Degenerate four-wave mixing as a spectrochemical analysis

Shih , Sanford P. Markey , and Mark W. Duncan ... Spectrochimica Acta Part B: Atomic Spectroscopy 1993 48 (6-7), 757-767 ... Optics Letters 1989 14 (1...
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Anal. Chem. 1087, 59,167-171

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CONCLUSION A simple procedure has been developed for the accurate determination of several elements in eastern coal fly ashes. The technique works well for a variety of other diverse materials that show similar elemental constituency. Applicability to high-sodium materials is currently under developmentusing selective time gating of observed emission and the development of secondary reference materials for standardization.

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ACKNOWLEDGMENT We are grateful to John S. Beaty and Richard Belmore TIME (SECONDS)

Figure 3. Volatilization time plot of a typical high-sodium (western) fly ash. All conditions are identical with those in Figure 2.

by Allied Analytical (10). Second, a new standard must be developed for high-sodium materials. Spiking of BCS 315 with NaPO, in order to more closely match the matrices, is one possible approach. In practice, the analyst often has prior knowledge as to whether the sample is an eastern or a western fly ash. In situations where this is not the case we envision a two-step analytical process. In the first the material will be rapidly “typed” to determine if the material is high in sodium. This could be done spectroscopically by examining the absolute counts generated by the Na photomultiplier tube. As an alternative approach, Platbrook and Barten (11)have published an infrared technique, utilizing clustering theory, to “type” these materials prior to application of other elemental techniques. Depending on the results of preliminary “typing” either a low-sodium (e.g., BCS 315) or a high-sodium standard will be selected for quantitation. Experiments to this end,

(Allied Analytical) and David Kehoe (Detroit Edison) for numerous helpful discussions. Registry No. FezOg, 1309-37-1;A1203,1344-28-1;CaO, 130578-8; MgO, 1309-48-4;TiOz, 13463-67-7;NazO, 1313-59-3;KzO, 12136-45-7;SiOz, 7631-86-9.

LITERATURE CITED Ng, K. C.; Zerezghi, M.; Caruso, J. A. Anal. Chem. 1984, 56, 417. Wheeler, B. D.; Jacobus, N. C. €G&G XRF Note XRF-7, 1972. Coleman, D. M.; Sainz, M. A. Anal. Chem. 1980, 52, 746. Allen, G. M.; Coleman, D. M. Anal. Chem. 1984, 56, 2981. Watters, R. L., Jr. Paper presented at Instut fur Spektrochemle und angewandte Spektroskople, Dortmund, Germany, April 13, 1978. Beaty, J. S.; Wohlers, C. C. Paper No. 61 presented at the Federation of Analytical Chemistry and Spectroscopy Societies (FACSS) V, Boston, Oct 1978. Beaty, J. S.; Belmore. R. J. JTEVA 1984, 12, 212. Kehoe, David, Research Laboratories, Detroit Edlson, personal communications. Norrls, J. A.; Watters, R. L. Paper No. 85 presented at the Federation of Analytical Chemistry and Spectroscopy Societies (FACSS) V, Boston, Oct 1978. Beaty, J. S., Allied Analytical, Waltham, MA, personal communication. Platbrood, G.; Barten, H. Anal. Chem. 1985, 57, 2504.

RECEIVED for review March 7,1986. Accepted July 16,1986.

Degenerate Four-Wave Mixing as a Spectrochemical Analysis Technique J. Michael Ramsey* and William B. Whitten Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

The nonlinear spectroscoplc technique of degenerate fourwave mixing (DFWM) is studied theoretically and experlmentally for use as a spectrochemlcal analyds tool. Speclflcaily, DFWM was evaluated for use In flame elemental analysls. The theoretical evaluation indicates that dectectbn Is fundamentally ilmited by Rayielgh scatterlng from flame gases. For the case of s0dlun-a detection limn is estimated to be 0.01 pptr (part per trillion) or 10 fg/mL. A pulsed Nd:YAG pumped dye laser was used for the experimental study where aqueous solutions of sodlum were aspirated into an air-C,H, flame. A comblnatlon d spatial filtering, poiarlratlon selection, and tlme resolution is used to dlscrlmlnate against background signals. A measured detection limit of 4 ppb sodium is obtained. Improved detectlon llmlts are expected for a contlnuous wave laser system.

