1. Introduction

Engineered composite materials and systems, including subwavelength cavities [1], waveguides [2], photonic crystals [3], plasmonic structures [4] and metamaterials [5], have revolutionized the fields of optics and photonics. They have opened the possibility of coupling electronic transitions in atoms and molecules to optical modes supported by plasmonic and photonic resonances, enabling the control and manipulation of light-matter interactions. Such hybridized coupled systems facilitate plethora of physical phenomena including, to name few, spontaneous and stimulated emission [6–9], control of Förster energy transfer [10–12] and Fano resonances [13–15], leading to applications in sensing [16,17], light harvesting [18–21], nanoscale lasing [9,22] and photonic circuitry [23,24]. Use of gain media (e.g. dye molecules or quantum dots) in photonic materials allows one to tackle the well-known problem of loss in metallic components [25] and makes possible a variety of active plasmonic and metamaterials devices and systems [9,26]. Coupling of excitons in gain media with optical and plasmonic resonances enriches the system’s performance and promises new advances in fundamental science and applications, for instance, nanoscale thermometers [19] and biosensors [12].

In many cases of fundamental and practical importance, the coupling between the interacting oscillators, e.g. excitons in dye molecules and surface plasmons (SPs), is weak. It affects the excitation dynamics but not the energy eigenstates of the system. However, when the coupling becomes stronger than all decay processes involved, one enters into the so-called strong coupling regime characterized by the splitting of the dispersion curve and its avoided crossing behavior [27]. Alternatively, the coupling energy can become comparable with the characteristic eigen-energy of the system – the regime known as ultra-strong coupling [28]. Strongly coupled systems open up a host of new applications, beyond the realm of weak coupling, enabling the modification of thermodynamic phenomena [29], vibrational transitions [30], work function [31], charge carrier mobility [32] and exciton transport [33].

Early demonstrations of the strong coupling have been done in the systems consisting of molecules interacting with surface plasmon polaritons (SPPs), where the splitting of the dispersion curve has been observed [34,35]. Subsequent experiments were carried out in the quantum optics regime, where the strong coupling between single atoms and cavities has been demonstrated in e.g [36–38]. More recently, strong coupling has been studied in a host of classical and quantum systems, including semiconductors, quantum dots, ensembles of dye molecules and J-aggregates coupled to cavities [39–41], localized plasmons [42–45], and SPPs [46–51] at both low and high (room) temperatures.

At this time, we report on the strong coupling of macroscopic ensembles of highly concentrated dye molecules with localized surface plasmons in the films of metallic nanoparticles (NPs) and nanoislands. We operate in the so-called classical framework of the strong coupling, involving interactions of plasmons with large ensembles of dye molecules, analogous to two coupled oscillators interacting with each other [27,52]. At the same time, molecules are treated as quantized systems, and the analytical methods and concepts known in quantum mechanics prove to be useful in the analysis of the experimental results.

2. Coupling with SPs supported by films of Ag nanoislands

In a lamellar stack of metallic and dielectric thin films, the effective dielectric permittivity in the direction of the layers can be negative and that in the orthogonal direction – positive. The isofrequency dispersion surface in such (meta)material is a hyperboloid, as opposed to a more conventional spheroid or ellipsoid, giving the name to the class of hyperbolic metamaterials [53–57]. Hyperbolic metamaterials can support propagation of light waves with nominally infinite wavevectors and have a broadband singularity of the photonic density of states (PDOS) [8]. The latter property leads to the phenomenon of a high significance: Light scattered by the metamaterial’s surface, which is intentionally roughened [58] or coated with nanoparticles [59], preferentially propagates into the metamaterial, which has high PDOS, and only small percentage of the light intensity is reflected back to the dielectric medium from which it was incident. The latter effect is prominent in the experiments outlined below.

