- Email: [email protected]
Femtosecond incoherent photon echo from rhodamine B in propylene glycol. Inhomogeneous broadening and spectral diffusion at room temperature
Volume 2 11, number 6
CHEMICAL PHYSICS LETTERS
27 August 1993
Femtosecond incoherent photon echo from rhodamine B in propylene glycol. Inhomogeneous broadening and spectral diffusion at room temperature Ruihua Zhang, Tzyy-Schiuan Yang and Anne B. Myers ’ Department ofChemistry, UniversityofRochester, Rochester,NY 14627-0216,USA Received 24 May 1993
Two-pulse degenerate four-wave mixing (photon-echo) experiments using “incoherent” light are reported for rhodamine B in propylene glycol and ethanol at 295 K. The signal detected in a particular direction is strongly asymmetric with respect to the time delay between the two pulses, implying that the electronic spectrum is inhomogeneously broadened on the time scale of the “waiting time” between interactions of the material system with the second and third electric fields. Similar experiments on nile blue yield a symmetric signal response characteristic of a homogeneously broadened system. The effectivewaitingtimes in exper-
imental configurationsemployingparalleland perpendicularlypolarizedexcitationpulsesare discussed.
1. Introduction Electronic absorption spectra of molecules in liquids and glasses are significantly broadened by intermolecular interactions. In most cases the environmentally induced spectral breadth is far greater than that arising from lifetime broadening alone, indicating that the electronic linewidth is due to some combination of processes generally referred to as “pure dephasing” (fast fluctuations in the energy gaps between spectroscopically coupled levels) and “inhomogeneous broadening” (a static distribution of local environments giving rise to different energy gaps for different molecules). While these distinctions may be fairly clear-cut in crystals or highly viscous glasses, in a normal liquid the local environment around a given chromophore is changing on a fairly rapid time scale, and whether a particular process contributes to pure dephasing or to inhomogeneous broadening depends on the time scale to which the particular spectroscopic measurement is sensitive. The term “spectral diffusion” is often used to describe broadening that is effectively static on some measurable time
’ To whom correspondence should be addressed.
scale but becomes averaged when observed over longer times. While some inferences about the nature of the environmentally induced spectral breadth can be obtained from the absorption lineshape alone, such conclusions are highly model dependent. Other experimental methods used to probe these questions include spectral hole burning [ l-81, fluorescence line narrowing [ 191, photon echoes and other time-resolved four-wave mixing techniques [ 10-301, fluorescence energy transfer [ 3 l-33 1, and resonance Raman and fluorescence lineshapes and quantum yields [ 34-401. Resonance Raman quantum yields are sensitive to the dynamics of electronic spectral broadening on a time scale that is determined by intrinsic molecular properties rather than by the temporal resolution of the laser pulses or detector, and the analysis of such experiments is far from straightforward [ 37,41,42 1. Time-domain techniques, particularly the photon echo, allow in principle a more direct resolution of “homogeneous” (lifetime broadening and pure dephasing) from “inhomogeneous” broadening. However, the expected fast time scale for spectral diffusion in liquids implies that very high time resolution will normally be required to observe any interesting dynamics. Indeed, while finite time
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
541
Volume 2 I 1.number 6
CHEMICAL PHYSICS LETTERS
scales for environmental fluctuations have been de-
duced through several experiments performed with femtosecond laser pulses [ 22,23,26], only a few timedomain studies have observed inhomogeneous electronic spectral broadening and/or spectral diffusion in room-temperature systems on picosecond or longer time scales [31-331. The photon echo is a particular type of four-wave mixing experiment in which the intensity of the signal in the phase-matched direction(s) is measured as a function of the time delay rd between the first and second laser pulses, which are normally derived by beam splitting a single pulse. The third incident field comes either from one of the first two pulses in the two-pulse configuration, or from a third pulse delayed by a “waiting time”, rw,,in the three-pulse or “stimulated” photon-echo configuration. In a simple two-level system, the dependence of the signal intensity on T, is given by the convolution of the dephasing time of the molecular system and the correlation time of the electric fields of the first two pulses. Thus, if the laser pulses are sufficiently short compared with the material dephasing time, one may determine the homogeneous linewidth even in the presence of strong inhomogeneous broadening. The signature of inhomogeneous broadening in a threepulse experiment is a signal that is asymmetric with respect to 7,. In liquids near room temperature the relevant dephasing times are typically well under 1 ps, so an experimental time resolution significantly better than this is required. Morita and Yajima [ lo] were perhaps the first to recognize that the actual requirement is not for an ultrashort pulse &ration but only for a short electric field correlation time, which can be obtained from spectrally broadband, temporally incoherent light. Such light sources are much easier to build and to operate over a wide wavelength range than are true femtosecond lasers. A number of workers have since built such “poor man’s ultrafast lasers” having correlation times ranging from picoseconds to tens of femtoseconds, and have demonstrated that they can indeed resolve dynamics occurring on time scales much shorter than the laser pulse envelopes [ 2543-491. There remains, however, a severe impediment to using these incoherent light sources to study electronic spectral broadening mechanisms in liquids. Weiner et al. [ 111, and Fayer and co-workers [ 12,50 ] 542
27 August 1993
have demonstrated clearly that it is the waiting time, r,, that defines whether a particular dynamic process will appear “homogeneous” or “inhomogeneous” in a photon-echo experiment. Only those contributions to the distribution of spectroscopic energy gaps that are static on a time scale long compared with T, will appear as inhomogeneous broadening in the photon echo. In experiments using short pulses, r, can be varied at will in a three-pulse configuration. However, in experiments with incoherent light the third field that stimulates the echo may come from any portion of the temporally long pulse that arrives after the first two fields have acted, and there will usually be a distribution of waiting times ranging from zero to the full pulse envelope. If the pulse duration is nanoseconds, it would appear that an inhomogeneous distribution has to persist for nanoseconds in order to show up as such in the photonecho decays. The purpose of this Letter is twofold. First, we demonstrate the observation of inhomogeneous broadening in a room-temperature liquid through the photon-echo technique performed with a broadband incoherent light source. For this demonstration we employ the molecular system of rhodamine B in propylene glycol in which Stein and Fayer have observed “dispersive” fluorescence energy transfer, a signature of inhomogeneous broadening on the fluorescence time scale [ 31,321. We then discuss the factors that determine the effective waiting time in such experiments, demonstrate that the waiting time can be made shorter than the full pulse duration, and evaluate the general utility of the method for examining electronic spectral broadening in liquids.
