1. Introduction

Organic dyes are widely used in biomedical imaging [1], biological and chemical sensing [2], and organic photovoltaics [3]. They also play an essential role in many proof-of-principle demonstrations in nanophotonics, plasmonics and metamaterials. In particular, they have been shown to compensate loss in plasmonic nanostructures [4–7], enable the smallest in the world spaser and nanolaser [8–11], and strongly couple with surface plasmons and resonant cavities, leading to the normal mode (or Rabi) splitting (of the order of 1eV!) and formation of hybrid polaritonic states.

Rhodamine 6G dye (R6G) is the material of choice in many applications and demonstrations because of its high absorption and emission cross-sections (~4x10⁻¹⁶ cm²) and high photo-stability. Its optical spectra are dominated by the singlet-singlet absorption (~532 nm) and emission (~570 nm) transitions. Most applications of R6G dye require high molecular concentrations. With increase of the dye concentration, its optical spectra undergo noticeable transformations, most notable of which are the red shift of both absorption and emission bands and the growth of the ~495 nm shoulder in the absorption spectra.

Some of these experimental features are commonly explained in terms of the exciton model [12,13] taking into account the formation of J, H, and oblique aggregates (dimers formed by molecular dipoles arranged head-to-tail (J), parallel (H), and at an angle to each other). In particular, the ~495 nm shoulder in the absorption spectrum is explained by some authors in terms of formation of dimer aggregates [14,15], while others attribute it to vibronic transitions [16–18].

At high dye concentrations, formation of larger molecular aggregates becomes possible [19], making interpretation of the optical spectra even more challenging. This ambiguity and a broad range of opinions and explanations motivated our study reported below. We have fabricated a series of polymeric films doped with R6G dye (in a broad range of molecular concentrations), studied their absorption, excitation, and emission spectra, and provided tentative interpretation of our findings.

2. Experimental samples and methods

The experimental samples in our studies were thin films of Poly(methyl methacrylate) (PMMA) doped with Rhodamine 6G (R6G) in the broad range of concentrations, ranging from c = 2.2x10⁻⁴ mol/L to 8.9x10⁻¹ mol/L. We first dissolved 0.15 mg of R6G perchlorate (M_R6G = 543.01 g/mol [20]) in approximately 10 mL of dichloromethane (DCM) and sonicated the solution in an ultrasonic bath at room temperature for ~5 min. After that, 1.70 g of PMMA (m.w. = 120,000 a.u.) was dissolved in the dye solution and sonicated for another ~15 min. Knowing the mass of the dye (m_R6G), the mass of PMMA (m_PMMA), and the densities of R6G (ρ_R6G = 1.26 g/cm³ [21]) and PMMA (ρ_PMMA = 1.18 g/cm³ [22]), we determined the concentration of R6G (in solid state) using the formula $c\left[\frac{mol}{L}\right]=\frac{m_{R6G}}{M_{R6G}}\cdot 1000\left[\frac{c{m}^3}{L}\right]\cdot {\left(\frac{m_{R6G}}{{\rho }_{R6G}}+\frac{m_{PMMA}}{{\rho }_{PMMA}}\right)}^{-1}$ [23].

The amount of the solvent (DCM) was chosen to optimize the viscosity of the solution, which affected the thickness of the deposited films. Fixed volumes of the prepared solutions were spin-coated onto glass substrates using a three-step recipe fine-tuned for the Model 6800 and Spincoat G3P-8 spin-coaters (from Specialty Coating Systems). The R6G:PMMA films were scratched in several locations and the film thicknesses were measured (using the DekTak XT profilometer from Bruker), after which the average value of several tests has been calculated. The thicknesses of the fabricated R6G:PMMA films were 120 ± 10 nm, except for the film with the lowest dye concentration, which was intentionally made thick, 3285 ± 10 nm.

Experimentally, we studied absorption, excitation, and emission spectra of the R6G:PMMA films. The absorption spectra were measured using the Lambda 900 spectrophotometer equipped with the 150 mm integrating sphere (from PerkinElmer). The excitation and the emission spectra were obtained using the FlouroLog 3 (from Horiba Jobin Yvon). All step-sizes and slit-widths in the spectral scans were much smaller than the characteristic widths of the spectral bands studied. All excitation and emission spectra were normalized to spectral emissivities and sensitivities of the corresponding light sources, monochromators, and detectors.

