An investigation of the origins and efficiencies of higher-order nonlinear spectroscopic processes

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Volume 206, number 5,6

An investigation of the origins and efficiencies of higher-order nonlinear spectroscopic processes * Joseph E.

Ivanecky III and John C. Wright

Departmentof Chemistry,Universityof Wisconsin-Madison, 1JO1 University Avenue,Madison, WI 53706, USA Received 10 August 1992;in final form 9 February 1993

We propose extending the site selection and mode selective capabilities of four-wave mixing spectroscopies to room-temperature samples using six-wavemixing to develop multiple Raman resonances. Calculationspredict a coherent higher-order Raman excitation spectroscopy (CHORES) should be observable at excitation intensities > 1 GW/cmz, but there is also competition from a sequential CARS (SCARS) process. Tbe SCARSmechanism dominates over CHORES for electronically non-resonant excitations Since SCARSand CHORES have identical dependencies on both input intensities and resonances, phase-matching considerations must be used to spatially separate their respective contributions.

1. Introduction There has been considerable interest in the development of nonlinear spectroscopic methods that are both highly selective and capable of high resolution. Among the resulting spectroscopies, four-wave mixing (FWM) has become of interest to researchers in a variety of disciplines. Although most work uses two separately tunable input fields, the incorporation of a third tunable field has provided some novel and unique spectroscopic capabilities. Steehler and Wright [l] first utilized fully resonant FWM (FRFWM ) to obtain site-selective vibrational spectra of the ground and lowest excited states of pentacene doped into pterphenyl crystals. The line-narrowing capabilities of coherent anti-Stokes Raman scattering (CARS), predicted by Ouellette and Denariez-Roberge [ 21, were confirmed by Riebe and Wright [ 31 and Hurst and Wright [4,5 J in results from mixed crystal and amorphous matrices, respectively. In addition to site-selection and line-narrowing, Carlson and Wright [ 61 have demonstrated that relationships and coupling coefficients between the selected vibrational resonances of the ground and excited electronic states determine the relative en* This research was supported by the National Science Foundation under grant CHE-9200535.

hancements in FRFWM. Although the additional resonances of FRFWM methods have resulted in enhanced sensitivity and selectivity, these spcctroscopic advantages have only been demonstrated for dilute guest-host systems at cryogenic temperatures since the electronic resonances required for FRFWM methods with typical lasers exhibit extensive homogeneous broadening at room temperature. If the multiple resonances could be achieved with ground state vibrational levels, the same site selection, line narrowing, and mode coupling measurements could be performed at room temperature. In isotropic media the lowest-order nonlinear polarization is generated through interaction with the third-order susceptibility, x@). Since at this level only a single vibrational Raman resonance may be developed using visible lasers, we consider here x(S) interactions that represent the next order of interaction that contributes to the nonlinear polarization. Although the number of coherent pathways increases rapidly with increasing order of interaction, we limit our discussion to a particular class ofX(‘) processes. A higher-order Raman spectral excitation study (HORSES) was previously’ reported by Chabay et al. [ 7 1. The HORSES mechanism can be either a sixwave mixing coherent higher-order Raman excitation spectroscopy (CHORES) or a sequential CARS (SCARS) process. Similar processes have appeared

0009-2614/93/S 06.00 0 1993 Elsevier Science Publishers B.V. All rights resewed.

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previously in the literature involving collisionallyenhanced multi-wave mixing in alkali-metal vapors

[8-l 01, phase-angle-resolved degenerate methods in semiconductor-doped glasses [ 11-I 31, and the observation of subharmonic resonances in molecular gases [ 14,15 1. Coherent interference effects involving such processes have also been reported in related systems [ 16,17 1. While there is growing interest in

the spectroscopic and analytical utilities of spontaneous z(5) processes, such as hyper-Raman scattering (HRS) [ 18,191, the use of coherent methods at this level of interaction has been extremely limited [ 20,2 1] with the notable exception of those interested in the development of coherent UV and WV sources. In this Letter, we present an investigation of the feasibility of the three-laser CHORES process shown in tig. la. Through the use of these three separately

