Photoacoustical and optical measurements on photochromic glasses Thomas Flohr and Reinhard Helbig Some predictions of a phenomenological theory describing the behavior of photochromic glasses were tested by photoacoustic measurements. The induced steady-state absorption wasinvestigated under the influence of strong optical bleaching. A depth profile of the induced steady-state absorption coefficient was measured by varying the glass thickness and described theoretically. Optical measurements were related to simulta- neously taken photoacoustical measurements. I. Introduction In photochromic glasses, the UV-induced absorp- tion coefficient is a function of the distance from the illuminated surface of the sample. As the exciting UV light is absorbed in the glass, its intensity decreases with increasing depth and fewer absorption centers are built up in the deeper layers of the sample. This is a problem in the interpretation of conventional optical investigations of photochromic glasses. Usually, the transmission is measured on a sample of finite thick- ness (a few millimeters). Therefore, only a mean value of the absorption coefficient will be obtained. This may prove a disadvantage if theoretical models for the behavior of the induced absorption coefficient have to be quantitatively compared to the experimental re- sults. In contrast to conventional optical studies, pho- toacoustical measurements largely avoid this difficul- ty, because the photoacoustic signal of photochromic glasses is due to the absorption to the depth of few microns beneath the sample surface. 2 With the pho- toacoustic method, some simple predictions of a phe- nomenological theory describing the behavior of pho- tochromic glasses in a rate equation from which we obtain the local absorption coefficient were tested. Furthermore, the results of optical measurements were compared to simultaneously taken photoacousti- cal measurements. The authors are with Universitat Erlangen-Nurnberg, Institut fur Angewandte Physik, Gluckstr. 9,8520Erlangen, Federal Republic of Germany. Received 13 December 1985. 0003-6935/86/122008-05$02.00/0. i) 1986 Optical Society of America. II. Basic Features of the Photoacoustic Method By nonradiating relaxation and recombination pro- cesses the light absorbed by a solid sample is trans- formed into heat. In a classical photoacoustic experi- ment, this heat is measured from the pressure change (photoacoustic signal) of the gas surrounding the sam- ple in a closed cell (usually in the lock-in technique). From the photoacoustic signal, information about thermal and optical properties of the sample may be derived (e.g., absorption coefficient, thermal diffusi- vity). According to Rosencwaig and Gersho,' a deter- mining parameter for the photoacoustic signal is the thermal diffusion length of the sample j= 2kp C'w. (k is the thermal conductivity, p the density, c the specific heat, and the chopping frequency of the measuring beam). Only the light absorbed within the lengthy contributes to the photoacoustic signal, which is proportional to the optical absorption coefficient in this region. As g is adjustable by varying the chopping frequency of the measuring beam, the penetration depth of photoacoustic measurements may in princi- ple be chosen arbitrarily. With a chopping frequency of 100 Hz, the thermal diffusion length of a photochromic glass is 40 ,gm. 2 The photoacoustic signal, therefore, comes from a thin surface layer, in contrast to the situation in optical transmission measurements. 111. Photochromic Glasses: Description of Their Optical Properties by a Rate Equation The glasses investigated were borosilicate with an admixture of silver chloride and some copper. Under exposure to ultraviolet light, the following reactions are induced 3 : 2008 APPLIED OPTICS / Vol. 25, No. 12 / 15 June 1986
Transcript
Photoacoustical and optical measurements on photochromicglasses
Thomas Flohr and Reinhard Helbig
Some predictions of a phenomenological theory describing the behavior of photochromic glasses were testedby photoacoustic measurements. The induced steady-state absorption was investigated under the influenceof strong optical bleaching. A depth profile of the induced steady-state absorption coefficient was measuredby varying the glass thickness and described theoretically. Optical measurements were related to simulta-neously taken photoacoustical measurements.
