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Abstract
The total internal refection ellipsometry (TIRE) method was used for the generation and study of the hybrid TPP-SPP mode on a photonic crystal structure with a thin layer of silver and graphene/PMMA. Raman spectroscopy showed a consistent monolayer graphene present on the Ag layer. Recent studies have also shown that TPP and SPP components in the hybrid plasmonic mode is sensitive to the variation of coupling strength due to presence of the graphene monolayer. The decrease of the TPP and SPP dip components in the TPP-SPP hybrid mode can be explained by the changes of the conductivity of the silver layer due to the presence of this additional graphene/PMMA structure, which results in the non-optimal resonance conditions for the hybrid plasmonic mode. The modified positions of the TPP and SPP components in the wavelength spectra when compared to their original, separate excitations, indicates a strong coupling regime. The design of these hybrid plasmonic/graphene-based nanostructures has attractive capabilities for the development of advanced optical sensors and integrated optical circuit technologies.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Graphene physics and plasmonics have become the subjects of wide spread studies and have led to numerous fundamental investigations and applications to novel optical devices [1–3]. Moreover, these fields strongly overlap, not only due to the intrinsic plasmons in graphene, which can be tunable in broadband range of wavelengths, but also due to the hybrid nanostructures of graphene and noble metals [4,5], where enhanced light-matter interactions can be expected [6]. Graphene is a 2D crystal consisting of carbon atoms arranged in a honeycomb lattice [7]. Such a crystal structure has very high quantum efficiency for light-matter interaction [2]. The unique optical properties and strong light-matter interactions which arise from the quasiparticles in graphene satisfies a linear dispersion relation [1]. However, the optical absorption of the graphene atomic monolayer is 2.3%, which is a rather large amount for a single layer, but is usually not enough to achieve an effective light-matter interaction for optical modulation, optical sensing and other purposes [8]. The combination of graphene with the traditional plasmonics on noble metals produce opportunities for the enhanced optical features of graphene, for example in Raman spectroscopy [9]. On the other hand, graphene could also be used to influence the optical responses of such hybrid graphene-plasmonic nanostructures [2,10]. These graphene-metal hybrid structures provide a number of advanced applications for conventional plasmonics [11,12].
Much attention has been given in the past years to optical surface states, especially to the so called Tamm plasmon polariton (TPP), which appears at the boundary between the photonic crystal and the metal layer [13–15]. This TPP phenomenon in wavelengths from the optical [16] to THz region [17] has a similar origin as the electron states proposed by I. Tamm [18], which can be realized in the energy band gap on a crystal surface. This photonic crystal band gap serves as the energy band gap in real crystals because of the Bragg reflections in its structure of alternating layers. Due to its different dispersion relations compared with those of the conventionally propagated surface plasmon polariton (SPP), the TPPs have several advantages. The TPPs have an in-plane wave vector, which is less than the wave vector of light in a vacuum, which allows for their direct excitation at the interface of the PC/metal. The Tamm plasmons can be excited in both p- and s- polarizations, instead of only the p-polarization for SPP. Moreover, it has been shown [19] that both the TPP and SPP surface modes can be excited simultaneously on the same metal layer and interact with each other in a strong coupling regime, when suitable conditions are satisfied [20]. In such cases, a new hybrid TPP-SPP mode appears and the repulsive nature of the TPP and SPP resonances is revealed [19,21]. The simultaneous excitation of the hybrid TPP-SPP mode requires a prism coupler (grating or other) for the SPP component to achieve the total internal reflection condition and to match the in-plane wave vector [22,23]. Meanwhile, for the TPP component, this excitation condition is always satisfied when the incident wavelength falls within the forbidden stop band of the photonic crystal.
The excitation of the hybrid plasmonic resonances and a full light polarization analysis can be achieved at the same time by employing the spectroscopic ellipsometry (SE) technique in its total internal reflection geometry (TIRE) [24]. In fact, TIRE utilizes the analytical power of ellipsometry by involving a glass prism as a coupler in its optical scheme [25], which is necessary for the SPP. This increases the sensitivity of the analyzed surfaces by introducing the plasmonic effect [26,27]. The large sensitivity of TIRE to changes of the polarization states enables one to analyze in detail the structures and properties of these ultra-thin layers [28,29].
