Anal. Chem. 1001, 63, 1927-1932
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Dual-Beam Optical Fiber Thermal Lens Spectroscopy Dorys Rojas,’ Robert J. Silva: Jonathan D. Spear, and Richard E. Russo* Lawrence Berkeley Laboratory, Applied Science Division, M S 90-2024, Berkeley, California 94720
A dual-beam thermal lens optlcal fiber spectrometer was doveloped and tasted wlth aqueous solutions of the rare-ecrrth lon N&+. An argon Ion pumped dye laser beam was dellvered to a mpk cuvette through optkal fibers of 100, 200, and 400 pm core diameter. The thermal lens signal was detected wlth a Ho-M h e r g u b d to a photodkck detector by an optical fiber of 200 pm core diameter. Theoretical values for tho optical aperture, excitation and probe beam radl, and dldaceo from the smpie to the probe beam walst and to the ap.rture4etector were cakdated and compared to exprlmental results. Theoretical thermal lens enhance “ ilacion that take hto account the radius of the exdlatkn wtth the expwhental values. A beam show good detectlon lhnit of 7 X lo4 M and an enhaccMlent factor of 0.9 were obtained for an Incident power of 25 mW and a power density of 31 W cm-*.
INTRODUCTION Thermal lens spectroscopy (TLS) is an optical absorption technique with characteristics of high sensitivity and small volume requirements, which are ideal for ultratrace measurements in aqueous and nonaqueous media (1-7). In contrast to conventional absorbance measurements, the thermal lens signal and therefore ita sensitivity are directly proportional to the incident power. Thus, by using lasers of high output power, sensitivities 2 and 3 orders of magnitude higher than those obtainable from conventional absorbance techniques have been achieved. Single- and dual-beam TLS optical configurations have been developed that have shown comparable sensitivities for equal spot size of the laser beams at the sample (2). However, higher sensitivities have been obtained by using a dual-beam mode-mismatched configuration, focusing the excitation beam at the center of the sample to provide the highest power density and locating the probe beam focus a t an optimal distance from the sample (6-8). Using optical fibers to transmit the laser beams makes the thermal lens technique amenable to remote, in situ analysis. Bialkowski (9) used a silica optical fiber to reduce the influence of mode and pointing variations in the laser. Ishibashi et al. (10, 11)used single-mode and multimode optical fibers for light introduction in single-beam thermal lens spectroscopy. They found that for the single-mode fiber, the coupling efficiency was lower, but the thermal lens enhancement factor was higher because of the Gaussian-like quality of the transmitted beam. In this work, we developed a compact optical fiber dualbeam thermal lens spectrometer for analysis of species in solution. Multimode optical fibers were used that minimized alignment procedures and noise problems encountered with single-mode fibers. The goal of this work was to develop an instrument for measuring sensitive optical absorption spectra
at a remote location from the large dye laser system, particularly in a environmentally controlled glovebox for actinide chemistry studies, process stream monitoring, and eventually remote environmental analysis. To achieve this goal, theoretical calculations were used to describe the behavior of optical parameters such as the distances from the sample to the detector and to the focus of the probe beam, the size of the aperture, and the radii of the excitation and the probe beams at their foci. The theoretical predictions are compared with the experimental results, and the performance of a compact optical fiber TLS system is described.
THEORETICAL SECTION I. Optical Parameters. Several theoretical models have been proposed to describe the behavior of the thermal lens effect, assuming parabolic lens behavior (1,12) and taking into account aberrant characteristics of the lens (13-15). From those models, an optimum distance from the sample to the probe beam waist has been predicted. However, the models have not been used to predict the optimum size of the aperture or the radii of the laser beams, the distance of the sample to the detector, nor the effect of the radius of the excitation beam on the thermal lens enhancement factor. In this section we will address those parameters that influence the sensitivity of an optical fiber thermal lens arrangement, without making an assumption about the relative size of the excitation and probe beams. As in previous work (I),we will use the conventional definition of the thermal lens signal as the relative variation of the intensity of the probe laser at the beam’s center. Figure 1 is a conceptual drawing of the dual-beam thermal lens configuration. When an optical aperture (in our case an optical fiber of diameter equal to 2b) is used to select the beam’s center, the power (P)a t the detector is given by (1)
P(t) = l b Z ( r , t ) 2 n rdr = P(l - e-2bz/Ulz2(t)) (1) 0
where the probe laser has a Gaussian spatial profile with e-2 radius equal to w2(t)at the aperture, I is the intensity (W m”) of the beam, and Po is the total optical power contained in the beam. The thermal lens signal s ( t ) , measured as the relative change of the probe beam’s center power becomes (I) e - 2 P / ~ 2 2 ( t = 0)
s(t) =
1 - e-2bZ/~z2(t=0)
(2)
When the sample cell is placed at a distance z1 before the probe beam waist and the aperture-detector is a t a distance z2, as shown in Figure 1, the radius of the probe beam at z2 is given by (16)
(‘3)
*Towhom correspondence should be addressed.