@j+da x

c) SCARS

b) HRS

a) CHORES

.ga+bt

m bd

0%

Fig. 1. Mixing schemes and LiouviIIediagrams for (a) coherent higher-order Ran-ranspectroscopy (CHORES), (b) hyper-Raman scattering (HRS), (c) sequential coherent anti-Stokes Raman scattering (SCARS). In the energy level diagrams horizontal solid and dashed lines indicate real and virtual energy levels, respectively. Solid and dashed vertical lines represent interactions with the ket and bra portions of the wavefunction, respcctively. In (b) the interaction indicated by the straight arrow between levelsg and b is provided by the vacuum field. The LiouvilIe diagrams show the elements of the density matrix, ps indicating the time evolution of the induced polarization with successive interactions. Evolution of the bra and ket are represented through interactions in orthogonal directions within the diagram. The initially populated state (a) and final coherent state are enclosed in boxes. For clarity the labels indicating the field responsible for each interaction have been omitted, for these the reader should refer to the corresponding energy level diagram.

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tunable fields, one is able to develop Raman resonances with two vibrational states of the ground electronic state. Resonances are achieved when ~I,-w~=L()~~ and 2wt-wz-c03=~~s. Conventional spectroscopies have shown these resonances provide excellent selectivity as a consequence of the very narrow linewidths associated with vibrational transitions. The only requirement is that each of the selected vibrations be Raman-active. We also consider the competition between this CHORES process and the SCARS process shown in fig. lc. SCARS is representative of a cascaded process, which has been previously reported in the coherent Raman scattering literature [ 14- 17,221, in which a field generated within the medium (at 2wr -w2, in this case) interacts further with the applied fields to produce the observed signal at (2w, -or) - o3 t w,. Finally, we compare both processes to HRS (see fig. lb) using parameters taken from experimental results which have appeared in the literature. Liouville space diagrams [23] are used to follow the evolution of the induced polarization through successive interactions for each process and provide insight into both their origins and differences. The Liouville diagrams of these respective processes are also given in fg 1. As guided by theoretical estimates formulated using the unified treatment of Lee and Albrecht [ 24 1, experimental results indicate phase-matching differences must be developed for the direct observation of a CHORES process in a condensed-phase system. While SCARS is seen to be several orders of magnitude less intense than a normal two-laser CARS process, it remains far more efficient than the CHORES process under present conditions. SCARS and CHORES are distinguished from one another by the coupling between their respective vibrational resonances. In CHORES, the induced coherence remains localized on an individual chromophore, whereas in SCARS an intermediate light field is generated and effectively decouples the molecular resonances. Consequently CHORES is capable of component selection while SCARS is not. Based on reports in the spontaneous HRS literature and agreement between the observed and theoretical intensities for CARS and SCARS, it is predicted CHORES processes may be made observable using laser intensities on the order of 1 GW/cm2.

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2. Theory

A Taylor series expansion in the electric field, P=x(‘)E+x(*)E’+x(‘)E~+ ... +x(“)E” provides a convenient means for describing the nonlinear response of a system. In this generalized scheme, the nlh-order susceptibility is proportional to a particular off-diagonal density-matrix element, pp). In turn, pp) is a product of n terms, each representing the ratio of a Rabi frequency, QO=@/fi, to a detuning, S,= wij- wL+ ir,, where wij is the transition frequency, wL is the algebraic combination of applied electromagnetic field frequencies closest to oii (including the vacuum field, in the case of spontaneous processes), and r;i is the dephasing rate (given by the homogeneous linewidth, half-width at halfmaximum or hwhm, of the transition). Consequently, one can increase the nonlinear response of a system either by increasing the Rabi frequencies, through stronger transitions or larger applied fields, or by reducing the detunings from a resonance. The dephasing rates of these resonances determine the magnitude of the enhancements and the lield strengths necessary to saturate the transitions. A system begins to exhibit optical nonlinearities as Q0 approaches 8, and is strongly saturated when Q, becomes comparable to, or exceeds, S,. In this regime, the contributions from higher orders become prevalent and may give rise to a number of observable effects, including line narrowing and dynamic Stark splitting [ 2,25 1. As a resonance is approached, one must consider the absorption effects that attenuate both the input and output fields at the same time the mixing efficiency is enhanced. While these absorption effects have received some attention in the literature [ 26,271, it remains unclear how they quantitatively affect the sensitivity and dynamic range of nonlinear spectroscopies. For clarity, we consider only the lowest-order expressions for CHORES and SCARS, excluding the effects of population transfer between excited states. Both Lukasik and Ducuing [ 141 and Debarre et al. [ 15 ] were able to identify the dominant nonlinear process in their respective experiments, based upon the scatterer number density dependence. This functionality follows from comparison of the respective intensity expressions (mks),

