- Email: [email protected]
Laser-induced incandescence of suspended particles as a source of excitation of dye luminescence
Journal of Luminescence 104 (2003) 27–33
Laser-induced incandescence of suspended particles as a source of excitation of dye luminescence S. Zelensky Physics Department, Kiev University, 6 Glushkova str., Kiev 03127, Ukraine Received 27 May 2002; received in revised form 31 October 2002; accepted 31 October 2002
Abstract The interaction of pulsed YAG-Nd3þ laser radiation with submicron light-absorbing particles suspended in an aqueous solution of Rhodamine 6G is investigated experimentally. The experiments demonstrate that the laser-induced incandescence of suspended particles excites the luminescence of the dissolved dye molecules. The mechanism of the luminescence excitation consists in the reabsorption of the thermal radiation within the volume of the sample cell. On the ground of this mechanism of excitation, a method of measurement of the luminescence quantum yield is proposed and realized. The method requires the knowledge of the geometrical parameters of the cell and does not require the use of reference samples. r 2002 Elsevier Science B.V. All rights reserved. PACS: 78.55.Bq; 33.70.Fd Keywords: Laser-induced incandescence; Reabsorption; Luminescence quantum yield; Suspensions; Rhodamine 6G
1. Introduction It is not a rare occasion in laser spectroscopy when an investigated transparent object contains a number of microscopic inclusions absorbing the laser light. For example, it can be dust particles in the air, soot particles in a flame or in a combustion engine, foreign inclusions in crystals or in glass, suspended particles in natural water or in artificial suspensions, etc. The presence of such inclusions can manifest itself in various optical properties of the object investigated. One of the ways to reveal the inclusions is to overheat them by the laser radiation. E-mail address: [email protected] (S. Zelensky).
Consider a black-body particle with the size of 0.1–1 mm which absorbs the pulsed laser radiation with the surface power density of 10– 100 MW cm2 (such radiation intensities can be easily obtained with laboratory-scale Q-switched lasers even without focusing). If the heat transfer from the particle to the environment can be neglected, the primitive treatment of the energy balance equation shows that the particle temperature can reach up to 104 K under the laser irradiation. Even if the thermal relaxation to the environment is taken into account, the estimated particle temperature exceeds the room temperature at least by a factor of ten. It is conceivable that such light-absorbing submicron particles in transparent condensed matter or in gaseous phase,
0022-2313/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-2313(02)00661-0
28
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
under the irradiation of a powerful laser, will emit measurable Planck’s radiation in the visible spectral region. The experimental observation of the mentioned laser-induced incandescence (LII) of suspended particles is reported, for example, in [1–4]. Another example of experiments in which the thermal radiation significantly manifests itself is the laser-induced visible emission of silicon nanoparticles in porous silicon [5,6]. In a number of earlier publications this emission was mistakenly interpreted as luminescence. The following features of LII in transparent condensed matrixes seem to be noteworthy. (i) The LII is usually observed at the conditions of strong scattering of the laser radiation by the suspended particles, so that the thermal radiation is significantly masked by the scattered light. To detect the LII signal, measures should be taken for the elimination of the scattered laser light (a single grating monochromator is suitable in most of the cases). (ii) For the above-mentioned values of laser intensity, the power of the LII optical signals is sufficient for reliable detection by a photomultiplier. If the infrared laser is employed, the LII is clearly visible to the naked eye. (iii) The phenomenological properties of LII are similar to the properties of broadband laser-induced luminescence. This circumstance makes it difficult to separate the luminescence and thermal radiation signals. For a suspension of light-absorbing particles irradiated by the infrared laser radiation, the LII looks like a homogeneous track of white color, without any signs of its polarization and anisotropy. In the paper [4] the signals of LII were detected within the spectral range of 220–750 nm: This spectral interval was not the feature of LII itself, but it was restricted by the characteristics of the employed photodetector. When the LII is detected at a fixed wavelength, the dependence of its intensity, I; on the laser intensity, F ; is essentially non-linear. For a moderate deviation of F ; the relationship between I and F can be approximated as DI=I ¼ gðDF =F Þ. The introduced index of non-linearity, g; is a function of F : g decreases with the increase of F : For example, the experiments demonstrated g ¼ 6–2 [3,4], gC3½6:
A promising situation arises when light-absorbing particles are suspended in a luminescent medium. In this case the chances are that the LII can serve as an internal source of excitation for the luminescence. The goal of this article is to demonstrate the reality of the mentioned mechanism of luminescence excitation.