Departamento de Quimica, Facultad de Ciencias, Universidad de Loe Andes, Merida 5101A,Venezuela. Lawrence Livermore National Laboratory, Nuclear Chemistry Division, L-396, Livermore, CA 94550.
e-2b2/~&t)
where wo is the radius of the probe beam at the focus, f ( t ) is the focal length of the thermal lens at time t, and z, = ?rwO2/X is the confocal distance of the probe beam (12),defined as the
This article not subject to U.S. Copyright. Published 1881 by the American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 63, NO. 18, SEPTEMBER 15. 1991
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n
excitation
'1
-
0.8
-
=
II
"z,+ f I
z*
Flg~we1. Optical configuration for the dusk" thermai lens systems. wand wo are the radius of the excttatkm and the probe beam, at their focus, respectlvely; w2 is the radius of the probe beam at the aperture; b is the radius of the aperture; z 1 is the distance from the center of the sample to the walst of the probe beam; z 2 is the distance from the center of the sample to the aperture. 0
20
10
22
M
40
(cm)
Figure 4. Theoretical thermal lens signal versus z 2 using flbers (apertures) of core diameter equal to 20 pm (a), 200 pm (b), 600 pm (c), and 1000 pm (d).
average power P,,, and e-2 radius equal to w, the focal length of the induced thermal lens is (12)
0.2
where f m is the focal length a t infinity (t >> t,; steady state) and t, is a time constant for the formation of the thermal lens. The parameters are determined by the characteristics of the excitation beam and the sample and are given by
i 50
0
100
I
I
150
200
f. = rkw2/alPaV(dn/dT)
(5)
t, = pCpw2/4k
(6)
Aperture Radius (pm) Figure 2. Theoretical thermal lens signal as a function of the radius b of the aperture, calculated for an average power of 100 mW, an excitation beam radius of 150 pm, a probe beam radius of 103 pm, z , = 7 cm, z 2 = 10 cm, and a 0.001 M concentration of Nd9+.
where a (cm-') is the absorptivity of the sample medium, 1 (cm) is the optical path length, p (g cmS) is the density, C, (cal g-' K-I) is the heat capacity at constant pressure, k (W em-' K-l) is the thermal conductivity, and dn/dT (K-l) is the change of refractive index with temperature. From eqs 3 and 4,the radius of the probe beam is given by
ir
1I ;)I
W22(t) = wo2
-1
+
22
12
+
fm(l+
!I
0.2
O f
0
I
1
I
I
I
I
I
1
20
40
60
80
100
120
140
160
Distance (cm)
Figure 3. Theoretical thermal lens signal as a function of the distance z 1 from the sample to the focus of the probe beam (a) and of the distance z2from the sample to the aperture-detector (b). For these curves we assumed values of z 2 = 10 cm and z1 = 7 cm for (a) and (b), respectively.
distance from the beam waist in which the diameter of the probe beam increases by a factor of 2lI2. For an excitation beam with a Gaussian spatial profile,
The influence of the experimental parameters b, zl,22, w , and woon the peak intensity of s(t) (TLS signal at a time equal to the inverse of twice the modulation frequency) can be predicted by substitution of eqs 7 and 8 into eq 2 and are shown in Figures 2 through 5. The curves in these figures were obtained by assuming a Nd3+concentration of 0.001 M, average power of 100 mW, excitation and probe beam waist radii of 150 and 103 pm, respectively, and values of z1and z2 of 7 and 10 cm, respectively. Thermal and optical parameters for water and neodymium are given in Table I. For dem-
ANALYTICAL CHEMISTRY, VOL. 63,NO. 18, SEPTEMBER 15, 1991
50
100
150
200
250
300
radius of the laser beam ( p m )
Flguro 5. Theoretical thermal lens slgnal versus the radius of the excitation (dashed line, w o = 103 pm) and the probe (solid line, w = 150 pm) beams. z 1 = 7 cm, z2= 10 cm.