(2) where N is the scatterer number density, z is the interaction length, nii is the refractive index of the medium at We, and co is the permittivity of free space. The constant term in (2) results from a conversion of the intensity generated at 2wi - w2 into a Rabi frequency. Note, optimal phase matching has been assumed here and throughout the remainder of this discussion. The initial observation of HORSES by Chabay consisted only of a determination of the power dependence of the output signal [ 71 and this measurement cannot distinguish between SCARS and CHORES processes since ( 1) and (2) have identical power dependences. CHORES and SCARS are differentiated from one another by the evolution of their respective pea coherences. As can be seen in fig. 1, the peacoherence for CHORES evolves directly to pm through interaction with the applied field at w3, In SCARS, the pea coherence produces an intermediate photon field (a two-laser CARS signal at 2w, - w2, see fig. lc) that in turn induces a& that can be larger than the orig inal peacoherence. This amplification is the result of a second interaction involving the ground state population, paa, and gives rise to the observed N4 dependence. This subtle distinction is reflected in the coupling between the resonances by which each process may be enhanced. CHORES is doubly resonant only when both vibrational resonances belong to the same chromophore, whereas in SCARS these resonances are coupled by the intermediate photon field and thus this restriction does not apply. Consequently one may distinguish between CHORES and SCARS on the basis of their ability to perform component selection - CHORES is capable of component selection while SCARS is not. From the ratio of their intensity expressions, one is able to not only determine the relative contribu439

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tions of the processes, but also the factors which control them, I 2 o&L~~NZz2 - SCARS=I CHORES tofi2c23e0n,c@a ’

(3)

The SCARS contribution is minimized by the same factors that reduce the intensity of the intermediate photon field generated by pea - lowering the concentration, reducing the interaction length, and increasing the detuning from the intermediate resonance. This expression does not consider absorption effects that could be important in determining the ratio. In addition to discriminating between CHORES and the competing cascade process, it is important to examine the absolute signal levels for CHORES, drawing comparisons to the signals observed in HRS experiments. One may derive a theoretical estimate for the spontaneous HRS intensity using the same approach that was taken in the formulations of eqs. (2) and (3). The spontaneous nature of this process is introduced through the Rabi frequency associated with the vacuum field interaction responsible for the evolution of ps. into pb. (see fig. 1~). Expressing the mean-squared amplitude associated with the vacuum field, 1E,.ac12,as fiw3Aw/4x2cen2c3, one finds in the limit of no pure dephasing

(4) where Aw,. and A$2 are the frequency interval and solid angle into which the radiation is scattered. Experimentally these quantities are associated with the bandpass and f/# of the collection optics, respectively. Consider a simple aromatic, such as toluene, which has two strong, Raman-active, vibrational modes at 786 and 1002 cm-‘. Electronic states lying in the far UV, around 120 nm [28], make the dominant contributions to the resonant enhancement of these modes. Assuming vibrational linewidths of 2 cm-’ (fwhm), Rabi frequencies of 3.6 cm-’ (corresponding to applied intensities of 60 MW/cm2 and a 1 D transition moment), and a collection bandwidth of 1 cm-’ with f/ 1 optics, one calculates a HRS intensity of about 6~ lo-” W/cm2 using eq. (4). This intensity is that seen by the detector and is typical of those calculated and measured by others [ 18,291. Under the same conditions, one predicts a 440