2. Experimental details The experiments were carried out with the following three objects denoted hereinafter as ‘‘A’’, ‘‘B’’, and ‘‘C’’. The object ‘‘A’’ was the aqueous suspension of light-absorbing particles. It was prepared by dilution of black gouache paint in distilled water. The suspension was filtered for the restriction of size of the suspended particles at a level of o2 mm: The concentration of suspended particles was low enough, so that the attenuation of optical signals within the cell volume can be considered as negligible (the optical transmittance of the suspension in the visible spectral region exceeded 0.95 at a thickness of 1 cm). The object ‘‘B’’ was prepared of the object ‘‘A’’ by adding Rhodamine 6G dye with the concentration of approximately 3 105 mol l1 : The absorption spectrum of the suspension ‘‘B’’ is given in Fig. 1, curve ‘‘Abs’’. The absorption band observed corresponds to the Rhodamine molecules. The third object, ‘‘C’’, was the aqueous solution of Rhodamine 6G with the same concentration as in the solution ‘‘B’’. The absorption spectrum of the solution ‘‘C’’ practically coincides with the absorption spectrum of the suspension ‘‘B’’, that indicates the absence of considerable interaction between the Rhodamine molecules and the suspended particles. The experiments were performed with a Qswitched YAG-Nd3þ laser (wavelength 1:06 mm; pulse duration B30 ns). The LII was detected by a photomultiplier through a single grating monochromator. The non-uniformity of spectral sensitivity of the spectrometer was corrected with the use of a standard tungsten lamp. The pulse duration of the optical signals, both the LII and the luminescence, was approximately the same as
κ , cm
-1
S. Zelensky / Journal of Luminescence 104 (2003) 27–33 6 4 2 0
29
Rectangular glass block
Abs Laser beam
Collimated laser beam
H
2.5 BCOR
2.0
Capillary orifice 2R
A
Excited volume (cylindrical)
Collimating slit
1.5
Pump flow
I (λ), a.u.
B
Fig. 2. The experimental layout. The direction of light collection is perpendicular to the plane of the drawing.
1.0
0.05
C, CCOR
0.00 (BCOR-A)
0.2 E 0.0 450
500
550
600
650
λ, nm
Fig. 1. The absorption spectrum (abs) of the suspension ‘‘B’’ and the emission spectra of the suspensions ‘‘A’’, ‘‘B’’, and ‘‘C’’. All of the spectra, except ‘‘abs’’, are given in equal arbitrary units. The suffix ‘‘COR’’ labels the spectra corrected for reabsorption. The spectrum C is plotted as circle points, the spectrum CCOR –as a solid line. The spectrum E is the difference ðBCOR A CCOR ).
of the laser. The laser repetition rate was approximately 1 pulse s1 : Every pulse from the photomultiplier was digitized and processed separately, the data averaging was implemented in the software. To prevent the laser-induced fading of the objects investigated, the suspensions were pumped through the optical cell with a flow of 0.5–1 cm3 s1 ; so that each of the laser pulses interacted with a ‘‘fresh’’ portion of the suspension. The rectangular glass block with the capillary orifice was used as an optical cell. The geometrical arrangement of the cell and laser beam is outlined in Fig. 2. The laser radiation passes through the collimating slit and hits the cell, thus the irradiated volume of the suspension is the cylinder with the
height of H ¼ 1:5 mm and with the radius of R ¼ 0:25 mm: The LII was collected with a fiber-optic bundle installed perpendicularly to the orifice and to the laser beam. The whole irradiated volume was located within the field of vision of the lightcollecting bundle. As it was mentioned, the emission investigated is non-linear. That is why it is important to keep the uniformity of laser excitation within the cell volume, otherwise the errors arise. For this purpose, the height of the collimating slit was approximately half as large as the laser beam diameter. Besides, the laser was equipped with a diaphragm in the resonator, so that its operation was close to the single-mode regime with the smooth bell-shaped distribution of surface power density across the beam.
3. Results and discussion The emission spectra of the objects ‘‘A’’, ‘‘B’’, and ‘‘C’’ are given in Fig. 1 (curves A, B, and C, respectively). The laser excitation intensity is approximately 10 MW cm2 : Each of the plotted points is the average of 5–10 laser pulses. The spectra A, B, and C in Fig. 1 were recorded at the same experimental conditions, i.e. the same photomultiplier gain voltage, the same level of excitation, the same geometrical arrangement. The emission of the object ‘‘A’’ (curve A, Fig. 1) shows all of the features of LII [3,4], namely, the essential non-linear behavior with F ðgC3Þ and the broad spectrum which can be fitted with a
30
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
Planck’s function with a particle temperature of 3500 K: For the emission considered, the method of particle temperature estimation proposed in [4] is inapplicable because of the relatively high level of laser excitation. As is seen from Fig. 1, in the spectral region of 540–640 nm; the emission of the suspension ‘‘B’’ exceeds the emission of the suspension ‘‘A’’ due to the Rhodamine luminescence. On the contrary, in the spectral region of 470–540 nm; the spectrum A exceeds the spectrum B due to the reabsorption of the LII by the Rhodamine molecules in the cell en route towards the photo-detector. The curve C in Fig. 1 is the spectrum of Rhodamine luminescence excited via the twophoton absorption of laser radiation (hereinafter referred to as the two-photon luminescence, TPL). For this luminescence, the experimental dependence of its intensity on the laser excitation intensity demonstrates the quadratic law which is naturally expected for the two-photon excitation. As one can see in Fig. 1, the contribution of Rhodamine luminescence to the spectrum B (the difference between the spectra B and A in the region 540–580 nm) exceeds the TPL spectrum of the solution ‘‘C’’. This fact indicates the presence of a new mechanism of excitation of Rhodamine luminescence in the experiments considered. It is plausible to suggest that in the experiments the LII serves as an intermediary agent (or an anti-Stokes energy transformer) between the infrared laser radiation and the dye molecules. As is clearly seen from Fig. 1, the mentioned reabsorption of LII significantly distorts the shape of the emission spectrum B, thus it is difficult to correctly separate the luminescence out of the spectrum B. For the elimination of the distortion, consider the following model (see Fig. 3). The cylindrical volume of radius R and height H contains the homogeneous suspension, that emits light with the constant power volume density, P: Denote the spectral density of P as PðlÞ: The photodetector is located on the X -axis, so that the light-collecting aperture of the photodetector is seen at a spatial angle of DO: Consider the element of volume, dV : The spectral density of optical signal emitted from dV towards the photodetector
y R
∆Ω
Photodetector aperture
dV
ρ sin ϕ
dI
ξ (ρ , ϕ )
ρ ϕ
0
R
ρ cos ϕ
x
R2 − ρ 2 sin2 ϕ
Fig. 3. The schematic drawing for the calculation of optical signals with the expressions (1)–(4).
