1700
Anal. Chem. 1984, 56,1700-1704
Theory for Laser-Induced Photothermal Refraction Norman J. Dovichi,* Thomas G. Nolan, and Wayne A. Weimer Department of Chemistry, University of Wyoming, Laramie, Wyoming 82071
Photothermal refraction is a novel thermooptlcal technlque which produces a linear measure of sample concentration and absorptlvtty wlth hlgh sensltivtty and spatial resolullon. I n thls technique, a cylindrical thermal lens Is formed wlthln a sample from absorptlon of a chopped Gaussian laser beam. The lens Is Interrogated at right angles with a contlnuous wave probe laser beam and detected as a change In the far-right probe beam center Intenslty. This paper develops a theoretlcai analysis of photothermal refractlon.
The use of lasers in optical instrumentation has produced spectacular gains in the temporal and spectral resolution of atomic and molecular species ( I , 2). Similarly, lasers may be used to produce high spatial resolution in the analysis of low concentration samples. Applications of high spatial resolution techniques are found in biochemistry, microchemistry, chromatography, combustion diagnostics, and microscopy. Unfortunately, conventional spectroscopic techniques produce a signal which is related to the integral of analyte concentration along the optical path; these line of sight techniques produce no information about the distribution of analyte along the optical path. Tomography (3)and the use of small path length samples (4) appear to be the only way to obtain spectroscopic information from a localized region using conventional optical techniques. Several laser techniques have been developed which produce spectroscopic information from a localized volume. These techniques are based on nonlinear effects wherein the signal is generated at the intersection region of two or more laser beams. Examples of techniques which produce or are capable of producing localized spectroscopic measurements include several coherent Raman techniques (5), multiphoton techniques (6), optically induced Stark spectroscopy (7),saturated absorbance spectroscopy (8),and thermal grating calorimetry (9). Unfortunately, none of these techniques produces a signal which is linearly related to conventional spectroscopic properties of the sample. This paper presents the theory for a new laser technique which not only produces a signal from a localized volume but also is linearly related to analyte concentration and absorptivity. In photothermal refraction, Figure 1, a modulated pump laser beam illuminates a sample. Absorption of the pump beam results in the formation of a cylindrically symmetrical temperature rise within the sample. A coplanar CW probe laser beam intersects the pump laser beam a t right angles. The heated sample acts as a cylindrical lens to defocus the probe beam along the axis perpendicular to the plane containing the two laser beams. The effect of the heated sample upon the probe beam is measured as a change in the far-field probe beam center intensity and is detected in phase with the pump laser modulation function. Since the refraction signal is generated only at the intersection region of the two laser beams, a measure of sample absorbance may be made with high spatial resolution. Photothermal refraction is part of a family of thermooptical techniques for absorbance measurements. In these techniques, an optical element is formed within a sample from a tem0003-2700/84/0356-1700$01.50/0
perature rise generated by absorption of a pump laser beam. This optical element perturbs the propagation properties of either the pump beam or a second probe laser beam. Thermooptical elements include a change of optical path length in interferometric techniques ( I O , I I ) , a lens in thermal lens calorimetry (12), a prism in photothermal deflection (13),and a grating in thermal diffraction (9). To this list we now add a cylindrical lens in photothermal refraction. Photothermal refraction is experimentally related to photothermal deflection. In the deflection technique, the temperature rise formed by the pump beam is probed off axis at the maximum of the temperature gradient; the probe beam is deflected away from the heated region. On the other hand, the temperature rise in photothermal refraction is probed on axis at the minimum of the temperature gradient; the probe beam is defocused equally on each side of the heated region. The theory for photothermal refraction draws heavily from that developed by Whinnery for thermal lens calorimetry (14, 15). In both experiments, the heated sample acts as a lens to defocus a probe beam. In thermal lens calorimetry, the heated sample has circular symmetry and is modeled as a simple lens. In photothermal refraction, the heated sample has cylindrical symmetry and is modeled as a cylindrical lens. In this paper, a theory is developed for photothermal refraction. In the following paper in this journal, the theory is verified with respect to a number of predictions.