Degenerate four-wave mixing, or DFWM, has been shown to have considerable potential as a technique for optical

spectrometry (1,2). Spectral resolution comparable to the natural line width can be obtained for atomic vapor samples due to the Doppler-free nature of the measurements. To our knowledge, however, the applicability of the DFWM technique to trace elemental analysis has not been explored. Pender and Hesselink (3)have shown that DFWM can take place in an &acetylene flame with sodium from an aspirated aqueous solution as the sample. However, they were attempting to show that DFWM could be used as a combustion diagnostic tool; thus their measurements involved relatively high concentrations. We present here the results of a study of degenerate four-wave mixing in atomic sodium produced in an analytical flame. DFWM is a coherent optical process where three input beams of identical frequency (degenerate)are coupled together in a nonlinear medium to generate a fourth output beam. The output beam is also the same wavelength as the inputs by the conservation of energy. The DFWM process (2) is shown schematically in Figure 1. Two of the input beams are spatially coherent and overlap in the nonlinear optical me-

0003-2700/87/0359-0167$01.50/00 1986 American Chemlcal Society

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Figure 1. Block diagram showing the geometry of the degenerate four-wave mixing experiment.

dium; i.e., the refractive index of the medium depends on the light intensity. The beams are called by convention the forward pump, I f , and probe, Ip, beams, as indicated in the figure. The intensity in the overlap region, and hence the refractive index, will have a periodic spatial variation due to the interference of the two beams. If a third beam, the backward pump beam, Ib, that is propagating opposite to the forward pump beam strikes this refractive index grating, a portion will be Bragg-scattered to form the output or phase-conjugate beam, IF Conservation of momentum requires that the output beam be counterpropagating to the input probe beam, Ip' This scattered beam is called the phase-conjugate beam because, except for polarization, its field strength is the complex conjugate or, effectively, a time reversal of the probe beam. The intensity of the phase-conjugate beam is a function not only of the incident intensities but also of the properties of the nonlinear medium. The reason the phenomenon is spectroscopically important is that the contribution to the nonlinear refractive index is large only when the light frequency is close to resonance with an allowed transition. Thus, if the frequency of the three input beams is scanned, the intensity of the output beam, IF, as a function of frequency should represent the spectra of the species present in the gaseous medium. DFWM processes in a gaseous sample were first observed by Bloom et al. ( 4 ) . They observed amplified reflection and spontaneous oscillation for a sample of sodium vapor strongly pumped by a pulsed laser. Further experiments by Liao et al. (1)were performed with a tunable continuous wave (CW) dye laser, again in sodium vapor. These experiments demonstrated several features of DFWM that are attractive for analytical spectroscopicmeasurements. The spectra observed by DFMW are "theoretically" background free; i.e., no signal is observed when no sample is present. This feature has obvious advantages for detecting trace quantities of materials. In addition, the Doppler-freenature of DFWM measurements provides spectral resolution superior to conventional techniques, improving the selectivity of the measurements. The high spectral resolution has made it possible to observe transitions between various hyperfine-split levels (1). The signal photons in DFWM are contained in a spatially coherent beam allowing near unity efficiency for collection with a high discrimination against background photons from incoherent processes. Polarization selection can also be used to discriminate against background signals present in "real" samples. Practical advantages of these measurements over other coherent techniques are the use of a single laser source and the wavelength-independentphase-matching conditions. Finally, spatially resolved measurements are inherently possible due to the crossed beam configuration of the experiment. We will first attempt to show the potential sensitivity of this technique by theoretical calculation of a fundamental detection limit; i.e., various background signals will be considered under ideal experimental conditions. Experiments using pulsed lasers will be described and the results discussed.