I. Introduction
In photochromic glasses, the UV-induced absorp-tion coefficient is a function of the distance from theilluminated surface of the sample. As the exciting UVlight is absorbed in the glass, its intensity decreaseswith increasing depth and fewer absorption centers arebuilt up in the deeper layers of the sample. This is aproblem in the interpretation of conventional opticalinvestigations of photochromic glasses. Usually, thetransmission is measured on a sample of finite thick-ness (a few millimeters). Therefore, only a mean valueof the absorption coefficient will be obtained. Thismay prove a disadvantage if theoretical models for thebehavior of the induced absorption coefficient have tobe quantitatively compared to the experimental re-sults. In contrast to conventional optical studies, pho-toacoustical measurements largely avoid this difficul-ty, because the photoacoustic signal of photochromicglasses is due to the absorption to the depth of fewmicrons beneath the sample surface. 2 With the pho-toacoustic method, some simple predictions of a phe-nomenological theory describing the behavior of pho-tochromic glasses in a rate equation from which weobtain the local absorption coefficient were tested.Furthermore, the results of optical measurementswere compared to simultaneously taken photoacousti-cal measurements.
The authors are with Universitat Erlangen-Nurnberg, Institut furAngewandte Physik, Gluckstr. 9,8520 Erlangen, Federal Republic ofGermany.
Received 13 December 1985.0003-6935/86/122008-05$02.00/0.i) 1986 Optical Society of America.
II. Basic Features of the Photoacoustic Method
By nonradiating relaxation and recombination pro-cesses the light absorbed by a solid sample is trans-formed into heat. In a classical photoacoustic experi-ment, this heat is measured from the pressure change(photoacoustic signal) of the gas surrounding the sam-ple in a closed cell (usually in the lock-in technique).From the photoacoustic signal, information aboutthermal and optical properties of the sample may bederived (e.g., absorption coefficient, thermal diffusi-vity). According to Rosencwaig and Gersho,' a deter-mining parameter for the photoacoustic signal is thethermal diffusion length of the sample
j= 2kp
C'w.
(k is the thermal conductivity, p the density, c thespecific heat, and the chopping frequency of themeasuring beam). Only the light absorbed within thelengthy contributes to the photoacoustic signal, whichis proportional to the optical absorption coefficient inthis region. As g is adjustable by varying the choppingfrequency of the measuring beam, the penetrationdepth of photoacoustic measurements may in princi-ple be chosen arbitrarily.
With a chopping frequency of 100 Hz, the thermaldiffusion length of a photochromic glass is 40 ,gm.2The photoacoustic signal, therefore, comes from a thinsurface layer, in contrast to the situation in opticaltransmission measurements.
111. Photochromic Glasses: Description of Their OpticalProperties by a Rate Equation
The glasses investigated were borosilicate with anadmixture of silver chloride and some copper. Underexposure to ultraviolet light, the following reactionsare induced3 :
The silver atoms from clusters of metallic silver whichcause an increase in absorption in the 350-900-nmwavelength region. Finally, a steady state is reacheddepending on the exciting UV intensity. When theUV light is removed, the glasses return to their initialstate. The regeneration process may be acceleratedby an additional illumination of red light.
Although some attempts have been made to explainthe behavior of photochromic silver halogenide glasseson a microscopic scale,- 8 the physical processes inphotochromic glasses are not well understood. Forthe present, most approaches are confined to a descrip-tion of photochromic properties in a phenomenologicalmanner, e.g., by a rate equation. Such a rate equationhas to include a term describing the generation ofabsorption centers, a term describing thermal regener-ation, and a term describing optical regeneration.
With k(x,t) as the induced absorption coefficient,kmax as the maximum absorption coefficient, Iv(x)and Ired(X) as the intensities of exciting and bleachinglight, respectively, and g and r and d as generation andregeneration coefficients, the rate equation reads asfollows:
dt = g [kma, - k(x,t)] - IUV(x) - r k2(x t)dt
(1)
A detailed explanation of this equation is given in Ref.9. Here, two simple predictions were tested:
(a) Case of dominating optical bleaching: the in-duced stationary state surface absorption coefficientwas measured as a function of the exciting UV intensi-ty and described theoretically.