can be written as follows: dIðlÞ ¼ PðlÞ
DO expðkðlÞxÞ dV ; 4p
ð1Þ
where kðlÞ is the absorption coefficient of the suspension, x is the distance in the OX direction between the element dV and the edge of the lightemitting volume (see Fig. 3). In the case of absence of the reabsorption, obviously, dI0 ðlÞ ¼ PðlÞ
DO dV : 4p
ð2Þ
The integration of (1) and (2) over the cylindrical volume gives the following expression: Z IðlÞ 2 1 GðlÞ ¼ ¼ r dr I0 ðlÞ p 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z p dj exp kðlÞR 1 r2 sin2 j r cos j ; 0
ð3Þ where r ¼ r=R: The function GðlÞ obtained can be used for the correction of spectral distortions caused by the reabsorption. It should be noted, in the experiments, the response of the photodetector, i; is proportional to the optical signal, I; as follows: iðlÞ ¼ SðlÞIðlÞL;
ð4Þ
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
where SðlÞ is the spectral sensitivity of the spectrometer, L is the spectral width of the monochromator’s slit. The correction procedure proposed can be applied to the spectrum B, Fig. 1, with the use of the spectrum Abs, Fig. 1, as kðlÞ in (3). The corrected spectrum is given in Fig. 1, curve BCOR : As is seen, the spectrum BCOR in the spectral region of Rhodamine’s absorption is in agreement with the spectrum A, so the correction performed can be rated as good. The emission spectrum of the suspension ‘‘B’’ (the spectrum BCOR ) includes the following signals: (i) the LII, (ii) the TPL of Rhodamine, and (iii) the luminescence of Rhodamine excited via the LII. After the elimination of the reabsorption-caused distortions, the luminescence spectrum can be separated out of the total emission spectrum BCOR : The difference of spectra BCOR and A, Fig. 1, is denoted as the curve (BCOR A). The difference of the spectrum (BCOR A) and the spectrum C corrected for reabsorption CCOR is given in Fig. 1, curve E. The final spectrum E represents the luminescence of Rhodamine 6G excited via the LII. The considered mechanism of excitation of luminescence via the LII seems to be intuitively obvious, however, the relative magnitude of the optical signals requires some additional treatment. In the experiments described in this article, the geometrical parameters of the light-emitting volume are fixed, thus providing the possibility to perform some numerical calculations of the signals. Consider the following simplified model. The cylindrical cell contains the suspension being irradiated by the laser radiation. Suppose the nondepleted pump approximation holds true for the laser light, i.e. the surface power density of the laser radiation, F ; is a constant. Therefore, the volume power density of LII, PLII ; can also be considered as a constant function of coordinates within the cell volume. At a point with the coordinates ~ r ; the integral number (over the absorption spectrum) of the LII photons absorbed by the dye molecules per unit time and per unit volume can be written: Z l nabs ðrÞ ¼ kðlÞ rl ðrÞ dl; ð5Þ h abs
31
where rl is the spectral density of LII energy in a unit volume, h is the Planck constant. The integration in (5) is performed over the spectral interval of the dye absorption spectrum. By integrating expression (5) over the cell volume, V ; the total number of the absorbed LII photons per unit time can be obtained: Z Z l Na ¼ dl kðlÞ d3 r rl ðrÞ: ð6Þ h V abs It should be noted, the volume density, rl ; is a function of the coordinates r; though F and PLII are constants. Within the cell volume, the elementary volumes, d3 r0 ; contribute to the value of rl according to the inverse square law, thus the following formula can be written: Z PLII ðlÞ rl ð~ rÞ ¼ d3 r0 ; ð7Þ 02 V 4pcjr -r j where c is the speed of light. Expression (7) does not take into account the absorption of LII by the dye molecules. The errors caused by this approach will be considered thereinafter. By substituting (7) into (6) we obtain: Z W Nabs ¼ kðlÞlPLII ðlÞ dl; ð8Þ 4phc abs where Z Z 3 d r W¼ V0
V
d3 r0
1 : jr r0 j2
ð9Þ
The introduced constant parameter, W ; can be computed for a given cell geometry. The optical signal measured experimentally is proportional to the total power of the light emitted in the cell. For the suspension ‘‘A’’, it can be written as follows: Z IA ðlÞ ¼ G PLII ðlÞ d3 r ¼ GPLII ðlÞ pR2 H; ð10Þ V
where G is the geometric factor. G accounts for the fraction of the total radiation emitted which falls into the photodetector’s field of view. It is assumed that G does not depend on r: With regard for (10), expression (8) can be transformed: Z W Nabs ¼ 2 kðlÞIA ðlÞldl: ð11Þ 4p hcGR2 H abs Now consider the signal of luminescence, IL ðlÞ: Denote the volume power density of the