THEORY The first attempt to develop a quantitative description of the DFWM process in an atomic vapor was by Abrams and

Lind ( $ 6 ) . They assumed that the effect was due to saturation of the excited-state population and calculated the phase-conjugate intensity based on a two-level atomic system. In later experimental work, however, new physical mechanisms were found to be important when the incident beams had different polarizations (7,8). These other mechanisms result from the degeneracy of the atomic levels and the way the atoms can be oriented or aligned by optical pumping. The theory for these processes is complicated by the provision for degenerate energy levels and the effects of atomic or molecular motion as well as the dependence on the intensities of the various beams. Theoretical treatments of these effects in various approximations have been given by Jabr et al. (8), Saikan (9),Lam and Abrams (101,and Bloch and Ducloy ( I I ) , to name but a few. For our purposes in the present investigation, however, the simpler model based on population saturation will be used. The use of the population saturation model is at least partially justified by the conditions in an analytical flame. For atoms in a flame at atmospheric pressure, the homogeneous collisional broadening of optical transitions will in general be equivalent to or slightly larger than the Doppler broadening (12). Furthermore, for sodium, the homogeneous broadening (5 GHz) is greater than the hyperfine splitting (1.7 GHz) as well, so optical pumping should not be as important as in a low-pressure sample. As long as the probe and forward pump beams have the same polarization and cross at a small angle, the two-level theory of Abrams and Lind (5,6) should be applicable. The population saturation theory has been extended to include the case of unequal pump intensities by Dunning and Steel (13). For small optical density within the sample, the ratio of phase-conjugate, IW, to probe intensity, Ip, or the reflection coefficient for the DFWM process can be written, approximately, as In this expression, L is the length of overlap of the four beams and r is the nonlinear coupling coefficient, given by

In eq 2, a. is the line center field absorption coefficient, Io Zb is the intensity of the counterpropagating pump beams, and I, is the saturation intensity for the transition being probed. The value 6 is the normalized detuning parameter (o- w0)T2,where wo is the transition frequency and T2is the dephasing time. The nonlinear coupling coefficient, r, contains contributions from both the real and imaginary parts of the electric susceptibility, i.e., the dispersion and absorption due to the transition. The line center field absorption coefficient and the sample absorbance, A (at line center), are related as shown in eq 3. The signal strength = In (10) A / 2 L (3) = If =

can be found by substituting eq 2 into eq 1 and multiplying by the probe intensity, Ip,as shown in eq 4. The nonlinear

[ A In ( ~ O ) I ' ~ I O / I ~ ) ~ I ~ Ipc =

( 1 + 6'

+~(Io/I,))~

(4)

coupling coefficient given in eq 2 is a maximum when the pump intensity equals half the saturation intensity. This pump intensity will yield the largest reflectivity and hence near optimum signal strength for a given transition. Setting the pump intensity to the value for maximum reflectivity at line center, Io = 18/2,gives [ A In ( l 0 ) ] * I p (5) Ipc = 4(3 + 6 2 ) 3

ANALYTICAL CHEMISTRY, VOL. 59, NO. 1, JANUARY 1987

109

lo-' sr. The analyzing polarizer in front of the photomultiplier

is set to pass horizontally polarized light. This polarizer greatly

Flgure 2. Schematic diagram of the optical setup: SF, spatial filter; ATN, variable attenuator: T, telescope with 10-pm spatial filter; P, Glan Thompson polarizer: BS, 50 % beam splitter; M, high-reflecting mirror; X/2, Fresnel rhomb pair at 45'; L, lens; PMT, photOmultlplier

tube. Equation 5 shows two interesting features of the DFWM signal from a two-level atom. The intensity of the signal beam or the phase-conjugatebeam is proportional to the square of the sample absorbance, provided pump absorption can be neglected. Therefore,the response will also depend on the square of the atom density or concentration. In addition, the signal decreases with the sixth order of the detuning, 6, rather than the square as with conventional spectroscopy. Also, note that the signal, IF, responds linearly to small changes in laser intensity about 412. Thus, this nonlinear technique does not appear to be any more susceptible to source flicker noise than conventional linear measurements. We evaluate eq 5 below and compare the reflected intensity with that arising from interfering effects to estimate a fundamental detection limit for the DFWM process. Theoretical Detection Limits. We can estimate the intensity of the signal beam using eq 5. Numerical values representative of sodium atoms in an air-C2Hz flame will be used in these calculations to allow comparison with the experimental results presented below. We can relate the DFWM signal expected for a given absorbance to a solution concentration by using the sensitivity value of sodium for the nebulizer/burner system used in this study (14). The absorption sensitivity of sodium for this system is 3 ppb; i.e., this concentration produces an absorbance of 0.0044. We will assume that the interaction length equals the flame length (10 cm), the measurements are made at line center (6 = 0), and Zp = Zo = Z8/2 = 37 W/cm2 (3). Using this information in eq 5, we can write the signal intensity in terms of the solution concentration, viz.