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CHORES intensity of 3 x 1O-’ W/cm2 using eq. ( 1) . While both .$‘) processes are enhanced near resonance as &+rba, CHORES exploits a second vibrational resonance at co, which accounts for its greater efficiency. The SCARS signal is predicted to be even larger, by a factor of about 6.5 x 1O3as calculated using eq. ( 3 ) , since it also is doubly resonant and exhibits a N4 dependence [ 14,15 1. In addition, spontaneous Raman scattering can mask the CHORES signal under the previously assumed conditions since its intensity should be comparable to that of the SCARS process. The phase matching requirements for SCARS and CHORES are different and can be used to discriminate between the two. For SCARS, the conditions Ak’=k,-kZfkl-kq and Ak”=k4-k3+kr-ks must be simultaneously satisfied, while the condition Ak = 3k, - k2 - k3 - k6 defines the phase matching for CHORES (see fig. 1 for the labelling). With a two-beam geometry, where phase matching is controlled by the single angle between the beams, it is not possible to simultaneously satisfy both conditions for SCARS but it is possible to phase match CHORES. For our experiments, an angle of x 1.22” phase matches CHORES and causes a 34% attenuation of the SCARS signal. With a three-beam geometry where phase matching is controlled by two crossing angles, it is possible to phase match both SCARS and CHORES but it is also possible to phase match only CHORES and to strongly attenuate the SCARS contribution. Additionally, the CHORES and SCARS signals can be made to propagate along different directions. This approach has been used in previous studies of susceptibilities up to x(“) [8,9,11,12].

3. Experimental A XeCl excimer laser is used to pump three homebuilt dye lasers at repetition rates below 20 Hz. These lasers have 5 ns pulses with bandwidths of x0.3 cm- ‘. They are calibrated with a Fizeau wavemeter to an accuracy comparable to their bandwidth. Phasematching conditions are initially established for a singly resonant, 20, -w2 process. Upon maximizing this signal, the third input field is introduced to phase match the SCARS process at 3wi- w2- w3. Inten-

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sities within the focal region are on the order of 60 MW/cm2 as the beams are focused with waists of 50120 pm within a 1 cm cuvette. The signal is spectrally filtered with a 0.85 m double monochromator, detected with a photomultiplier, and averaged with a gated integrator. The entire system is controlled by a laboratory computer capable of synchronously scanning any two frequency elements, including the monochromator, while acquiring the data. Details on the optical system and operational procedures have been described elsewhere [ 301.

a>

:I-

4. Results and discussion Studies of the vibrational motions of mono-substituted benzenes [ 3 1,32 ] have revealed coupling between modes 1 and 12 (vi and viz) [ 331. In toluene y1 and yIz dominate the spontaneous Raman spectrum, appearing at 786 and 1002 cm-‘, respectively [ 341. Fig. 2 shows separate two-laser CARS spectra of these modes obtained by synchronously scanning the Stokes field (oz) and the monochromator (u,) with w1= 17 186 cm-‘. The resonances were scanned in separate spectra as a result of phasematching considerations. While wider scans are possible, most spanned 100 cm-‘, or less, so as to minimize such extraneous effects. The signals generated on both vibrational resonances greatly exceeded the dynamic range of the detection electronics necessitating optical attenuation prior to detection. Under these conditions it is also possible to observe a singly resonant nonlinear signal at 3w, - 20, by opening the spatial filter in the collection optics and scanning the monochromator. As expected these 30, -20, signals were much weaker than the twolaser CARS signals. Based on the estimated input intensities, transition moments, and detunings as used earlier, a quantitative comparison of the 2wi -w2 and 3w, -20~ signals indicates the 3wi-2~ signal is most likely originating from a SCARS process as the experimental ratio of these signals is x 5 x 1O4compared to a value of 1O5calculated using eq. (2) and an analogous expression for the CARS intensity. Using two input fields, only a single vibrational Raman resonance can be achieved, when w, - o2 =wa. By adding a third tunable field, an additional resonance can be developed when 20, -w2-o3