The purpose of the experiments described in this section was to study the effect of metamaterials with hyperbolic dispersion on the strong coupling between SPs in the films of Ag nanoislands and ensembles of dye molecules. The films of Ag nanoislands were deposited on lamellar metal/dielectric metamaterials and coated with dye-doped polymeric films (Fig. 1(a)). The control samples were similar Ag nanoislands + dye composites deposited on glass – the system studied in detail in [60], Fig. 1(b). The lamellar metamaterials consisted of five Ag (25 nm) layers and five MgF₂ (35 nm) layers deposited by thermal evaporation (“Nano 36” from Kurt J. Lesker) on top of glass slides, as described in e.g [61].). MgF₂ was the top-most layer. The material with such parameters has hyperbolic dispersion at λ>374 nm [62].

 

Fig. 1 Schematics of the Ag nanoislands sample on top of lamellar hyperbolic metamaterial (a) and glass (b). Scanning electron microscope (SEM) image of a typical Ag nanoislands film (c).

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Discontinuous Ag films (conglomerates of Ag nanoislands) were deposited onto glass and hyperbolic metamaterial substrates using the same thermal evaporator, Fig. 1(c). Thin silver films are known to consist of nanoscopic islands, whose sizes, increasing with the increase of the nominal film thickness, are determined by the time and the temperature of the thermal vapor deposition process [60]. In our experiments, the targeted Ag film thicknesses, monitored using a quartz crystal oscillator, ranged between 1 nm and 14 nm. The substrates were not heated.

Further, thin (~30 nm) films of the poly(methyl methacrylate) (PMMA) polymer impregnated with the rhodamine 6G (R6G) laser dye in concentration ~30 g/l (in solid state) were spin coated on top of the Ag island films, as described in [61]. The absorption spectrum of the R6G:PMMA film deposited on glass (recorded using the Lambda 900 spectrophotometer from Perkin Elmer), can be decomposed into two bands with the maxima at λ = 545 nm and λ = 507 nm, corresponding to the peak and the shoulder in the R6G absorption spectrum for Figs. 2(a) and 2(b). Some authors assign the former band to the R6G monomers (M) and the latter band to the R6G dimers (D) [60], while the others associate them with different vibrational states [63]. In the text below, we will refer to these bands as M and D, however, without implying any particular physical origin.

 

Fig. 2 Absorbance spectra of the Ag nanoislands films (deposited on glass) without (a) and with (b) R6G:PMMA film on top. Black trace – absorbance spectrum of the R6G:PMMA film on glass and its decomposition into two bands (dashed lines). With increase of the nominal thickness of silver, Ag nanoislands become larger and the SP resonance shifts to longer wavelengths.

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The extinction spectra of the Ag nanoislands samples deposited on top of transparent glass substrates (measured in the transmission mode) and the reflection spectra of the samples on top of non-transparent reflecting metamaterial substrates, before and after deposition of the R6G:PMMA film (Figs. 2 and 3), were acquired in the same spectrophotometer equipped with an integrating sphere.

 

Fig. 3 Reflectance spectra of the Ag nanoislands films (deposited on metamaterial) without (a) and with (b) R6G:PMMA film on top. Dashed green trace, corresponding to the same sample as solid green traces in figures (a) and (b), depicts typical reflectance spectrum of the lamellar metamaterial substrate before deposition of Ag nanoislands.

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The extinction spectra of silver nanoislands on glass featured a broad band, associated with the surface plasmon resonance in Ag nanoparticles, whose wavelength position depends on the nominal thicknesses of Ag films and corresponding sizes of Ag islands [60], Fig. 2(a). The spectra of the same nanoislands samples with the R6G:PMMA film deposited on top, have up to three narrower peaks and shoulders, Fig. 2(b), which are consistent with Fano resonances expected at strong coupling of broadband SP oscillators and much more narrow molecular absorption transitions [15,44,60,64]. The positions of the multiple absorption peaks in the spectra of hybridized “dye+nanoislands” samples ${\lambda }_{\max }^{SP+R6G}$ are plotted against the SP maxima ${\lambda }_{\max }^{SP}$ in the same Ag nanoislands films but without R6G:PMMA film on top in Fig. 4(a). The resultant plot, which (following [60]) we refer to as the dispersion curve, clearly shows three well separated branches.