Zpc = KC2 where C is the solution concentration of Na in nanograms per milliliter and K is a constant equal to 1.2 X 10" (W-mL2)/ (cm2.ng2). In the current experimental setup the beam diameter is 0.35 cm. Thus, eq 6 predicts a signal power of 1.1 pW for a 1 ppb Na solution or 3.4 X 10l2photons/s. The pulsed laser used in this experiment would produce 1.7 X lo4 signal photons/pulse with its 5-1-15 pulse duration. While the DFWM process is intrinsically background-free, other effects can generate a background signal that will degrade the detection limit. As will be seen below, the experimental arrangement used in the present investigation provides a high degree of discrimination against unwanted light, through collimation and polarization selection and by time resolution. For example, potentially the greatest source of stray light would be that scattered from the probe beam by the beam splitter that directs the phase-conjugate beam to the detector, Figure 2. Much of this stray light can be eliminated by spatial filtering of the signal beam. A lens and pinhole combination at the photomultiplier tube will accept only that portion of scattered light in the solid angle ird2/4f2, where d is the pinhole diameter and f the lens focal length. The minimum solid angle is limited by diffraction because of the finite beam diameter, D, to 7~(1.22X/D)~ (15),or 1.3 X

attenuates the scattered light from the vertically polarized probe beam. The signal beam results from the Bragg scattering of the backward pump beam off of the photogenerated index grating in the atomic vapor; thus the signal beam is horizontally polarized and passes the analyzing polarizer nearly unattenuated. Finally, the scattered photons from the beam splitter travel an optical distance -300 cm shorter than the signal photons, so the scattered light arrives about 10 ns before the signal. The PMT response to the scattered light is a pulse of 10-nsduration while the signal duration is somewhat less. We can exclude about 90% of the remaining scattered light by setting the gate on the boxcar integrator to measure the signal preferentially. Since the light beams are highly collimated, it would be possible in principle to enlarge the dimensions of the apparatus to give even further temporal discriminationif desired. These three forms of discrimination greatly reduce the background signal due to scattering from optical components. Another contribution to the background is from Rayleigh scattering of the incident beams. The backward pump is polarized in the same direction as the phase-conjugate signal beam. Light scattered from this beam by the flame gases will be a major contribution to the background since neither polarization nor time resolution provides effective dmcrimination. The magnitude of the Rayleigh scattering background can be estimated by using the experimentallydetermined differential scattering cross section for nitrogen (16), the predominate component of the flame gases. This cross section was determined to be 2.12 X cm2/sr at 694.3 nm. Assuming the flame gases are 100% nitrogen at 2480 K and 1 atm pressure, a background signal of 4.6 X W or -1.4 X lo4 photons/ s would result from Rayleigh scattering. Fluorescence from the sample atoms can in some cases be an interference. Even though this contribution is proportional to the sample concentration and hence more like signal than noise, the fluorescence will be Doppler-broadened and potentially results in a broad background for the Doppler-free DFWM measurement. In the present case, this would not be a severe limitation because colliiion broadening is a significant contributor to the line width as stated above. The fluorescence intensity can be related to the sample absorbanceor sensitivity given above for this system, provided the fluorescence quantum efficiency is known. The fluorescence intensity, ZFL, at the detector is given in eq 7, where A

(7) is the sample absorbance, Zo is the pump beam intensity, QF is the fluorescence quantum efficiency and dfl is the solid angle collected. A factor of 2/3 has been included in eq 7 to account for the reduced absorbance due to saturation by the pump beam intensity, Io= I,/2 (17). The fluorescence quantum efficiency is the ratio of the measured fluorescence lifetime to the natural lifetime. The experimentally determined lifetime of the sodium D lines in an air-C2H2flame is 0.72 ns (18). The natural lifetime of sodium determined from the measured natural line width is 106 ns (19). These experimental values suggest a fluorescence quantum efficiency of 6.6 X By use of the above values in eq 7, ZFL = (6.6 X 10-l2)CW/cm2, where C is the concentration in solution in nanograms per milliliter. The concentration where the DFWM signal and the fluorescence signal are equal is 5.6 X lo-' ng/mL. A background signal that cannot be discriminated against by the above methods is the nonresonant DFWM signal from the other gases in the flame. The contribution from these gases can be approximated by treating them like two-level