2. Experimental The experimental arrangement is shown in fig. 1. The frequency-doubled output of a Q-switched Nd:YAG laser (Continuum 660-A)) consisting of 532 nm pulses at a 20 Hz repetition rate, is used to pump an open-cavity dye laser. The “oscillator” consists of a broadband flat rear reflector and a 1 cm path length flow cell at Brewster’s angle, transversely pumped with approximately 3 mJ/pulse of the 532 nm light. In order to maximize the overall bandwidth and spectral smoothness of the output, no out-
CHEMICAL PHYSICS LETTERS
Volume 2 11, number 6
DyeLaser
PMT
?PC
BOXCAR
Fig. 1.Experimental configuration for two-pulse four-wave mixing with “incoherent” light. BS, beamsplitter; DL, delay line; P, and P,, polarizers; L, and L,, lenses; R1 and R2, right angle prisms; S, and S2,shutters. This configuration allows either signal beam, k3or k4, to be detected.
put coupler or tuning element is used, The amplified spontaneous emission from the “oscillator” is then amplified in a second 1 cm flow cell transversely pumped by another 3 mJ/pulse. Both oscillator and amplifier cells contain a methanol solution of a mixture of dyes adjusted empirically to provide the broadest possible emission bandwidth; the approximate composition of the final dye mixtures used for these experiments is rhodamine 590 (69%), rhodamine 610 (lo%), rhodamine 560 (lo%), rhodamine 640 (5%), kiton red (4%), and DCM (2%). The resulting pulses have a bandwidth of 39 nm at a central wavelength of 580 nm, a measured pulse duration of 8 ns, and an energy of 50 uJ/pulse. The spectra of the laser output are obtained with a Princeton Instruments IRY-700/N/R intensified diode array multichannel detector mounted on a Spex 1870 0.5 m spectrograph. This detection system allows us to obtain the spectra of individual pulses, and the single-pulse spectra are essentially indistinguishable from the time-averaged laser spectrum. The pulse is attenuated to an energy of 1 uJ or less and split equally into two excitation pulses, ki and kZ, in an interferometric setup. One arm of the interferometer is stationary while the retroreflecting mirrors of the other arm are positioned on a computer-controlled, stepper-motor-driven translation stage (Aerotech) providing a resolution of 0,7 fs. The pulses are recombined through a 20 cm El. lens at
27 August 1993
an angle of 15 mrad and overlapped on the sample contained in a 1 mm flow cell. The signals are collected from both phase matching directions, k3=2kl-kz and k,=2kz-k,, and recorded as a function of delay time by a photomultiplier interfaced to a boxcar averager (Stanford Research Systems). Typically signals are obtained from 25 laser shots at each delay setting, and approximately 20 separate sweeps of the delay line are averaged to give the final signal traces. All experiments are carried out at ambient temperature (about 23°C). In preliminary experiments it was found that interaction with almost any optical element caused some distortion of these spectrally broad pulses, and unequal distortions suffered by the two pulses led to artifactual oscillations in the signal. Thus we have taken care to choose optics that are spectrally as flat as possible and to match the optical elements in the two arms of the interferometer as closely as possible. The beamsplitter (reflective neutral density filter, Esco Products) is nearly flat in this spectral region, and in the configuration employed (see fig. 1) both pulses undergo one reflection and either two or three transmissions through the splitter; the beam that undergoes only two transmissions is passed through an additional glass flat to match the dispersive broadening of the two pulses. Aluminum mirrors are used throughout the setup. For experiments employing orthogonally polarized pulses, the polarization rotation is achieved by reflection and matched polarizers are used in both beams. The power spectra of the two beams appear identical. The samples consist of rhodamine B (Exciton) dissolved in propylene glycol, ethanol, or methanol at concentrations of 5 X 10d5 to 8 X 1O-’ M. The formation of dimers or higher aggragates was reported by Stein and Fayer [32] to be unimportant up to concentrations much higher than this. The resulting optical density in a 1 mm path length is 0.07 to 0.12 near the center of the laser spectrum (580 nm). No change in the four-wave mixing signal was observed upon addition of a drop of concentrated HCl to some samples to insure complete protonation of the weakly acidic rhodamine B. Fig. 2 shows the absorption spectrum of rhodamine B in propylene glycol, superimposed on the power spectrum of the laser pulses.
543
Volume 2 11,number 6
CHEMICAL PHYSICS LETTERS
27 August 1993
level structure, the dependence of the three-pulse four-wave mixing signal on pulse delay time Td is given by [ll] 2 WG)cc
/I
dwexP[i(w-w,)~,la(w)#(w)
, (1)
510
550
590
630
Wavelength (tnn) Fig. 2. Absorption bandshape of rhodamine B in propylene glyco1 superimposed on laser powerspectrum. The laser spectrum changes slightly in shape and width from day to day but is stable over the short term (minutes to hours).
3. Theoretical
An enormous number of theoretical treatments of the dependence of the four-wave mixing signal on pulse delay time have been published for both twoand three-beam scattering with both ultrashort and incoherent, broadband long pulses [ 1O-12,20-23,5 l531. However, due to the complexity of the most general expressions, all of the existing treatments of which we are aware make one or more simplifying assumptions that render them inadequate for quantitative modeling of our experimental data. The treatments of Bai and Fayer [ 121 and of Hartmann and Manassah [ 53 ] do explicitly consider spectral diffusion, but they assume that the inhomogeneous width is very large compared with the laser spectral bandwidth, which is inappropriate for our very large excitation bandwidth. We are presently developing a complete theoretical treatment of time-delayed four-wave mixing with incoherent light that properly includes the finite correlation time of the light, a nonzero but finite inhomogeneous linewidth within which spectral diffusion occurs, and the multilevel vibrational substructure of the electronic absorption band, and can describe signals obtained with either parallel or perpendicular polarizations of the two pulses. However, qualitative conclusions can still be drawn from the experimental data in the absence of a complete theoretical description. In the case of pure homogeneous broadening and for an arbitrary vibronic 544
where IX,_is the center laser frequency, a(w) is the measured optical absorption spectrum, and Q(w) is the measured power spectrum of the laser pulses. This expression holds for scattering into either direction, k,+(k,-k2) or k,- (k,-k2), as long as the third pulse (wavevector k,) is separated in time from pulses 1 and 2 and comes after any rapid excited state relaxation processes are complete. Eq. (1) is similarly applicable to two-pulse scattering with “incoherent” light in the homogeneous broadening limit as long as the pulse envelopes are long compared with the pulse coherence time, such that most of the scattering arises from processes in which the third pulse acts long after the coherence induced by the first two pulses has decayed. If, on the other hand, there is inhomogeneous broadening that persists for times longer than the pulse duration, then the signal ‘detected in a particular direction will be asymmetric with respect to rd=O. Finally, if spectral diffusion within an “inhomogeneous” distribution occurs, the spectrum will appear homogeneously broadened if the spectral diffusion time is short compared with the effective waiting time. Thus, for experiments performed with true femtosecond pulses, the spectral diffusion rate can be determined by looking for a transition from asymmetric to symmetric signals as the time delay of the third pulse is increased [ 11 1, In a two-pulse scattering configuration with incoherent long pulses, we do not have direct control over the waiting time, and in general there will be a broad distribution of ~,,,scorresponding to the long period of time during which there is still light on the sample after the first two fields have acted. In other words, the long incoherent pulse can be thought of as a random train of femtosecond pulses, and once two of these pulses have interacted with the medium to create a grating, any one of the later pulses may scatter off it for as long as that grating survives [ 10,12,17]. The length of time for which the grating persists is determined by several factors including the
Volume 2 11, number 6
27 August 1993
CHEMICAL PHYSICS LETTERS
excited state lifetime and the polarizations of the two pulses. When a grating is formed using parallel polarized pulses in an electronically resonant material, the electronic population grating present at short times decays to form thermal and/or acoustic gratings that are typically weaker than the population grating but persist for times much longer than the excited state lifetime [ 541. Thus, in an experiment employing nanosecond duration incoherent pulses, waiting times ranging from femtoseconds to the full pulse duration can contribute to the signal. If, on the other hand, the grating-forming beams are chosen to have orthogonal polarizations, an orientational grating is formed which decays on the time scale of the molecular reorientation time [ 54-561. Thus the effective waiting time can often be limited to times much shorter than the incoherent pulse envelope, although there will still be a distribution of waiting times involved.