The optical response of graphene layer in PC/metal structures which supports hybrid plasmonic modes in strong coupling has been studied by numerical simulations [30,31]. A rather small number of works have been dedicated to experimental studies on the influence of graphene layers on coupled plasmonic excitations [2]. In this sense, the behavior of the dispersion relations of the hybrid Tamm-plasmon polariton modes in a strong coupling regime under the influence of graphene have not been investigated before, although such newly acquired knowledge could be a substantial contribution to the development of advanced optical elements and nanodevices with reduced Ohmic losses due to such hybrid modes. In these studies, variable angle spectroscopic ellipsometry, total internal reflection ellipsometry and Raman spectroscopy were used for the characterization of the optical responses of such hybrid 1D photonic crystal/metal nanostructures. This was done in order to estimate the changes of their optical responses due to the adlayer of the graphene monolayer with the supporting PMMA film on the top of graphene and their resulting influence on the interaction strength of the TPP and SPP components in the strong coupling regime of the hybrid TPP-SPP mode. The motivation of this work was to evaluate the variation of coupling strength due to the graphene and PMMA layers, because this is not directly detectable from the optical responses. The interest in the study systems which are able to support the strong coupling effect arises from their promising applications to optical information processing, lasing, also to fundamental studies of light-matter interaction and even for employing such structures in biosensors.
2. Methods
The sample used for the hybrid TPP-SPP mode excitation consisted of a 1D PC and a porous SiO2 layer of approximately 90 nm thickness with a thin silver layer (∼40 nm) on its top. The PC being used was made of 6 alternating TiO2 (∼60 nm) and SiO2 (∼110 nm) bilayers deposited onto a BK-7 glass substrate by means of ion beam sputtering. The porous SiO2 and Ag films were deposited on PC using glancing angle deposition method [32]. The thickness of the metal had to be thin enough for the coupling of the TPP and the SPP in a hybrid mode. The morphology of the structure was evaluated from scanning electron microscopy (SEM) micrographs. The thicknesses of the layers of the sample were determined from the cross sections of the SEM micrographs (Fig. 1).
Fig. 1. Cross section of the sample. A PC composed of 6 TiO2 and SiO2 bilayers of 60 nm and 110 nm respectively, with a 90 nm thick layer of porous SiO2 and a thin coat (40 nm) of Ag on top.
A commercially available single layer graphene (SLG) deposited via CVD growth onto Cu film with a poly(methyl methacrylate) (PMMA) layer on top was used [33]. The Cu film was then chemically dissolved from the Cu/SLG/PMMA structure, leaving the single layer graphene with the PMMA floating on a solution surface. The SLG/PMMA was then transferred onto the surface of the sample.
Raman spectroscopy was used to ensure that the graphene was deposited onto the surface of the Ag layer. The Raman spectra were recorded using an inVia Raman (Renishaw, UK) spectrometer equipped with a thermoelectrically cooled (−70 °C) CCD camera and a microscope. The Raman spectra were excited with 532 nm wavelength light from a continuous-wave diode-pumped solid-state laser (Renishaw, UK). A 20x/0.40 NA long working distance objective lens and an 1800 lines/mm grating were used to record the Raman spectra. The accumulation time was 100 s. To avoid damage to the sample, the laser power at the sample was restricted to 0.06 mW. The Raman scattering wavenumber axis was calibrated by the polystyrene Standard Raman spectrum. The parameters of the bands were determined by fitting the experimental spectra with Gaussian-Lorentzian shape components using GRAMS/A1 8.0 (Thermo Scientific) software.
Resonance Raman (RR) spectroscopy is able to provide significant structural information on graphene based materials [34–37]. The number of graphene layers can be determined from an analysis of the intensity ratio of the 2D and G bands (I(2D)/I(G)) [38,39]. The Resonance Raman spectrum of the graphene layer on the sample is shown in Fig. 2. An enhancement of the I(2D)/I(G) ratio is expected for single layer graphene; usually this is I(2D)/I(G) > 2. However, other factors such as a charge-transfer or a stacking order may affect the I(2D)/I(G) ratio [35,40]. In the case of our studied sample, the I(2D)/I(G) ratio was found to be 2.4. This was consistent with the previously reported data for single layer graphene [38–40]. The defects in the graphene structure can be probed by an analysis of the D band (“disorder induced” band) near 1350 cm−1 [39]. Such band is not visible in our RR spectrum (Fig. 2), indicating the high structural quality of the graphene film being studied.