THEORY A model for the far-field probe beam center intensity in photothermal refraction consists of three parts: a description of the temperature rise generated within the sample by the pump beam, the identification of the focal length for a cylindrical lens equivalent to the heated sample, and finally a computation of the change in the far-field probe beam center intensity caused by the equivalent cylindrical lens. The appendix of this paper develops an expression for the relative change in far-field probe beam center intensity for pulsed pump laser excitation, This impulse response function is of value in modeling not only experiments using a pulsed pump laser but also experiments with an arbitrary excitation function; convolution of the impulse response function with the pump laser wave form yields the response for an arbitrary excitation function (16,17). Figure 2 summarizes the results obtained for impulse, step function, square pulse, and chopped excitation functions. The impulse response for photothermal refraction, Figure 2a, is given by eq 22 of the appendix:
where AI(t) is the relative change in the far-field probe laser beam center intensity and E is the energy per pump laser pulse. The sensitivity of the effect is proportional to 8 4.606t.C(dn/dT)ZI 8= (2) (2~)l/~uk where c is molar absorptivity, C is concentration, d n l d T is the change in sample refractive index with temperature 0 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
1701
Step excitation, Figure 2b, models the case where the farfield probe laser intensity is sampled some time, t , after a chopper unblocks a CW pump laser beam. The step response of the photothermal refraction signal is given simply by the time integral of the impulse response (16, 17)
AI@) = OP
[
(1
+ 2t/tC)'/2- 1 1
(4)
where P is the average pump laser power. The next case considered is a square pulse excitation function, Figure 2c. The expected signal in this case is given at a time, t , after the pulse is turned off
Figure 1. Photothermal refraction diagram. The pump beam is directed along the Y axis and probe beam is directed along the X axis. Refraction of the probe beam 1s generated at the intersectlon region and occurs in the Z direction. The photothermal refractlon signal is measured as the relative change in the intensity which passes through a pinhole located at the far-fleld probe beam center. EXCITATION FUNCTION
RESPONSE FUNCTION I
Ib STEP
TIME
I
I C
where T is the pulse width. The last excitation function to be considered is a square wave, which models the photothermal refraction signal when the pump laser is chopped in an infinite square wave, Figure 2d. We chose to consider the case where the square wave is symmetric; that is, when the blocked and unblocked periods, T , of the chopping cycle are equal. It is convenient to treat separately the signal with the pump beam blocked and unblocked. The signal with the pump beam blocked is the sum of the signals from the previous square pulses
where teff is the time measured from the blocking of the pump beam. The summation is made over an infinite number of chopper cycles. When the pump beam illuminates the sample, the signal includes a contribution from both the current heating cycle and all previous cycles. The signal is given as a function of to,, the time measured from the unblocking of the pump beam
[ c-
AI(t,,) = -0P 1 -7
O
T
TIME
I d
Figure 2. Excitation and response functions considered for photothermal refraction. On the left is the pump laser excitation function and on the right Is the probe laser response. (a) Impulse. The excitation function is an impulse of energy E at time T = 0. (b) Step. The excitation function is a step function starting at T = 0. The response function is plotted on a scale corresponding to haif the steady state response. (c) Square pulse. The excitation function is a square pulse of length T . The response function is plotted for T = t,. (d) Infinite square wave. The excitation function is an infinite square wave train with equal blocked and unblocked periods. The time scale to, is measured from the start of the blocked period. The time scale ton is measured from the start of the unblocked period. The response function is plotted for T = t,.
m=o(l
-1m
+ 2(t,, + r n T ) / t , ) ' / 2
]
(7)
The last two equations are internally consistent. The signals at the blocking and unblocking transitions are equal as verified by substitution. In some cases, it is weful to consider the frequency response of the photothermal refraction signal. The frequency response for a given excitation function is simply the product of the frequency spectra of the excitation function and the impulse response function (16). The real portion of the impulse response spectrum is obtained from the cosine Fourier transform of eq 1evaluated on the half-line, F,IAI(t)}(16). The imaginary portion of the spectrum is found from the sine Fourier transform on the half-line, F,(hl(t)J(16). Integration by parts gives the transforms in terms of the Fresnel integrals
evaluated at the probe laser wavelength, Z1is the distance from the probe laser beam waist to the beam intersection region, w is the pump laser beam spot size, and k is the sample thermal conductivity. The time constant for the effect is given by
t, = w2C,/4kp
where p capacity.