4. Results Fig. 3 shows the dependence of the signal scattered into both directions on the time delay rd for rhodamine B in propylene glycol with both parallel and perpendicularly polarized pulses. Both polarization configurations exhibit a marked asymmetry of the two signals with respect to time delay, and both exhibit a “quantum beat” separated from the main maximum by 40-50 fs. The signals in the two directions are approximately related by reflection across the t =O point, as anticipated. The similarity of the signals in the two polarization configurations suggests that the distribution of waiting times contributing to the signal in the two experiments is not significantly different. This may not be surprising given that the rotational diffusion time for rhodamine B in the highly viscous propylene glycol is comparable to the excited state lifetime [ 321. In this solvent, the excited state population grating that is expected to dominate the scattering in the parallel polarized configuration should not persist for a much longer time than the orientational grating that dominates the signal in the perpendicularly polarized configuration. Fig. 4 shows the corresponding result for rhodamine B in ethanol with parallel polarized pulses. Similar results are obtained with perpendicularly po-
-160
-80
0
80
160
Delay time (fs) Fig. 3. Solid and dashed curves: four-wave mixing signals for rhodamine B in propylene glycol observed in the two directions k, and k4 as a function of time delay between k, and A2(see fig. 1). k, and k2 have parallel polarizations in the upper plot, and perpendicular polarizations in the lower. The dotted curve in the upper plot is the theoretical response for a homogeneously broadened system calculated from eq. ( I ). The theoretical curves are the same for both polarization configurations.
-160
-80
0
80
160
Delaytime (fs)
Fig 4. Four-wave mixing signals for rhodamine B in ethanol observed in the two directions k, and k4 asa function of time delay between k, and kz. k, and k2 have parallel polarizations.
larized pulses and in methanol rather than ethanol as the solvent. The asymmetry of the signals and the beats are very similar to those observed in propylene glycol. This suggeststhat substantial inhomogeneous 545
Volume 211, number 6
CHEMlCAL PHYSICS LETTERS
-n
-160
-80
0
80
160
Delay time (fs) Fig. 5. Four-wave mixing signals for nile blue in methanol observed in the two directions ks and k4 as a function of time delay between k, and k,. k, and k2 have parallel polarizations. The dotted curve is the theoretical response for a homogeneously broad-
ened system calculated from eq. ( I ).
broadening of the electronic spectra persists even in these relatively low-viscosity solvents. Fig. 5 presents results on nile blue in methanol. The scattering into the two directions is essentially symmetric, indicating that this system appears to be homogeneously broadened; i.e. spectral diffusion is fast relative to the effective waiting time r, in the incoherent pulse experiment. This result is in agreement with the recent report of Moshary et al. [24] and indicates that our observation of asymmetric responses for rhodamine B is not simply an experimental artifact. Similar results are obtained from nile blue in propylene glycol. Figs. 3 and 5 also compare the experimental curves with those calculated from eq. (1) for pure homogeneous broadening, i.e. the Fourier transform of the product of the chromophore’s absorption spectrum with the experimental laser power spectrum. For nile blue the agreement is reasonably good, while the experimental and calculated curves clearly do not correspond well for rhodamine B. Again these results are consistent with the conclusion that the electronic spectrum of nile blue in methanol is homogeneously broadened on our experimental time scale, whereas rhodamine B in hydrogen-bonding solvents exhibits substantial inhomogeneous broadening.
5. Discussion One potentially confusing point needs to be clar546
27 August 1993
ified at the outset. It has been stated that for two-pulse scattering the signal intensities should always be asymmetric with respect to 7d=0 regardless of the nature of the broadening [ 11,231. That is true when short pulses are used, and merely reflects the fact that the third field cannot scatter off the grating until the two fields needed to form the grating have arrived, and the third field is the same as one of the two grating-forming fields. In the limit of delta-function pulses there would be no scattering at all for h
Volume 2 11, number 6
CHEMICAL PHYSICS LETTERS
during which the effects of spectral diffusion can manifest themselves. Thus the signal profiles should appear more asymmetric, indicating more inhomogeneous broadening when the excitation pulses have perpendicular polarizations than when they are parallel. Therefore it is somewhat surprising that the signals we observe in the two polarization configurations are so similar, particularly in methanol and ethanol in which the rotational reorientation is fast. The “quantum beats” observed in the rhodamine B data remain to be fully interpreted. The experimental 40-50 fs time interval between the main maximum and the “beat” is extremely reproducible from one day to the next and is observed over a wide range of rhodamine concentrations and laser powers. The spacing of 40-50 fs corresponds to a vibrational frequency of 700-800 cm-‘; alternatively, the position of the beat relative to the zero time corresponds to a vibrational frequency near 1500 cm-‘. These are not frequencies that we would obviously expect to observe, as the absorption spectrum, aIthough only weakly structured, appears to have dominant Franck-Condon activity in a mode or group of modes closer to 1300 cm-‘, and the laser spectrum, centered on the red side of the absorption spectrum, does not overlap this structure. The theoretical signals, calculated from the experimental absorption spectrum and laser power spectrum with the assumption of homogeneous broadening, do not exhibit any beats. Wiersma and co-workers have recently explored, both experimentally and theoretically, time-resolved four-wave mixing using deliberately chirped femtosecond pulses [ 26,30,58]. They demonstrate that “quantum beats” due to CARS and CARS-type resonances can appear at time delays that have no clear relationship to the system’s vibrational frequencies when the pulses carry a linear chirp in the appropriate range of magnitudes. We have not yet attempted to evaluate the possible role of frequency chirping of our long pulses which are, in any case, very far from the transform limit. More theoretical and experimental work will be required before any firm conclusion can be drawn about the role of inhomogeneous broadening and the time scale for spectral diffusion in the electronic spectrum of rhodamine B. A more rigorous theoretical development than any yet presented, together with much more thorough characterization of our
27 August 1993
laser pulses, will be needed before these experiments can be interpreted quantitatively. Even then, the utility of such experiments for probing dynamics in liquids will probably be limited to a few special systems in which the effective waiting time is constrained to be short by other aspects of the system’s dynamics (e.g. fast rotation with the perpendicularly polarized geometry). Although broadband, temporally long laser pulses are undoubtedly easier to generate than true femtosecond pulses, adequate control over and characterization of the former is difficult, and the latter are far more useful for photon-echo applications because the waiting time can be controlled accurately in three-pulse geometries. As continuing improvements in ultrafast technology make the generation of femtosecond pulses increasingly straightforward, techniques based on incoherent light are likely to become progressively less interesting, at least for application to liquid state dynamics.
Acknowledgement This work was supported in part by NSF grant CHE-9020844. ABM is the recipient of a Packard Fellowship in Science and Engineering, a Sloan Research Fellowship, an NSF Presidential Young Investigator Award, and a Dreyfus Teacher-Scholar Award.