Fig. 2. Resonance Raman spectrum of graphene on the PC/SiO2/Ag substrate. Excitation wavelength is 532 nm (0.06 mW).
The structure described above was measured using spectroscopic ellipsometry (SE). The ellipsometer used for these measurements was a J. A. Woollam M-2000X with a rotating compensator. The light source was a Xe lamp with a spectral range of 245–1000 nm. As the sample with SLG/PMMA had rather small area, the microspot focusing option was used. The longer axis of the light spot ellipse on the sample surface were about 180 µm in the case of VASE measurements, meanwhile in TIRE configuration due to the glass prism, beam was slightly defocused and the long axis of the ellipse was about 290 µm. For the excitation of the Tamm plasmon, a conventional configuration of variable angle spectroscopic ellipsometry (VASE) without a prism coupler was used. For the excitation of the hybrid TPP-SPP mode, a total internal reflection (TIR) configuration of spectroscopic ellipsometry with a 45° prism coupler was used. The measured ellipsometric spectra Ψ (λ) and Δ (λ) were then analyzed and compared to the multi-layer model designed with a CompleteEASE program. By using the regression analysis method, the thicknesses and the optical constants of the layers were determined.
3. Results and discussion
During this study, two different measurement configurations, the conventional variable angle spectroscopic ellipsometry and the TIRE, were used for the excitation of the single TPP and hybrid TPP-SPP modes, respectively. VASE measurements were first conducted in order to examine the optical response of the PC/SiO2/Ag structure with the SLG and PMMA on top of the Ag. In it, the single TPP excitations manifested themselves as a dip in the ellipsometric spectra of Ψ (λ). The dependence of the ellipsometric spectra Ψ (λ) and Δ (λ) on the angle of incidence (θinc) can be seen in Fig. 3(a). The PC/SiO2/Ag sample’s incident angle measurement range was 45° − 75° degrees. Accordingly, the dips of the TPP optical states [Fig. 3(a)] corresponded to 555 nm, 536 nm, 519 nm, 505 nm for the 45°, 55°, 65° and 75° angles, respectively. The ellipsometric spectra of the sample, before and after the SLG and PMMA deposition, were compared at a 65° angle of incidence [Fig. 3(b)], where the contribution to the optical response of the SLG/PMMA layers were the greatest. The TPP resonance dips can be seen at 519 nm for the PC/SiO2/Ag, 520 nm for the PC/SiO2/Ag/PMMA and 522 nm for the PC/SiO2/Ag/SLG/PMMA, respectively. A red shift of ∼1 nm in the ellipsometric spectra Ψ (λ) was observed after deposition of PMMA onto the PC/SiO2/Ag sample and a ∼3 nm shift to longer wavelengths in the PC/SiO2/Ag/PMMA and the PC/SiO2/Ag/SLG/PMMA samples.
Fig. 3. Modeled (solid lines) and experimental (circles and squares) results of (a) a single Tamm plasmon-polariton Ψ and Δ spectra for the PC/SiO2/Ag structure at different angles (θinc∈[45°-75°]), (b) Ψ and Δ parameters of the samples PC/SiO2/Ag (1 - orange), PC/SiO2/Ag/PMMA (2 - green) and PC/SiO2/Ag/SLG/PMMA (3 - blue) at an angle of incidence of 65°.
For the measurement of the VASE ellipsometric spectra of the PC/SiO2/Ag structure with typical TPP curves, the optical model consisted of a BK-7 glass substrate, a PC constructed of 6 bilayers of TiO2/SiO2 of 60 nm/110 nm thicknesses and a 90 nm porous SiO2 layer on its top with a 40 nm Ag layer over it. The porous SiO2 layer was defined by effective media approximation (EMA) with a percentage composition of 70% SiO2 and 30% void. A regression analysis of the PC/SiO2/Ag structure was then conducted where the thicknesses of the layers were the fitting parameters. Secondly, the TPP optical state supporting structures with the PMMA and the SLG/PMMA on the top of the silver surface were fitted. The model parameters of the PC obtained before were then fixed, while the thicknesses of the porous SiO2, Ag, PMMA and SLG were varied. From the fitting procedure of the PC/SiO2/Ag/PMMA structure, the obtained thickness of the PMMA layer was ∼10 nm. From the regression analysis of ellipsometric spectra where the SLG was between the Ag and PMMA layers, the obtained SLG thickness was about ∼0.8 nm (1 − 2 graphene layers), while the PMMA thickness stayed the same (∼10 nm). The optical constants of the Ag and the graphene layers were taken from the literature [41,42] and others (SiO2, TiO2, PMMA) were obtained from the CompleteEASE program software package.