(b) A depth profile of the induced stationary stateabsorption coefficient was obtained by varying theglass thickness. The depth profile was compared witha theoretical model derived from the rate equation.
IV. Experimental Setup
The experimental setup is shown schematically inFig. 1. The sample is located within a photoacousticcell which is shielded from the acoustic noise of theenvironment. The absorption in the sample is in-duced by light from a 200-W Hg lamp. A SchottGlassfilter UG1 transmits only the 330-390-nm spec-tral region. Since the Hg lamp has a strong emissionline at -366 nm, irradiation is almost monochromatic.The exciting intensity is adjusted by a variable aper-ture and measured relatively using a photomultiplier.The photoacoustic signal is produced by a choppedHe-Ne laser (wavelength 632 nm, 5 mW). Choppingfrequency is 44 Hz. The laser is simultaneously usedto bleach the sample. Changes of the sample trans-mission can be detected by measuring the transmittedlaser intensity by a photodiode.
He-Ne-Laser
Chopper
Fig. 1. Schematic plot of the experimental setup.
Photoacoustic CellExciting Beam
Sample | Herasil
Fig. 2. Schematic arrangement of exciting and measuring beamsfor photoacoustic studies of photochromic glasses.
V. Measurements and Discussion
A. Equilibrium Absorption Under the Influence of StrongOptical Bleaching
1. Experiment
For photoacoustic studies of photochromic glasses,the configuration of exciting and measuring beams isimportant. In Fig. 2, exciting and measuring beamsare incident on the sample from the same direction.The photoacoustic signal is a measure for the inducedabsorption coefficient k(0) of the uppermost glass lay-er at the inside of the photoacoustic cell. The photoa-coustic signal as a function of the exciting UV intensityis shown in Fig. 3. The different symbols representresults of measurements for different glass thicknesses(0.2-2 mm), which do not affect the result because ofthe small thermal diffusion length.
2. DiscussionFor a theoretical fit, Eq. (1) was regarded under the
assumptions (dk)/(dt) = 0 (steady state) and r = 0(dominating optical bleaching, optical bleaching at fulllaser intensity proved to be much more effective thanthermal regeneration). If we consider only a thin layernear the surface (x = 0), we get Iuv(x) = Iuv(O) andIred(X) = Ired(O). Equation (1) yields, with Iuv(0) as avariable,
Fig. 3. Photoacoustic signal as a measure of the induced stationary-state absorption coefficient k(OIuv) under the influence of strong
optical bleaching as a function of the exciting UV intensity.
Photoacoustic Cell
Exciting eam _ Laser
1 Sample J Herasit
Fig. 4. Schematic arrangement of exciting and measuring beamsfor photoacoustic studies of photochromic glasses.
.2 .4 .6 .8 1 1.2 1.4Sample Thickness (mm)
uva
0. 24*1UV,
0.0 55
*1 UV. 0
0.011* UVO
Fig. 5. Photoacoustic signal after reaching stationary-state absorp-tion as a function of sample thickness for various UV exciting inten-
sities (uv = 366 nm).
consider the decrease of Iuv(d) with increasing depthd, the following approximation was made:
Iuv(d) = Iuv(O) exp[-(kUV+ktat d) * d], (3)
where kuv is the UV absorption coefficient of the un-darkened glass. Additionally, the UV light is ab-sorbed by the induced absorption centers. This isdescribed by the mean value kstatd of the inducedabsorption coefficient at a certain Iuv(O) in the region 0(= sample surface) to d. Now Eq. (1) yields, with d as avariable,
k,.t.t[x = 0Ouv(0)I = km=- IUV(O)
Iuv(O) + Ired(O)
(2)
For small exciting intensities, kstat [x = 0, Iuv(O)]should be proportional to Iuv(O), but for increasing UVintensities, a constant limit should be reached. Theexperimental points shown in Fig. 3 together with atheoretical curve confirm this prediction.
