Volume 138. number
Michael T. RIEBE and John C. WRIGHT Department of Chemutry, Umverslty of Wisconsrn, Madison. WI 53706. USA Received
24 April 1987; in final form 11 May 1987
We report the elimination of inhomogeneous broadening m mixed organic crystals with multiply resonant four-wave mixing methods. Lute narrowing and the line shifts characteristic of site selective methods are observed for both coherent anti-Stokes Raman spectroscopy (CARS) and multiply enhanced non-parametric spectrosocopy (MENS). The sate selective capability of CARS is in agreement with the model proposed by Ouellette and Denariez-Roberge.
Fluorescence line narrowing (FLN) was the first example of site selective laser spectroscopy that was capable of resolution within the inhomogeneous linewidth of a solid [ 11. A laser positioned within an inhomogeneously broadened line excites the sites resonant with the laser and the resulting fluorescence is narrower than the inhomogeneous width. The position of the resonance shifts as the laser position is changed to excite different sites in the band. Ever since the predictions of Druet, Taran, and BordC [ 21 and later Oudar and Shen [ 31 that multiply resonant four-wave mixing methods were capable of Doppler-free spectroscopy, there has been much interest in extending site selective methods to non-linear spectroscopy where sample fluorescence is not required. Dick and Hochstrasser [ 41 predicted similar promise for three-wave mixing which could also be surface sensitive. Hochstrassser and co-workers developed multiply resonant techniques for both three-wave and fourwave mixing spectroscopy and applied them to mixed organic crystals [ 5-91. Decola, Andrews, Hochstrasser, and Trommsdorff [ 51 and Chang, Johnson, and Small [ lo] reported observing a narrowing of the resonance lines but neither presented data. Steehler and Wright later developed three-laser methods that were capable of site selective spectroscopy in systems with unique crystallographic sites [ 111. In this paper, we show that the same three-laser methods remove inhomogeneous broadening and that the mechanism is site selection since the resonances shift as different sites within the inhomogeneous band are selected. We also report that a fourwave mixing process usually considered parametric and not capable of eliminating inhomogeneous broadening was observed to remove the inhomogeneous broadening. We show that saturation effects are responsible for the observation and that the results are consistent with a more complete theory developed by Ouellette and Denariez-Roberge [ 12 1. Site selection is accomplished by tuning lasers to match the transition energy for one or more sites within the ensemble of sites that constitutes the inhomogeneous width of that transition. A scan across other transitions can then contain an enhanced contribution from the selected sites giving a spectral line that is narrower than the inhomogeneous linewidth. This enhanced contribution is not always observed however, depending upon a number of factors. The prime factor determining the relative size of the enhancement is the nature of the interference that occurs between the sites that are multiply resonant with the lasers and the other sites within the inhomogeneous distribution [ 31. The type of interference depends upon whether either of the two states associated with the output resonance were initially populated (a parametric process) or not (a non-parametric process). In the usual theory, if a lattice strain shifts all relevant energy levels in the same direction, parametric non-linear processes cannot give * This research
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by the National
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under grant CHE-85 15&92.
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Fig. 1. Relevant energy levels of pentacene-doped benzoic acid and the resonances used for CARS and MENS spectroscopy. The resonances are described by the parameters defined at the right.
line narrowing while non-paramet~c processes can. The situation is reversed if one of the levels involved in the multiple resonance shifts oppositely from the others [ 2-41. If the system is initially in the ground state, coherent anti-Stokes Raman scattering (CARS) is a parametric method and coherent Stokes Raman scattering (CSRS) is a non-parametric method. Lee et al. [ 131 and Nguyen and Wright [ 141 developed a related threelaser technique called multiply enhanced non-parametric spectroscopy (MENS) that has interference characteristics similar to CSRS but avoids the fluorescence inerference that plagues that technique. MENS was predicted to be important for resolving inhomogeneous broadening in molecular spectroscopy where an excited electronic state and its associated vibronic levels shift together. The resonance schemes, laser frequencies and the energy levels described in this Letter for the CARS and MENS methods are diagrammed in fig. 1. The expectations become complicated because the resonant lasers can induce saturation effects where large excited state populations or higher-order effects change the predicted behavior [ 6,1.5J. Ouellette and DenariezRoberge [ 12 ] showed that a narrowed line will develop in a parametric process like CARS at higher laser powers where excited state populations become important. These complications are the result of appreciable excited state populations and from fifth-order processes that are non-parametric. An inhomogeneously broadened line will be present at very low laser powers but a narrowed line becomes dominant as the powers are increased. For