Regression analysis in its conventional VASE configuration for the TPP excitation showed that the values for the substrate structure supporting the TPP excitation, namely the PC/ SiO2/Ag layer, were very close (Table 1) to those obtained from the SEM cross-section (Fig. 1), which were used as the starting values in fitting procedure for the thicknesses of the SiO2, TiO2 and Ag layers. The evaluated ratio of the graphene peaks (2.4) in the Raman spectra, which were measured at five different spots, supports the assumption that the most probable dominating structure on the silver surface was the single layer of graphene (0.34 nm as stated in the literature [43,44]) and this was taken as the starting value in the fitting procedure. The regression analysis showed that the thickness of the graphene layer was about 0.8 nm. Since the light spot diameter was ∼250-300 µm, the optical response gave the average value of the graphene layer, which might have some wrinkles or non-homogeneities due to the influence of the PMMA layer on its top. It is thus possible that the average thickness may be thicker. The simulated data were fitted to the experimental VASE results in the range of AOI 45°−75° simultaneously with mean square error (MSE) values of about 20 for the TPP excitation. Also accounted for were the ∼1.33 ± 0.06 nm thick mix of Ag and porous SiO2. The thicknesses of the PC layers obtained from the PC/SiO2/Ag model corresponded to 57 ± 0.1 nm and 110.6 ± 0.2 nm for the TiO2 and SiO2, respectively.
Table 1. Thicknesses of the investigated sample layers and the porosity of the SiO2 determined from regression analysis. EMA expresses the percentage of air in the SiO2 layer.
The TIRE configuration was used in order to achieve the hybrid TPP-SPP mode excitation and to study the influence of the graphene layer on the strong coupling regime between the TPP and SPP components. The dependence of the ellipsometric parameter Ψ (λ) on the AOI of the PC/SiO2/Ag structure is shown in Fig. 4. The experimental results are presented as circles and the solid lines show the fitting results. For the TIRE configuration, the same approach of optical model design and regression analysis was applied as for the VASE, taking into consideration the inverse problem of the multi-layer model and the prism coupler. The fitting procedure gave values of the thicknesses, which were very close to those of the VASE. The only corrections involved were due to the glass prism. The contributions of the graphene monolayer to the optical response of the PC/SiO2/Ag/SLG/PMMA structure were measured at 47.5° AOI due to the broad gap between the TPP and SPP components in hybrid mode, thus indicating their intense interaction in a strong coupling regime [45].
Fig. 4. Hybrid TPP-SPP mode ellipsometric parameter Ψ spectral dependence on the incident angle in a PC/SiO2/Ag structure. The dots and solid curves correspond to the experimental and theoretical results, respectively.
The experimental TIRE results of the PC/SiO2/Ag, PC/SiO2/Ag/PMMA and PC/SiO2/Ag/SLG/PMMA structures at θinc=47.5° are shown in Fig. 5. The TPP and SPP excitation dips in ellipsometric parameter Ψ (λ) of the PC/SiO2/Ag structure (Fig. 5 blue line) were at 427 nm and 492 nm, respectively. After the PMMA deposition (Fig. 5 green line) on the top of the PC/SiO2/Ag, the hybrid TPP-SPP mode shifted to 448 nm (TPP) and 511 nm (SPP). The red shifts of the TPP and SPP components in their hybrid plasmonic mode were 21 nm and 19 nm, respectively. For the PC/SiO2/Ag/SLG/PMMA structure with the graphene layer between the silver layer and the PMMA (Fig. 5 red line), the plasmonic components manifested themselves at 456.4 nm (TPP) and 527.7 nm (SPP). The shift to longer wavelengths [29.4 nm (TPP) and 35.8 nm (SPP)] corresponded to those of the PC/SiO2/Ag structure. Thus, the difference between the corresponding TPP and SPP resonances with and without the graphene layer were 8.4 nm for the TPP and 16.7 nm for the SPP. The spectral distance, which indicates the coupling strength between the TPP and the SPP excitations in their hybrid mode was 65 nm, 63 nm and 71.3 nm for the PC/SiO2/Ag, PC/SiO2/Ag/PMMA and PC/SiO2/Ag/SLG/PMMA structures, respectively.