3. Absorption, emission, and excitation spectral studies

At small dye concentrations, c≤2.2x10⁻³ mol/L, the absorption band has a maximum at 532 nm and a shoulder at ~495 nm (Fig. 1(a), trace 1). With increase of the dye concentration, the shoulder gets larger (Fig. 1(b), trace 1) and at c = 8.9x10⁻¹ mol/L, it becomes a peak on its own (Fig. 1(c), trace 1). The absorption spectrum can be adequately fitted (in a frequency domain) with a sum of two Gaussian functions, see traces 2, 3 and 4 in Figs. 1(a)-1(c). With increase of the dye concentration, both Gaussian bands constituting the absorption spectrum experience a red shift, broaden, and the distance between them increases, see traces 3 and 4 in Figs. 1(a)-1(c). Note that we intentionally restricted the fitting procedure to the smallest number of Gaussian bands (two) providing for an adequate fit. Although an increase in the number of the Gaussian bands used in the fitting procedure reduces the mismatch between the experimental and the calculated spectra, the excessive Gaussian bands (which are highly sensitive to the experimental noise) may have no direct correspondence with the centers contributing to the absorption spectra, leading to erroneous interpretation of the experimental data. A better fit could sometimes be obtained if a convolution of Lorentzian and Gaussian functions was used instead of Gaussian shapes. However, for consistency, all spectra in this study were fitted with combinations of Gaussian functions.

 

Fig. 1 Absorption spectra of R6G:PMMA films. Trace 1 – experiment; trace 2 – fit with the sum of two Gaussian functions, traces 3 and 4 – Gaussian functions corresponding to the main peak and the shoulder, respectively. (a) c = 2.2x10⁻⁴ mol/L, (b) c = 6.7x10⁻¹ mol/L, (c) c = 8.9x10⁻¹ mol/L.

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With an increase of the dye concentration, the area of the Gaussian band representing the shoulder of the absorption spectrum increases linearly (the slope in log-log coordinates is equal to η = 1.01), while the growth of the area of the Gaussian band corresponding to the maximum of the dye absorption is slightly sublinear (the slope in log-log coordinates is equal to η = 0.89), Fig. 2(a). Note that the error bars for the data points in Fig. 2(a) are smaller than the size of the characters and the uncertainties in the slopes are ~3%.

 

Fig. 2 (a) Concentration dependence of the area under the Gaussian bands, representing the main peak (red circles) and the shoulder (blue squares) of the absorption spectrum (blue squares). (b) Dependence of the concentration of monomers (red trace) and dimers (blue trace) on the total concentration of molecules, predicted by the aggregation/dissociation model. The slopes of the curves at low and high molecular concentrations are shown in the figure.

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Expectedly, the emission spectra at low dye concentrations (c≤2.2x10⁻³ mol/L) were nearly mirror images of the corresponding absorption spectra [16,24], with the zero phonon line at 543 nm. They, too, could be decomposed into the sum of two Gaussian bands representing the main peak at ~555 nm and the shoulder at ~573 nm, Fig. 3(a). Similar to the absorption spectra, with increase of the dye concentration, the emission band experienced a red shift, broadened, and the spectral distance between the two fitting Gaussian bands increased, Fig. 3(b). Furthermore, the ratio between the areas of the two Gaussian bands representing the shoulder and the main peak increased with increase of the dye concentration, Figs. 3(a) and 3(b) – the behavior already seen in the absorption spectra.

 

Fig. 3 Emission and excitation spectra of R6G:PMMA: (a) c = 2.2x10⁻³ mol/L. Trace 1 – experimental emission spectrum; trace 2 – its fit with the sum of two Gaussian functions, traces 3 and 4 – Gaussian functions corresponding to the main peak and the shoulder of the emission band. Trace 1’ – experimental excitation spectrum; trace 2’ – its fit with the sum of two Gaussian functions; traces 3′ and 4’ – Gaussian functions corresponding to the main peak and the shoulder of the excitation band. (b) c = 6.7x10⁻¹ mol/L. Traces 1,2-4 and 3′,4’: same as in Fig. 3(a). Emission spectra 1, 5 and 6 were collected when the samples were excited at 400 nm, 485 nm and 530 nm, respectively. Excitation spectra 7, 9 and 10 were collected when the emission was collected at 606 nm, 555 nm and 620 nm, respectively. Trace 8 – fit of trace 7 with the sum of two Gaussian functions.