MENS, the four-wave mixing from both the ground and excited states are non-parametric processes and similar changes with laser power do not occur. Several different researchers have reported line na~owing in non-linear four-wave mixing, but none have demonstrated site selection within an inhomogeneously broadened line [ 5, lo]. The key observation to demonstrate site selection is the correlated shifting of a narrowed resonance within an inhomogeneous band of one transition as the narrow-line laser is stepped across another transition’s broad inhomogeneous profile. This effect can be seen from the form of the equations describing the third-order susceptibility, xc3). The four-wave mixing signal is proportional to 1~‘~’I’, which for an inhomogeneously broadened distribution can be approximated by expressions for CARS and MENS that appear in the literature [ 1O-l 3 1. These equations assume a Lorentzian distribution of strains [ 43, a, with a half-width given by ca and neglect contributions from any excited state population. The CARS expression for xc3) has only one term of the form 0) x
where < is a constant, 6, = o”, - mlasers- ir;,, oz represents the center of the transition between levels i and j as defined in fig. 1, mlarersrepresents the combination of laser frequencies associated with the resonances in fig. 1, T,, is the dephasing rate, and Aot represents the size of the level shifts induced by the strains. The three resonance denominators for CARS all contain the inhomogeneous broadening parameter a,Ao$ and no narrowing is possible. The MENS expression has some inhomogeneously broadened terms with the same form of the resonance denominator but it also contains terms of the form
(2) A=Aw&,lAo$o. 566
These terms do not contain the inhomogeneous width and the position of the resonance shifts
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17755 17740 17745 17750 wt-w2+wg ENH#;Y (cm-t)
17735 17745 17745 17750 wl-wg+w5 [email protected]
Fig. 2. Spectra of 5 x 10m5mole% pentacene in 2% p-terphenyll benzotc acid. (a) FIuorescence excitation and CARS spectra for different detunings, c+~-o,, w, -02=260 cm-‘, incident laser powers of 2.1, 3.2, and 6.4 MWlcm2 for o ,, w2, and w,, respectively. Y-axis scales are arbitrary. (b) Fluorescence excitation and MENS spectra for different detunings, o,,.~-o~, or-wX=260 cm-‘, incident laser powers of 2.8, 0.3, and 12.4 MWlcm’ for o ,, wz, and wX,respectively. Y-axis scales are arbitrary.
of the relative laser frequencies. If the o2 laser is constant and the w , laser is scanned over the w,,~ resonance (see fig. 1), the narrowed line appears at w , = wEso- ( w$~ - w2)/A. The shift given (w&, 0,)/A is analogous to the shifting observed in fluorescence line-narrowing studies and occurs because the w2 laser is selectively enhancing the contribution from different sites within the inhomogeneous envelope of the molecular transition. The instrumentation for this experiment has been described elsewhere [ 131. Fully resonant four-wave mixing in benzoic acid crystals doped with = 5 x 1OP5 mole% pentacene and O-2 moleoh p-terphenyl was performed at 1.9 K. The concentration of the p-terphenyl determined the amount of inhomogeneous broadening in the pentacene transitions. Fluorescence excitation was used to measure widths of x 3 and z 8 cm-’ for the 0 and 2 mole% concentrations respectively. Fig. 2a shows the results of a CARS experiment in a crystal where the p-terphenyl concentration was 2 mole%. Successive scans are shown for different values of 08,~ -w , in the resonance denominator of the CARS expression. The laser at wj is scanned across the w,,~ resonance and the value of w , - w 2 is held constant at w to by incrementing the value of w2 in step with w , . The scans show a vibronic feature that is much sharper than the 8 cm-’ width of the vibronic level measured in the fluorescence excitation spectrum also shown in fig. 2. The width is limited by the bandwidth of the three lasers. The peak shifts to different values of w 1- w2+ w3 as the relative value of w~.~- w , is changed. Fig. 2b shows comparable scans using MENS. Here, successsive scans correspond to different values for ~8,~ - w2, wZ- ~3 is kept constant at the value of wzo, and w , is scanned across the position of the w,,~ resonance. The same narrow line feature and the same shifting of the peak position occurs as seen in the CARS experiment. The narrow feature and the shifting of the vibronic resonance in the MENS spectra are predicted by perturbative solutions for xc3’. A fit of the shifts to the equation shows that A= 1.0, in agreement with the Aw$,~IAw;~ ratio measured from absorption and fluorescence excitation scans. The terms in the expression for MENS that do exhibit inhomogeneous broadening are not observed to contribute to the experimentally observed spectrum because the inhomogeneous width is much wider than the homogeneous width and the intensity of the broader line is too weak to appear in fig. 2. On the other hand, the features in the CARS spectra are not consistent with a perturbative solution for CARS since the experiments show that line narrowing is occurring within the inhomogeneous envelope. A more exact expression for the density matrix element p4, was used to describe the four-wave CARS mixing using the equaas a function
Volume 138, number 6 U, =16996
CHEMICAL PHYSICS LETTERS cm-’
, 16996 cm-’
7 August 1987
17760 17744 &a4 Energy [cm-t]
Fig. 3. Simulations of spectral scans about the v’ level in fig. 1 as a function of the w , detuning form the 0’ resonance at 17000 cm-’ and the inhomogeneous linewidth (in cm-‘), u,.