Fig. 5. Experimental data of the ellipsometric Ψ and Δ parameters at three different stages of the sample: plain PC/SiO2/Ag (blue), after PMMA is added (green), with graphene and PMMA (red). The angle of incidence is 47.5°.
The graphene and PMMA layers noticeably modify the optical response of the hybrid TPP-SPP mode and hence change the coupling strength between TPP and SPP components in their hybrid plasmonic mode. In Fig. 5, the green curve corresponds to the evolution of the hybrid plasmonic component dips due to presence of the PMMA layer on the silver surface. The diminishment of both the TPP and SPP states indicates non-optimal resonance conditions, while the red shift of both resonances can be attributed to an increase of the refractive index due to the PMMA. The red curve in Fig. 5 shows the optical response of the ellipsometric parameters due to presence of the graphene layer between the silver layer and the PMMA. The graphene layer slightly increases the spectral gap between the TPP and SPP components. At the same time, it weakens the SPP resonance due to changes of metal layer conductivity. It should be noted that the TPP and SPP components in the hybrid TPP-SPP mode show different behavior when the SLG/PMMA layer is deposited on the top of the silver surface. As is well-known [19,24] the TPP and SPP resonances excited at the different interfaces, the TPP at the inner, while the SPP at the outer. Therefore, the SPP is more sensitive to changes of the refractive index on the top of the metal surface, while the changes of the optical response of the TPP is more related to the alteration of the coupling strength between the TPP and SPP in their hybrid TPP-SPP mode.
The graphene transfer via polymer does not permit one to measure the amount of pure graphene on the PC/Ag structures without the PMMA layer. Moreover, as was shown before [46], this variation of the coupling strengths is not directly equal to the change of the general optical response of the system. The conducted evaluation takes into account not only the gap Ω (Rabi splitting) between resonances, but also the widths (FWHM) of both resonances. As was shown, the ambiguities in distinguishing between the strong and weak coupling were raised in various systems, especially in the widely studied exciton-plasmon based structures [46,47]. In order to reveal the varying in the coupling strength between TPP and SPP components, we applied the expression proposed in the previously mentioned study:
The system is in the strong coupling regime when where g is the coupling strength, Ω is the Rabi splitting, ωSPP and ωTPP – SPP and TPP are the resonance positions in the spectra, γSPP and γTPP are the corresponding widths of the resonances. According to these evaluations, the strong coupling regime were estimated for all three cases of experimentally studied multi-layered structures as being: PC/Ag (g=0.33 eV; Γ=0.034 eV; ωTPP=2.9 eV; ωSPP=2.5 eV; γTPP=0.1 eV; γSPP=0.06 eV), PC/Ag/PMMA (g=0.32 eV; Γ=0.052 eV; ωTPP=2.7 eV; ωSPP=2.3 eV; γTPP=0.08 eV; γSPP=0.14 eV) and PC/Ag/SLG/PMMA (g=0.31 eV; Γ=0.053 eV; ωTPP=2.7 eV; ωSPP=2.4 eV; γTPP=0.1 eV; γSPP=0.11 eV). The obtained results have shown that such changes in the optical response of hybrid mode were sensitive enough to distinguish the variation of coupling strength being contributed by the graphene layer. It should be noted that the general optical response of the system masks the variations of the coupling strength.Additionally, to reveal the contribution of the graphene single layer and PMMA to the coupling strength in the hybrid TPP-SPP mode, numerical simulations were performed. This evaluation was conducted using the same parameters of the model structure as in the TIRE experiment. The map of the ellispometric parameter Ψ was chosen, because the plasmonic minimas of TPP and SPP in Ψ (λ) resemble the minima observed in the reflectance intensity of the plasmonic resonances. The shape of these minimas in Ψ is close to the square root of the plasmonic reflectance, which indicates that the Ψ minima, in fact, are sharper than corresponding plasmonic minima in reflectance [48]. This advantage gives more precise detection of the gap and the widths of the TPP and SPP components in the hybrid mode, which have an influence