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atoms but far from resonance. The contribution from molecular nitrogen is again presumed to be most significant. The strong absorption bands of N2 are in the range of 85-100 nm with an average absorption cross section of 4 X lo-'* cm2 (20). We will assume that the transition is centered at 90 nm, that the integrated cross section is cm2, and that the flame is 100% nitrogen. By use of the temperature of the flame given above to determine the density of nitrogen molecules, an absorbance at line center for Nzcan be calculated. The absorbance and the 500-nm detuning can be used in eq 5 to estimate the nonresonant background at the pump wavelength. For this experiment a nonresonant background of 4.4 x W or an average of 1.3 X photons/s is predicted. We have implicitly assumed a saturation intensity equal to that of sodium in this calculation, which would lead to an overestimate for the nonresonant background. Mie scattering from particulate in the flame can also contribute to the background signal. The source of the particulate might be from nebulized droplets that have failed to desolvate or from unvaporized analyte. The quantity of particulate in the flame will depend greatly on the nebulizer and spray chamber used and is therefore very difficult to estimate. Although Mie scattering is observed in our measurements, we do not consider this source of background signal to be a fundamental limitation to the technique because it can presumably be eliminated or reduced by improving the nebulization process. According to the above estimates, the largest contribution to the background signal originating from the sample or flame is the Rayleigh scattering of the incident beams. At least one of the incident beams must be polarized parallel to the signal polarization so that the scattered light from this beam will be detected. Thus, Rayleigh scattering appears to limit the fundamental sensitivity of DFWM measurements in analytical flames. To calculate a fundamental detection limit, we will assume that shot noise on the background signal is the limiting source of noise. A signal-to-noise ratio of 2 and a 1-s time constant then correspond to a concentration of -10 fg/mL of sodium in aqueous solution. The background signal produced by sodium resonance fluorescence at this concentration is a factor of 10 below the DFWM signal. The sample absorbance a t this level is lo-* in the 10-cm slot flame. This detection limit is undoubtedly optimistic for a real experimental system but does give an indication of the potential sensitivity of the technique. Experimental detection limits will probably be limited by a combination of flame and laser noise sources.

EXPERIMENTAL SECTION The optical arrangement is shown schematically in Figure 2. The air-acetylene burner is a Varian Techtron Mark V burner and spray chamber with a Hi-Vac barrel-type nebulizer. The burner produces a flame with a 10-cm length. NaCl/distilled water solutions of various concentrations are aspirated into the slot burner. The three incident liiht beams are split from the output beam of a Quanta-Ray PDL-1pulsed dye laser. All of the measurements reported here were made with Kiton Red dye, with the laser grating-tuned to the sodium D2 line at 589 nm. The line width of the laser pulses is 8 GHz and the pulse duration 5 ns. The beam is 0.35 cm in diameter and has a near uniform intensity distribution. The three beam splitters shown in Figure 2 are nominally 50%, so the three beams are of about equal intensity. The dye laser output is attenuated, spatially filtered, and vertically polarized before the beam splitters. The backward pump beam passes through a Fresnel rhomb pair to rotate the polarization to horizontal. This polarization rotation serves two purposes. Scattering of the backward pump beam creates the signal beam; thus, the signal beam is also horizontally polarized. This allows polarization discrimination against background resulting from the forward pump and probe beams. In addition, all beams directed back to the dye laser are rotated to horizontal polarization

c

10'1

10

ioo

io'

io2

10'

10'

CONCENTRATION (ppb)

