Open Access
Add to BibSonomyAbstract
A modified spatial filtering method that improves the sensitivity of single-beam and mode-mismatched thermal lens spectroscopy (TLS) for fluorescence quantum yield measurement is presented. The method is based on the detection of the external part of a laser beam transmitted by the fluorescent sample (eclipsing detection mode). The experimental results show that the signal/noise (S/N) ratio of the absolute quantum yield of Rh6G can be enhanced up to ~1400% using the eclipsing detection mode on the TLS experimental setup. The method was evaluated by measuring the fluorescence quantum yield of varying concentration of ethanolic solutions of Rhodamine 6G.
©2013 Optical Society of America
1. Introduction
Thermal Lens Spectroscopy (TLS) is a powerful and well-established tool for material characterization. TLS can be applied to the measurement of analyte concentrations [1,2], characterization of trace elements in gases [3], measurement of absolute absorption coefficients [4], and spectrometry for liquid chromatography [5,6]. In particular, TLS has been established as an accurate technique to evaluate quantum yield, diffusivity and thermal conductivity of liquid and transparent solid media [7]. The first reports of the thermal lens effect were made by Gordon et. al [8] and by Leite et. al [9]. Since then, the TLS experimental configurations have evolved (i) from intra to extra-cavities setups and (ii) from the use a single-beam to a dual-beam excitation-probe detection mode, which is considered to be the most sensitive extra-cavity configuration [10–12].
In the optical characterization of organic laser dyes, η is also an essential parameter on laser threshold determination [13,14].The fluorescence quantum efficiency is the rate between radiative and nonradiative processes occurring in luminescent materials. The techniques to determine η can be classified into absolute and relative method [14–16].Earlier quantum yields measurements based mostly in fluorometry were wrong mainly due to lack of care of experimental conditions and suffered from the low resolution of the measuring instruments. Therefore, TLS emerges as a technique which presents more accurate results for η values when compared with methods that directly explore relative and absolute fluorescence analysis [14–18], which involve the characterization of total light emitted by the sample or require comparison between the emission of the unknown and standard sample [15,19–22]. The TLS high sensitivity allows the evaluation of samples with low analyte concentration (10−11 mol/L) or with low absorptivities of 10−7 cm−1 [2,17]. In this sense, the TLS may be 100 times more sensitive than methods that direct explore fluorescence analyses [2]. Using a suitable experimental design, thermal lens techniques can detect variations of the refractive index across the probe beam waist as small as 10−8, which corresponds to temperature variations of 10-5 0C in liquids [18]. Other techniques based on thermal processes, as photothermal radiometry [23] and photoacoustic methods [21] can be used to determine the quantum yield of fluorescent materials.
To determine η with the TLS technique, a Gaussian beam from a modulated cw or pulsed laser is focused onto a liquid or solid medium containing fluorophores. After the absorption of the excitation beam, the fluorophores at ground energy state are promoted to higher excited states, from which they decay by radiative and nonradiative processes. The latter process relies on the transference of heat to the host, heating it, and thus leading to a time-dependent transverse spatial profile of the temperature ΔT(r,t) in the sample. The temperature gradient ΔT(r,t) creates a refractive index gradient (dn/dT)normal to the beam axis. The resulting gradient (dn/dT) produces a lens-like object, which is known as a thermal lens (TL). The spatial and temporal evolution of ΔT(r,t) in the medium can be described by the heat transfer equation [8,10,12].The diffraction theory predicted that when a probe laser beam propagates through the TL, its wavefront changes. A consistent theoretical model for the TL effect based on Fresnel diffraction approximations for excitation-probe configuration was developed by Sheldon et. al [12] for both the mode-matched (also valid for single-beam scheme) and by Shen et. al [11] for mode-mismatched conditions. Equation (1) is the analytical expression for the intensity of probe beam reaching the detector in the mode-mismatched configuration [10].
