thicker TDBC-PVA films. ATR dip shifts to higher angles and broadens as the thickness of the overlayer increases. For the fixed wavelength of 632.8 nm, the TDBC-PVA acts as a dielectric layer with real and imaginary parts given in Table 1; and a dielectric overlayer shifts the dispersion relation of surface plasmons to higher coupling, i.e. larger resonance angle and momentum³⁴. Fresnel fits to experimental data yielded the values of $\:{\epsilon\:}^{{\prime\:}}$ and $\:{\epsilon\:}^{"}$ at 632.8 nm, for all films, which show good agreement with the literature, (Table 1), as well as the data of Fig. 1(c): for $\:{\epsilon\:}_{1}$, $\:{\epsilon\:}_{632.8\:nm}^{{\prime\:}}=2.6$; and $\:{\epsilon\:}_{632.8\:nm}^{{\prime\:}{\prime\:}}=0.04$. The values of $\:{\epsilon\:}^{{\prime\:}}$ and $\:{\epsilon\:}^{{\prime\:}{\prime\:}}$ in Table 1 are dictated by the quality of the Fresnel fit. The fit for the first mode is excellent (mode 1 in Fig. 2) with real and imaginary parts nearly equal to those obtained by Lorentz model. The real part $\:{\epsilon\:}^{{\prime\:}}$ is the same for all three samples, and the imaginary parts are slightly off the 0.04 value of the Lorentz model.

Fig. 2

(a) Angular reflectivity scans of a bare 48 nm thin Ag layer (left), and Ag layers covered with TDBC-PVA films having same concentration and different thicknesses (right). Scatters are experimental data, and full lines are Fresnel reflectivity theoretical fits. The inset shows the images of the samples 0 to 3. FDTD calculations of Electric field distribution of bare Ag, thickness: 48 nm (b), and samples 0 to 3 (c to e; respectively). The color scale indicates the amplitude of electric field normalized by the amplitude of the incident electric field. The red spots on Fig. (a) indicate the incidence angles which correspond to reflectivity minima and maximum EFE. Note a strong EFE at the Ag/air interface and an appreciable one at the TDBC-PVA/air interface, i.e. in the bulk of the TDBC-PVA film and at its surface. For all samples, some light is localized in the TDBC-PVA layer and the rest is evanescent in air, and a strong light localization is observed at the TDBC-PVA film, and it becomes broader with the observed broadening of the mode corresponding to an increased thickness of TDBC-PVA layer (Fig. (a)).

Table 1 Complex dielectric constants, i.e. Real and imaginary parts $\:{\epsilon\:}^{{\prime\:}}$ and $\:{\epsilon\:}^{{\prime\:}{\prime\:}}$, of PVA-TDBC samples having the same concentration and different thicknesses. $\:{\epsilon\:}^{{\prime\:}}$ and $\:{\epsilon\:}^{{\prime\:}{\prime\:}}$ of ag are close to those of Ref³⁵. Other works refer to data from the literature at $\:\lambda\:=632.8\:nm$ for TDBC-PVA on glass substrates^26,36.

Samples 2, i.e. glass/PVA-TDBC, exhibit featureless reflectivities at the analysis wavelength, i.e. 632.8 nm (Figure S1). Featureless modes are observed for metallic TDBC-PVA as well when the analysis wavelength is outside the range of negative $\:Re\left(\epsilon\:\right)$^26,27. We calculated $\:R\left(\theta\:\right)$, using Fresnel formula and the data of our samples at four different wavelengths ($\:\lambda\:=582;\:590;600;632.8\:nm$) corresponding to different regions of the energy spectrum (Figure S2). In particular, at $\:590\:nm$, which corresponds to maximum absorption, with $\:\epsilon\:\left(590\right)=2+0.45\:i$, $\:R\left(\theta\:\right)$ exhibits a minimum value even though $\:Re\left(\epsilon\:\right)$ is positive. That is to say that shallow reflectivity is not a proof of ESP mode excitation. Besides, there is negligible electric field enhancement (EFE) when TDBC-PVA is deposited on glass (Figure S1). Indeed, electric field (EF) distribution calculations using Fresnel reflectivity show that while there is an appreciable enhancement of the optical field when TDBC-PVA is deposited as an outerlayer on silver (Figure S3), there is a negligible change in the EFE at the prism’s interface when TDBC-PVA is added as an overlayer directly on the prism (inset to Fig. S1(a) and FDTD (Fig. S1(b and c)). There is no enhancement and no confinement caused by TDBC at these structures confirming the optically nonmetallic behavior of our TDBC-PVA layers. Optically metallic TDBC-PVA support light enhancement and confinement (Figure S1).