(3) is the sample density and C, is the sample heat
where vo = r v t , is the normalized frequency and v is the reference frequency in cycles per second. C2 and Sz are the alternate definitions of the cosine and sine Frensnel integrals given in ref 18. The amplitude and phase of the signal are
1702
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
given by the well-known expressions for the polar form of complex numbers amplitude = [Fc(AI(t)}2 + F,(AI(t)}2]1/2(10) phase = arctan
[
z]
Table I. Thermooptical Properties of Gases for Photothermal Refraction Measurementsn
103(dn/dT)/k,
(11)
An asymptotic expansion of the amplitude of the photochemical signal may be evaluated (18,19). The signal develops a 20 dB/decade roll-off at high chopping frequencies and is similar to the behavior of a low pass electronic filter.
ASSUMPTIONS Several assumptions are implicit in this model. These include: 1. The sample is sufficiently large so that the semiinfinite heat equation may be used. It has been stated for other thermooptic techniques that the sample must be ten times larger than the pump beam spot size to satisfy this assumption (14). However, if the sample holder or cuvette has similar thermal properties as the sample, it is only necessary that the sample be large enough not to vignette the laser beams. 2. The sample is homogeneous. 3. The quantum yield of fluorescence, qf, of the sample is negligible. This assumption may be removed with the introduction of (1- Sqf) in eq 1 where S is the Stokes loss in energy between the excitation and emission wavelengths (15). 4. The pump and probe beams are in the TEM, mode. 5. The temperature rise must be small enough that the derivative of refractive index with temperature is a constant. 6. The absorbance of the sample must be sufficiently small, A < 0.05, so that there is negligible power loss in the pump beam as it traverses the probe beam. 7. Focusing conditions must ensure that the pump laser beam spot size is constant over the probe beam diameter. 8. The pump laser beam spot size must be sufficiently large so that the probe beam only interacts with the central portion of the temperature distribution. This assumption allows the truncation of the Taylor's series expansion of An at the squared term. If the probe beam is influenced by higher order terms in the refractive index expansion, either a ray tracing routine or diffraction theory may be used to compute the photothermal refraction signal (13). 9. The detector field of view is restricted to the center of the probe beam. This assumption is satisfied if the pinhole radius is a few percent of the far-field probe beam spot size. 10. The detector is located in the far-field of the probe beam. This assumption is valid if Zz is much greater than 2, and f. It should be noted that the latter assumption will not hold for small time under impulse or step function excitation. 11. The relative change in the far-field probe beam center intensity is sufficiently small to justify the use of the binomial expansion of eq 20. A relative change of 10% or less produces an expansion good to better than 2%. DISCUSSION Several analytically important observations may be made on the basis of the photothermal refraction model. First, the signal is linearly dependent upon absorptivity and concentration. The independence of signal upon path length, assuming the sample plus cuvette is several times the size of the pump beam, is important in the analysis of small volume samples since there is no loss of sensitivity for small path length samples. Path length independence is also noted in thermal grating theory (9). The sample volume for the absorbance measurement is defined by the intersection of the pump and probe laser beams. To a good approximation, this volume is given by
gas
cm/ W
carbon dioxide argon methane nitrogen oxygen
-8.3 -4.9 -3.9 -3.5 -3.1 -0.23 -0.073
hydrogen helium
103t,,b s
23 12
11 11 11 1.6 1.4
Data from Mori, Imasaka, and Ishibashi (28). *Timeconstant computed for a 1-mm spot size pump beam. Table 11. Thermooptical Properties of Liquids for Photothermal Refraction Measurementsa
liquid
cc1,
isooctane benzene acetone
methanol water
(dnldT)lk, cm/ W -0.57 -0.50 -0.44 -0.31 -0.19 -0.013
tWb
9
3.2 3.9 2.4 2.7 2.4 1.8
