PRESSURE DEPENDENCE OF DEGENERATE FOUR-WAVE MIXING IN SOz : EFFECT OF THE THERMAL GRATINGS

The degenerate four wave mixing (DFWM) spectrum of the A(1A2)--X(1AI) and B(B) X(1A1) transitions of SO2 in the 299.5-305 nm region is presented. It has been found that the DFWM signal intensities are proportional to the cube of laser intensity and the square of SO2 pressure. The DFWM signal increases dramatically with the pressure of N2 as a buffer gas. The enhancement of the DFWM signal can be mainly attributed to the thermal grating contribution.


INTRODUCTION
There has been increasing interest in degenerate four wave mixing (DFWM) as sensitive spectroscopic probes of molecules [1].Degener- ate four wave mixing involves the interaction of three input beams of identical frequency with a nonlinear medium to produce a fourth signal beam of the same frequency u;.The generated coherent signal beam, propagating in a unique and well defined direction, is spectrally *Corresponding author.Tel." +86 21 65102777, Fax: +86 21 65102777, e-mail: qzqin@ fudan.ac.cn 168 S. SHI et al.
bright and highly collimated.To date DFWM has been successfully used to monitoring atoms, molecules and free radicals in the gas phase.It is generally found that laser induced fluorescence (LIF) is a very sensitive detection technique, however, LIF suffers from colli- sional quenching which at worst can remove the signal completely.DFWM could prove more applicable in the high pressure regime or inhomogeneous mixtures.Mann et al. [2] and Ishii et al. [3] de- monstrated that dramatic increase of the DFWM intensity could be achieved with the addition of buffer gas.Recently several groups [2,4] have studied the collision effects on the DFWM signals and provided convincing results which showed that various mechanisms can con- tribute to the formation of laser-induced gratings.
In this paper, we choose SO2 as the subject to study its DFWM because its spectroscopy has been extensively studied and SO2 is a major air pollutant contributing to the formation of smog and acid rain.We observed the DFWM spectrum of SO2 in the 299.5-305 nm range for the first time, which is characterized by broad vibronic bands from a complex interaction between the A(1A2)+ X(1A1) and B(1B1)---X(1A1) transitions.The intensities of DFWM signals were measured as a function of SO2 pressure, the laser intensity and ni- trogen buffer gas pressure.A simple model proposed by Dahney [4] was employed to fit the experimental results, and the reason for the DFWM signal intensity enhancement is discussed.

EXPERIMENTAL
A schematic diagram of the experimental set-up is shown in Figure 1.The 532 nm frequency doubled output of a Nd :YAG laser (Spectra- Physics GCR-190) at 10 Hz pumps a PDL-2 dye laser with a band- width of 0.6cm-1 using a R-640 dye, and the output is frequency doubled with an associated wavelength extension (WEX-1C).The laser is scanned from 299 to 305 nm to obtain SO2 spectrum.A length of 12 cm glass sample cell equipped with two silica windows is used.The laser beam, collimated to approximately 3 mm in diameter, is splitted into a strong forward pump beam and a weak probe beam.After passage through the interaction region in the cell, the strong beam is retroreflected by a mirror to form the backward pump beam.These two pump beams are of approximately the same intensity.The probe beam is directed at an angle of about one degree against the forward pump beam to achieve a maximum spatial overlap with the pump beams.The DFWM signal of SO2 is so bright that can be observed by naked eyes, and is extracted by one of the beam splitters and directed approximately 6m away from the interaction region through several irises.The signal is detected with a photomultiplier tube and fed to a gated integrator (PAR 162 and 165 Boxcar) for pro- cessing.Data acquisition and storage are performed with a PC com- puter.The dependencies of the DFWM signal on the laser intensity and SO2 pressure are measured by monitoring the signal intensity at 300nm.The effect of added N2 buffer gas on the DFWM signal is examined by monitoring the signal intensity as a function of total pressure of gas mixtures containing 1.0 Torr SO2.The laser intensity is measured with energy ratiometer (RJ-7200), and kept constant during each scan.To compare with the DFWM spectrum, a linear absorption spectrum of SO2 is also taken via the measurement of SO2 absorption with the same laser beam.
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RESULTS AND DISCUSSION
The DFWM and absorption spectra in the region of the A(1A2)< X(1A1) and B(1B)+-X(A) transitions of SO2 are presented in Figure 2. The DFWM spectrum is taken with 1.0 Torr SO2 and 206 IxJ of pump laser beam energy.Because the relative absorption of 1.0 Torr SO2 in a 12cm cell is about 7 percent, which will attenuate the in- tensities of all the pumps, probe and signal beams.spectrum are quite similar to the absorption spectrum.The three bands can be assigned to G, F, E bands, respectively, proposed by D. J. Brassington [5].However, the bandwidth of the DFWM spec- trum is narrower than that of the absorption spectrum.This result can be explained as it is known that the spectral intensities obtained by DFWM are proportional to the squared modulus of the complex third-order susceptibility tensor IX (3) 2, while perturbation in the index of the refraction and absorption coefficient correspond to resonances in X 3).Thus, the DFWM spectrum often resembles the square of the absorption spectrum, in the case of unsaturation, the DFWM profile is narrower than the absorption band by roughly a factor of 2.
We have measured the dependences of the DFWM signal inten- sity on the laser intensity and the SO2 pressure.When both the laser intensity and SO2 pressure are low and no buffer gas is added, the DFWM signal generation can mainly attribute to an optical absorp- tion induced population grating.According to the theoretical analysis of the formation of the population grating, an approximate expression describing the pressure and laser intensity dependences of the DFWM signal is derived by Danehy et al. [4] in the form: crANoL IpG 7"13 where Ip is the intensity of the DFWM signal originating from the population grating, 7" is the pulse duration, r is the peak (line-center) absorption cross section, AN0 is the unperturbed population differ- ence between ground and excited states, L is the interaction length, I is the laser intensity (assumed equal for each laser beam) and /sat is the saturated intensity defined by Abrams et al. [6] with pressure (P) and temperature (T) dependences.In the case of I<</sat, Eq. ( 1) can be simplified and the DFWM signal intensity is proportional to the cube of the laser intensity and the square of the gas pressure of SO2.
Figure 3 represents the DFWM signal intensity as a function of the laser intensity in a log-log plot.An i2.9 dependence is obtained with the pump beam energy (Ep) in the range of 160 to 3301,tJ, while an i0.7 is observed at Ep above 330 tJ, indicating that the DFWM signal of SO2 has been saturated above 330ktJ.Our result for a multilevel system of SO2 is consistent with the results of a single rovibronic  transition of NO2 which also obeyed an 13 laser power dependence [2].The DFWM signal intensity dependence on the pressure of pure SO2 is shown in Figure 4.It can be seen that a linear relationship in a log-log plot gives a slope of 1.95 which is in good agreement with the expected value of 2 from Eq. (1).
In order to examine the enhancement of the DFWM signal inten- sity of SO2 with added N2 as buffer gas, the signal intensities are meas- ured by varying the N2 pressure for a fixed SOa pressure of 1.0 Torr.
The result shows a 25 fold increase in the signal intensity at a total pressure of 760 Torr.This enhancement of DFWM signal intensity can be explained in term of the formation of collisionally induced thermal grating when the added buffer gas pressure is much higher than the pressure of SO.It has been suggested that collisions between the ex- cited molecules and the surrounding buffer gas transfer their internal energy into translational motion of the buffer gas, thus producing a -0 7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