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At both small (c = 2.2x10⁻³mol/L) and large (c = 8.9x10⁻¹ mol/L) concentrations, the shapes of the emission spectra practically did not depend on the wavelength at which the emission was excited (Fig. 3(b), traces 1, 5, and 6).

Likewise, the excitation spectra (Fig. 3(b), traces 7, 9 and 10) were practically independent of the emission detection wavelengths. This suggests that all electronic excitations, regardless of the wavelength at which they were excited, ended up either at the same emitting metastable state or went to heat. Correspondingly, no emission originating from any other excited state was observed. Similar to the absorption and emission spectra, with an increase of the dye concentration (above 6.7x10⁻¹ mol/L), the excitation spectra red-shifted, broadened, and the spectral distance between the Gaussian bands representing the main peak and the shoulder increased, compare traces 3 and 4 in Figs. 4(a) and 4(b).

 

Fig. 4 Comparison of the excitation and the absorbance spectra: Trace 1 – experimental excitation spectrum, trace 2 – its fit with the sum of two Gaussian functions, traces 3 and 4 – Gaussian functions corresponding to the main peak and the shoulder, respectively, trace 5 – experimental absorbance spectrum (a) c = 2.2x10⁻⁴ mol/L, (b) 6.7x10⁻¹ mol/L. Insets: zoomed maxima of the excitation and absorbance bands.

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Despite the qualitative resemblance of the excitation and the absorption spectra, they had noticeable differences. Thus, the maximum of the excitation spectra was blue shifted relative to that of the absorption spectrum, Figs. 4(a) and 4(b). This spectral shift, which was modest at small dye concentrations (0.8 nm at c = 2.2x10⁻⁴ mol/L and 2.8 nm at c = 2.2x10⁻³ mol/L), became substantially large at high dye concentrations (8 nm at c = 6.7x10⁻¹ mol/L), see insets in Figs. 4(a) and 4(b).

The absorption and the excitation spectra, once scaled appropriately, overlapped at large frequencies (short wavelengths). However, the overlap was poor at low frequencies (long wavelengths), Figs. 5(a) and 5(b), suggesting that the dye molecules excited close to the long-wavelength edge of the absorption spectrum did not contribute to emission. This effect was stronger at large concentrations than at small concentrations.

 

Fig. 5 Normalized absorbance spectrum (trace 1), scaled excitation spectrum (trace 2), and their difference (trace 3), suggest that the molecules excited close to the long-wavelength edge of the absorption spectrum contribute to spontaneous emission less than the molecules excited close to the short-wavelength edge of the absorption spectrum. (a) c = 2.2x10⁻³ mol/L, (b) c = 6.7x10⁻¹ mol/L.

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4. Discussion

The major experimental results of our study are summarized and discussed below.

The origin of the shoulder in the absorption, excitation and emission spectra of R6G and some other dye molecules is a subject of controversy. While some authors attribute it to vibronic transitions within individual dye molecules [16–18,25], others ascribe it to molecular dimers [14,15], which are known to exist at high molecular concentrations [12,13].

The aggregation/dissociation model governing the concentrations of monomers n and dimers m in ensembles of molecules [14] yields

(2) With an increase of the dye concentration, the absorption, excitation, and emission spectra red-shift, broaden, and spectral differences between the Gaussian bands representing the main peak and the shoulder become larger.

The overall red shift of the absorption and emission spectral bands, observed at high dye concentrations, agrees with the Lorentzian model predicting that dipole-dipole interactions of head-to-tail aligned molecular dipoles weaken effective spring constants of molecular oscillators and reduce the oscillation frequency [26]. The qualitatively similar explanation of this experimental result originates from the exciton theory predicting, among others, formation of J-aggregates (dimers with head-to-tail arrangement of molecular dipoles [12,13]).