I

795

785 @l-(4,

775 cm-'

Fig. 2. Two-laser CARS oJo, scans, in neat toluene with 0,=17186 cm-‘, over (a) the 1002 cm-’ (YJ and (b) 786 cm-’ (u,) modcs.The dipappearingat the rightin (b) isa measure of optical zero obtained by blockingone of the input fields. = o, (see figs. la and Ic). The enhancements provided by each of these resonances are shown separately in the spectrum in fig. 3a obtained by synchronously scanning w2 and w, (w2/w,) such that c0,=30,-02-w3. In an w2/w, scan one is simultaneously scanning both resonances. The number of features one should expect in such a scan is determined by the value of o, used to obtain the spectrum. As both resonance conditions are satisfied when wi - w3=o,c&=r&,, this indicates only a single, doubly resonant feature should be observed in a synchronous scan where @z/W, O,-W~=OY,*-WYL. These conditions have been achieved in the 02/o, scan which appears in fig. 3b as the resonances with the vi and vi2 modes of toluene are developed simultaneously. The spectrum in fig. 3a, a synchronous 02/o, scan where w1-w~=w,,~ -CO,, + 15 cm-‘, exhibits two, singly

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I

795

:I

780

765

3 b) j a ?

il

?

795

I

780 765 (WI-w*) I cm-’

-, 1020 1000 (2w,-02-03),

980 cm

-1

Fig. 3. (a) Three-laser,synchronousw,/w.scan over the 786cm-’ (v,) mode witho,= cm-’ andoi--W3=q,--0,,+15 cm - ‘. The feature on the right corresponds to the resonance developed as 2o,-wx-w~ is scanned over the 1002 cm-i (viz) mode. The difference in the relative.intensities of these features is due, in part, to inequivalent laser powers. (b) Repeat of the scan in (a) with ol--w,=w,,,--w.,. Now the two featuresin (a) have been made to overlap. (c) Three-laser, synchronous 0,/w. scan over the 1002cm-’ modewith wi -wz resonant with the 786 cm-i mode.

resonant features separated by an amount equal to the w, -wg detuning. The enhancement provided solely by the 20, -02-w3 resonance is seen in the spectrum in fig. 3c obtained by a synchronous ws/ o, scan with w, -02 resonant with the v1 mode at 786 cm-‘. In addition to the expected viz peak of toluene at 1002 cm-‘, one also sees a weak feature around 1028 cm- ’ which has been assigned to V,s of toluene. Power dependences of the doubly resonant signal at 30, - wZ-wJ were obtained through successive WJW, scans over a,,,, varying the power of each input field. Least-squares fits of the data to the form z(3w,-w*-w~)=~P(w~)“P(w~)~P(w~)’ 442

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showed no unexpected behavior. The values of x, y, and z obtained from these fits were 2.87, 1.02, and 0.948, respectively. In order to identify which process, CHORES or SCARS, was responsible for these features, a 1: 1 mixture of benzene and toluene was placed in the focal region. With o1 - w2 tuned to the vi mode of toluene, the WJW, scan in fig. 4 shows signal enhancements by both the vi2 of toluene and v, of benzene (appearing at 992 cm-‘). This spectrum is identical b a two-laser CARS w2/w, scan over the same region (with the exception of the absolute intensity), and shows no evidence of selective enhancements caused by having 01--02 tuned to the toluene v, mode resonance. For this reason, we assign the resonances in fig. 4, as well as those of Chabay et al., to a SCARS mechanism. The coherence initially developed through vi of toluene does not remain localized but rather it radiates a photon field at 2w, - o2 which then interacts with w3 to drive both the toluene v12 and benzene vl vibrations as the w3 field is tuned. Although it would be possible, as discussed, to spatially resolve the CHORES and SCARS processes with appropriate phase matching, the observed SCARS signals are sufficiently weak that a CHORES signal would bc below our detection lim-

e

G,-

02

-w3),

cm-’

