June 1, 1992 / Vol. 17, No. 11 / OPTICS LETTERS 775

Resonance-enhanced time-resolved optical Kerr effect of,B-carotene in solution

Paolo Foggi, Valey E Kamalov, Roberto Righini, and Renato Torre

European Laboratory of Nonlinear Spectroscopy, University of Florence, Largo E. Fermi 2, Florence, Italy

Received November 18, 1991

A sharp resonant amplification of the third-order susceptibility of a diluted ,B-carotene solution in dodecane isobserved by means of the time-resolved optical Kerr effect when the wavelength of the probe is tuned in therange of 490-570 nm. The resonance is well in the red with respect to the 0-0 first electronic transition; someevidence is given of the possible role of higher excited states and of two-photon resonance.

The time-resolved optical Kerr effect (OKE) has re-cently been applied to study the molecular dynamicsof simple liquids' with the use of laser pulses in thefemtosecond time scale. We recently improved thistechnique to investigate large organic mole-cules in solution at low concentration: 13-carotenemolecular dynamics was studied in different dilutedsolutions in n-alkanes.2 With this technique the ob-servation of the OKE signal is made possible by theenhancement of the third-order susceptibility owingto the probe-beam resonance with one electronictransition of the solute molecules. The differenttemporal response allows the separation of the ori-entational contribution to y(3) from the other termsthat are present only at zero delay.

In this Letter we present our results on the reso-nance enhancement of the OKE signal when thelaser probe pulse is tuned near the first one-photon-allowed electronic transition of 13-carotene. Thedetails of the experimental apparatus of the time-resolved OKE technique have been described else-where.' An angle of 450 was used between thepolarization vectors of the pump and probe pulses.The intensity of the probe beam passed throughcrossed polarizers was measured as a function of thepump-probe delay; the duration of the pulses, ob-tained from autocorrelation and cross-correlationtraces with the assumption of a biexponential shapeof the pulses (correlation width 1.5 pulses FWHM),was 150-200 fs for the pump and 250 fs for theprobe. The energy of the pump pulse at A = 604 nmwas approximately 10 ,uJ, with a spot diameter of150 /,tm; the frequency-tunable probe beam was ob-tained by selecting, with the help of a couple of 60°prisms and a slit, a portion of the continuum gener-ated by focusing part of the pump beam into a watercell.2 The sample consisted of a 300-,um-thickjet stream of a 5 X 10-i M solution of all-trans-,1-carotene in dodecane.

In Fig. 1 the temporal response of the opticalanisotropy created in the 13-carotene solution(5 X 10-4 M) in dodecane at 298 K is shown fordifferent probe-beam frequencies. In all curvestwo components can be easily observed: a narrowstrong peak followed by a slowly decaying compo-

nent, which appear as a plateau in the 2-ps timescale of the figure.

The nonlinear polarization, responsible for the in-duced birefringence, can be conveniently expressedas the convolution of the time profiles of the laserpulses and of the sample third-order susceptibility,which consists of an electronic term (related to themolecular hyperpolarizability) and a term that de-pends on the nuclear coordinates.3 The expressionfor the ith component is then

i= X( 1 Ej (t)Ek(t)E(t)+t+ Ej (t) d dX,13)ln(t _t')Ek*(t')E1(t).

_co jk(1)

The first term on the right-hand side corresponds tothe instantaneous response that is due to the distor-tion of the electron cloud, and its contribution to theOKE signal corresponds to the peak at zero delay inFig. 1. The second term is the nuclear contribution,which may contain vibrational and orientationalterms; the decay time constant of the rotational con-tribution has been found to be 215 ps for 13-carotenein dodecane,2 which corresponds to a rotational re-laxation time of 430 ps. The enhancement of bothcontributions in Eq. (1), when the probe frequencyapproaches the electronic resonance, is the key con-dition for this experiment; in fact, no OKE signalfrom 13-carotene could be detected by using a red-shifted (620 nm) probe beam.

It should be noted that Eq. (1) was derived withinthe Born-Oppenheimer approximation, i.e., far fromelectronic resonance. This condition does not applystrictly to the present case; however, the breakdownof the Born-Oppenheimer approximation is slowenough to allow the extension of the treatmentalso to preresonance conditions (see Ref. 3). Wethen consider that Eq. (1) can be safely utilized inour case.

The absorption spectrum of 13-carotene in dode-cane is shown in Fig. 2, where the wavelengths ofthe pump (604 nm) and probe beams are also indi-cated. The ratio of the instantaneous to the orien-tational components changes essentially when theprobe frequency is tuned on the red side of the ab-

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776 OPTICS LETTERS / Vol. 17, No. 11 / June 1, 1992

.FCc)

-1 -0.5 0 0.5 1 1.5 2 2.5time delay (ps)

Fig. 1. Time-resolved OKE signal of ,3-carotene solu-tion in dodecane (5 X 10-4 M, T = 298 K) measured atdifferent probe wavelengths. Apump = 604 nm, Aprobe =490-507 nm.

.?TCa)

0

wavelength (nm)

Fig. 2. Absorption spectrum of ,-carotene in dodecane.The wavelengths of the pump and probe beams aremarked; also shown is the position Aoo of the purely elec-tronic resonance for ,B-carotene in hexane at T = 298 K.4

The hatched area shows the spectral range of C0pump +Wprobe. The inset shows a scheme of the electronic levelsof 1B-carotene.

sorption band from A = 570 nm to A = 490 nm.This behavior is apparent from the different curvesof Fig. 1, in which the intensities have been normal-ized to the height of the plateau.