 

Fig. 4 (a) Positions of the spectral peaks in the “Ag nanoislands+dye” samples, ${\lambda }_{\max }^{SP+R6G}$_, plotted versus localized surface plasmon resonance maxima in pristine Ag nanoisland films deposited on glass, ${\lambda }_{\max }^{SP}$. Solid lines: fitting with Eq. (2). Dashed horizontal lines correspond to the peak (M) and the shoulder (D) in the R6G absorption spectrum. The dotted line is the function y = x. (b) Same for the dips in the reflectance spectra of the Ag nanoislands sample deposited on the hyperbolic metamaterial substrate.

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Following [58], we assumed that M and D absorption bands are coupled equally to the surface plasmon (SP) oscillation, with Δ being the coupling energy, and described the hybridized “SP+dye” system with the Hamiltonian

Note that Eq. (2) predicts repulsion of the perturbed states (branches of the dispersion curve) under the perturbation (coupling) – the behavior well known in quantum mechanics [65]. Thus, the upper branch is always above the y = x line (the maximal values ${\lambda }_{\max }^{SP+R6G}$ are larger than the values ${\lambda }_{\max }^{SP}$) while the lower branch is always below the y = x line (the minimal values ${\lambda }_{\max }^{SP+R6G}$ are smaller than the values ${\lambda }_{\max }^{SP}$).

In accord with the discussion above, Ag nanoislands scatter incident light and preferentially re-direct it into the volume of hyperbolic metamaterial, where the photonic density of states is high. This results in the reduced sample’s reflectance in the nanoislands’ SP spectral band, where the scattering is strongest. Correspondingly, SP maxima of the pristine nanoislands films on top of hyperbolic metamaterials are seen in the reflectance spectra as minima, Fig. 3(a). Likewise, multiple absorption peaks in the spectra of strongly coupled SPs and excitons in dye molecules result in multiple reflectance dips, Fig. 3(b). For comparison, the reflectance of pristine hyperbolic metamaterial (without Ag nanoislands or dye) is high (≈90%) and nearly flat in the spectral range of interest, Figs. 3(a) and 3(b). (Note that the reflectance in the metamaterial/nanoislands/dye samples, ~1.5%, was much smaller than that of black soot, ~4% [66].)

The positions of the spectral dips in the “Ag nanoislands+dye” composites, ${\lambda }_{\max }^{SP+R6G}$, are plotted against the SP maxima in pristine Ag nanoisland films, ${\lambda }_{\max }^{SP}$, in Fig. 4(b). When this dispersion curve was fitted with Eq. (2), using Δ, E_M, and E_D as fitting parameters, the best agreement between the theory and the experiment was found at E_M = 2.30 eV (corresponding to ${\lambda }_M^{fit}$ = 540 nm) and E_D = 2.43 eV (corresponding to ${\lambda }_D^{fit}$ = 510 nm), close to the experimentally measured ${\lambda }_M^{\exp }$ = 545 nm and ${\lambda }_D^{\exp }$ ₌ 507 nm. At the same time, the coupling energy Δ = 0.221 eV was 34% larger than that on top of the glass substrate, ($\Xi$ = 0.64 eV ≈3Δ). We infer that lamellar metal/dielectric metamaterials can confine and enhance electric fields [67], causing more efficient coupling of dipoles in vicinity of their surface.

(Note that if we will “swap” the coupling energies found on top of glass and on top of the metamaterial and fit the dispersion curve in Fig. 3(a) with fixed Δ = 0.221 eV (like that on top of the metamaterial) and the dispersion curve in Fig. 3(b) with fixed Δ = 0.165 eV (like that on top of glass), using energies E_M and E_D as the fitting parameters, the resultant wavelengths ${\lambda }_M^{fit}$ and ${\lambda }_D^{fit}$ will be strongly (by ~10 nm) different from the experimental ones. This validates the accuracy of the fitting procedure and proves that the determined coupling energies on top of glass and on top of the metamaterial are, indeed, different from each other.)