Fig. 4. Three-laser, synchronous 0,/w. scan in a 1: 1 (v/v) mixture of toluene and benzene, where o, -02 is resonant with the 786 cm-’ mode of toluene and wi= 17186 cm-‘. Vibrational features of toluene and benzene appear at 1002 and 992 cm-‘, respectively, indicating the detected signal is generated through a SCARSmechanism (see text). The dip at the right is a measure of optical zero obtained by blocking one of the input fields.

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its, especially considering the quantitative estimate discussed earlier. As discussed previously, the nonlinear response of a system may be increased by working closer to resonance since x(“) scales as (Q/J)n. Ziegler and Roebber [ 35 J have utilized this approach to produce HRS signals comparable to those encountered in spontaneous Raman scattering through the use of an electronic resonance at o_~~Since CHORES should be analogously enhanced by reducing the detuning from the excited state (thus reducing the &, S,, and S,, detunings, see eq. ( 1) ), we have attempted to utilize this strategy to enhance the CHORES signal. p nitroaniline (DNA) has a very intense SO+ transition around 24000 cm-’ and strong nonlinear properties [ 36 1. Using o1 energies within the red tail of this absorption band and the 992 cm-’ mode of benzene as an internal standard, we were able to observe two-laser CARS signals from solutions containing pNA which were in agreement with the relative intensities observed in spontaneous Raman scattering. However the absolute intensities of both the benzene and pNA features were always several orders of inagnitude lower than those obtained from neat benzene despite the reduced detuning from the excited electronic state of pNA. The intensity decrease appears to be larger than would be predicted from a theoretical treatment of absorption effects in FWM [27] and we do not understand the reasons for the large decrease. Nevertheless, the decrease is sufficiently large that a CHORES process would be below our detection limits. Although these experiments indicate that CHORES processes cannot be observed with the nanosecond laser systems used in our work, there is theoretical justification for believing that it can be observed with picosecond systems. Estimates based on applied intensities of 1 GW/cm’ indicate the proposed CHORES process should develop signals roughly two orders of magnitude brighter than the SCARS signals reported here. Such intensities are readily achieved using existing picosecond laser technology and have been shown to improve the S/N ratio in HRS spectra [ 29,37,38 1.Additionally, shorter duration pulses should lower detection limits as material damage thresholds increase with the reciprocal square root of the laser pulse width. Mazur and co-workers [ 39 ] have been able to obtain CARS spectra in reflection

7 May 1993

from surfaces and from 50 8, films using subpicosecond lasers. These higher peak powers should also allow for more definitive experimentation regarding the utility of electronic resonances. As such studies will likely involve the use of thinner samples, the SCARS/CHORES intensity ratio, eq. (3), should decrease due to their differing z dependences. Similar arguments may be made regarding trade-offs involving absorption effects and number density dependences and these should reduce the SCARS/ CHORES ratio further. Any such reductions which can be made in this ratio will be of considerable importance as they reduce the need for separating the SCARS and CHORES signals via phase-matching considerations.

References [l] J.K. Steehler and J.C. Wright, J. Chem. Phys. 83 (1985) 3188.