where I0 is the intensity of the probe beam at t = 0, m = (wp/wex)2, wp and wex are the beam waist of probe and excitation beams in the sample, respectively. V is given by:where focus of the probe is considered the origin of z-axis. Z and Z2 represent the sample and the detector positions (see Fig. 1), respectively. Z0P is the probe beam Rayleigh range, tc is the characteristic heat diffusion time , with as the thermal diffusivity, ρ is the volumetric density, and CP is the specific heat of sample. θ is the thermal phase shift, whose amplitude is given by Eq. (3) [10, 17].with φ being the fraction of absorbed energy transformed in thermal energy, also called the absolute nonradiative quantum efficiency; λp is the probe beam wavelength, κ is the thermal conductivity of solvent, dn/dT is the thermo-optic coefficient, and Pabs is the absorbed power from excitation beam, given by Pabs = Pex (1-e-αL), where α is the linear optical absorption coefficient at the excitation wavelength (λex) and L is the thickness of sample. For nonfluorescent materials, φ = 1 and for fluorescent materials φ < 1, withwhere is the average emission wavelength and is the number of photons emitted per second in an incremental wavelength centered at. Defining and [24], and using Eq. (3) and (4), the expression to fluorescence quantum yield is [16].
Fig. 1 Scheme of the geometric position of the laser beams in a dual-beam mode-mismatched TL (DTL) configuration.
The use of a spatial filter to increase the TL sensitivity was first proposed by Slaby [25,26] and by Bloisi et. al [27], who observed the enhanced of the S/N ratio of the diffracted beam. The use of a spatial filter was also introduced in the Z-scan technique (Eclipse Z-Scan) to improve the sensitivity in nonlinear refraction measurements [28]. As consequence of the presence of the wavefront spatial filter, the transmitted beam appears like a solar eclipse. In eclipse detection mode, significant intensity changes are expected to be measured in the wings of the transmitted beam rather than near the center [28,29].
In this work, we present a modified detection mode for a single-beam and a mode-mismatched TLS on quantum yield measurements that improves the sensitivity of the technique. The proposed modified setup, detects only the external fraction of the transmitted beam by blocking the central part using a spatial filter. This mode is referred to as the eclipsing detection mode.
To evaluate the modified system, we measured the fluorescence quantum yield of Rh6G dye molecule in an ethanolic solution and recorded the (S/N) ratio of the detected beam. It is known that, in addition to the background noise own of detector, the spatial noise due the fluctuations of the beam intensity also contributes to the overall background signal. The spatial noise originates from convective motions in the TL region and the laser’s instability. If the background signal is large, the detection limit of TLS is reduced and the experimental errors become considerable. We show that the S/N ratio during the measurement of absolute quantum yield of Rh6G can be enhanced up to ~1400% when an eclipsing detection mode is explored in the TLS experimental setup.
From here on, the new methodology will be referred to as Eclipse Thermal Lens (ETL) and S-ETL or D-ETL when a single-beam laser or dual-beam (excitation-probe lasers).
2. Experimental Details
The experimental setup for TLS used to evaluate the quantum yield of Rh6G is shown in Fig. 2. The excitation beam was a modulated frequency-doubled cw Nd:YAG laser (Compass 215M-20; Coherent, Inc.) emitting at 532 nm. The fluorescent samples for TL experiments were ethanolic solutions of Rh6G with concentrations between 10−4 and 10−7 M. The samples were enclosed into a 1 mm optical length quartz cuvette. Two additional samples for fluorescence characterization were prepared, 5 × 10−4 and 1 × 10−3 M. Both, the Rh6G (dye content 99%) and the ethyl alcohol (puriss. P.A. > 99.8%) were provided by Sigma Aldrich Co., with the Rh6G being used without further purification. The acquisition of absorption spectra was performed using a UV-Vis spectrophotometer model evolution 600 BB (Thermo Scientific Inc.). The emission spectra were acquired by a spectrometer model HR400 (Ocean Optics Inc.). To focus the excitation beam onto the Rh6G samples, spherical lenses were used, with a f = 10cm lens used in the single-beam and a f = 15cm lens used in the mode-mismatched configuration). The excitation beam waist at the sample was ~15 µm in S-ETL and ~20 µm in the D-ETL mode-mismatched configuration. In the D-ETL setup a HeNe laser (632.8 nm) was used as the probe beam. It was focused on the sample in a counter-propagating direction, establishing an angle of ≈3.5° with the excitation beam. The red laser power at the sample was 1.1 mW. The probe beam diameter at the sample was measured as approximately 56 µm. A chopper was used to control the excitation the laser exposure time on the sample (duty cycle = 0.05, rotation frequency: 200 Hz for the S-ETL configuration and 20 Hz for the mode-mismatched configuration). The difference in the chopper frequencies implies an increase of an order of magnitude in the transient time of TL signal in the excitation-probe mode mismatched configuration. This longer time to detect of TL signal can be explained as a consequence of how fast the effect is created and how long a measurement is performed. In the conventional single-beam TL the same laser is used to create and measure the TL effect, resulting in characteristic transient time. In the mode-mismatched configuration, the probe’s diameter is larger than the excitation beam (2.8, in this experiment), resulting in the increase time needed for the system to reach steady-state [30].