to the coupling strength. The dependence of the ellipsometric parameter Ψ (λ) on the angle of incidence was modeled (Fig. 6), which allowed an estimation of the dispersion relation of the hybrid TPP-SPP mode. The spectral gap between the components in the hybrid mode for the PC/SiO2/Ag, PC/SiO2/Ag/SLG, PC/SiO2/Ag/PMMA and PC/SiO2/Ag/SLG/PMMA structures were evaluated at θinc=47.5° and was found to be 68.5 nm, 67.3 nm, 59.4 nm and 60.7 nm, respectively. These calculation results clearly demonstrated that both resonances were red-shifted after the graphene and PMMA deposition. The evaluated coupling strength between the TPP and SPP components weakened due to the graphene layer (g=0.34; Γ=0.038) [Fig. 6(b)]. In Fig. 6(c), the decreased bending of dispersion curves were observed and the evaluated coupling strength was (g=0.28; Γ=0.03). When the analyzed structure contained the SLG/PMMA layers [Fig. 6(d)], the Rabi splitting Ω and the widths of both resonances increase, what leads to the decrease of the coupling strength for (g=0.27; Γ=0.043). Despite the fact that the dispersion curves of the TPP and SPP components slightly increased for the SLG/PMMA structure, both excitations were diminished, and the widths of the resonances became wider [Fig. 6(d)]. The coupling strength also slightly decreased. As can be seen in graphs Figs. 6(c) and 6(d), the bending of the TPP and SPP dispersion branches diminishes, however, the strong coupling conditions were still satisfied for Figs. 6(c) and 6(d). This decrease of the TPP and SPP dip components in the TPP-SPP hybrid mode can be explained by changes of the conductivity of the silver layer due to the addition of the SLG/PMMA structure and, as a result, the creation of non-optimal resonance conditions for the hybrid plasmonic mode. The numerical calculations and the evaluation of the coupling strengths for expressions (1) and (2) clearly show the hybrid origin of the coupled TPP and SPP optical states. The modified positions of the TPP and SPP components in the wavelength spectra, compared with their original, separate excitations, indicate the strong coupling regime [45]. The alteration of the splitting modes (the gap between the TPP and SPP dips and the widening of the resonances) indicate a variation of the coupling strength g [45]. In TIRE configuration, the TPP and SPP states cannot be generated separately at a given angle or wavelength. Hence, both excitations are in superposition and satisfy the same wave equation [19]. This leads to the hybrid modes and the coupling of the TPP and SPP.
Fig. 6. Image plot of the modeled ellipsometric parameter Ψ of the PC/SiO2/Ag (a), PC/SiO2/Ag/SLG (b). PC/SiO2/Ag/PMMA (c), PC/SiO2/Ag/SLG/PMMA (d) samples. The photonic band gap (PBG) edges are marked with the white dashed line. The yellow dot line marks the gap between the TPP and SPP modes.
4. Conclusions
Summarizing, the TIRE method was used for the generation and study of the hybrid TPP-SPP modes on a PC structure with a thin layer of silver and SLG/PMMA. Raman spectroscopy showed the presence of a consistent graphene monolayer on the Ag layer. Recent studies have shown that noticeable changes in the general optical response can have a rather weak impact on strong coupling. Despite of this, the variation of the coupling strength between the PMMA and SLG/PMMA structures in the hybrid plasmonic mode was big enough to evaluate the differences between them. The higher sensitivity was achieved in the hybrid TPP-SPP plasmonic mode, than during the single TPP optical state excitation, due to the optical response to the PMMA and SLG/PMMA. The analysis of the in-plane wave vector, which the plasmonic mode gives, allows one to obtain more sensitive optical responses from such graphene-based hybrid nanostructures. The widening of the TPP and SPP resonance width weakens the coupling strength and decreases the Q-factor. Moreover, the monitoring of the coupling strength between the TPP and SPP components gives additional information about the optical responses of such hybrid optical devices.
Acknowledgment
Authors of this article thank Dr. Algirdas Selskis for providing SEM micrographs.
Disclosures
The authors declare no conflicts of interest.
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