[ 2 ] E Ouellette and M.-M. Denariez-Roberge,Can. J. Phys. 60 (1982) 1477. [3] M.T.RiebeandJ.C. Wr$ht, J.Chem. Phys. 88 (1988) 2981. [4] G.B.HurstandJ.C. Wright,J. Chem. Phys. 95 (1991) 1479. [ 51 G.B.Hurst and J.C. Wright,J. Chem. Phys. 97 (1992) 3940. [6] R.J. Carlson and J.C. Wright, J. Chem. Phys. 92 (1990) 5186. [ 711. Chabay, G.K. Klauminzer and B.S. Hudson, Appl. Phys. Letters 28 (1976) 27. [8] R.K. Raj, Q.F. Gao, D. Bloch and M. Ducloy, Opt. Commun. 51 (1984) 117. [ 9 1R. Trebino and L.A. Rahn, Opt. Letters I2 ( 1987) 9 12. [ 101G.S. Agarwaland N. Nayak, Phys. Rev. A 33 (1986) 391. [ 111L.H. Acioli, A.S.L. Gomes and J.R. Rios Leite, Appl. Phys. Letters 53 (1988) 1788. [ 12] A. Blouin, P. Galarneauand M.-M. Denariez-Roberge,Opt. Commun. 72 (1989) 249. [13] E.J. Canto-Said, D.J. Hagen, J. Young and E.G. Van Stryland, IEEEJ. Quantum Electron. 27 ( 1991) 2274. [ 141I. Lukasik and J. Ducuing, Phys. Rev. Letters 28 (1972) 1155. [ 151D. Dbbarre, M. Lcfebvre and M. Ptalat, Opt. Commun. 69 (1989) 362. [ 161F. Yablonovitch, C. Flytzanis and N. Bloembergen, Phys. Rev. Letters 29 (1972) 865. [ 17] D.S. Chemla, A. Maruani and F. Bonnouvier, Phys. Rev. A 26 (1982) 3026. [ 1S] L.D. Ziegler, J. Raman Spcctry. 21 (1990) 769. [ 191C.C. Bonangand S.M. Cameron, Opt. Commun. 86 ( 1991) 504. [20] K. Duppcnand D.A. Wiersma, Opt.Lctters 13 (1988) 318. [21] Q.Z. Wang, P.P. Ho, R.R. Alfano and R. Kashyap, Phys. Rev. A 45 (1992) 1951.

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[22] D. von der Linde, M. Maier and W. Kaiser, Phys. Rev. 178 (1969) 11. [23] S. Mukamel, Phys. Rev. A 28 (1983) 3480. [24] D. Lee and A.C. Albrecht, in: Advances in infrared and Raman spectroscopy, Vol. 12, eds. R.J.H. Clark and R.E. Hester ( Wiley-Heyden, Chichester, 1985) p. 179. 1251F. Guellette and M.-M. Denariez-Roberge,Can. I. Phys. 60 (1982) 877. 126I J.R. Andrews, R.M. Hochstrasser and H.P. Trommsdorff, Chem. Phys. 62 (1981) 87. 1271R.J. Carlson and J.C. Wright, Appl. Spectry. 43 (1989) 119s. [28] L.D. Ziegler and AC. Albrecht, J. Chem. Phys. 70 (1979) 2634. [29] W.P. Acker, D.H. Leach and R.K. Chang, Chem. Phys. Letters 15s (1989) 491, [JO] J.C. Wright, R.J. Carlson, G.B. Hurst, J.K. Steehler, M.T. Riebe, B.B. Price, D.C. Nguyen and S.H. Lee, Intern. Rw. Phys. Chem. 10 (1991) 349.

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[31]K.S.PitzerandD.W.Scott, J.Am.Chem.Soc. 65 (1943) 803. [32] J.B. Hopkins, D.E. Powers, S. Mukamel and R.E. Smalley, J. Chem. Phys. 72 (1980) 5049. [ 331E.B.Wilson Jr., Phys. Rev. 45 (1934) 706. [ 341B. Schrader, Raman/infrared atlas of organic compounds (VCH, Weinheim, 1989). [ 351L.D. Ziegler and J.L. Roebber, Chem. Phys. Letters 136 (1987) 377. [ 361B.F. Levine, Chem. Phys. Letters 37 (1976) 516. (371 J.P. Neddersen, S.A. Mounter, J.M. Bostick and C.K. Johnson, J. Chem. Phys. 90 (1989) 4719. [ 381S. Nie, L.A. Lipscomb, S. Feng and N.-T. Yu, Chem. Phys. Letters 167 (1990) 35. [39] E. Mazur, Harvard University (1991), private communication.