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
32
luminescence as PL ðl; rÞ: Unlike PLII ; it depends on the coordinates r: Similarly to expression (10), one can write: Z PL ðl; rÞ d3 r: ð12Þ IL ðlÞ ¼ G V
At the point with the coordinates r; the integral number (over the spectrum) of the luminescence photons emitted per unit time and per unit volume can be presented: Z l PL ðl; rÞ dl nlum ðrÞ ¼ ð13Þ lum hc where the integration is performed over the dye luminescence spectrum. On the ground of (12) and (13), the total number of the luminescence photons emitted per unit time in the cell can be written: Z 1 Nlum ¼ IL ðlÞl dl: ð14Þ hcG lum Now, using expressions (11) and (14), it is possible to compute the absolute value of the luminescence quantum yield, Z; according to its definition Z ¼ Nlum =Nabs : With the use of the experimental spectra given in Fig. 1, the calculations result in the value of ZE0:86: For the comparison of the value of Z obtained, the additional experiment was performed. Using the second harmonic of YAG : Nd3þ laser radiation as a source of excitation, the luminescence intensities of Rhodamine 6G in aqueous and alcoholic solutions were compared. Assuming ZE1 for the alcoholic solution, the experiment gives the value of ZE0:75 for the aqueous solution used. So, it can be concluded that the values of Z obtained by different methods are in agreement with the accuracy of approximately 15%. This agreement substantiates the supposition about the mechanism of excitation of the luminescence investigated in this article. Obviously, the above-given procedure (expressions (11) and (14)) can be considered as a new method of measurement of luminescence quantum yield. The method gives the absolute value of Z and does not require the use of reference luminescent samples. However, the attained accuracy shows that the improvement of the method would be desirable. Consider some of the sources of errors actual in the experiments and derivations.
As it was already mentioned, expression (7) is approximate. To investigate the errors caused by this approximation, the test calculations were performed with expression (7) which was modified to take into account the reabsorption of LII as follows: Z PLII ðlÞ exp½kðlÞjr r0 j 3 0 rl ðrÞ ¼ d r: ð15Þ 4pcjr -r0 j2 V For a given cell parameters and the absorption spectrum, kðlÞ; the estimating calculations show that the use of expression (15) instead of (7) leads to the increase of the computed value of quantum efficiency by 5–8%. However, the account for the reabsorption according to (15) gives rise to the spectral dependence of the parameter W (9) and, consequently, to the essential loss of simplicity of the calculations, that now seems to be inexpedient. The method considered does not account for the absorption of LII in the short-wavelength ðlo450 nmÞ absorption bands of the dye molecules. As is seen from Fig. 1 (curve A), the LII intensity decreases with the decrease of the wavelength, that is why the short-wavelength absorption is neglected, though the errors caused by this disregard are not estimated. Obviously, the short-wavelength radiation can be significantly reduced by adding an absorption agent to the solution, however, such an approach requires thorough investigation of possible interactions between the ingredients of the solution. Finally, it should be noted, the method is sensitive to the errors of the experimental data, especially to those caused by the laser instabilities.
4. Concluding remarks In this paper, the experiments demonstrate that the laser-induced incandescence of light-absorbing submicron particles can coexist with the luminescence of the suspension matrix. It is also demonstrated that the possibility exists for the excitation of the luminescence via the LII up-conversion. The experiments in this paper were carried out with the purpose-made suspension of particles in the Rhodamine 6G aqueous solution. Nevertheless,
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
the effects investigated are not unique, and they can occur in various media. For a specific object, the question is whether the LII is of detectable magnitude or not. The answer depends on the experimental conditions. Whether or no, in experiments with powerful laser excitation in turbid media, an investigator should be aware of possible LII effects.
33
References [1] [2] [3] [4] [5]
A.C. Eckbreth, J. Appl. Phys. 48 (1977) 4473. R.L. Vander Wal, Appl. Opt. 35 (1996) 6548. S. Zelensky, J. Phys.: Condens. Matter 10 (1998) 7267. S. Zelensky, J. Opt. A: Pure Appl. Opt. 1 (1999) 454. P. Roura, J. Costa, M. Lopez-de Miguel, et al., J. Lumin. 80 (1998) 519. [6] P. Roura, P.J. Costa, Eur. J. Phys. 23 (2002) 191.