3. Coupling with SPs supported by films of layer-by-layer (LBL) deposited Au NPs

In the set of experiments described below, we have studied thin films composed of Au nanoparticles deposited onto the glass substrate using the layer-by-layer (LBL) technique [68], Fig. 5(a). The advantage of LBL in comparison with other methods is that it affords deposition of high uniformity, high optical density NP films with tunable plasmonic frequency [69].

 

Fig. 5 (a) Schematics of the LBL Au nanoparticles film. (b) Transmission electron microscope (TEM) image of Au NPs. (c) Photograph of the [(PDDA/PSS)₅ (PU/Au)₃]₅ LBL film.

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Gold nanoparticles (Au NPs) were prepared according to the procedure reported earlier [70]. In brief, HAuCl₄ (180.0 mg, 0.458 mmol) was dissolved in 950 mL ultrapure deionized water. The mixture was heated to boiling under vigorous stirring. Then, 50 ml of 34 mM sodium citrate solution was quickly injected into the boiling HAuCl₄ solution. The mixture was kept boiling until the color turned from transparent to deep red, which indicated the formation of Au NPs. After cooling to the room temperature, the aqueous Au NP dispersions have been obtained. The diameter of the citrate-stabilized gold nanoparticles was ≈11 nm (Fig. 5b). The citrate layer on the surface of the nanoparticles makes Au NPs negatively charged.

The suspensions of Au NPs were further concentrated and used as the dipping solution in preparation of the LBL films. For the concentration process, the as-made aqueous Au NPs dispersions were transferred into centrifuge tubes and concentrated 10 × by centrifuging at 10,000 r.p.m. for 1 h. Finally, the resultant nanoparticles were collected for the LBL deposition.

Glass slides (25 mm × 75 mm) were cleaned in piranha solution (sulphuric acid and hydrogen peroxide, in a 3:1 volume ratio) overnight and then thoroughly rinsed with deionized water prior to the use. For LBL assembly, a glass slide was immersed in 0.5 wt % solution of positively charged poly(diallyldimethylammonium chloride) (PDDA) for 5 min, rinsed with deionized water for 1 min, dried, immersed in 1.0 wt % solution of negativelycharged polystyrene sulfonate (PSS) with negative charges for 5 min, and rinsed with deionized water (for 1 min) again. The procedure was then repeated with PDDA and PSS solutions. After depositing x LBL layers of PDDA/PSS, we immersed the glass slide with the film into 1.0 wt % solution of Polyurethane (PU) for 5 min, then rinsed it with deionized water (for 2 min) and dried. Then the slide was dipped into a dispersion of concentrated Au NPs solution for 10 min, rinsed for 2 min, and dried with air again. This PU/Au sequence has been repeated y times, producing [(PDDA/PSS)_x(PU/Au)_y]₁ single cycle composite. As a rule, the deposition cycle was repeated several (m) times, resulting in the lamellar material designated as [(PDDA/PSS)_x(PU/Au)_y]_m. The LBL samples used in our experiments are summarized in Table 1 below.

Table 1. List of the Au LBL samples studied

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Thick Au LBL films, such as [(PDDA/PSS)₅ (PU/Au)₃]₅ sample in Table 1, had typical dark gold coloration with a tendency toward yellowish luster of bulk gold, Fig. 5(c).

To measure the transmission spectra of the R6G dye films, the glass slides were immersed in the methanol solutions of R6G (5 g/l and 15 g/l) for 10 seconds and then dried in air. The corresponding absorbance spectra, featuring the peak and the shoulder or the two maxima, have been fitted with the sum of two Gaussian bands, as shown in Fig. 6(a). The positions of these bands (denoted as M and D), depended on the dye concentration and ranged within the following limits: 556 nm<${\lambda }_M^{\exp }$<560 nm, 506 nm<${\lambda }_D^{\exp }$<512 nm. We assumed that the corresponding characteristic energies E_M and E_D did not change much when the dye molecules were deposited on Au NPs films.