References [ 1] T. Sesselman, W. Richter, D. Haarer and H. Morawitz, Phys. Rev. B 36 (1987) 7601. [2] P.J. van der Zaag, J.P. Galaup and S. VGlker,Chem. Phys. Letters 166 (1990) 263. [3]T.J. Kang, J. Yu and M. Berg, Chem. Phys. Letters 174 (1990) 476. [4] J. Yu, T.J. Kang and M. Berg, J. Chem. Phys. 94 (1991) 5787. [5] J. Zollfrank and J. Friedrich, J. Phys. Chem. 96 (1992) 7889. [6] J. Yu and M. Berg, J. Chem. Phys. 96 (1992) 8741. [7] L. Shu and G.J. Small, J. Opt. SOC.Am. B 9 ( 1992) 724. [8] T. BaschC, W.P. Ambrose and W.E. Moemer, J. Opt. Sot. Am. B 9 ( 1992) 829. [9] J. Yu, P. Earvolino and M. Berg, J. Chem. Phys. 96 (1992) 8750. [lo] N. Morita and T. Yajima, Phys. Rev. A 30 (1984) 2525.
547
Volume 2 11, number 6
CHEMICAL PHYSICS LETTERS
[ 111A.M. Weiner, S. De Silvestri and E.P. Ippen, J. Opt. Sot. Am. B 2 ( 1985) 654. [ 121Y.S. Bai and M.D. Fayer, Chem. Phys. 128 (1988) 135. [ 131P.C. Becker, H.L. Fragnito, J.Y. Bigot, C.H.B. Cruz, R.L. Fork and C.V. Shank, Phys. Rev. Letters 63 (1989) 505. [ 141 H. Fidder, S. de Boer and D.A. Wiersma, Chem. Phys. I39 (1989) 317. [ 151 I.A. Walmsley and C.L. Tang, J. Chem. Phys. 92 ( 1990) 1568. [ 161 S. Saikan, A. Imaoka, Y. Kanematsu, K. Sakoda, K. Kominami and M. Iwamoto, Phys. Rev. B 41 ( 1990) 3185. [ 171K. Misawa and T. Kobayashi, Mol. Cryst. Liquid Cryst. 182A (1990) 125. [ 181A. Elschner, L.R. Narasimhan and M.D. Fayer, Chem. Phys. Letters 171 (1990) 19. [19]A.M. Walsh and R.F. Loring, Chem. Phys. Letters 186 (1991) 77. [20] Y.J. Yanand S. Mukamel, .I. Chem. Phys. 94 (1991) 179. [ 211 L.R. Narasimhan, Y.S. Bai, M.A. Dugan and M.D. Fayer, Chem. Phys. Letters 176 ( 1991) 335. [ 221 E.T.J. Nibbering, D.A. Wiersma and K. Duppen, Phys. Rev. Letters66 (1991) 2464. ]23‘I J.-Y. Bigot, M.T. Portella, R.W. Schoenlein, C.J. Bardeen, A. Migus and C.V. Shank, Phys. Rev. Letters 66 ( 1991) 1138. 124 F. Moshary, M. Arend, R. Friedberg and S.R. Hartmann, Phys. Rev. A 46 ( 1992) R33. ]25 Y. Nomura, Y. Fujimura, M. Takahashi, M. Fujii and M. Ito, Chem. Phys. Letters 197 ( 1992) 405. [26] E.T.J. Nibbering, D.A. Wiersma and K. Duppen, in: Coherence phenomena in atoms and molecules in laser fields, eds. A.D. Bandrauk and SC. Wallace (Plenum Press, New York, 1992). [ 27 ] M. Cho, N.F. Schererand G.R. Fleming, J. Chem. Phys. 96 (1992) 5618. [ 281 M. Cho and G.R. Fleming, J. Chem. Phys. 98 ( 1993) 2848. [29] C.J. Bardeen and C.V. Shank, Chem. Phys. Letters 203 (1993) 535. [ 30 ] K. Duppen, F. de Haan, E.T.J. Nibbering and D.A. Wiersma, Phys. Rev. A, in press. [ 3 1]A.D. Stein and M.D. Fayer, Chem. Phys. Letters 176 ( 1991) 159. [32] A.D. Stein and M.D. Fayer, J. Chem. Phys. 97 ( 1992) 2948. [33] M.J.E. Morgenthaler, S.R Meech and K. Yoshihara, Chem. Phys. Letters 197 ( 1992) 537.
548
27 August 1993
[ 341 A.B. Myers, M.O. Trulson and R.A. Math&, J. Chem. Phys. 83 (1985) 5000. [ 351 A.B. Myers, M-0. Trulson, J.A. Pardoen, C. Heeremans, J. Lugtenburg and R.A. Mathies, J. Chem. Phys. 84 (1986) 633. (361 E.T.J. Nibbering, K. Duppen and D.A. Wiersma, J. Chem. Phys. 93 (1990) 5477. [37]A.B.MyersandB.Li,J.Chem.Phys.92(1990)3310. [38] A.B. Myers, J. Opt. Sot. Am. B 7 (1990) 1665. [ 391 T.-S. Yang and A.B. Myers, J. Chem. Phys. 95 (1991) 6207. [40] M.K. Lawless and R.A. Mathies, J. Chem. Phys. 96 (1992) 8037. [41] J. Sue,Y.J. YanandS. Mukamel, J. Chem. Phys. 85 (1986) 462. [42] Y.J. Yan and S. Mukamel, J. Chem. Phys. 86 (1987) 6085. 1431R. Beach, D. DeBeer and S.R. Hartmann, Phys. Rev. A 32 (1985) 3467. [44] M. Tomita and M. Matsuoka, J. Opt. Sot. Am. B 3 (1986) 560. [45] T. Hattori and T. Kobayashi, Chem. Phys. Letters 133 (1987) 230. [46] T. Hattori, A. Terasaki and T. Kobayashi, Phys. Rev. A 35 (1987) 715. [47]Z.Q. Huang, Y.J. Xie, G.L. Huang and H.S. Kwok, Opt. Letters 15 ( 1990) 501. [48]T. Hattori and T. Kobayashi, J. Chem. Phys. 94 (1991) 3332. [ 491 T. Matsumoto, K. Ueda and M. Tomita, Chem. Phys. Letters 191 (1992) 627. [5O]M. Berg, CA. Walsh, L.R. Narasimhan, K.A. Littau and M.D. Fayer, J. Chem. Phys. 88( 1988) 1564. [ 5 1 ] S. Sailan, T. Nakabayashi, Y. Kanematsu and A. Imaoka, J. Chem. Phys. 89 (1988) 4609. [ 521 X. Cheng and T. Kobayashi, Mol. Cryst. Liquid. Cryst. A 182 (1990) 139. [53] S.R. Hartmann and J.T. Manassah, J. Phys. B 23 (1990) 1363. [54] A.B. Myers and R.M. Hochstrasser, IEEE J. Quantum Electron. QE-22 ( 1986) 1482. [55] B.S. Wherrett, A L. Smirl and T.F. Boggess, IEEE J. Quantum Electron. QE-19 ( 1983) 680. [56] J.T. Fourkas, R. Trebino and M.D. Fayer, J. Chem. Phys. 97 (1992) 69. [ 571 E Lopez Arbeloa, T. Upez Arbeloa, M.J. Tapie EstCvezand I. Lopez Arbeloa, J. Phys. Chem. 95 (1991) 2203. [58] E.T.J. Nibbering, D.A. Wiersma and K. Duppen, Phys. Rev. Letters 68 (1992) 514.