Figure 3. Working curve for the degenerate four-wave mixing experiment. The analyte is sodium in aqueous solution. The lowest concentration (4 ppb) represents the detection limit for the current apparatus. The signal at the detection limit is =8 photons/iaser pulse. The relative uncertainty at 4 and 8 ppb is 74% and 25%, respectively. All other measurements have a relative uncertainty of = 10%. The curvature at high concentration is due to absorption of the optical

beams. by the Fresnel rhombs, effectively isolating the experiment from the laser. The probe beam undergoes additional spatial filtering before entering the sample. The phase-conjugate signal beam is in principle a time-reversed replica of the probe beam and should therefore pass completely back through the spatial filter while only a portion of the stray light will be transmitted. The probe beam crwes the pump beam at an angle of -20 mrad. The small crossing angle and large beam diameter provide significant beam overlap through the entire length of the flame. The signal beam is directed by a third beam splitter through a horizontal polarizer, lens, and pinhole to an RCA Model C31034 photomultipliertube. The photomultiplier output is averaged on a boxcar integrator, digitized, and stored as a function of time on a laboratory computer. The laser power is adjusted to give the largest signal-tobackground ratio at some intermediate concentration (100 ppb), and this intensity is used for all measurements. The power level used in the experiments reported here is 90 nJ/pulse (&50%) for the input beams, which corresponds to an average intensity of N 100 W/cm2. This intensity is approximately the saturation intensity given above for Na in an air-C2H2flame. The theory given above predicts the maximum signal-to-background ratio with a pump intensity of I J 2 .

RESULTS AND DISCUSSION A plot of phaseconjugate intensity vs. sodium concentration is shown in Figure 3. Because of the quadratic dependence of output signal on sample concentration at low optical density, the dynamic range of the detection system is strained by only a few-decade range of concentration. Accordingly, a neutral density filter was placed in front of the detector as needed and the results normalized to measurements with the previous attenuation. The quadratic dependence on sample concentrations is evident a t low concentrations. At higher values, absorption of the optical beams reduces the output intensity. We have found that the linear range can be extended to higher concentrations a t the expense of low-end sensitivity by moving the laser frequency away from line center. Presumably a wavelength scan over the transition followed by peak integration would give the greatest dynamic range. The detection limit shown in Figure 3 , 4 ppb, produced a signal of approximately 1photoelectron/pulse. This signal

ANALYTICAL CHEMISTRY, VOL. 59, NO. 1, JANUARY 1987

corresponds to -8 signal photons/pulse given the photocathode quantum efficiency of 13%. Equation 6 predicts that 20 parts-per-trillion (pg/mL) of sodium would produce this same signal; a detection limit lo2 lower than observed experimentally. The reduced signal that we observe could be attributed to a number of effects. A reduction of one-half is expected due to thermal washout of the small spaced grating formed by the probe and backward pump beams. Also, beam self-focusing and self-defocusing take place a t the optical resonance reducing the phase conjugate efficiency (8). Finally, the most significant effect is suspected to be beam distortion by the refractive index gradients caused by the spatial temperature profile within the slot flame. These distortions are quite evident from observing the pump beams before and after passing through the flame. The phase conjugation process is optimum when the pump beams are two counterpropagating plane waves or a phase-conjugate pair (2). Wave-front distortion of the pump beams results in similar distortion of the signal beam, thus reducing the collection efficiency of signal photons. Both of the beam distortion problems could be avoided by phase conjugating one pump beam to form the other. The relative uncertainty of the measurement at the lowest concentration, 4 ppb, is 74% and drops to 25% at 8 ppb. The remainder of the measurements in Figure 3 have a relative uncertainty of 10%. The major background signal observed was due to Mie scattering from either solution droplets or unvaporized analyte particles. The dominant noise source at the lowest two concentrations measured was from fluctuations in this background signal due to flame and laser variations. The Mie scattering could be reduced by using an improved nebulizer/spray chamber system. At the higher concentrations, signal-dependent noise dominated and resulted largely from laser pulse-to-pulse power fluctions. A further improvement should result from the use of a CW dye laser instead of the pulsed laser that was available for the present measurements, both because of the increased integration time of the CW measurement and the pulse-to-pulse intensity fluctuations that add noise to the signal and background for the pulsed measurements. Signal modulation could be conveniently achieved with a CW laser by modulating one of the incident beams, or a form of sample modulation could be used. Some of these techniques have been tried by Raj et al. (21). These detection limits can be compared to those for other measurement techniques that also use an air-acetylene flame as an atomizer. Tong and Yeung (22) found a detection limit for sodium of 30 pptr with a CW polarization modulation scheme. Detection limits of 100 pptr and 8 ppb were reported for atomic fluorescence spectrometry with laser (23) and continuum (24) sources, respectively. A limit of 0.2 ppb has been given for atomic absorption spectrometry (14). Our preliminary results show that DFWM measurements are