B. Depth Profile by Variation of the Glass Thickness
1. Experiment
With the setup of Fig. 2, the surface absorptionkstat[x = 0,Iuv(0)] for Iuv(O) is measured. If the excit-ing beam, however, is sent into the glass from theopposite direction (see Fig. 4), the exciting light has topass through the glass thickness d until it reaches theglass surface inside the photoacoustic cell where theabsorption is measured. Here the light is absorbedcorresponding to a steady-state absorption coefficientktt(d) which is caused by Iv(d). Keeping the inten-sity of the exciting beam constant, the steady-stateabsorption coefficient ktat(d) may be determined as afunction of the sample thickness d by varying thesample thickness d. (A set of glasses of differentthicknesses from the same ingot was available.) Theresults are shown in Fig. 5 for various UV intensities.
2. DiscussionAs in Sec. V.A.2, the rate equation was considered
assuming (dk)l(dt) = 0, r = 0, and Ired(X) = Ired(O). To
ket(d) = kmax Iuv(d)
Iuv(d) + Ired(0)g
(4)
Keeping in mind that only one curve is fitted in Fig. 5,whereas the others were obtained from this one byvarying IUV(O), the agreement with the simple theoret-ical model is quite good.
C. Simultaneous Photoacoustical and TransmissionMeasurements
1. Experiment
We measured the photoacoustic signal with the set-up in Fig. 2 and plotted the measurement points vs thetransmission simultaneously determined with a photo-diode. This is shown in Figs. 6-9 for samples of vari-ous thicknesses both for darkening and for bleaching.For the darkening, steady-state absorption was await-ed. With comparable transmission, the photoacousticsignal for the darkening is always larger than that forthe bleaching. This effect grows with increasing sam-ple thickness. Furthermore, the photoacoustic signalfor the darkening reaches a constant limit with de-creasing transmission (this may be seen clearly for the2-mm thick sample, see Fig. 9 in particular).
2. DiscussionThe spatially inhomogeneous absorption of the sam-
ple and the origin of the photoacoustic signal from thedepth of a few microns beneath the sample surfaceexplain the behavior observed. Figure 10 is given as anillustration.
Fig. 6. Photoacoustic signal as a function of the sample transmis-sion for darkening and for bleaching with a 0.2-mm sample thick-
ness.
0
d
-a.
1n7
So8.2
. 6
. 5
. 4
. 3
.I
0I
.5 - 2 rmm,
4 ~~~~~~~~~Darkening3
2 2z . B20 eaching
.1. E.
.1 .2 . .4 .5 .6 .7 .8 9
Transmission
Fig. 8. Photoacoustic signal as a function of the sample transmis-sion for darkening and for bleaching with a 2.0-mm sample thick-
ness.
aid
75
Transmission
Fig. 7. Photoacoustic signal as a function of the sample transmis-sion for darkening and for bleaching with a 0.5-mm sample thick-
ness.
Phoaoad ade
Sample ~ I
I>2
Photoacoustic cell
ironsmissian
Fig. 9. Curves for darkening from Figs. 6 to 8.
Exciting eam
Laser
Fig. 10. Schematic plot to illustrate the behaviorof the photoacoustic signal shown in Figs. 6-8.
(a) Darkening The photoacoustic signal is a mea-sure of the absorption in a thin surface layer at theinside of the photoacoustic cell. Here, however, theinduced steady-state absorption coefficient is alwayslarger than the mean absorption coefficient k whichwould be obtained from the transmission measuredwith the photodiode if the Lambert-Beer law werevalid. Therefore, an enhancement of the photoacous-tic signal may be observed, which grows with increas-ing sample thickness. Furthermore, in the thin sur-face layer maximum absorption will already bereached when the absorption coefficient in the depth
of the sample is still growing with increasing UV inten-sity. In spite of the decreasing transmission, the pho-toacoustic signal will no longer increase. Saturationoccurs, which is especially observed for the 2-mm thicksample.