CHEMICAL PHYSICS LETTERS
27 August 1993
Femtosecond incoherent photon echo from rhodamine B in propylene glycol. Inhomogeneous broadening and spectral diffusion at room temperature Ruihua Zhang, Tzyy-Schiuan Yang and Anne B. Myers ’ Department ofChemistry, UniversityofRochester, Rochester,NY 14627-0216,USA Received 24 May 1993
Two-pulse degenerate four-wave mixing (photon-echo) experiments using “incoherent” light are reported for rhodamine B in propylene glycol and ethanol at 295 K. The signal detected in a particular direction is strongly asymmetric with respect to the time delay between the two pulses, implying that the electronic spectrum is inhomogeneously broadened on the time scale of the “waiting time” between interactions of the material system with the second and third electric fields. Similar experiments on nile blue yield a symmetric signal response characteristic of a homogeneously broadened system. The effectivewaitingtimes in exper-
imental configurationsemployingparalleland perpendicularlypolarizedexcitationpulsesare discussed.
1. Introduction Electronic absorption spectra of molecules in liquids and glasses are significantly broadened by intermolecular interactions. In most cases the environmentally induced spectral breadth is far greater than that arising from lifetime broadening alone, indicating that the electronic linewidth is due to some combination of processes generally referred to as “pure dephasing” (fast fluctuations in the energy gaps between spectroscopically coupled levels) and “inhomogeneous broadening” (a static distribution of local environments giving rise to different energy gaps for different molecules). While these distinctions may be fairly clear-cut in crystals or highly viscous glasses, in a normal liquid the local environment around a given chromophore is changing on a fairly rapid time scale, and whether a particular process contributes to pure dephasing or to inhomogeneous broadening depends on the time scale to which the particular spectroscopic measurement is sensitive. The term “spectral diffusion” is often used to describe broadening that is effectively static on some measurable time
’ To whom correspondence should be addressed.
scale but becomes averaged when observed over longer times. While some inferences about the nature of the environmentally induced spectral breadth can be obtained from the absorption lineshape alone, such conclusions are highly model dependent. Other experimental methods used to probe these questions include spectral hole burning [ l-81, fluorescence line narrowing [ 191, photon echoes and other time-resolved four-wave mixing techniques [ 10-301, fluorescence energy transfer [ 3 l-33 1, and resonance Raman and fluorescence lineshapes and quantum yields [ 34-401. Resonance Raman quantum yields are sensitive to the dynamics of electronic spectral broadening on a time scale that is determined by intrinsic molecular properties rather than by the temporal resolution of the laser pulses or detector, and the analysis of such experiments is far from straightforward [ 37,41,42 1. Time-domain techniques, particularly the photon echo, allow in principle a more direct resolution of “homogeneous” (lifetime broadening and pure dephasing) from “inhomogeneous” broadening. However, the expected fast time scale for spectral diffusion in liquids implies that very high time resolution will normally be required to observe any interesting dynamics. Indeed, while finite time
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
541
Volume 2 I 1.number 6
CHEMICAL PHYSICS LETTERS
scales for environmental fluctuations have been de-
duced through several experiments performed with femtosecond laser pulses [ 22,23,26], only a few timedomain studies have observed inhomogeneous electronic spectral broadening and/or spectral diffusion in room-temperature systems on picosecond or longer time scales [31-331. The photon echo is a particular type of four-wave mixing experiment in which the intensity of the signal in the phase-matched direction(s) is measured as a function of the time delay rd between the first and second laser pulses, which are normally derived by beam splitting a single pulse. The third incident field comes either from one of the first two pulses in the two-pulse configuration, or from a third pulse delayed by a “waiting time”, rw,,in the three-pulse or “stimulated” photon-echo configuration. In a simple two-level system, the dependence of the signal intensity on T, is given by the convolution of the dephasing time of the molecular system and the correlation time of the electric fields of the first two pulses. Thus, if the laser pulses are sufficiently short compared with the material dephasing time, one may determine the homogeneous linewidth even in the presence of strong inhomogeneous broadening. The signature of inhomogeneous broadening in a threepulse experiment is a signal that is asymmetric with respect to 7,. In liquids near room temperature the relevant dephasing times are typically well under 1 ps, so an experimental time resolution significantly better than this is required. Morita and Yajima [ lo] were perhaps the first to recognize that the actual requirement is not for an ultrashort pulse &ration but only for a short electric field correlation time, which can be obtained from spectrally broadband, temporally incoherent light. Such light sources are much easier to build and to operate over a wide wavelength range than are true femtosecond lasers. A number of workers have since built such “poor man’s ultrafast lasers” having correlation times ranging from picoseconds to tens of femtoseconds, and have demonstrated that they can indeed resolve dynamics occurring on time scales much shorter than the laser pulse envelopes [ 2543-491. There remains, however, a severe impediment to using these incoherent light sources to study electronic spectral broadening mechanisms in liquids. Weiner et al. [ 111, and Fayer and co-workers [ 12,50 ] 542
27 August 1993
have demonstrated clearly that it is the waiting time, r,, that defines whether a particular dynamic process will appear “homogeneous” or “inhomogeneous” in a photon-echo experiment. Only those contributions to the distribution of spectroscopic energy gaps that are static on a time scale long compared with T, will appear as inhomogeneous broadening in the photon echo. In experiments using short pulses, r, can be varied at will in a three-pulse configuration. However, in experiments with incoherent light the third field that stimulates the echo may come from any portion of the temporally long pulse that arrives after the first two fields have acted, and there will usually be a distribution of waiting times ranging from zero to the full pulse envelope. If the pulse duration is nanoseconds, it would appear that an inhomogeneous distribution has to persist for nanoseconds in order to show up as such in the photonecho decays. The purpose of this Letter is twofold. First, we demonstrate the observation of inhomogeneous broadening in a room-temperature liquid through the photon-echo technique performed with a broadband incoherent light source. For this demonstration we employ the molecular system of rhodamine B in propylene glycol in which Stein and Fayer have observed “dispersive” fluorescence energy transfer, a signature of inhomogeneous broadening on the fluorescence time scale [ 31,321. We then discuss the factors that determine the effective waiting time in such experiments, demonstrate that the waiting time can be made shorter than the full pulse duration, and evaluate the general utility of the method for examining electronic spectral broadening in liquids.