Fig. 2 Experimental setup for S-ETL/D-ETL method. L1 and L7 (f = 3.5 cm), L2 (f = 25 cm), L3 and L4 (f = 10 cm), L5 (f = 15 cm), L6 (f = 20 cm) are spherical lens; M1, M2 and M3 are aluminum mirrors; D is a silicon photodiode.
A convergent lens was positioned just after to the wavefront spatial filter to collect and direct the light to the photodetector, allowing for the detection not only of the diffracted beam but also the external part of transmitted beam, increasing the TL signal. The photodetector used to measure the TL signal scanned by both the green and red lasers was a silicon photodiode model BPW21R with spectral response peak at 565 nm, its low performance at 632 nm reduce the sensitivity of the dual-beam TLS technique.
3. Results and Discussions
3.1. single-beam configuration
We measured the values of η of Rh6G and the S/N ratio of the TL signal using the S-ETL and the traditional single-beam TL methods. Figure 3 shows the transient signals (focal and post-focal) due to the thermal effect in a sample of 10−6 M of Rh6G measured using single-beam TLS [Fig. 3(a)] and when a spatial filter was used [Fig. 3(b)]. No averaging was performed on the oscilloscope detected signals. The signal in Fig. 3(b) appears inverted with respect to Fig. 3(a) due to convergent role of lens L4. The optical power of excitation beam was 8 mW. The inset in Fig. 3(b) is a digital image of transmitted beam. Comparing Figs. 3(a) and 3(b), clearly, we can observe an enhanced in the S/N ratio when the S-ETL method is used. The S/N ratios were evaluated at a stationary regime (t = 2.5 ms). S/N values were measuring assuming different values for the beam waist (at the filter position)/wavefront filter diameter ratio as shown in Table 1. An enhanced of ~300% on the S/N ratio was observed by exploring the S-ETL method when compared with its respective values obtained by the conventional single-beam TL.
Fig. 3 TL signal from a 10−6 M of Rh6G in ethanol solution obtained by (a) single-beam TL and (b) S-ETL methods. The inset image in (b) is a digital image of excitation beam after the wavefront filtering. N and S indicate noise and signal respectively.
Table 1. Signal/noise ratios for three different beam/filter diameters ratio. The Rh6G concentration was 10−6 M and the excitation power was 8 mW.