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potentially competitive with the other methods. DFWM could also be used to probe molecular transitions. Reduced sensitivity would be expected because of the generally smaller optical cross sections for molecular transitions, but this can be partially compensated for by the increased saturation intensity (increased optimum input intensity). The detection limit will depend inversely on the square root of the optical cross section assuming a given excited-state relaxation rate. Another feature of DFWM that may add to the possible utility of the technique is two-photon phase conjugation (19) which permits the study of UV transitions with visible input and signal beams. In summary, we have explored the possibility of using degenerate four-wave mixing with an air-acetylene burner/ atomizer for analytical atomic spectrometry. The theoretical analysis based on a two-level atom approximation gives an estimated fundamental detection limit of 0.01 pptr (10 fg/mL) for sodium in aqueous solution. This detection limit can only be approached by the ideal experimental apparatus. The experimentally observed detection limit with the pulsed laser system described here is 4 ppb. Higher detection limits are observed because of reduced signal intensity, laser noise, and Mie scattering. Improved detection limits are expected for a CW laser system and with modifications to the experimental setup.

LITERATURE CITED (1) Liao. P. F.; Bloom. D. M.; Economou, N. P. Appl. Phys. Lett. 1978, 32. 813-815. (2) F O a ~ general review of DFMW processes, see: ~ p t i c aphase l Conjugation; Fisher, R. A., Ed.; Academic Press: New York, 1983. (3) Pender, J.; Hessellnk, L. Opt. Left. 1985, 10, 264-266. (4) Bloom, D. M.; Llao, P. F.; Economou, N. P. Opt. Lett. 1978, 2, 58-60. (5) Abrams, R. L.; Lind. R. C. Opt. Lett. 1978, 2. 94-96. (6) Abrams, R. L.; Lind, R. C. Opt. Lett. 1978, 3, 205. (7) Lam, J. F.; Steel, D. G.; McFarlane, R. A.; Lind, R . C. Appl. Phys. Lett. 1981, 38, 977-979. (8) Jabr, S. N.; Lam, L. K.; Hellwarth. R. W. Phys. Rev. A 1981, 24, 3264-3267. (9) Salkan, S. J . Opt. SOC.Am. Lett. 1982, 72, 514-516. (10) Lam, J. F.; Abrams, R. L. Phys. Rev. A 1982, 26, 1539-1546. (11) Bloch, D.; Ducloy, M. J . Opt. SOC.Am. 1983, 73,635-646. (12) Parsons, M. L.; McCarthy, W. J.; Winefordner, W. D. Appl. Spectrosc. 1986, 20, 223-230. (13) Dunning, G. J.; Steel, D. G. I€€€ J. Quanf. Electron. 1982, QE-18, 3-5. (14) Varian product literature, 1984; publication 85-100421-00. (15) Koechner, W. SolM State Laser Engineering; Springer-Verlag: New York, 1976. (16) Rudder, R. R.; Bach, D. R. J . Opt. SOC.Am. 1988, 58, 1260-1266. (17) Yarlv, A. Quantum Electronics; Wiley; New York, 1975; Chapter 8. (16) Russo, R. E. Ph.D. Thesis, Indiana Universlty, Bloomington, IN, 1981. (19) Liao, P. F.; Economou, N. P.; Freeman, R. R. Phys. Rev. Lett. 1977, 39, 1473-1476. (20) Wantanabe, K.; Marmo, F. F. J . Chem. Phys. 1958, 25, 965-971. (21) Raj, R. K.; Bloch, D.; Snyder, J. J.; Camy, G.; Ducioy, M. Phys. Rev. Lett. 1880, 1257-1254. (22) Tong, W. 0.;Yeung, E. S. Anal. Chem. 1985, 57, 70-73. (23) Weeks, S. J.; Haraguchi, H.; Winefordner, J. D. Anal. Chem. 1978, 50, 360-368. (24) Wlnefordner, J. D. CH€MECH 1975, 123-127.

RECEIVED for review May 15,1986. Accepted August 25,1986.