2. Experimental The experimental arrangement is shown in fig. 1. The frequency-doubled output of a Q-switched Nd:YAG laser (Continuum 660-A)) consisting of 532 nm pulses at a 20 Hz repetition rate, is used to pump an open-cavity dye laser. The “oscillator” consists of a broadband flat rear reflector and a 1 cm path length flow cell at Brewster’s angle, transversely pumped with approximately 3 mJ/pulse of the 532 nm light. In order to maximize the overall bandwidth and spectral smoothness of the output, no out-
CHEMICAL PHYSICS LETTERS
Volume 2 11, number 6
DyeLaser
PMT
?PC
BOXCAR
Fig. 1.Experimental configuration for two-pulse four-wave mixing with “incoherent” light. BS, beamsplitter; DL, delay line; P, and P,, polarizers; L, and L,, lenses; R1 and R2, right angle prisms; S, and S2,shutters. This configuration allows either signal beam, k3or k4, to be detected.
put coupler or tuning element is used, The amplified spontaneous emission from the “oscillator” is then amplified in a second 1 cm flow cell transversely pumped by another 3 mJ/pulse. Both oscillator and amplifier cells contain a methanol solution of a mixture of dyes adjusted empirically to provide the broadest possible emission bandwidth; the approximate composition of the final dye mixtures used for these experiments is rhodamine 590 (69%), rhodamine 610 (lo%), rhodamine 560 (lo%), rhodamine 640 (5%), kiton red (4%), and DCM (2%). The resulting pulses have a bandwidth of 39 nm at a central wavelength of 580 nm, a measured pulse duration of 8 ns, and an energy of 50 uJ/pulse. The spectra of the laser output are obtained with a Princeton Instruments IRY-700/N/R intensified diode array multichannel detector mounted on a Spex 1870 0.5 m spectrograph. This detection system allows us to obtain the spectra of individual pulses, and the single-pulse spectra are essentially indistinguishable from the time-averaged laser spectrum. The pulse is attenuated to an energy of 1 uJ or less and split equally into two excitation pulses, ki and kZ, in an interferometric setup. One arm of the interferometer is stationary while the retroreflecting mirrors of the other arm are positioned on a computer-controlled, stepper-motor-driven translation stage (Aerotech) providing a resolution of 0,7 fs. The pulses are recombined through a 20 cm El. lens at
27 August 1993
an angle of 15 mrad and overlapped on the sample contained in a 1 mm flow cell. The signals are collected from both phase matching directions, k3=2kl-kz and k,=2kz-k,, and recorded as a function of delay time by a photomultiplier interfaced to a boxcar averager (Stanford Research Systems). Typically signals are obtained from 25 laser shots at each delay setting, and approximately 20 separate sweeps of the delay line are averaged to give the final signal traces. All experiments are carried out at ambient temperature (about 23°C). In preliminary experiments it was found that interaction with almost any optical element caused some distortion of these spectrally broad pulses, and unequal distortions suffered by the two pulses led to artifactual oscillations in the signal. Thus we have taken care to choose optics that are spectrally as flat as possible and to match the optical elements in the two arms of the interferometer as closely as possible. The beamsplitter (reflective neutral density filter, Esco Products) is nearly flat in this spectral region, and in the configuration employed (see fig. 1) both pulses undergo one reflection and either two or three transmissions through the splitter; the beam that undergoes only two transmissions is passed through an additional glass flat to match the dispersive broadening of the two pulses. Aluminum mirrors are used throughout the setup. For experiments employing orthogonally polarized pulses, the polarization rotation is achieved by reflection and matched polarizers are used in both beams. The power spectra of the two beams appear identical. The samples consist of rhodamine B (Exciton) dissolved in propylene glycol, ethanol, or methanol at concentrations of 5 X 10d5 to 8 X 1O-’ M. The formation of dimers or higher aggragates was reported by Stein and Fayer [32] to be unimportant up to concentrations much higher than this. The resulting optical density in a 1 mm path length is 0.07 to 0.12 near the center of the laser spectrum (580 nm). No change in the four-wave mixing signal was observed upon addition of a drop of concentrated HCl to some samples to insure complete protonation of the weakly acidic rhodamine B. Fig. 2 shows the absorption spectrum of rhodamine B in propylene glycol, superimposed on the power spectrum of the laser pulses.
543
Volume 2 11,number 6
CHEMICAL PHYSICS LETTERS
27 August 1993
level structure, the dependence of the three-pulse four-wave mixing signal on pulse delay time Td is given by [ll] 2 WG)cc
/I
dwexP[i(w-w,)~,la(w)#(w)
, (1)
510
550
590
630
Wavelength (tnn) Fig. 2. Absorption bandshape of rhodamine B in propylene glyco1 superimposed on laser powerspectrum. The laser spectrum changes slightly in shape and width from day to day but is stable over the short term (minutes to hours).
3. Theoretical
An enormous number of theoretical treatments of the dependence of the four-wave mixing signal on pulse delay time have been published for both twoand three-beam scattering with both ultrashort and incoherent, broadband long pulses [ 1O-12,20-23,5 l531. However, due to the complexity of the most general expressions, all of the existing treatments of which we are aware make one or more simplifying assumptions that render them inadequate for quantitative modeling of our experimental data. The treatments of Bai and Fayer [ 121 and of Hartmann and Manassah [ 53 ] do explicitly consider spectral diffusion, but they assume that the inhomogeneous width is very large compared with the laser spectral bandwidth, which is inappropriate for our very large excitation bandwidth. We are presently developing a complete theoretical treatment of time-delayed four-wave mixing with incoherent light that properly includes the finite correlation time of the light, a nonzero but finite inhomogeneous linewidth within which spectral diffusion occurs, and the multilevel vibrational substructure of the electronic absorption band, and can describe signals obtained with either parallel or perpendicular polarizations of the two pulses. However, qualitative conclusions can still be drawn from the experimental data in the absence of a complete theoretical description. In the case of pure homogeneous broadening and for an arbitrary vibronic 544
where IX,_is the center laser frequency, a(w) is the measured optical absorption spectrum, and Q(w) is the measured power spectrum of the laser pulses. This expression holds for scattering into either direction, k,+(k,-k2) or k,- (k,-k2), as long as the third pulse (wavevector k,) is separated in time from pulses 1 and 2 and comes after any rapid excited state relaxation processes are complete. Eq. (1) is similarly applicable to two-pulse scattering with “incoherent” light in the homogeneous broadening limit as long as the pulse envelopes are long compared with the pulse coherence time, such that most of the scattering arises from processes in which the third pulse acts long after the coherence induced by the first two pulses has decayed. If, on the other hand, there is inhomogeneous broadening that persists for times longer than the pulse duration, then the signal ‘detected in a particular direction will be asymmetric with respect to rd=O. Finally, if spectral diffusion within an “inhomogeneous” distribution occurs, the spectrum will appear homogeneously broadened if the spectral diffusion time is short compared with the effective waiting time. Thus, for experiments performed with true femtosecond pulses, the spectral diffusion rate can be determined by looking for a transition from asymmetric to symmetric signals as the time delay of the third pulse is increased [ 11 1, In a two-pulse scattering configuration with incoherent long pulses, we do not have direct control over the waiting time, and in general there will be a broad distribution of ~,,,scorresponding to the long period of time during which there is still light on the sample after the first two fields have acted. In other words, the long incoherent pulse can be thought of as a random train of femtosecond pulses, and once two of these pulses have interacted with the medium to create a grating, any one of the later pulses may scatter off it for as long as that grating survives [ 10,12,17]. The length of time for which the grating persists is determined by several factors including the
Volume 2 11, number 6
27 August 1993
CHEMICAL PHYSICS LETTERS
excited state lifetime and the polarizations of the two pulses. When a grating is formed using parallel polarized pulses in an electronically resonant material, the electronic population grating present at short times decays to form thermal and/or acoustic gratings that are typically weaker than the population grating but persist for times much longer than the excited state lifetime [ 541. Thus, in an experiment employing nanosecond duration incoherent pulses, waiting times ranging from femtoseconds to the full pulse duration can contribute to the signal. If, on the other hand, the grating-forming beams are chosen to have orthogonal polarizations, an orientational grating is formed which decays on the time scale of the molecular reorientation time [ 54-561. Thus the effective waiting time can often be limited to times much shorter than the incoherent pulse envelope, although there will still be a distribution of waiting times involved.