"Data taken from Solomini (29) and Stone (7). bTime constant is computed for 1-mm spot size pump beam. where usis the spot size of the smaller beam and is the spot size of the larger beam (4). The use of very tightly focused laser beams, on the order of 1pm, will produce L. spatial resolution on the order of The sensitivity of photothermal refraction is inversely related to the pump beam spot size. This behavior is quite valuable since a decrease in the pump beam spot size not only improves the spatial resolution of the technique but also improves the sensitivity of the measurement. Similar behavior has been predicted for double beam thermal lens calorimetry (20) and thermal diffraction (9). The sensitivity of the measurement is predicted to increase linearly with Z1, the distance from the probe beam waist to the sample. However, the probe beam spot size increases with this distance. As 2, increases, the assumption that the pump beam spot size is greater than the probe beam spot size eventually will be violated. Only a limited improvement in sensitivity is available by changing Z1. On the other hand, it should be possible to take advantage of this distance dependence in the development of a differential spectrometer as in thermal lens calorimetry (21). The differential spectrometer would rely upon the sign change in the photothermal signal for samples located across the probe beam waist. The signal is linearly dependent upon the pump laser power. An increase in source power yields a corresponding increase in sensitivity. Under conditions of constant noise, an increase in pump laser power will yield an improved detection limit. The sensitivity of the signal, as in other thermooptical techniques, is a function of solvent composition and depends on the ratio of d n / d T to k. The time constant of the effect also is a function of the solvent composition. Tables 1-111 list the ratio of dn/dT to k and the time constant for several gases (22),liquids (12,23),and solids (24,25),respectively. Note that dn/dT is usually negative with exceptions found among certain solids. In general, liquids generate the highest sensitivity and largest time constant. Gases and solids tend to have similar sensitivity and time constant. Finally, the temporal dependence of the photothermal refraction signal allows the use of powerful techniques such as phase sensitive detection and signal averaging to improve the ~ T W , ~ / W L
WL
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
1703
Table 111. Thermooptical Properties of Solids for Photothermal Refraction Measurements' 103(dn/d T )/ k , solid
cm/ W
103t,,b 8
Ge BK-7 (optical glass)
0.45 0.23 0.056 -0.07 -0.56 -8.9
70 48 30 62 46 20
sapphire quartz (Approx) NaCl
CSI
Data taken from Sparks (24) except for BK-7 data which were taken from the Melles Griot Optics Guide (25). bTime constant computed for a 1-mm spot size pump beam. signal-to-noise ratio of the measurement. As in thermal lens calorimetry, the frequency dependence of the signal is an important considerationwith lock-in detection (26). The time dependence of the signal may be used to extend the dynamic range of the measurement (27). In the frequency domain, the photothermal refraction signal acts as a low pass filter on the pump beam; that is, high frequency noise on the pump beam does not influence the measurement, One obvious source of high-frequency noise occurs a t harmonics of line frequency and is due to imperfect regulation of the pump laser power supply. APPENDIX: IMPULSE RESPONSE FUNCTION The impulse response function for photothermal refraction is found in this appendix. First, the temperature rise within the sample is computed, then the focal length of a cylindrical lens equivalent to the heated sample is found, and finally the influence of the cylindrical lens upon the probe beam is considered. Temperature Rise. Fortunately, Twarowski and Kliger have developed an expression for the temperature rise within a semiinfinite homogeneous sample excited by a pulsed TEM, laser (20). In the coordinate system of Figure 1, the temperature rise, AT(x,z,t),at a time t after the excitation pulse is given by AT(x,z,t) =
2.303E~C
2(x2
+ 22)/"2
where the terms are defined after eq 1 and 2. It is assumed that the excitation pulse is much shorter than the thermal time constant. Focal Length. The next task in the development of an expression for the far-field probe beam center intensity is to identify the focal length of a cylindrical lens equivalent to the heated region. For a small temperature rise, the change in sample refractive index, An, is simply related to the temperature rise by dn An = - AT dT The refractive index change may be expanded in a Taylor's series along the Z axis 1 a2An An=-JZ=Oz2 + Higher Order Terms (14) 2 az2 The even symmetry of the temperature distribution ensures that all odd power terms in the expansion are zero. Furthermore, we chose to define the change in refractive index so that the zeroth power term drops out of the equation. It is well known that a differential sample element with a quadratic variation in refractive index acts as a lens whose differential inverse focal length is given by (14,15, 28)