Table I. Thermal and Optical Parameters param dn/dT CP n
k P
A probe A excn e
(Nd at 575 nn)
values -8 X lod K-' 0.998 cal g1K-' 1.33 1.43 X lo-* cal cm-' 1 g cmmS 632.8 nm 575 nm 6.93 L mol-' em-'
6-l K-' =
6.11 mW em-'
K-'
onstration in Figures 2-5, all parameters were kept constant except the one under study. In all cases,we report the absolute value of the thermal lens signal, as its sign depends on the relative position of the sample with respect to the focus of the probe beam, negative if the beam is converging (as in our optical configuration) and positive if the beam is diverging. As shown in Figure 2, the theory predicts that the signal s ( t ) is essentially independent of the radius of the optical aperture below approximately 25 pm and decreases as the aperture's size increases. In spite of the maximum signal b e i i predicted for the smallest aperture, mechanical vibrations and the pointing instabilities of the lasers make these apertures unsuitable for practical experimental work (9,17). A 100 pm radius aperture would provide approximately 90% of the maximum signal level. Figure 3 shows the behavior of the thermal lens signal as a function of the distances z1 (z2 = 10 cm) and z2 (z, = 7 cm), predicted by eq 2 for an aperture radius b equal to 100 pm. For distances smaller than 18 cm, the TLS signal increases linearly with zl. For greater values, the signal increases only slightly as z1 increases and levels off at distances greater than 40 cm. Similarly, for distances of z2 smaller than 15 cm, the signal increases linearly with distance. For z2 greater than 50 cm, the signal tends to level off. This behavior demonstrates that it is not necessary to place the detector and/or the optical aperture at long distances from the sample cell, as has been commonly reported in the literature for larger aperture diameters (4-8). Figure 4 presents the variation of the signal s ( t ) as a function of the distance z2for apertures with radii equal to 20,200,600, and lo00 wm. From this figure we see that the distance z2 necessary for maximum response increases as the aperture's size increases. The curve for the lo00 pm diameter
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aperture indicates the large spacing needed to obtain a maximum TLS response. Thus, in order to minimize the thermal lens spectrometer's size, the smallest apertures would ensure maximum signal response with shorter z2distances. Figure 5 shows the calculated variation of the thermal lens signal as a function of the e-2 radius of the excitation and the probe beams, w and wo, respectively. The thermal lens signal exponentially decreases as the radius of the excitation beam increases and slowly increases as the radius of the probe beam increases. Therefore, the maximum signal will be obtained with the smallest w (which provides the maximum power density), and the largest wo that would provide an optimum b/wo ratio. For large values of wo combined with small w, the aberration effeds of the thermal lens may become important, reducing the observed signal. We varied several parameters simultaneously to study the effect of cross terms on the calculated TLS signal, s ( t ) . The simultaneous variation of z1 and z2 showed the greatest influence; however, when z1 > 6 cm and z2 > 50 cm, the calculated theoretical intensity only increases by a factor of 2. For our case, in which a compact system configuration is desired, the values chosen for the experimental parameters are not optimum for maximum signal intensity but represent a compromise based on signal intensity and minimum distances. 11. TLS Enhancement Factor. Thermal lens spectroscopy provides an enhancement in sensitivity over conventional optical absorption spectroscopy, described by an enhancement factor. In this work, the enhancement factor will take into account the radius of the excitation beam which has not been addressed previously for continuous-wave TLS (13,18-20). Previously, it has been appropriate to assume a limiting case where (a) b > zl, and (c) zz/f(t) > t,, the focal length becomes f.. (see eq 6) and the signal reaches a steady-state value, S,. According to eq 9 S, = 2zlalPaV(dn/dT)/akw2
(10)
For small values of the absorbance (A), the relative change in the intensity AI/Ioas would be measured by conventional spectrophotometry is equal to 2.3034, which is equal to elC or al. Equation 10 becomes
S,, = 2.303EJ
(11)
where E, is the thermal lens enhancement factor, given by
E, = [2z,(dn/dT)/kI(P,,/aw2)
(12)
From this expression we see that for a given average power, the power density (Pav/aw2) and therefore the enhancement factor increase as the radius of the excitation beam decreases. Furthermore,for z1 equal to 3ll2z,, the steady-state signal and the enhancement factor vary directly with the radius of the probe beam and inversely with the probe beam wavelength.