Laser-induced incandescence of suspended particles as a source of excitation of dye luminescence S. Zelensky Physics Department, Kiev University, 6 Glushkova str., Kiev 03127, Ukraine Received 27 May 2002; received in revised form 31 October 2002; accepted 31 October 2002
Abstract The interaction of pulsed YAG-Nd3þ laser radiation with submicron light-absorbing particles suspended in an aqueous solution of Rhodamine 6G is investigated experimentally. The experiments demonstrate that the laser-induced incandescence of suspended particles excites the luminescence of the dissolved dye molecules. The mechanism of the luminescence excitation consists in the reabsorption of the thermal radiation within the volume of the sample cell. On the ground of this mechanism of excitation, a method of measurement of the luminescence quantum yield is proposed and realized. The method requires the knowledge of the geometrical parameters of the cell and does not require the use of reference samples. r 2002 Elsevier Science B.V. All rights reserved. PACS: 78.55.Bq; 33.70.Fd Keywords: Laser-induced incandescence; Reabsorption; Luminescence quantum yield; Suspensions; Rhodamine 6G
1. Introduction It is not a rare occasion in laser spectroscopy when an investigated transparent object contains a number of microscopic inclusions absorbing the laser light. For example, it can be dust particles in the air, soot particles in a flame or in a combustion engine, foreign inclusions in crystals or in glass, suspended particles in natural water or in artificial suspensions, etc. The presence of such inclusions can manifest itself in various optical properties of the object investigated. One of the ways to reveal the inclusions is to overheat them by the laser radiation. E-mail address: [email protected] (S. Zelensky).
Consider a black-body particle with the size of 0.1–1 mm which absorbs the pulsed laser radiation with the surface power density of 10– 100 MW cm2 (such radiation intensities can be easily obtained with laboratory-scale Q-switched lasers even without focusing). If the heat transfer from the particle to the environment can be neglected, the primitive treatment of the energy balance equation shows that the particle temperature can reach up to 104 K under the laser irradiation. Even if the thermal relaxation to the environment is taken into account, the estimated particle temperature exceeds the room temperature at least by a factor of ten. It is conceivable that such light-absorbing submicron particles in transparent condensed matter or in gaseous phase,
0022-2313/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-2313(02)00661-0
28
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
under the irradiation of a powerful laser, will emit measurable Planck’s radiation in the visible spectral region. The experimental observation of the mentioned laser-induced incandescence (LII) of suspended particles is reported, for example, in [1–4]. Another example of experiments in which the thermal radiation significantly manifests itself is the laser-induced visible emission of silicon nanoparticles in porous silicon [5,6]. In a number of earlier publications this emission was mistakenly interpreted as luminescence. The following features of LII in transparent condensed matrixes seem to be noteworthy. (i) The LII is usually observed at the conditions of strong scattering of the laser radiation by the suspended particles, so that the thermal radiation is significantly masked by the scattered light. To detect the LII signal, measures should be taken for the elimination of the scattered laser light (a single grating monochromator is suitable in most of the cases). (ii) For the above-mentioned values of laser intensity, the power of the LII optical signals is sufficient for reliable detection by a photomultiplier. If the infrared laser is employed, the LII is clearly visible to the naked eye. (iii) The phenomenological properties of LII are similar to the properties of broadband laser-induced luminescence. This circumstance makes it difficult to separate the luminescence and thermal radiation signals. For a suspension of light-absorbing particles irradiated by the infrared laser radiation, the LII looks like a homogeneous track of white color, without any signs of its polarization and anisotropy. In the paper [4] the signals of LII were detected within the spectral range of 220–750 nm: This spectral interval was not the feature of LII itself, but it was restricted by the characteristics of the employed photodetector. When the LII is detected at a fixed wavelength, the dependence of its intensity, I; on the laser intensity, F ; is essentially non-linear. For a moderate deviation of F ; the relationship between I and F can be approximated as DI=I ¼ gðDF =F Þ. The introduced index of non-linearity, g; is a function of F : g decreases with the increase of F : For example, the experiments demonstrated g ¼ 6–2 [3,4], gC3½6:
A promising situation arises when light-absorbing particles are suspended in a luminescent medium. In this case the chances are that the LII can serve as an internal source of excitation for the luminescence. The goal of this article is to demonstrate the reality of the mentioned mechanism of luminescence excitation.