tions developed by Dick and Hochstrasser and weak probe lasers [ 151:
Fig. 4. Fluorescence excitation and CARS spectra of 5x lo-’ mole% pentacene in pure benzoic acid for different detunings, o&-o,, w, -02=260 cm-‘, incident laser powers of 2.1, 7.2, and 4.4 MW/cm* for w ,, w2, and oj, respectively. Y-axis scales are arbitrary.
for the case of fully resonant
mixing with a strong pump
where D=-B&d,S,6,+~Q,~* (6,6~6,-6,6,6,+6,lm,I'). Wehaveusedthisexpressiontogetherwiththe relationship between poO and pose, to numerically model the four-wave mixing that occurs for a Gaussian distribution of inhomogeneously broadened sites with parameters that correspond to the pentacene: benzoic acid system. The results are shown in fig. 3 for a series of different values of the inhomogeneous width, 0, and detunings of o, from 08.~ at 17000 cm- ‘. A Rabi frequency B, of 1.8 GHz was used in the simulations. Fig. 3 shows similar features to those obtained by Ouellette and Denariez-Roberge. There are two resonances in CARS scans when saturation effects become important, one an inhomogeneously broadened resonance and the other a sharp resonance that is associated with an excited state population. The relative intensity of the two features depends upon the inhomogeneous broadening. We observe only the sharp resonance in fig. 2a, presumably because the inhomogeneous broadening is large enough that the relative intensity of the broad peak is much lower than the sharp peak. In order to investigate this possibility, a CARS experiment was performed in a crystal without p-terphenyl where the inhomogeneous broadening is much smaller. The spectra are shown in fig. 4 for conditions similar to those in fig. 2a. One now sees a second broader resonance which does not shift with different values of o , . If the o , laser is detuned below the w o,o transition, the narrowed resonance quickly disappears while the broader resonance decreases by the amount predicted in eq. (1). Both observations are consistent with the simulations shown in fig. 3. If the laser is tuned above the 0’ level, the sharp peak is more 568
intense than the peak predicted by the simulations. The simulations in fig. 3 assumed that po.o, and poo can be related as a simple two-level system connected by a strong radiation field. There is a very strong phonon sideband in the pentacene spectrum which is comparable in importance to the O-+0’ transition so there will be a larger excited state population than predicted by a simple two-level picture. If simulations are done with an enhanced value for po,o,, the sharp feature is increased in agreement with the observations. More detailed simulations would have to account for the shape of the phonon sideband in order to arrive at a realistic estimate of the spectral features. The relative intensities of the resonances in fig. 4 do not change significantly as a function of the laser intensity over a range of x 2 x 1O6 to 7 x lo3 W/cm2 (corresponding to laser energies of 5 uJ to 20 nJ in 5 ns pulses focused to a 260 urn diameter spot). Lower intensities were not used because the signals could not be detected. Although one would expect that the narrowed process would have a non-linear power dependence, the intensities are still in the range where saturation effects are expected. Homogeneous linewidths of = 0.00 1 cm- ’ have been measured by hole-burning [ 161 and photon-echo [ 171 methods so only a small fraction of the measured laser intensity will be within the homogeneous linewidth. For the 0.25 cm-’ width of our laser, a Rabi frequency of 0.005 cm-’ would be estimated for the lowest laser intensity used, still appreciably larger than the homogeneous width of the transition. Broadening or dynamic Stark effects are not detected at these intensities because the laser linewidth obscures them. It is also clear experimentally the system is saturated because the two pentacene resonances continue to increase relative to the benzoic acid host resonances which do not saturate as the pulse intensities are lowered to 7 x 1O3W/cm’. The sharp and broad pentacene resonances maintain the same relative intensities because the transitions remain strongly saturated. There are other processes that can have a narrowed line. An excited state CARS process that is resonantly enhanced by higher electronic levels like that observed in the experiments of Dallinger and Woodruff would cause the same narrowed line that shifts with different positions of the lasers [ 181. This process however would not have a resonance with the wXo transition. We performed a series of CARS and MENS scans where either w , for CARS or w2 for MENS (see