E, = [2&'.Jdn/dT)
/Ah1 ( w o / w ) ~
(13)
In many cases,w was assumed to be equal to wo, although this assumption is not generally valid (2, 6,10, 11). If this assumption is made, the influence of power density on the TLS enhancement factor is ignored. EXPERIMENTAL SECTION Instruments. We employed these theoretical considerations to develop a small TLS spectrometer using optical fibers. A diagram of the dual-beam TLS spectrometer developed for this
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 18, SEPTEMBER 15, 1991 0.3 -
0.25 -
m
L
0.2-
.-E
B
e.
Figure 6. Block diagram of the dual-beam optical fiber thermal lens spectrometer. M, L, BS, and F are mirror, lens, beam Spmter,and filter, respectively. fp and fd are the optical fibers used for the transmission of the excltatlon and probe beams, respecthrely. See text for discussion.
work is shown in Figure 6. A dye laser (Coherent Radiation 590) pumped by an argon ion laser (Spectra Physics 171) was used as the excitation beam. A He-Ne laser (Uniphase 1303P, X = 632.8 nm) was used as the probe beam. The excitation beam, modulated at 10 Hz, was coupled to the optical fiber fp (Fiberguide Ind., Anhydroguide graded index, NA (numerical aperture) = 0.22, length = 10 m) with a 1OX microscope objective (Ll). At the distal end of the fiber, the beam was collimated with lens L2 (4.5 cm focal length) and then focused on the sample with lens L3 (15 cm focal length). The probe beam was focused with lens L4 (15 cm focal length), with the beam waist occurring after the sample. Reflections of the dye laser beam into the He-Ne laser cavity, and resultant oscillations in the probe beam intensity, were prevented by an interferencefilter F1 (Corion D1-633-F). A 50% beam splitter (Newport 2OQ20) was used to direct the excitation and the probe beams collinearly into the sample cuvette. A 1cm path length fluorescence cuvette (Starna Cells Inc.) was employed as the sample cell. To eliminate variations of the position of the cuvette, it was epoxied to the holder and the solutions were changed with a micropipet. The laser power incident on the sample cell was monitored from the split beam of the dye laser (Scientech 365). The transmitted beam was blocked after the sample with an interference filter F2 (Corion D1-633-F). A second optical fiber (Fiberguide Ind., Anhydroguide graded index 200 pm core diameter, NA = 0.22, length = 10 m) served as the aperture and as a lightguide of the probe beam to the photodiode detector (UDT Pin lODF 238-10). The ends of the fiber were cleaved and then polished by using lapping paper (3M Co.) with grit sizes of 12, 1,and 0.3 pm, successively. The fiber was mounted in fiber chucks and XYZ translators (Newport Corp.). The enclosed region represents the sample area that was located “remotely” from the large excitation laser system. dc (UDT lOlC), ac (Ithaco 1201),and differential (Stanford Research System SR 235) amplifiers were used for signal processing. The thermal lens signal was recorded as the ratio of the ac and dc signals with a digital averaging oscilloscope (Tektronix 7854), which provides a complete time representation of the signal and avoids the distortion produced with the long-time constants required with a lock-in amplifier (I). Low-frequency noise produced by vibrations of the optical holders made the optical alignment and optimization in real time difficult. However, when the TLS signal was differentially amplified, the low-frequency noise was eliminated and the optimization of the signal could be performed in real time. In addition, the differential signal had a magnitude approximately 40 times greater than the nondifferential signal. Reagents. A stock solution of 0.2 M Nd3+in 0.01 M hydrochloric acid was prepared from neodymium chloride (Aldrich, 99.9%). Sample solutions of lower concentrations were prepared by dilution of the stock solution with 0.01 M hydrochloric acid. The alignment and optimization procedures were carried out with a solution of 0.001 M Nd9+. RESULTS AND DISCUSSION Effect of t h e Size and t h e Distance of the Optical Aperture. Employing pinholes of 5-25 pm in front of the detector, no appreciable change (