4. Results Fig. 3 shows the dependence of the signal scattered into both directions on the time delay rd for rhodamine B in propylene glycol with both parallel and perpendicularly polarized pulses. Both polarization configurations exhibit a marked asymmetry of the two signals with respect to time delay, and both exhibit a “quantum beat” separated from the main maximum by 40-50 fs. The signals in the two directions are approximately related by reflection across the t =O point, as anticipated. The similarity of the signals in the two polarization configurations suggests that the distribution of waiting times contributing to the signal in the two experiments is not significantly different. This may not be surprising given that the rotational diffusion time for rhodamine B in the highly viscous propylene glycol is comparable to the excited state lifetime [ 321. In this solvent, the excited state population grating that is expected to dominate the scattering in the parallel polarized configuration should not persist for a much longer time than the orientational grating that dominates the signal in the perpendicularly polarized configuration. Fig. 4 shows the corresponding result for rhodamine B in ethanol with parallel polarized pulses. Similar results are obtained with perpendicularly po-
-160
-80
0
80
160
Delay time (fs) Fig. 3. Solid and dashed curves: four-wave mixing signals for rhodamine B in propylene glycol observed in the two directions k, and k4 as a function of time delay between k, and A2(see fig. 1). k, and k2 have parallel polarizations in the upper plot, and perpendicular polarizations in the lower. The dotted curve in the upper plot is the theoretical response for a homogeneously broadened system calculated from eq. ( I ). The theoretical curves are the same for both polarization configurations.
-160
-80
0
80
160
Delaytime (fs)
Fig 4. Four-wave mixing signals for rhodamine B in ethanol observed in the two directions k, and k4 asa function of time delay between k, and kz. k, and k2 have parallel polarizations.
larized pulses and in methanol rather than ethanol as the solvent. The asymmetry of the signals and the beats are very similar to those observed in propylene glycol. This suggeststhat substantial inhomogeneous 545
Volume 211, number 6
CHEMlCAL PHYSICS LETTERS
-n
-160
-80
0
80
160
Delay time (fs) Fig. 5. Four-wave mixing signals for nile blue in methanol observed in the two directions ks and k4 as a function of time delay between k, and k,. k, and k2 have parallel polarizations. The dotted curve is the theoretical response for a homogeneously broad-
ened system calculated from eq. ( I ).
broadening of the electronic spectra persists even in these relatively low-viscosity solvents. Fig. 5 presents results on nile blue in methanol. The scattering into the two directions is essentially symmetric, indicating that this system appears to be homogeneously broadened; i.e. spectral diffusion is fast relative to the effective waiting time r, in the incoherent pulse experiment. This result is in agreement with the recent report of Moshary et al. [24] and indicates that our observation of asymmetric responses for rhodamine B is not simply an experimental artifact. Similar results are obtained from nile blue in propylene glycol. Figs. 3 and 5 also compare the experimental curves with those calculated from eq. (1) for pure homogeneous broadening, i.e. the Fourier transform of the product of the chromophore’s absorption spectrum with the experimental laser power spectrum. For nile blue the agreement is reasonably good, while the experimental and calculated curves clearly do not correspond well for rhodamine B. Again these results are consistent with the conclusion that the electronic spectrum of nile blue in methanol is homogeneously broadened on our experimental time scale, whereas rhodamine B in hydrogen-bonding solvents exhibits substantial inhomogeneous broadening.
5. Discussion One potentially confusing point needs to be clar546
27 August 1993
ified at the outset. It has been stated that for two-pulse scattering the signal intensities should always be asymmetric with respect to 7d=0 regardless of the nature of the broadening [ 11,231. That is true when short pulses are used, and merely reflects the fact that the third field cannot scatter off the grating until the two fields needed to form the grating have arrived, and the third field is the same as one of the two grating-forming fields. In the limit of delta-function pulses there would be no scattering at all for h
Volume 2 11, number 6
CHEMICAL PHYSICS LETTERS
during which the effects of spectral diffusion can manifest themselves. Thus the signal profiles should appear more asymmetric, indicating more inhomogeneous broadening when the excitation pulses have perpendicular polarizations than when they are parallel. Therefore it is somewhat surprising that the signals we observe in the two polarization configurations are so similar, particularly in methanol and ethanol in which the rotational reorientation is fast. The “quantum beats” observed in the rhodamine B data remain to be fully interpreted. The experimental 40-50 fs time interval between the main maximum and the “beat” is extremely reproducible from one day to the next and is observed over a wide range of rhodamine concentrations and laser powers. The spacing of 40-50 fs corresponds to a vibrational frequency of 700-800 cm-‘; alternatively, the position of the beat relative to the zero time corresponds to a vibrational frequency near 1500 cm-‘. These are not frequencies that we would obviously expect to observe, as the absorption spectrum, aIthough only weakly structured, appears to have dominant Franck-Condon activity in a mode or group of modes closer to 1300 cm-‘, and the laser spectrum, centered on the red side of the absorption spectrum, does not overlap this structure. The theoretical signals, calculated from the experimental absorption spectrum and laser power spectrum with the assumption of homogeneous broadening, do not exhibit any beats. Wiersma and co-workers have recently explored, both experimentally and theoretically, time-resolved four-wave mixing using deliberately chirped femtosecond pulses [ 26,30,58]. They demonstrate that “quantum beats” due to CARS and CARS-type resonances can appear at time delays that have no clear relationship to the system’s vibrational frequencies when the pulses carry a linear chirp in the appropriate range of magnitudes. We have not yet attempted to evaluate the possible role of frequency chirping of our long pulses which are, in any case, very far from the transform limit. More theoretical and experimental work will be required before any firm conclusion can be drawn about the role of inhomogeneous broadening and the time scale for spectral diffusion in the electronic spectrum of rhodamine B. A more rigorous theoretical development than any yet presented, together with much more thorough characterization of our
27 August 1993
laser pulses, will be needed before these experiments can be interpreted quantitatively. Even then, the utility of such experiments for probing dynamics in liquids will probably be limited to a few special systems in which the effective waiting time is constrained to be short by other aspects of the system’s dynamics (e.g. fast rotation with the perpendicularly polarized geometry). Although broadband, temporally long laser pulses are undoubtedly easier to generate than true femtosecond pulses, adequate control over and characterization of the former is difficult, and the latter are far more useful for photon-echo applications because the waiting time can be controlled accurately in three-pulse geometries. As continuing improvements in ultrafast technology make the generation of femtosecond pulses increasingly straightforward, techniques based on incoherent light are likely to become progressively less interesting, at least for application to liquid state dynamics.
Acknowledgement This work was supported in part by NSF grant CHE-9020844. ABM is the recipient of a Packard Fellowship in Science and Engineering, a Sloan Research Fellowship, an NSF Presidential Young Investigator Award, and a Dreyfus Teacher-Scholar Award.