2. Experimental details The experiments were carried out with the following three objects denoted hereinafter as ‘‘A’’, ‘‘B’’, and ‘‘C’’. The object ‘‘A’’ was the aqueous suspension of light-absorbing particles. It was prepared by dilution of black gouache paint in distilled water. The suspension was filtered for the restriction of size of the suspended particles at a level of o2 mm: The concentration of suspended particles was low enough, so that the attenuation of optical signals within the cell volume can be considered as negligible (the optical transmittance of the suspension in the visible spectral region exceeded 0.95 at a thickness of 1 cm). The object ‘‘B’’ was prepared of the object ‘‘A’’ by adding Rhodamine 6G dye with the concentration of approximately 3 105 mol l1 : The absorption spectrum of the suspension ‘‘B’’ is given in Fig. 1, curve ‘‘Abs’’. The absorption band observed corresponds to the Rhodamine molecules. The third object, ‘‘C’’, was the aqueous solution of Rhodamine 6G with the same concentration as in the solution ‘‘B’’. The absorption spectrum of the solution ‘‘C’’ practically coincides with the absorption spectrum of the suspension ‘‘B’’, that indicates the absence of considerable interaction between the Rhodamine molecules and the suspended particles. The experiments were performed with a Qswitched YAG-Nd3þ laser (wavelength 1:06 mm; pulse duration B30 ns). The LII was detected by a photomultiplier through a single grating monochromator. The non-uniformity of spectral sensitivity of the spectrometer was corrected with the use of a standard tungsten lamp. The pulse duration of the optical signals, both the LII and the luminescence, was approximately the same as
κ , cm
-1
S. Zelensky / Journal of Luminescence 104 (2003) 27–33 6 4 2 0
29
Rectangular glass block
Abs Laser beam
Collimated laser beam
H
2.5 BCOR
2.0
Capillary orifice 2R
A
Excited volume (cylindrical)
Collimating slit
1.5
Pump flow
I (λ), a.u.
B
Fig. 2. The experimental layout. The direction of light collection is perpendicular to the plane of the drawing.
1.0
0.05
C, CCOR
0.00 (BCOR-A)
0.2 E 0.0 450
500
550
600
650
λ, nm
Fig. 1. The absorption spectrum (abs) of the suspension ‘‘B’’ and the emission spectra of the suspensions ‘‘A’’, ‘‘B’’, and ‘‘C’’. All of the spectra, except ‘‘abs’’, are given in equal arbitrary units. The suffix ‘‘COR’’ labels the spectra corrected for reabsorption. The spectrum C is plotted as circle points, the spectrum CCOR –as a solid line. The spectrum E is the difference ðBCOR A CCOR ).
of the laser. The laser repetition rate was approximately 1 pulse s1 : Every pulse from the photomultiplier was digitized and processed separately, the data averaging was implemented in the software. To prevent the laser-induced fading of the objects investigated, the suspensions were pumped through the optical cell with a flow of 0.5–1 cm3 s1 ; so that each of the laser pulses interacted with a ‘‘fresh’’ portion of the suspension. The rectangular glass block with the capillary orifice was used as an optical cell. The geometrical arrangement of the cell and laser beam is outlined in Fig. 2. The laser radiation passes through the collimating slit and hits the cell, thus the irradiated volume of the suspension is the cylinder with the
height of H ¼ 1:5 mm and with the radius of R ¼ 0:25 mm: The LII was collected with a fiber-optic bundle installed perpendicularly to the orifice and to the laser beam. The whole irradiated volume was located within the field of vision of the lightcollecting bundle. As it was mentioned, the emission investigated is non-linear. That is why it is important to keep the uniformity of laser excitation within the cell volume, otherwise the errors arise. For this purpose, the height of the collimating slit was approximately half as large as the laser beam diameter. Besides, the laser was equipped with a diaphragm in the resonator, so that its operation was close to the single-mode regime with the smooth bell-shaped distribution of surface power density across the beam.
3. Results and discussion The emission spectra of the objects ‘‘A’’, ‘‘B’’, and ‘‘C’’ are given in Fig. 1 (curves A, B, and C, respectively). The laser excitation intensity is approximately 10 MW cm2 : Each of the plotted points is the average of 5–10 laser pulses. The spectra A, B, and C in Fig. 1 were recorded at the same experimental conditions, i.e. the same photomultiplier gain voltage, the same level of excitation, the same geometrical arrangement. The emission of the object ‘‘A’’ (curve A, Fig. 1) shows all of the features of LII [3,4], namely, the essential non-linear behavior with F ðgC3Þ and the broad spectrum which can be fitted with a
30
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
Planck’s function with a particle temperature of 3500 K: For the emission considered, the method of particle temperature estimation proposed in [4] is inapplicable because of the relatively high level of laser excitation. As is seen from Fig. 1, in the spectral region of 540–640 nm; the emission of the suspension ‘‘B’’ exceeds the emission of the suspension ‘‘A’’ due to the Rhodamine luminescence. On the contrary, in the spectral region of 470–540 nm; the spectrum A exceeds the spectrum B due to the reabsorption of the LII by the Rhodamine molecules in the cell en route towards the photo-detector. The curve C in Fig. 1 is the spectrum of Rhodamine luminescence excited via the twophoton absorption of laser radiation (hereinafter referred to as the two-photon luminescence, TPL). For this luminescence, the experimental dependence of its intensity on the laser excitation intensity demonstrates the quadratic law which is naturally expected for the two-photon excitation. As one can see in Fig. 1, the contribution of Rhodamine luminescence to the spectrum B (the difference between the spectra B and A in the region 540–580 nm) exceeds the TPL spectrum of the solution ‘‘C’’. This fact indicates the presence of a new mechanism of excitation of Rhodamine luminescence in the experiments considered. It is plausible to suggest that in the experiments the LII serves as an intermediary agent (or an anti-Stokes energy transformer) between the infrared laser radiation and the dye molecules. As is clearly seen from Fig. 1, the mentioned reabsorption of LII significantly distorts the shape of the emission spectrum B, thus it is difficult to correctly separate the luminescence out of the spectrum B. For the elimination of the distortion, consider the following model (see Fig. 3). The cylindrical volume of radius R and height H contains the homogeneous suspension, that emits light with the constant power volume density, P: Denote the spectral density of P as PðlÞ: The photodetector is located on the X -axis, so that the light-collecting aperture of the photodetector is seen at a spatial angle of DO: Consider the element of volume, dV : The spectral density of optical signal emitted from dV towards the photodetector
y R
∆Ω
Photodetector aperture
dV
ρ sin ϕ
dI
ξ (ρ , ϕ )
ρ ϕ
0
R
ρ cos ϕ
x
R2 − ρ 2 sin2 ϕ
Fig. 3. The schematic drawing for the calculation of optical signals with the expressions (1)–(4).