where dx is the differential length measured along the probe beam path. The quadratic term in the Taylor's series expansion of the refractive index about the Z axis is used to identify the differential inverse focal length of the equivalent cylindrical lens. The derivative of the temperature distribution is evaluated at z = 0 and substituted into eq 15 to find the inverse focal length for a differential element of sample, d(l/f)
d[
f1
+
= -4.606~CE aw2ktc(l d2t/tc)2 n / d T exp[
lT:T:c]
(16)
The differential inverse focal length next is integrated over the probe beam path. It is convenient to assume the sample is sufficiently large to be treated as infinite, an assumption made in the development of the temperature distribution. Performing the spatial integration yields an expression for the focal length of a cylindrical lens equivalent to the heated sample _1 -- 4.606cCE d n / d T (17) f (2a)1/2wkt,(i 2t/tc)3/2
+
where the time dependence of the focal length is explicitly shown. Far-FieldProbe Beam Center Intensity. The final task in this model is to compute the influence of the cylindrical thermal lens upon the far-field probe beam center intensity, I@). A cylindrical lens transforms a circular laser beam into an elliptically shaped beam (28). The far-field probe beam center intensity is given by
where wy and w, are the beam spot size aligned along the Y and Z axis, respectively. Fortunately, the ABCD law for Gaussian beam propogation i s valid for elliptically shaped beams as long as the law is applied independently to each axis (28). The cylindrical thermal lens does not influence the Y axis of the probe beam profie since there is no refractive index variation along that axis. Our attention therefore is focused upon w,. Harris and Dovichi have presented the result of an ABCD law computation which may be used in this problem as eq 18 of ref 12
where Z1 is the distance from the sample to the probe beam waist, 2, is the distance from the sample to the detector, wo is the probe beam waist spot size, and the confocal distance 2, = m o ~ / Xwhere X is the probe laser wavelength. It is assumed that the detector is located in the far-field of the probe beam. Substitution of eq 18 into eq 19 gives a formal expression for the far-field probe beam center intensity as a function of time
where I(0) is the beam center intensity with no lens present. Equation 20 may be simplified if the relative change in I ( t ) is small, 10% or less, with a binominal expansion. This result is written in terms of the relative change in far-field probe
1704
Anal. Chem. 1904, 56, 1704-1707
laser beam center intensity, h l ( t )
An explicit expression for the impulse response function for the photothermal refraction signal is found by substitution of eq 17 to eq 21
(10) (11) (12) ($3) (14) (15) (16) (17) (18) (19) (20) (21) (22)
where 0 is defined in eq 2.
LITERATURE CITED Fujimoto, J. G.; Ippen, E. P. Opt. Lett. 1983, 8 , 446-448. Hall, J. L.; Hollberg, L.; Baer, T.: Robinson, H. G. Appl. Phys. Lett, 1981. 39. 680-682. Harris, S. J.; Weiner, A. M. Opt. Lett. 1981, 6 , 434-436. Dovichi, N. J.; Martin, J. C.; Jett, J. H.; Trkula, M.; Keller, R. A. Anal. Chem. 1984, 5 6 , 348-354. Harvey, A. B. "Chemical Applications of Nonlinear Raman Spectroscopy"; Academic Press: New York, 1981. Huff, P. 6.; Tromberg, B. J.; Sepaniak, M. J. Anal. Chem. 1982, 5 4 , 946-950. Farrow, R. L.; Rahn, L. A. Opt. Left. 1981, 6 , 108-110. Goldsmith, J. E. M. Opt. Lett. 1981, 6 , 525-527. Pelletier, M. J.; Thorsheim, H. R.; Harris, J. M. Anal. Chem. 1982, 5 4 , 239-242.
(23) (24) (25) (26) (27) (28)
Stone, J. J. Opt. SOC.Am. 1972, 6 2 , 327-333. Woodruff, S. D.; Yeung. E. S.Anal. Chem. 1982, 5 4 , 174-178. Harris, J. M.; Dovichi, N. J. Anal. Chem. 1980, 5 2 , 695A-706A. Wetsei, G. C.; Stotts, S. A. Appl. Phys. Lett. 1983, 42, 931-933. Whinnery, J. R. Acc. Chem. Res. 1974, 7, 225-231. Hu, C.; Whinnery, J. R. Appl. Opt. 1973, 72, 72-79. Carslaw, H. S. "Mathematical Theory of the Conduction of Heat in Solids", 2nd ed.; Dover: New York, 1945; Chapter 10. Schwartz, M. "Information Transmission, Modulation and Noise", 2nd ed.; McGraw Hili: New York, 1970; Chapter 2. Abromowitz, M.; Stegun, I."Handbook of Mathematical Functions", 2nd ed.; Dover: New York, 1972; Chapter 7. Boersma, J. Math. Comp. 1960, 7 4 , 380. Twarowski, A. J.; Kliger, D. S.Chem. Phys. 1977, 20, 253-258. Dovichi, N. J.; Harris, J. M. Anal. Chem. 1980, 5 2 , 2338-2342. Mori, K.; Imasaka, T.: Ishibashi, N. Anal. Chem. 1983, 55, 1075-1079. Solimlni, D. J. Appl. Phys. 1986, 37, 3314-3315. Sparks, M. J. Appl. Phys. 1971, 4 2 , 5029-5046. "Optics Guide 2"; Melles Grlot: Irvlne, CA, 1981; p 66. Dovichi, N. J.; Harris, J. M. Los Alamos Conference on Optics '81, D. L. Liebenberg, Ed., Proc. SPIE 1981, 288, 372-374. Dovichi, N. J.; Harris, J. M. Anal. Chem. 1981, 53, 106-109. Yariv, A. "Introduction to Optical Electronics", 2nd ed.; Holt, Rinehart, and Winston: New York, 1976.