Fig. 3

Reflectivity spectra for samples 1–3 (Table 1), calculated by FDTD, plotted versus the energy of the incident light. The spectra are arbitrarily shifted for clarity and the incidence angles are indicated. The spectra from figures (a) to (c) correspond to those of samples 1 to 3; respectively. The dashed vertical lines correspond 632.8 nm (1.95 eV) (red) and TDBC absorption maximum 590 nm (2.1 eV) (black).

Fig. 4

Energies of reflectivity minima versus the wavevector for samples 1 to 3 (a to c; respectively). The dashed lines correspond to the TDBC absorption maximum 590 nm (2.1 eV) and the red light (632.8 nm) energy (1.96 eV). The full lines are calculated polaritons energies. The thickness of Ag and TDBC-PVA layers is indicated on each figure.

To study the interaction between TDBC excitons and SPPs, we performed FDTD calculations, explained in the supplemental material, of light reflectivity as a function of the incidence angle $\:\left(\theta\:\right)$, in the 1.7–2.76 eV energy range, for the samples which we studied experimentally, i.e. samples 1, 2, 3 of Fig. 2; Table 1. For the calculations, we used our experimental data (Fig. 1(c), and Table 1) and data from Palik for silver³⁷. The incidence angles ranged from 43° to 63°, with a step of 1°, i.e. we calculated 22 spectra for each sample. For all three samples, two dips occur for each spectrum, i.e. for each incidence angle (Fig. 3). These dips correspond to the upper and lower polariton branches due to strong coupling of surface plasmons and excitons (Fig. 4). In the case of weak coupling, observed for glass/TDBC-PVA/Ag/air structure, i.e. an inverted structure, the dips correspond to uncoupled surface plasmon and exciton resonances (Fig. 5). The position of the dips depend on the incidence angle, and they present a minimum separation of 173 meV for $\:\theta\:=55^\circ\:$, and 210 meV for $\:\theta\:=58^\circ\:$ and 215 meV for $\:\theta\:=59^\circ\:$ for samples 1, 2 and 3; respectively. In Fig. 4, we plotted the energies of the dips versus the in-plane wavevector $\:k=\left(2\pi\:/\lambda\:\right){n}_{p}\text{s}\text{i}\text{n}\left(\theta\:\right)$, where $\:{n}_{p}$ is the prism’s refractive index. The bulk plasmon energy of silver is 3.76 meV, and it is much smaller than the energies studied. The SPP energy can be tuned, by tuning $\:\theta\:$, to cross the TDBC exciton energy. A clear anti-crossing behavior is observed, which is indicative of strong coupling between the surface plasmon mode and the TDBC excitons.

The dispersion relations which we obtained are presented by open circles, and we observe a large splitting, i.e. Rabi splitting, between the upper and the lower branches (Fig. 4). The splitting depends on the thickness of the excitonic material. $\:{E}_{Rabi}$ increases with the increased thickness, d, of the insulator ($\:173\:meV$ for $\:d=35\:nm$; $\:210\:meV$ for $\:d=46\:nm$; and $\:215\:meV$ for $\:d=48\:nm$). The energy of Rabi splitting is determined by adjusting to experimental results the following theoretical expression of $\:{E}_{\pm\:}\left(k\right)$ which represents coupled-mode dispersion³⁸; a feature which we did for our results.

$$\:{E}_{\pm\:}\left(k\right)=\frac{{E}_{p}\left(k\right)+{E}_{ex}}{2}\pm\:\frac{1}{2}\sqrt{{E}_{Rabi}^{2}+{\left[{E}_{p}\left(k\right)-{E}_{ex}\right]}^{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)$$

$\:{E}_{\pm\:}\left(k\right)$ are adapted from the well-known solutions of the dispersion relation for microcavity polaritons, i.e. upper and lower polariton branches, by replacing the dispersion relation of the cavity modes by the dispersion relation of surface plasmons^15,38. $\:{E}_{p}\left(k\right)$ the uncoupled plasmon dispersion, and $\:{E}_{ex}$ is the energy of the excitonic transition, independent of $\:k$, taken to be 2.1 eV from the absorption maximum of J-aggregate TDBC. In our fitting, $\:{E}_{Rabi}$ is the only free fitting parameter. $\:{E}_{Rabi}$ is obtained for each sample, using $\:{E}_{p}\left(k\right)$, with $\:k$ near $\:0.013\:{nm}^{-1}$and differing slightly from this value, for each sample studied. The polaritons branches which we obtained by this procedure are shown in full lines in Fig. 4, and they fit quite well our results, with a little deviation in the small wavevector regime owing to precisions in the fitting procedure of the measured $\:{E}_{Rabi}$, i.e. the best fit is shown as full lines in the figure (Table 2). The values of Rabi splitting which we obtained for our samples are close to the values measured experimentally by, for example, Bellessa et al. who reported $\:{E}_{Rabi}=180\:meV$for a 44 nm TDBC-PVA on top of a 50 nm Ag film¹⁵. The thicknesses of Ag and TDBC-PVA were slightly varied in our experiments; i.e. 54–60 nm for Ag, and 35–48 nm for TDBC-PVA, and are close to those of Bellessa et al.. We found that $\:{E}_{Rabi}$ increases (173 to 215 meV) for the increased thickness of TDBC-PVA (35 to 48 nm).