References [ 1] T. Sesselman, W. Richter, D. Haarer and H. Morawitz, Phys. Rev. B 36 (1987) 7601. [2] P.J. van der Zaag, J.P. Galaup and S. VGlker,Chem. Phys. Letters 166 (1990) 263. [3]T.J. Kang, J. Yu and M. Berg, Chem. Phys. Letters 174 (1990) 476. [4] J. Yu, T.J. Kang and M. Berg, J. Chem. Phys. 94 (1991) 5787. [5] J. Zollfrank and J. Friedrich, J. Phys. Chem. 96 (1992) 7889. [6] J. Yu and M. Berg, J. Chem. Phys. 96 (1992) 8741. [7] L. Shu and G.J. Small, J. Opt. SOC.Am. B 9 ( 1992) 724. [8] T. BaschC, W.P. Ambrose and W.E. Moemer, J. Opt. Sot. Am. B 9 ( 1992) 829. [9] J. Yu, P. Earvolino and M. Berg, J. Chem. Phys. 96 (1992) 8750. [lo] N. Morita and T. Yajima, Phys. Rev. A 30 (1984) 2525.
547
Volume 2 11, number 6
CHEMICAL PHYSICS LETTERS
[ 111A.M. Weiner, S. De Silvestri and E.P. Ippen, J. Opt. Sot. Am. B 2 ( 1985) 654. [ 121Y.S. Bai and M.D. Fayer, Chem. Phys. 128 (1988) 135. [ 131P.C. Becker, H.L. Fragnito, J.Y. Bigot, C.H.B. Cruz, R.L. Fork and C.V. Shank, Phys. Rev. Letters 63 (1989) 505. [ 141 H. Fidder, S. de Boer and D.A. Wiersma, Chem. Phys. I39 (1989) 317. [ 151 I.A. Walmsley and C.L. Tang, J. Chem. Phys. 92 ( 1990) 1568. [ 161 S. Saikan, A. Imaoka, Y. Kanematsu, K. Sakoda, K. Kominami and M. Iwamoto, Phys. Rev. B 41 ( 1990) 3185. [ 171K. Misawa and T. Kobayashi, Mol. Cryst. Liquid Cryst. 182A (1990) 125. [ 181A. Elschner, L.R. Narasimhan and M.D. Fayer, Chem. Phys. Letters 171 (1990) 19. [19]A.M. Walsh and R.F. Loring, Chem. Phys. Letters 186 (1991) 77. [20] Y.J. Yanand S. Mukamel, .I. Chem. Phys. 94 (1991) 179. [ 211 L.R. Narasimhan, Y.S. Bai, M.A. Dugan and M.D. Fayer, Chem. Phys. Letters 176 ( 1991) 335. [ 221 E.T.J. Nibbering, D.A. Wiersma and K. Duppen, Phys. Rev. Letters66 (1991) 2464. ]23‘I J.-Y. Bigot, M.T. Portella, R.W. Schoenlein, C.J. Bardeen, A. Migus and C.V. Shank, Phys. Rev. Letters 66 ( 1991) 1138. 124 F. Moshary, M. Arend, R. Friedberg and S.R. Hartmann, Phys. Rev. A 46 ( 1992) R33. ]25 Y. Nomura, Y. Fujimura, M. Takahashi, M. Fujii and M. Ito, Chem. Phys. Letters 197 ( 1992) 405. [26] E.T.J. Nibbering, D.A. Wiersma and K. Duppen, in: Coherence phenomena in atoms and molecules in laser fields, eds. A.D. Bandrauk and SC. Wallace (Plenum Press, New York, 1992). [ 27 ] M. Cho, N.F. Schererand G.R. Fleming, J. Chem. Phys. 96 (1992) 5618. [ 281 M. Cho and G.R. Fleming, J. Chem. Phys. 98 ( 1993) 2848. [29] C.J. Bardeen and C.V. Shank, Chem. Phys. Letters 203 (1993) 535. [ 30 ] K. Duppen, F. de Haan, E.T.J. Nibbering and D.A. Wiersma, Phys. Rev. A, in press. [ 3 1]A.D. Stein and M.D. Fayer, Chem. Phys. Letters 176 ( 1991) 159. [32] A.D. Stein and M.D. Fayer, J. Chem. Phys. 97 ( 1992) 2948. [33] M.J.E. Morgenthaler, S.R Meech and K. Yoshihara, Chem. Phys. Letters 197 ( 1992) 537.
548
27 August 1993
[ 341 A.B. Myers, M.O. Trulson and R.A. Math&, J. Chem. Phys. 83 (1985) 5000. [ 351 A.B. Myers, M-0. Trulson, J.A. Pardoen, C. Heeremans, J. Lugtenburg and R.A. Mathies, J. Chem. Phys. 84 (1986) 633. (361 E.T.J. Nibbering, K. Duppen and D.A. Wiersma, J. Chem. Phys. 93 (1990) 5477. [37]A.B.MyersandB.Li,J.Chem.Phys.92(1990)3310. [38] A.B. Myers, J. Opt. Sot. Am. B 7 (1990) 1665. [ 391 T.-S. Yang and A.B. Myers, J. Chem. Phys. 95 (1991) 6207. [40] M.K. Lawless and R.A. Mathies, J. Chem. Phys. 96 (1992) 8037. [41] J. Sue,Y.J. YanandS. Mukamel, J. Chem. Phys. 85 (1986) 462. [42] Y.J. Yan and S. Mukamel, J. Chem. Phys. 86 (1987) 6085. 1431R. Beach, D. DeBeer and S.R. Hartmann, Phys. Rev. A 32 (1985) 3467. [44] M. Tomita and M. Matsuoka, J. Opt. Sot. Am. B 3 (1986) 560. [45] T. Hattori and T. Kobayashi, Chem. Phys. Letters 133 (1987) 230. [46] T. Hattori, A. Terasaki and T. Kobayashi, Phys. Rev. A 35 (1987) 715. [47]Z.Q. Huang, Y.J. Xie, G.L. Huang and H.S. Kwok, Opt. Letters 15 ( 1990) 501. [48]T. Hattori and T. Kobayashi, J. Chem. Phys. 94 (1991) 3332. [ 491 T. Matsumoto, K. Ueda and M. Tomita, Chem. Phys. Letters 191 (1992) 627. [5O]M. Berg, CA. Walsh, L.R. Narasimhan, K.A. Littau and M.D. Fayer, J. Chem. Phys. 88( 1988) 1564. [ 5 1 ] S. Sailan, T. Nakabayashi, Y. Kanematsu and A. Imaoka, J. Chem. Phys. 89 (1988) 4609. [ 521 X. Cheng and T. Kobayashi, Mol. Cryst. Liquid. Cryst. A 182 (1990) 139. [53] S.R. Hartmann and J.T. Manassah, J. Phys. B 23 (1990) 1363. [54] A.B. Myers and R.M. Hochstrasser, IEEE J. Quantum Electron. QE-22 ( 1986) 1482. [55] B.S. Wherrett, A L. Smirl and T.F. Boggess, IEEE J. Quantum Electron. QE-19 ( 1983) 680. [56] J.T. Fourkas, R. Trebino and M.D. Fayer, J. Chem. Phys. 97 (1992) 69. [ 571 E Lopez Arbeloa, T. Upez Arbeloa, M.J. Tapie EstCvezand I. Lopez Arbeloa, J. Phys. Chem. 95 (1991) 2203. [58] E.T.J. Nibbering, D.A. Wiersma and K. Duppen, Phys. Rev. Letters 68 (1992) 514.