RECEIVEDfor review February 2 , 1984. Accepted April 18, 1984. The authors acknowledge funding of this work by the Research Corporation and the University of Wyoming Faculty Development Award program.
Laser- Induced Photothermal Refraction for Small Volume Absorbance Determination Thomas G. Nolan, Wayne A. Weimer, and Norman J. Dovichi*
Department of Chemistry, University of Wyoming, Laramie, Wyoming 82071
Laser-Induced photothermal refractlon Is demonstrated as a new technique for the measurement of small absorbance wlthln a few plcollter volume. A 4-W hellum-cadmlumlaser beam Is used to form a cyllndrlcal thermal lens wkhln a sample. A 5-mW hellum-neon laser beam probes the cyllndrlcal thermal lens at right angles. Refraction of the probe laser beam Is detected as a change In the far-field probe beam center Intensity. The signal Is llnearly related to both pump laser power and sample concentration-absorptlvlty product. The sensltlvity of the effect also changes wtth solvent, modulation frequency, and optlcal alignment. The best detection limit, In terms of the concentratlon-absorptivity product, was 1.1 X lo4 an-'in CCl,. The absorbance across the probe beam profile at the detectlon llmlt was 1.1 X Determlnatlon of Iron 1,lO-phenanthrohe In a mixed watermethanol solvent ylelded a concentration detection llmlt of 3 X M within a 25 pL probed volume, correspondlng to a mass detectlon llmlt of 0.4 fg of iron.
The incorporation of lasers into instrumentation designed for absorbance measurementrs has produced outstanding gains in detection limit (1-3). These improvements arise from not only the high power but also the spatial coherence of the laser beam. The preceding paper in this journal presents the theory for a novel laser technique which produces a linear measure of sample absorptivity and concentration with high spatial resolution ( 4 ) . In photothermal refraction, a cylindrical lenslike optical element is formed within a sample from a temperature rise generated by absorption of a pump laser 0003-2700/84/0356-1704$01.50/0
beam. This thermooptical element is probed at right angles with a second laser beam. The probe beam is refracted or defocused by the thermal cylindrical lens and detected as a change in the far-field probe beam center intensity. Since the technique only measures sample absorbance at the intersection of the pump and probe laser beams, the technique should produce absorbance measurements with good spatial resolution. This paper verifies much of the theory developed for photothermal refraction and demonstrates the low detection limits produced by the technique.
EXPERIMENTAL SECTION Instrument. A block diagram for the photothermal refraction instrument is shown in Figure 1. The system was constructed on a 4 ft by 8 f t optical table, NRC Model KST-48. The helium-cadmium pump laser, Liconex Model 4210B, delivered to the sample a linearly polarized 4-mW beam at 441.6 nm. The beam was modulated in a symmetricsquare wave with a variable speed chopper, Scitec Model 300, typically at 25 Hz.A microscope slide was used to split a small portion of the pump beam to a reference photodetector, described below. The main beam was reflected from two mirrors, M1 and M2, onto a focusing lens. For the frequency dependence study, this focusing lens was a 10 mm focal length microscope objective, Melles Griot. For all other experiments, the focusing lens, L1, was a 27 mm focal length lens, Edman Scientific. The focusing lens was mounted on a translation stage which could be moved along the beam path to adjust the pump beam spot size within the sample. A 1cm by 5 mm quartz flow cuvette, Precision Cells Model 59FL, was used to hold the sample. The use of a flow cuvette allowed the transfer of sample without disturbing the optical alignment. The cuvette was tilted slightly to avoid introducing retroreflectionsinto the laser cavities. A 5-mW helium-neon probe laser, Melles Griot Model 05LHP151, produced a linearly polarized beam at 632.8 nm. The probe beam 0 1984 American Chemical Society