can be written as follows: dIðlÞ ¼ PðlÞ
DO expðkðlÞxÞ dV ; 4p
ð1Þ
where kðlÞ is the absorption coefficient of the suspension, x is the distance in the OX direction between the element dV and the edge of the lightemitting volume (see Fig. 3). In the case of absence of the reabsorption, obviously, dI0 ðlÞ ¼ PðlÞ
DO dV : 4p
ð2Þ
The integration of (1) and (2) over the cylindrical volume gives the following expression: Z IðlÞ 2 1 GðlÞ ¼ ¼ r dr I0 ðlÞ p 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z p dj exp kðlÞR 1 r2 sin2 j r cos j ; 0
ð3Þ where r ¼ r=R: The function GðlÞ obtained can be used for the correction of spectral distortions caused by the reabsorption. It should be noted, in the experiments, the response of the photodetector, i; is proportional to the optical signal, I; as follows: iðlÞ ¼ SðlÞIðlÞL;
ð4Þ
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
where SðlÞ is the spectral sensitivity of the spectrometer, L is the spectral width of the monochromator’s slit. The correction procedure proposed can be applied to the spectrum B, Fig. 1, with the use of the spectrum Abs, Fig. 1, as kðlÞ in (3). The corrected spectrum is given in Fig. 1, curve BCOR : As is seen, the spectrum BCOR in the spectral region of Rhodamine’s absorption is in agreement with the spectrum A, so the correction performed can be rated as good. The emission spectrum of the suspension ‘‘B’’ (the spectrum BCOR ) includes the following signals: (i) the LII, (ii) the TPL of Rhodamine, and (iii) the luminescence of Rhodamine excited via the LII. After the elimination of the reabsorption-caused distortions, the luminescence spectrum can be separated out of the total emission spectrum BCOR : The difference of spectra BCOR and A, Fig. 1, is denoted as the curve (BCOR A). The difference of the spectrum (BCOR A) and the spectrum C corrected for reabsorption CCOR is given in Fig. 1, curve E. The final spectrum E represents the luminescence of Rhodamine 6G excited via the LII. The considered mechanism of excitation of luminescence via the LII seems to be intuitively obvious, however, the relative magnitude of the optical signals requires some additional treatment. In the experiments described in this article, the geometrical parameters of the light-emitting volume are fixed, thus providing the possibility to perform some numerical calculations of the signals. Consider the following simplified model. The cylindrical cell contains the suspension being irradiated by the laser radiation. Suppose the nondepleted pump approximation holds true for the laser light, i.e. the surface power density of the laser radiation, F ; is a constant. Therefore, the volume power density of LII, PLII ; can also be considered as a constant function of coordinates within the cell volume. At a point with the coordinates ~ r ; the integral number (over the absorption spectrum) of the LII photons absorbed by the dye molecules per unit time and per unit volume can be written: Z l nabs ðrÞ ¼ kðlÞ rl ðrÞ dl; ð5Þ h abs
31
where rl is the spectral density of LII energy in a unit volume, h is the Planck constant. The integration in (5) is performed over the spectral interval of the dye absorption spectrum. By integrating expression (5) over the cell volume, V ; the total number of the absorbed LII photons per unit time can be obtained: Z Z l Na ¼ dl kðlÞ d3 r rl ðrÞ: ð6Þ h V abs It should be noted, the volume density, rl ; is a function of the coordinates r; though F and PLII are constants. Within the cell volume, the elementary volumes, d3 r0 ; contribute to the value of rl according to the inverse square law, thus the following formula can be written: Z PLII ðlÞ rl ð~ rÞ ¼ d3 r0 ; ð7Þ 02 V 4pcjr -r j where c is the speed of light. Expression (7) does not take into account the absorption of LII by the dye molecules. The errors caused by this approach will be considered thereinafter. By substituting (7) into (6) we obtain: Z W Nabs ¼ kðlÞlPLII ðlÞ dl; ð8Þ 4phc abs where Z Z 3 d r W¼ V0
V
d3 r0
1 : jr r0 j2
ð9Þ
The introduced constant parameter, W ; can be computed for a given cell geometry. The optical signal measured experimentally is proportional to the total power of the light emitted in the cell. For the suspension ‘‘A’’, it can be written as follows: Z IA ðlÞ ¼ G PLII ðlÞ d3 r ¼ GPLII ðlÞ pR2 H; ð10Þ V
where G is the geometric factor. G accounts for the fraction of the total radiation emitted which falls into the photodetector’s field of view. It is assumed that G does not depend on r: With regard for (10), expression (8) can be transformed: Z W Nabs ¼ 2 kðlÞIA ðlÞldl: ð11Þ 4p hcGR2 H abs Now consider the signal of luminescence, IL ðlÞ: Denote the volume power density of the
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