fig. 1) was incremented across the o $. position, (o,---02+w3) forCARS or o , for MENS was set for resonance with c&O, and the oUo resonance was scanned by changing either o , - w2 for CARS or w2 - w3 for MENS. These scans showed one resonance when w , - w2 (CARS) or w2 - w3 (MENS) matched wZo. The resonance position did not shift with the position of the laser about oo.o. These scans show there is not an important contribution from CARS processes with resonances in higher excited states. Dephasing-induced coherent emission (DICE) will cause additional resonances characteristic of excited state vibronics when the difference frequency between two lasers matches the resonances [ 191. DICE occurs at elevated temperatures where dephasing induces the extra resonance. It is of negligible importance at the temperatures of these experiments. There can also be very sharp line structure produced in four-wave mixing scans because of the selection caused by strong index of refraction changes near absorption lines that affect the phase matching [ 201. This effect occurs for more strongly absorbing samples and the selectivity in the phase mataching is of negligible importance in this study. The use of site selective line narrowing in non-linear spectroscopy should have important applications in a variety of systems, particularly those where the sample does not fluoresce. Site selective spectroscopy has become an important technique for obtaining detailed static and dynamic information about condensed phase molecular spectroscopy [ 2 11, for ultratrace analysis of polyaromatic hydrocarbons [ 221, and recently has been shown to be capable of high resolution surface spectroscopy of adsorbed molecules [ 231. The elimination of inhomogeneous broadening with non-linear spectroscopy demonstrated in this Letter also shows the feasibility of Doppler-free spectroscopy as predicted by Druet et al. [ 21. Dick and Hochstrasser  pointed out that the same considerations can be used for three-wave mixing spectroscopy with xc2’ instead ofx’3’ so inhomogeneous broadening could be removed with sum or difference frequency spectroscopies. The latter methods are expected to have important applications in systems where it is important to look selectively at sites where the inversion symmetry of the sample is removed such as surfaces and interfaces. The demonstration of the site selective nature of both parametric and non-parametric four-wave mixing methods reported here extends the capability 569
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of high resolution laser spectroscopy to non-emissive quantum states and disordered systems that do not fluoresce.
[ 1 ] A. Szabo, Phys. Rev. Letters 25 (1970) 924. [ 21 S.A. Druet, J.-P. Taran and C.J. Bordt, J. Phys. (Paris) 40 (1979) 8 19.  J.L. Oudar and Y.R. Shen, Phys. Rev. A22 (1980) 1141.  B. Dick and R.M. Hochstrasser, J. Chem. Phys. 78 (1983) 3398. [ 51P.L. Decola, J.R. Andrews, R.M. Hochstrasser and H.P. Trommsdorff, J. Chem. Phys. 73 (1980) 4695. [ 61 J.R. Andrews, R.M. Hochstrasser and H.P. Trommsdorff, Chem. Phys. 62 (198 1) 87. [ 71 B. Dick and R.M. Hochstrasser, Phys. Rev. Letters 51 (1983) 2221. [ 81 R.M. Hochstrasser and H.P. Trommsdorff, Accounts Chem. Res. 16 (1983) 376.  R. Bozio, P.L. Decola and R.M. Hochstrasser, in: Time resolved vibrational spectroscopy, ed. G.H. Atkinson (Academic Press, New York, 1983). [ IO] T.C. Chang, C.K. Johnson and G.J. Small, J. Phys. Chem. 89 (1985) 2984. [ II] J.K. Steehler and J.C. Wright, J. Chem. Phys. 83 (1985) 3200. [ 121 F. Ouellette and M.-M. Denariez-Roberge, Can. J. Phys. 60 (1982) 1477. [ 131 S.H. Lee, J.K. Steehler, DC. Nguyen and J.C. Wright, Appl. Spectry. 39 (1985) 243. [ 141 D.C. Nguyen and J.C. Wright, Chem. Phys. Letters 117 (1985)224. [ 151B. Dick and R.M. Hochstrasser, Chem. Phys. 75 (1983) 133. [ 161 R.W. Olson, H.W.H. Lee, F.G. Patterson, M.D. Fayer, R.M. Shelby, D.P. Burum and R.M. MacFarlane, J. Chem. Phys. 77 (1982) 2283. [ 171 L.W. Molenkamp and D.A. Wiersma, J. Chem. Phys. 80 (I 984) 3054. [ 181 R.F. Dallinger and W.H. Woodruff, J. Am. Chem. Sot. 101 (1979) 439 1. [ 191 J.R. Andrews and R.M. Hochstrasser, Chem. Phys. Letters 82 (198 1) 38 1.  D.A. Ender, MS. Otteson, R.L. Cone, M.B. Rttter and H.J. Guggenheim, Opt. Letters 7 (1982) 611. [2 I] RI. Personov, in: Spectroscopy and excitation dynamics of condensed molecular systems, eds. V.M. Agranovich and R.M. Hochstrasser (North-Holland, Amsterdam, 1983) ch. 10. [ 221 E.L. Wehry, in: Analytical applications of lasers, ed. E.H. Piepmeter ( Wiley-Interscience, New York, 1986) ch. 7.  F.W. Deeg and Chr. Brauchle, J. Chem. Phys. 85 (1986) 4201.