The dependence of η as a function of the excitation power using the S-ETL and the traditional single-beam TL methods was also evaluated. Figure 4(a) shows the excitation power dependence of η, obtained by the S-ETL method, for a 10−6 M of Rh6G. No significant change of the fluorescence quantum yield value was observed at excitation powers between 4.2 and 8.0 mW. Below 4.2 mW, the TL signal was not detectable. In this study, the maximum power density of excitation laser was ~11 × 106 W/m2, closed to the value (≈106 W/m2) for optical saturation in the majority of laser dyes [31–33]. The optical saturation produces a nonlinear dependence of TL signal with the excitation power limiting the sensitivity of photothermal effects. To guarantee the sensitivity of TLS in Rh6G solutions is necessary to ensure the full transference of thermal energy from nonradiative decays to the solvent. The TL signal was faint for Rh6G concentrations lower than 10−6 M. Table 2 shows the mean values of quantum yield (<η>) obtained considering excitation powers between 4.2 and 8 mW. In Table 2, the <η> values obtained here, with the S-ETL method, are compared with those reported in the literature using different methods. Table 2 also shows that the measured quantum yield values decrease as concentration of the dye increase. The η dependence with dye concentration can be better observed in Fig. 4(b). A decrease of ~10% in the quantum yield was measured when the Rh6G concentration increase from 10−6 M (η ~94%) to 10−4 M (η ~84%). Evaluating the samples fluorescent spectra, a red shift (up to 12 nm) of the emission peak was observed as the dye concentration increased, which can be attributed to reabsorption of light emitted by monomers and by fluorescents (J-type) and non-fluorescents (H-type) dimers [34–36]. Moreover, considering a dimerization constant for Rh6G in ethanol as Kd = 0.22 [35], we estimate that dimers concentration in our most concentrated sample (1 × 10−4 M) was Cd = 2.2 × 10−9 M. Therefore, the observed decrease of the quantum efficiency can be mainly attributed to reabsorption processes of monomers, which are a consequence of the overlaps between absorption and emission spectrum of Rh6G, as discussed in reference [37,38].
Fig. 4 Fluorescence quantum yield values of Rh6G obtained by S-ETL method as a function of, (a) the excitation power and (b) its molar concentration.
Table 2. Mean values of quantum yield values for different Rh6G concentrations obtained by S-ETL methods.
3.2. Dual-beam configuration
In this section, the dual-beam mode-mismatched TL (DTL) configuration exploring the eclipse detection mode (D-ETL) is evaluated. Figures 5(a) and 5(b) respectively, show the normalized postfocal TL signal measured with and without the presence of the wavefront spatial filter. No average was performed on the oscilloscope detected signals. A large increment in the TL signal is observed when the eclipse is used. The eclipse detection mode provides 14-fold increase in the ratio S/N of the DTL signal, when the beam excitation power was 9 mW. Table 3 shows the S/N values obtained at different power excitations of the Nd:YAG laser. The Rh6G concentration was 2 × 10−5 M. Note that the ratio S/N is reduced from 14.1 to 11.9 when the power of laser beam was increased from 9 mW (7.2 W/cm2) to 11 mW (8.8 W/cm2), due probably to detector saturation.
Fig. 5 Normalized TL signal of a HeNe probe beam (632 nm) passing through a sample of 2 × 10−5 M of Rh6G in ethanol solution when excited by 9 mW from a cw Nd:YAG laser (532 nm). Signal obtained using (a) dual-beam mode mismatched TL (DTL) and (b) D-ETL method. The inset image in (b) is a digital image of the probe beam, before and after the wavefront filter.
Table 3. Ratio S/N between the D-ETL and the conventional DTL techniques. The Rh6G concentration was 2 × 10−5 M.
The dependence of quantum yield of Rh6G with the dye concentration was also observed using D-ETL. Table 4 shows the medium values of η for different Rh6G concentrations. One can note that η values decrease as the dye concentration increases. Moreover, the obtained values agree very well with those reports by others authors.
Table 4. Mean values of quantum yield values for different Rh6G concentrations obtained by D-ETL method compared with those obtained by other authors
Figure 6(a) and 6(b) show η values for Rh6G versus the excitation power, obtained with and without the use of the wavefront spatial filter, respectively. Note that in the presence of spatial filter, it was possible to measure values to η of samples with concentration of 2 × 10−7 M. Without spatial filter, no η values were obtained for Rh6G concentrations bellow 10−6 M. The comparison between the η values, for concentrations ~10−5 M, in Fig. 6(a) with those in Fig. 6(b), shows that the greater sensitivity of D-ETL method allows measure η with a laser power 1.6 times lower (2.7 mW) than using S-ETL or single-beam TL method (4.2 mW). Figure 7 shows values of η as a function of Rh6G concentration. Fluorescence quantum yield decrease as the Rh6G concentration increase, as observed in the S-ETL [Fig. 4(b)].
Fig. 6 Fluorescence quantum yield of Rh6G dissolved in ethanol as function of excitation power. Measurements performed (a) with and (b) without a wavefront filter in the dual-beam TL.