In Fig. 3 the ratio of the instantaneous and orien-tational contributions is superimposed onto the redtail of the absorption spectrum. The orientationalcontribution was measured at a delay time AT =2 ps, where the instantaneous contribution is negli-gible. The actual contribution of the instantaneousterm to the signal at AT = 0 was obtained by sub-tracting the orientational part at zero delay. Anapproximated value for the latter quantity was ob-tained by convoluting a single exponential function(decay time constant 215 ps) with the pulse profiles,according to Eq. (1); this procedure discriminatesthe delayed signal from the instantaneous one. Inaddition to the purely electronic term X(,el the in-stantaneous part of the nonlinear polarization in

Eq. (1) may contain contributions from the nuclearpart when the difference of the pump and probe fre-quencies coincides with a Raman vibrational transi-tion; of course such a contribution requires thatboth the pump and the probe pulses are present atthe same time. The resonance observed at 514 nmis very sharp (FWHM = 400 cm-') and has a typicaldispersive shape; similar shapes are usually ob-served in coherent Raman spectroscopy.5 As shownin Fig. 3, the frequency of the purely electronic

'BE+ -1Ag- transition differs substantially fromthe observed resonance; thus it cannot be invoked asan explanation of our experimental data. The solidcurve in Fig. 3 is reminiscent of the coherent Ramanspectroscopy excitation profile of 13-carotene intetrahydrofurane measured by Ferrante et al.,6 inwhich a narrow band is observed at 503 nm.

Different mechanisms can be proposed as an ex-planation of the observed resonance:

(a) Raman resonance: The frequency differencebetween the pump (A = 604 nm) and the probe at510 nm is 3050 cm-', which corresponds quite closelyto the first overtone of the C=C stretching mode of13-carotene (vc=c = 1525 cm-'). The bandwidth ofthe Raman resonance is expected to be much smaller(2F = 30 cm-' from the Raman spectrum7) thanthat of the resonant peak. However, the largebandwidth of our pulses (-150 cm-') and the limitednumber of experimental points in the curve of Fig. 3make this argument not conclusive enough to ex-clude the possibility that the observed effect is dueto such vibrational resonance. A more convincingargument is that we did not observe any intensifica-tion when the frequency difference of the pump andprobe pulses equaled the fundamental coc=c fre-quency, whose Raman intensity is of course muchhigher than that of the overtone. We are then led toconclude that the Raman resonance can be ruled outas a possible explanation. On the other hand, it isnot obvious why we do not observe in any case am-plification due to Raman resonance. The Raman-induced Kerr effect has in fact been described widely

wavelength (nm)

Fig. 3. Ratio of instantaneous to orientational contribu-tions to the OKE signal of P-carotene in dodecane versusthe probe wavelength (ApUmp = 604 nm). The dotted curveis the red tail of the absorption spectrum of 13-carotene.The solid curve is merely a guide to the eye.

June 1, 1992 / Vol. 17, No. 11 / OPTICS LETTERS 777

and observed in several systems. We should, how-ever, consider that the Raman-induced Kerr effectis a typical frequency-domain experiment, in whichnarrow-linewidth lasers are employed; on the con-trary, the intrinsic linewidths of our short pulses arequite large (-150 cm-'). As a result, only a smallfraction of the incident photons can be on resonancewith the much narrower Raman transition, thus re-ducing drastically the efficiency of the excitation.Of course the same does not hold for the electronicresonance, owing to the large linewidth of suchtransitions.

(b) Two-photon resonance: As shown in Fig. 2,the sum frequency &)pump + C

0probe coincides with the

second allowed transition (S0 -- S0 ) of 13-carotene.Furthermore an increase of the two-photon crosssection is expected owing to the near coincidence of(Oprobe with the broad 1'B0 <- 1'Ag transition. Themeasurement of the two-photon absorption by meansof four-wave-mixing techniques has been describedpreviously.8'l0 Further support of this mechanismis provided by the results obtained by changing thepump-beam frequency: By shifting C)pUmp from 604to 580 nm, with Coprobe fixed at 514 nm, the observedratio of instantaneous to orientational componentsdecreases from 16.1 to 3.1; the resonance then de-pends on the frequency of both beams.

Mechanism (b) then appears as the most convinc-ing explanation of the effect shown in Fig. 3; how-ever, the nature of the excited state that leads to theresonance observed in the OKE experiment remainsuncertain: it can be due to the two-photon-allowedn'Ag <- 1'Ag electronic transition. The band-width of the observed resonance (400 cm-') is similarto those of the narrow features observed in the ab-sorption spectra of J aggregates" and is attributedto molecular excitons. The molecular structure of13-carotene characterized by a long conjugated chainis compatible with such exciton states. The assign-ment of the observed resonance to an exciton state,however, requires further experiments, which arecurrently in progress.

This research was supported by the ItalianMinistero della Ricerca Scientifica e Tecnologica

and the Consiglio Nazionale delle Ricerche. ValeyE Kamalov gratefully thanks A. C. Albrecht andK. Yoshihara for helpful discussions. We are in-debted to C. Ferrante and R. Bozio for providing uswith a preprint of their article.

Paolo Foggi and Roberto Righini are also with theDepartment of Chemistry, University of Florence,via G. Capponi 9, 50121 Florence, Italy.

Valey F. Kamalov is also with the PhotochemistryDepartment, Institute of Chemical Physics, Acad-emy of Sciences, Kosygin Street 4, Moscow 117977,Russia.

Renato Torre is also with the Department ofPhysics, University of Florence, Largo E. Fermi 2,50125 Florence, Italy.

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