(b) Bleaching If the whole sample is saturated, itmay be assumed that during bleaching the absorptioncoefficient decreases homogeneously along the samplethickness (not considering the 'red dependence on thetransmitted sample thickness). The sample transmis-sion decreases as expected when the Lambert-Beer lawis valid. The absorption coefficient measured with the
photoacoustic method is equal to the averaged absorp-tion coefficient determined from the transmission.
The measurement points in Figs. 6-9 were fittedwith a complete formula for the photoacoustic signal.For bleaching, the special case of spatially homoge-neous absorption given by Rosencwaig and Gersholwas used; for darkening, an expression for spatiallyinhomogeneous absorption derived on the basis of theRosencwaig theory by Afromowitz et al. was used.10
Here, k[x,Iuv(x)] was obtained from Eq. (4).
VI. Summary
We have demonstrated that photoacoustic measure-ments are useful for the study of an optical mediumwith spatially varying absorption coefficients. Photo-chromic glasses are convenient for this purpose, astheir absorption may be varied without changing theother sample properties. Additional information canbe obtained from transmission and photoacousticalmeasurements taken simultaneously.
We are obliged to H. J. Hoffmann, Schott GlaswerkeMainz, for providing the samples.
References
1. A. Rosencwaig and A. Gersho, "Theory of the PhotoacousticEffect with Solids," J. Appl. Phys. 47,64 (1976).
2. G. Gliemeroth, "Fotoakustische Messungen an fototropen Gld-sein," Glastech. Ber. 56, 313 (1983).
3. G. P. Smith, "Photochromic Glasses: Properties and Applica-tions," J. Mater. Sci. 2, 139 (1967).
4. R. J. Araujo, "Kinetics of Bleaching of Photochromic Glass,"Appl. Opt. 7, 781 (1968).
5. R. J. Araujo and N. F. Borelli, "Diffusion-Model Interpretationof the Darkening and Fading of Photochromic Glasses," J. Appl.Phys. 47, 1370 (1976).
6. R. J. Araujo, "Photochromic Glass," in Treatise on MaterialsScience, Vol. 12, M. Tomozawa and R. H. Doremus, Eds. (Aca-demic, New York, 1977).
7. R. J. Araujo, N. F. Borrelli, and D. A. Nolan, "The Influence ofElectron-Hole Separation on the Recombination Probability inPhotochromic Glasses," Philos. Mag. B 40, 279 (1979).
8. R. J. Araujo, N. F. Borrelli, and D. A. Nolan, "Further Aspects ofthe Influence of Electron-Hole Separation on the Recombina-tion Probability in Photochromic Glasses," Philos. Mag. B 44,453 (1981).
9. T. Flohr, diploma thesis, Erlanger 1985.10. M. Afromowitz, P-S. Yeh, and S. Yee, "Photoacoustic Measure-
ments of Spatially Varying Optical Absorption in Solids: ATheroetical Treatment," J. Appl. Phys. 48, 209 (1977).
OPTICAL POTENTIAL FOR UTILITIES IS FOCUS OF STUDYDetermining the value to electric utilities of using newoptical technology for voltage and current measurements is theaim of a government/industry project under way at NBS. Suchmeasurements--traditionally made using bulky but accuratetransformer systems--are crucial to ensure proper operation ofpower stations and substations. The project brings NBStogether with the Bonneville Power Administration, ElectricPower Research Institute, and the Empire State Electric EnergyResearch Corporation to answer a common question: Are thereeconomic or technical payoffs to using the new techniques?Though optical methods for electricity measurements have beenavailable for some time, these have been mainly for specialapplications. New developments now offer the promise of widermeasurement applications for the utility industry. In fact,several manufacturers in the United States and abroad areproducing optical measuring systems aimed at utilities. TheNBS study will help the industry determine those opticalsystems that may offer advantages over conventional or improvedtransformer-based measurement techniques.