Fig. 7 Fluorescence quantum yield of ethanolic solutions of Rh6G as a function of its molar concentration for different excitation powers measured by D- ETL method.
4. Conclusions
A modified method for thermal lens spectroscopy called of Eclipse Thermal Lens (ETL) was used to measure the quantum yield of Rh6G solution. By using a wavefront spatial filter, the sensitivity in the TL detection was increased by a factor of ~3 in the traditional single-beam TL technique and by ~14 in the dual-beam mode-mismatched configuration. The larger sensitivity and the low excitation powers required on the presented method allow the evaluation of quantum yield reducing photoblenching and optical saturation effects. Moreover, the TL technique, with the eclipse detection mode, is of special interest for the evaluation of fluorescence quantum yield at low concentration of fluorophore, whose quantum efficiency is large, condition where the thermal effects are not well pronounced, reducing the performance of conventional TL methods.
Acknowledgments
This study was support by CAPES, the Center of Excellence of Nanophotonics and Biophotonics (PRONEX/FACEPE/CNPq), and INCT Fotônica (CNPq).
References and links
1. N. J. Dovichi and J. M. Harris, “Laser induced thermal lens effect for calorimetric trace analysis,” Anal. Chem. 51(6), 728–731 (1979). [CrossRef]
2. T. Imasaka, K. Miyaishi, and N. Ishibashi, “Application of the thermal lens effect for determination of iron(II) with 4,7-diphenyl-1,10-phenanthroline disulfonic acid,” Anal. Chim. Acta 115(1), 407–410 (1980). [CrossRef]
3. G. C. Nieman and S. D. Colson, “Pressure effects on the two-photon spectrum of trans-butadiene as detected by gas phase transient lensing spectroscopy,” J. Chem. Phys. 68(6), 2994–2996 (1978). [CrossRef]
4. J. R. Whinnery, “Laser measurement of optical absorption in liquids,” Acc. Chem. Res. 7(7), 225–231 (1974). [CrossRef]
5. C. E. Buffett and M. D. Morris, “Thermal lens detection for liquid chromatography,” Anal. Chem. 54(11), 1824–1825 (1982). [CrossRef]
6. R. A. Leach and J. M. Harris, “Thermal lens calorimetry,” J. Chromatogr. A 218, 15–19 (1981). [CrossRef]
7. D. R. Snook and R. D. Lowe, “Thermal lens spectroscopy. A review,” Analyst (Lond.) 120(8), 2051–2068 (1995). [CrossRef]
8. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36(1), 3–8 (1965). [CrossRef]
9. R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurement by mean of the thermal lens effect using a He:Ne laser,” Appl. Phys. Lett. 5(7), 141–143 (1964). [CrossRef]
10. J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992). [CrossRef]
11. M. L. Baesso, J. Shen, and R. D. Snook, “Time-resolved thermal lens measurement of thermal diffusivity of soda-lime glass,” Chem. Phys. Lett. 197(3), 255–258 (1992). [CrossRef]
12. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21(9), 1663–1669 (1982). [CrossRef] [PubMed]
13. P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, and E. C. Hammond, “Flashlamp‐pumped organic‐dye lasers,” J. Chem. Phys. 48(10), 4726–4742 (1968). [CrossRef]
14. G. A. Crosby and J. N. Demas, “The measurement of fluorescence quantum yields. Review,” J. Phys. Chem. 75(8), 991–1024 (1971). [CrossRef]
15. C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Comparison of methods and achievable uncertainties for the relative and absolute measurement of photoluminescence quantum yields,” Anal. Chem. 83(9), 3431–3439 (2011). [CrossRef] [PubMed]
16. R. A. Cruz, V. Pilla, and T. Catunda, “Quantum yield excitation spectrum (UV-visible) of CdSe/ZnS core-shell quantum dots by thermal lens spectrometry,” J. Appl. Phys. 107(8), 083504 (2010). [CrossRef]
17. A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem. 20(2–4), 99–110 (2002). [CrossRef]
18. C. Hu and J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt. 12(1), 72–79 (1973). [CrossRef] [PubMed]