 

Fig. 6 Sample [(PDDA/PSS)₅ (PU/Au)₃]₅. (a) Reflectance spectra of the pristine (1), single dipped (2) and double dipped (3) sample. Absorbance spectra of the R6G film and its fit with two Gaussian bands (black solid and dashed lines, respectively). The error bar in the bottom shows the accuracy of the reflectance measurement. (b) Transmittance spectra of the pristine (1) and single dipped (2) sample. The red arrow shows the reflectance maximum in Figure a. Inset of Figure a: Reflectance maximum of the pristine [(PDDA/PSS)₅ (PU/Au)₃]_m film as the function of the number of deposition cycles m.

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The reflectance and transmittance spectra of the Au LBL films, recorded in the spectrophotometer setup described above, featured the SP resonance band, whose position in the reflectance spectrum was red shifted relative to that in the transmittance spectrum (see Figs. 6(a) and 6(b). This is the regular ordering of the scattering and absorption cross section bands in the Mie spectra of plasmonic nanospheres. As one can see in Table 1, in the [(PDDA/PSS)₅ (PU Au)₃]_m samples, the plasmon resonance wavelength got blue-shifted (from 650 nm to 628 nm) with increase of the number of cycles m from 1 to 5, inset of Fig. 6(a). This behavior formally corresponds to reduction of the effective dielectric permittivity of the host medium, which is possible in layered metal/dielectric metamaterials [53–56,71], such as [(PDDA/PSS)₅ (PU/Au)₃]_m structures.

When the spectral measurements of pristine Au LBL films were completed, the samples were dipped into the methanol solution of R6G dye (5 g/l) for 10 seconds and dried in air, after which the spectral recordings have been repeated. In the dipped samples, the reflection spectra had three maxima (Fig. 6(a)), resembling those in Fig. 2(b). The minima in the transmission spectra of the same samples were much less pronounced, Fig. 6(b). Therefore, we concentrated on the analysis of the reflection spectra.

When the positions of the reflectance peaks, ${\lambda }_{\max }^{SP+R6G}$, were plotted against those of SP peaks in pristine Au LBL films before dipping, ${\lambda }_{\max }^{SP}$, the dispersion curve featuring the three branches, resembling those in Fig. 4, has emerged (Fig. 7(a)). This suggests that the strong exciton-plasmon coupling does exist in Au LBL films covered with R6G dye. When the dispersion curve was fitted with Eq. (2), using Δ, E_M and E_D as fitting parameters, the best agreement between the theory and the experiment was found at E_M = 2.22 eV (corresponding to ${\lambda }_M^{fit}$ = 560 nm) and E_D = 2.40 eV (corresponding to${\lambda }_D^{fit}$ = 516 nm), which were reasonably close to the spectral ranges evaluated experimentally: 553 nm<${\lambda }_M^{\exp }$<560 nm, 506 nm<${\lambda }_D^{\exp }$<512 nm.

 

Fig. 7 (a) Positions of spectral peaks in single dipped “Au LBL+dye” samples, ${\lambda }_{\max }^{SP+R6G}$, plotted versus localized surface plasmon resonance maxima in pristine Au LBL films, ${\lambda }_{\max }^{SP}$. Solid lines: fitting with Eq. (2). The dotted line is the function y = x. (b) Same as above for double dipped “Au LBL+dye” samples. The solid lines are linear trendlines.

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The determined coupling energy Δ = 0.12 eV was smaller than the one in the Ag nanoislands samples discussed above. However, since the span of the surface plasmon maxima, ${\lambda }_{\max }^{SP}$, in this particular experiment was rather small, the accuracy of the retrieved energy values was relatively low as well.

After the second series of measurements described above was completed, the same Au nanoparticle films were dipped into even more concentrated methanol solution of R6G (15 g/l) and dried in air. The maxima and minima in the new series of reflection spectra became even more pronounced, resembling Fano resonances in ensembles of interacting plasmonic nanoparticles [72], and their spectral positions shifted, Figs. 6(a), 7(a) and 7(b). Correspondingly, the new (high concentration) dispersion curve substantially deviates from the old (lowconcentration) one. The most dramatic difference is observed in the branch corresponding to the long-wavelength reflection peak, which has a negative slope, Fig. 7(b). One of the samples, [(PDDA/PSS)₅ (PU/Au)₃]₁, had four (instead of three) reflection peaks. The corresponding data points, which did not match the dispersion curve, are shown in Fig. 7(b) as open circles. In accord with our earlier comment, we surmise that the changes in the spectra of the double dipped samples were so strong that they could not be accurately described by the perturbation model of Eq. (2).