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luminescence as PL ðl; rÞ: Unlike PLII ; it depends on the coordinates r: Similarly to expression (10), one can write: Z PL ðl; rÞ d3 r: ð12Þ IL ðlÞ ¼ G V
At the point with the coordinates r; the integral number (over the spectrum) of the luminescence photons emitted per unit time and per unit volume can be presented: Z l PL ðl; rÞ dl nlum ðrÞ ¼ ð13Þ lum hc where the integration is performed over the dye luminescence spectrum. On the ground of (12) and (13), the total number of the luminescence photons emitted per unit time in the cell can be written: Z 1 Nlum ¼ IL ðlÞl dl: ð14Þ hcG lum Now, using expressions (11) and (14), it is possible to compute the absolute value of the luminescence quantum yield, Z; according to its definition Z ¼ Nlum =Nabs : With the use of the experimental spectra given in Fig. 1, the calculations result in the value of ZE0:86: For the comparison of the value of Z obtained, the additional experiment was performed. Using the second harmonic of YAG : Nd3þ laser radiation as a source of excitation, the luminescence intensities of Rhodamine 6G in aqueous and alcoholic solutions were compared. Assuming ZE1 for the alcoholic solution, the experiment gives the value of ZE0:75 for the aqueous solution used. So, it can be concluded that the values of Z obtained by different methods are in agreement with the accuracy of approximately 15%. This agreement substantiates the supposition about the mechanism of excitation of the luminescence investigated in this article. Obviously, the above-given procedure (expressions (11) and (14)) can be considered as a new method of measurement of luminescence quantum yield. The method gives the absolute value of Z and does not require the use of reference luminescent samples. However, the attained accuracy shows that the improvement of the method would be desirable. Consider some of the sources of errors actual in the experiments and derivations.
As it was already mentioned, expression (7) is approximate. To investigate the errors caused by this approximation, the test calculations were performed with expression (7) which was modified to take into account the reabsorption of LII as follows: Z PLII ðlÞ exp½kðlÞjr r0 j 3 0 rl ðrÞ ¼ d r: ð15Þ 4pcjr -r0 j2 V For a given cell parameters and the absorption spectrum, kðlÞ; the estimating calculations show that the use of expression (15) instead of (7) leads to the increase of the computed value of quantum efficiency by 5–8%. However, the account for the reabsorption according to (15) gives rise to the spectral dependence of the parameter W (9) and, consequently, to the essential loss of simplicity of the calculations, that now seems to be inexpedient. The method considered does not account for the absorption of LII in the short-wavelength ðlo450 nmÞ absorption bands of the dye molecules. As is seen from Fig. 1 (curve A), the LII intensity decreases with the decrease of the wavelength, that is why the short-wavelength absorption is neglected, though the errors caused by this disregard are not estimated. Obviously, the short-wavelength radiation can be significantly reduced by adding an absorption agent to the solution, however, such an approach requires thorough investigation of possible interactions between the ingredients of the solution. Finally, it should be noted, the method is sensitive to the errors of the experimental data, especially to those caused by the laser instabilities.
4. Concluding remarks In this paper, the experiments demonstrate that the laser-induced incandescence of light-absorbing submicron particles can coexist with the luminescence of the suspension matrix. It is also demonstrated that the possibility exists for the excitation of the luminescence via the LII up-conversion. The experiments in this paper were carried out with the purpose-made suspension of particles in the Rhodamine 6G aqueous solution. Nevertheless,
S. Zelensky / Journal of Luminescence 104 (2003) 27–33
the effects investigated are not unique, and they can occur in various media. For a specific object, the question is whether the LII is of detectable magnitude or not. The answer depends on the experimental conditions. Whether or no, in experiments with powerful laser excitation in turbid media, an investigator should be aware of possible LII effects.
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A.C. Eckbreth, J. Appl. Phys. 48 (1977) 4473. R.L. Vander Wal, Appl. Opt. 35 (1996) 6548. S. Zelensky, J. Phys.: Condens. Matter 10 (1998) 7267. S. Zelensky, J. Opt. A: Pure Appl. Opt. 1 (1999) 454. P. Roura, J. Costa, M. Lopez-de Miguel, et al., J. Lumin. 80 (1998) 519. [6] P. Roura, P.J. Costa, Eur. J. Phys. 23 (2002) 191.