19. J. H. Brannon and D. J. Magde, “Absolute quantum yield determination by thermal blooming. Fluorescein,” J. Phys. Chem. 82(6), 705–709 (1978). [CrossRef]
20. K. Suzuki, A. Kobayashi, S. Kaneko, K. Takehira, T. Yoshihara, H. Ishida, Y. Shiina, S. Oishi, and S. Tobita, “Reevaluation of absolute luminescence quantum yields of standard solutions using a spectrometer with an integrating sphere and a back-thinned CCD detector,” Phys. Chem. Chem. Phys. 11(42), 9850–9860 (2009). [CrossRef] [PubMed]
21. C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta 90, 30–37 (2012). [CrossRef] [PubMed]
22. A. M. Brouwer, “Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report),” Pure Appl. Chem. 83(12), 2213–2228 (2011). [CrossRef]
23. A. Mandelis, M. Munidasa, and A. Othonos, “Single-ended infrared photothermal radiometric measurement of quantum efficiency and metastable lifetime in solid-state laser materials: The Case of Ruby (Cr3+:A1203),” IEEE J. Quantum Electron. 29(6), 1498–1504 (1993). [CrossRef]
24. S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett. 78(21), 3220 (2001). [CrossRef]
25. J. Słaby, “Application of spatial filtering in thermal lensing detection,” Opt. Commun. 64(2), 89–93 (1987). [CrossRef]
26. J. Slaby, “Background illumination filtering in thermal lens spectroscopy,” Anal. Chem. 61(22), 2496–2499 (1989). [CrossRef]
27. F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun. 68(6), 391–395 (1988). [CrossRef]
28. T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wavefront distortion,” Opt. Lett. 19(5), 317–319 (1994). [CrossRef] [PubMed]
29. A. S. L. Gomes, E. L. Filho, C. B. de Araújo, D. Rativa, and R. E. de Araujo, “Thermally managed eclipse Z-scan,” Opt. Express 15(4), 1712–1717 (2007). [CrossRef] [PubMed]
30. R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara Jr, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv. 1(2), 022154 (2011). [CrossRef]
31. B. Li and R. Gupta, “Optical saturation in continuous-wave photothermal deflection spectroscopy: quantitative investigation of fundamental and harmonic components,” Appl. Opt. 40(9), 1563–1569 (2001). [CrossRef] [PubMed]
32. Y. M. Biosca and G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in non-polar solvents,” Anal. Chim. Acta 345(1–3), 257–263 (1997). [CrossRef]
33. S. E. Bialkowski, A. Chartier “Using slow measurement systems to measure fast excited-state kinetics with nonlinear rate-competitive optical bleaching,” in Photoacoustic and Photothermal Phenomena:Tenth International Conference, F. Scudieri, M. Bertolotti, eds., AIP Conf. Proc. 463, 14–17 (1999). [CrossRef]
34. M. Fischer and J. Georges, “Fluorescence quantum yield of rhodamine 6G in ethanol as a function of concentration using thermal lens spectroscopy,” Chem. Phys. Lett. 260(1–2), 115–118 (1996). [CrossRef]
35. F. López Arbeloa, P. Ruiz Ojeda, and I. López Arbeloa, “The fluorescence quenching mechanisms of rhodamine 6G in concentrated ethanolic solution,” J. Photochem. Photobiol., A 45(3), 313–323 (1988). [CrossRef]
36. C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett. 464(4–6), 245–248 (2008). [CrossRef]
37. R. F. Kubin and A. N. Fletcher, “Fluorescence quantum yields of some rhodamine dyes,” J. Lumin. 27(4), 455–462 (1982). [CrossRef]
38. R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol. 53(3), 317–322 (1991). [CrossRef]
39. C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B 13(16), 563–576 (1999). [CrossRef]
40. L. S. Rohwer and J. E. Martin, “Measuring the absolute quantum efficiency of luminescent materials,” J. Lumin. 115(3–4), 77–90 (2005). [CrossRef]
41. R. R. Hammond, “Selfabsorption of molecular fluorescence, the design of equipment for measurement of fluorescence decay, and the decay times of some laser dyes,” J. Chem. Phys. 70(8), 3884–3894 (1979). [CrossRef]