We also would like to note that the reflectance of the double dipped samples was equal to zero (within the experimental accuracy) at λ~470 nm. This suggests that at this wavelength the effective index of refraction crossed the point n~1 and moved toward the epsilon near zero (ENZ) regime at shorter wavelengths. Correspondingly, “Au LBL+dye” composite can potentially be used as a simple platform for realization of the ENZ regime desirable for many applications [73].

4. Summary

We have studied two classes of composite materials combining plasmonic nanoparticles and highly concentrated R6G dye. The first group of samples consisted of the films of Ag nanoislands, deposited on glass or lamellar metamaterials with hyperbolic dispersion, coated by the dye-doped polymer. The second group was composed of LBL deposited films of Au NPs dipped in highly concentrated dye solution and dried in air. All pristine metallic NPs films studied, featured the spectral maximum (or minimum) corresponding to the localized surface plasmon (SP) resonance. The spectra of the same films coated by the dye molecules had three maxima (minima) or shoulders (resembling Fano resonances routinely reported in ensembles of plasmonic NPs [14,15,72]), originating from the strong coupling of the surface plasmons and two bands composing the absorption spectrum of the R6G dye.

The positions of the spectral maxima (minima) in the dye-doped films, ${\lambda }_{\max }^{SP+R6G}$, plotted against those in pristine films, ${\lambda }_{\max }^{SP}$, resulted in the dispersion curve with three branches, qualitatively similar to those in [60]. The latter dispersion curve was described by the analytical model based on the Hamiltonian matrix accounting for the unperturbed energies of SP and two absorption bands as well as the coupling energy of the SP band with the dye absorption bands.

Fitting of the experimental dispersion curves measured in the Ag nanoislands samples deposited on glass with the model described above, resulted in a good agreement of the experimental and calculated wavelength positions of the dye absorption bands. The determined coupling constant, Δ = 0.165 eV, was in a good agreement with that in [60]. The coupling energy measured on top of the hyperbolic metamaterial [57], Δ = 0.221 eV, was ~34% larger than that on top of glass. We infer that lamellar metal/dielectric metamaterials can confine and enhance electric fields [67], causing more efficient coupling of dipoles in vicinity of their surface.

The dispersion curves in the Au LBL films, which were dipped in the R6G dye solution one time, were fitted with the same Hamiltonian operator equation, yielding reasonable agreement between the calculated and the experimental spectral positions of the dye absorption bands. The determined coupling constant was slightly smaller than that in Ag nanoislands films. However, the accuracy of the retrieval procedure could be somewhat lower because the spread of SP wavelengths in pristine Au LBL films was smaller than that in Ag nanoislands films. In the same Au LBL films, which were dipped in the highly concentrated dye solution in the second time, the Fano-like spectral features became more pronounced and the dispersion curve changed significantly. In particular, the upper branch got an unusual negative slope and the dispersion curve could not be described any longer with the analytical model successfully used above. We surmise that the changes in the spectra of the double dipped samples were so strong that they could not be accurately described by the perturbation model of Eq. (2).

We, finally, remark that the band positions in the reflectance spectra are somewhat different from those in the absorbance spectra. (In hyperbolic material, this happens due to spectral dispersion of the photonic density of states [74,75].) Correspondingly, the value of the coupling constant retrieved from the fitting of the reflectance spectra can be slightly different from that obtained from the fitting of the absorbance spectra. Therefore, the conclusion regarding the effect of the hyperbolic metamaterial substrate on the coupling energy should be made with some degree of caution. The studies of the effect of the photonic density of states and non-local dielectric environments on the strong exciton-plasmon coupling will be continued and their results will be published elsewhere.