Table 2 Fitting values of E_Rabi according to eq. 1.

$\:{E}_{Rabi}$ is influenced by the thickness of Ag, $\:{d}_{Ag}$, and increases with the increased $\:{d}_{Ag}$ due to silver thickness dependent plasmon damping³⁹. In our experiments, we decreased $\:{d}_{Ag}$ when the thickness of the excitonic material increased, to overrule the effect $\:{d}_{Ag}$ on the observed increase of $\:{E}_{Rabi}$. Excitonic damping is a possible explanation for the increased Rabi splitting. The photonic mode broadens owing to losses which increase with the increased thickness of the excitonic material as can be clearly seen from both the experimental results and FDTD simulations (Fig. 1). One reason for the occurrence of strong coupling is sharp absorption, i.e. width of the excitonic transition of the J-aggregates of TDBC $\:\left(67\:meV\right)$ smaller than Rabi splitting $\:\left(173\:meV\right)$, and large oscillator strength which is proportional to Rabi splitting squared. Another reason for strong coupling occurrence is the photon confinement at the excitonic structures caused by small field penetration in the air and high angular confinement; see e.g. Figure 2. Indeed, Fig. 2(c) to (e) show that EFE occurs inside the TDBC-PVA overlayer as well as at the interface of the later with air. The TDBC molecules get exposed to field enhancement not only in the bulk of the film but at its surface as well. In an inverted structure, i.e. glass/TDBC-PVA/Ag/air, where the TDBC molecules are exposed to the incident laser light only through refraction at the glass/polymer interface or reflection at the polymer/metal interface, weak coupling occurs because the surface plasmon mode is confined only at the Ag/air interface, i.e. TDBC molecules are not exposed to confined light (Fig. 5). In other words, strong light confinement is necessary for the observation of strong coupling.

Fig. 5

(a) Reflectivity spectra for the glass/TDBC-PVA (35 nm)/Ag (60 nm/Air structure (shown as an inset to figure (b)), inverted with respect to that of Fig. 2 with the same thicknesses of the Ag and TDBC-PVA layers as those of sample 1, calculated by FDTD, plotted versus the energy of the incident light. The spectra are arbitrarily shifted for clarity and the incidence angles are indicated. A sharp and broad dip occur for each incidence angle. The sharp dip, which corresponds to the SPR mode, see e.g. the spectrum at $\:\theta\:=42^\circ\:$ corresponding to excitation at 1.95 eV (632.8 nm) and angular reflectivity scan (b), spans through the broad one, which remains at the same energy position, i.e. 2.1 eV corresponding to the excitonic transition of TDBC, when the angle is changed, and moves to larger angles for larger energies. (c) Energies of reflectivity minima versus the wavevector for this structure. Open and full circle scatters correspond to the energies of the exciton and plasmon resonances, respectively; and the dashed horizontal lines correspond to the energies of the 632.8 nm (1.95 eV) excitation laser (red) and TDBC absorption maximum 590 nm (2.1 eV) (black). FDTD calculations of (b) the angular reflectivity scan and (d) the electric field distribution at the structure for 632.8 nm light excitation. The color scale indicates the amplitude of electric field normalized by the amplitude of the incident electric field.

In summary, we studied strong coupling between surface plasmons and excitons in nonmetallic TDBC-PVA of varying thickness using theoretical calculations of reflectometry, by rigourous FDTD numerical simulations and electromagnetic theory. We also did experiments of angular scans of reflectivity, using prism coupling of light to the interacting metal and excitonic materials, and we measured absorption and applied the model of Lorentz for the dielectric constant. We observed anti-crossing of the polariton modes due to strong coupling owing to high light confinement at the excitonic material and large and sharp excitonic absorption. We found values of Rabi splitting at room temperature which is sample dependent ($\:173-215\:meV$) and which increases with the increased thickness of the excitonic material. Future works could focus on the effect of the metallic versus nonmetallic optical character of TDBC-PVA on strong coupling of excitons with surface plasmons or surface exciton polaritons or cavity photonic modes or other highly confined photonic modes.