Log(P[Torr])
Log-Log plot of the DFWM signal intensity versus the pressure of SO 2.
spatial modulation of gas temperature and leading to the formation of thermal gratings [7].An approximate expression for the thermal grating signal has been derived by Danehy et al. [4].When I/Isat < O. 1, the thermal grating signal intensity can be written as TG 16r3I (Anbuff) ]e(rrecrANoL) 2   A,p T ATCp (1 + 41/Isat) 2 (2)   where is the excitation wavelength, Cp is the specific heat of the buffer gas, e is an empirical parameter that accounts for the fraction of absorbed energy converted to heat, Anbuir is density-induced varia- tions in the buffer-gas refractive index, Ap is gas density variation, and the other parameters are the same as in Eq. ( 1).
Since the DFWM signal mainly originates from the population grating and thermal gratings, total signal intensity obtained in the S. SHI et al.
added buffer gas can be given by IDFWM IPG --ITG (3)   Using Eqs. ( 1), ( 2) and (3), the DFWM signal intensity can be simu- lated as a function of the pressure of N2 buffer gas.In Eqs. ( 1) and ( 2), /sat is buffer gas pressure dependent, give by FO'Vl2crff [4] when the pressure of SO2 is fixed.Here ro is the line-integrated absorption cross section, Fo and 712 are the population and coherence decay rates.In a situation where collision dominates lifetimes, they are both propor- tional to pressure Pbum This lead to /sat (3( p2, but this relationship is not in good agreement with experimental observations [7,8,9].The N2 pressure dependence of DFWM signal of 1.0Torr of SO2 at Ef 300mJ and the simulation results along with the contributions of population grating and thermal gratings are shown in Figure 5.Our  results show that the above equations are satisfactorily used to describe the dependence of the DFWM signal upon the N2 pressure with/sat 0( P 1.4.It can be seen that the intensity of the DFWM signal originating solely from a population grating IpG almost drops to zero in the presence of buffer gas N2.Different from IpG, the contribution of the thermal gratings increases dramatically with the pressure of N2.It is evident that collisionally induced thermal grating is domi- nant in the higher N2 pressure region, and plays a major role in the enhancement of the DFWM signal intensity.

CONCLUSION
An excitation spectrum of the A(1A2).--X(1A1)and B(1B1).--X(1A1)transitions of SO2 is observed by using the DFWM technique for the first time.The dependences of the DFWM signal on the laser in- tensity and the SO2 pressure are in good agreement with the pre- diction from the population grating signal equation deviated by Danehy et al. [4].The addition of N2 buffer gas can enhance the DFWM signal significantly and it can be attributed to the contribu- tion of the collisionally induced thermal gratings at high buffer gas pressure.
FIGURESchematic diagram of the experimental apparatus for DFWM.

FIGURE 2 A
FIGURE 2 A Comparison of the absorption (a) and DFWM (b) spectra of A(1A2) X(IA) and B(B) X(A) transitions of SO2.Pump beam energy: 2601xJ; probe beam energy: 160

FIGURE 3
FIGURE 3 Log-Log plot of the DFWM signal intensity versus the laser intensity.
So we calibrate the measured DFWM signals with taking the SO2 absorption into account.It can be seen that the overall features of the DFWM