The increase of the spectral distance between the main peak and the shoulder with increase of the dye concentration is in agreement with the arguments of the quantum theory, predicting repulsion of the energy eigenstates under perturbation [27], provided, in our case, by interactions between dye molecules.

Different dye molecules could have weaker or stronger interactions with other surrounding molecules, leading to inhomogeneous broadening of the spectral bands.

(3) The excitation spectra are blue-shifted relative to the absorption spectra. Correspondingly, the dye molecules excited close to the long-wavelength edge of the absorption band (almost) do not contribute to emission. The effect becomes stronger with an increase of the dye concentration.

We tentatively explain this result in terms of the strong coupling of dye molecules. In a simplified case of molecular dimers, the strong coupling causes splitting of the excited states of interacting molecules, whose magnitude increases with an increase of the dye concentration (reduction of the inter-molecular distances). The corresponding wavefunctions may have same or different parities, determining whether the transition is allowed or forbidden. In Ref [23], by combining conceptual models of the (i) strong coupling (resulting in energy-split excited states of opposite parity), (ii) parabolic potentials for the ground and the excited states, and the (iii) parity selection rule, we have shown that the emission (originating from the lower excited state) can be observed at excitation of the upper excited state but not the lower excited state, see Appendix Fig. 6. By applying this heuristic model to our experiment, one can see why pumping into the low-energy edge of the absorption spectral band does not contribute to the emission and why the spectral shift between the maximum of the excitation band (presumably corresponding to excitation of the upper excited state) and the maximum of the absorption band grows with increase of the dye concentration. Note that a qualitatively similar experimental observation has been reported in Ref [19].

 

Fig. 6 Energy level diagram of coupled molecules (the configuration coordinate is plotted on the horizontal axis). Parabola S₀ represents the ground state. Parabola S₁ represents the first excited state of uncoupled molecules. Parabolas S₁^- and S₁⁺ represent the two branches of the split excited state of the strongly coupled molecules. The transition $|2P-〉\to |3P-〉$ is parity forbidden. Correspondingly, the molecules excited at the transition $|1〉\to |2P-〉$ do not emit. This explains the shift between the absorption and excitation bands observed in our experiment. (Adopted and modified from Ref [23].).

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(4) In the discussion above, we have made two major statements: (i) that many features in the spectra of highly doped R6G:PMMA films point at the dimer formation and strong coupling of molecular oscillators and (ii) that the shoulder in the absorption spectrum of R6G dye is chiefly not due to molecular dimers. These statements are not in contradiction with each other. In fact, although dimers of R6G molecules may (and probably do) contribute to the ~490 nm absorption shoulder, this contribution is relatively insignificant and does not noticeably affect the nearly linear growth of the absorption shoulder over four orders of magnitude.

The existence of higher molecular aggregates and their spectroscopic signatures require more studies, which are outside of the scope of this work. However, their contributions to the ~490 nm absorption shoulder are expected to be even smaller than those of molecular dimers.

5. Conclusions

We have experimentally studied spectroscopic properties of R6G:PMMA films in a broad range of molecular (R6G) concentrations. The linear growth of the shoulder of the absorption band with increase of the dye concentration (over nearly four orders of magnitude), suggests that it is, chiefly, not due to formation of dimers or larger molecular aggregates, as it has been claimed in earlier works [14,15,19]. This conclusion is in line with Ref [16], ascribing the shoulder to vibronic transitions in individual R6G molecules, and Refs [17,18,25] discussing vibronic transitions in spectra of organic dyes.

The red shift of the absorption and emission bands with an increase of the dye concentration can be explained by the head-to-tail interactions of interacting molecular dipoles. The increase of the spectral distance between the major peak and the shoulder is in line with repulsion of the energy states under perturbation, and the broadening of the spectral bands can be explained by inhomogeneous molecular environments.

The blue shift of the excitation spectral band with respect to the corresponding absorption spectral band suggests that some photons absorbed near the low-energy edge of the absorption spectra do not contribute to emission (which originates from the same branch of the excited state). Following Ref [23], we tentatively explain this effect in terms of the parity selection rule prohibiting energy relaxation within the same excited state parabola.