J. Phys. Chem. 1989, 93, 75-83
75
Nonlinear Absorption by a//-trans-@-Carotene Studied by Diffraction from Laser-Induced Anharmonic Thermal Gratings X. R. Zhu and J. M. Harris* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: March 18, 1988; In Final Form: May 31, 1988)
The nonlinear optical absorption of all-trans-/3-carotenein hexane and chloroform has been studied by measuring the diffraction from laser-inducedanharmonic thermal gratings. Nonradiative relaxation following nonlinear absorption at a crossed-laser-beam interference pattern generates a thermal grating containing harmonics of the spatial frequencies present in the interference pattern. Observation of diffraction at the second Bragg angle provides a zero-background measurement of deviation from linear absorption. The measured angular sensitivity and decay rates of the diffraction transients are consistent with Bragg diffraction theory. A two-step absorption model is proposed to interpret the observed results. The kinetic parameters of the model are determined by simultaneously fitting the first- and second-order diffraction intensity versus excitation intensity. The results indicate that nonlinear absorption of trans-/3-carotenein hexane is primarily caused by excited-state absorption, and while in chloroform it is dominated by photoisomerization and subsequent photoisomer absorption. In hexane solution, the ground-state recovery time is found to be less than 35 ps, consistent with previously reported results. Photoisomerization of trans-&carotene is an efficient process in chloroform but not in hexane; the photoisomerization quantum yields in the two solvents are 0.026 and 57.0 X lo4, respectively.
Introduction Observing diffraction from laser-induced dynamic gratings’-’ has recently been applied to the study of molecular photophysics and photochemistry. In particular, transient grating experiments have been used to investigate photophysical and photochemical processes of molecules in polymer matrices.e6 Picosecond pulsed lasers have been used to probe excitation transport in molecular Moving gratings created with nondegenerate pump beams have provided a frequency domain technique for measuring subpicosecond excited-state l i f e t i m e ~ . ~Absorptive J~ heating can be used to generate propagating acoustic gratings as well as isobaric thermal gratings which relax diffusively. Acoustic have been used to measure weak overtone absorption spectra, crystal elastic constants, and excited-state absorption. Thermal gratings have also been used to determine radiationless’’ and fl~orescence’~ quantum yields of dye solutions. Thermal grating technique has recently been used to measure weak optical absorptions, as small as cm-’, from one- and two-photon transition^.'^ Nonlinear absorption from two- and three-photon and from saturated one-photon transitions18 in liquids create a thermal grating containing higher harmonics of (1) Eichler, H. J. Opt. Acta 1977, 24, 631. (2) Pohl, D. W. IBM J . Res. Deu. 1979, 23, 604. (3) Eichler, H. J.; Gunter, P.; Pohl, D. W. Laser-Induced Dynamic Gratings; Springer Series Optical Science Vol. 50; Springer-Verlag: New York, 1986. (4) Deeg, F. W.; Pinsl, J.; Brauchle, C. J . Phys. Chem. 1986, 90, 5710. (5) Deeg, F. W.; Pinsl, J.; Brauchle, C. IEEE J. Quantum Electron. 1986, QE-22, 1476. (6) Brauchle, C.; Burland, D. M. Angew. Chem., Int. Ed. Engl. 1983,22, 582 and references cited therein. (7) Salcedo, J. R.; Siegman, A. E.; Dlott, D. D.; Fayer, M. D. Phys. Reu. Lett. 1977, 41, 131. (8) Fayer, M. D. Annu. Reu. Phys. Chem. 1982,33,63and references cited therein. (9) Yajima, T.; Souma, H.; Ishida, Y. Phys. Reu. A 1978, 17, 324. (10) Tribino, R.; Barker, C. E.; Siegman, A. E. IEEE J . Quantum Electron. 1986, QE-22, 1413 and references cited therein. (11) Eichler, H.; Stahl, H. J . Appl. Phys. 1973, 44, 3429. (12) Fayer, M. D. IEEE J . Quantum Electron. 1986, QE-22 8, 1437 and references cited therein. (13) Andrews, J. R.; Hochstrasser, R. M. Chem. Phys. Lett. 1980,76,207. (14) Petukhov, V. A.; Popov, M. B.; Krymova, A. I. Sou. J . Quantum Electron. 1986, 16, 503. (15) McGraw, D. J.; Harris, J. M. J . Opt. SOC.A m . 1985, B2, 1471. (16) McGraw, D. J.; Harris, J. M. Opt. Lett. 1985, IO, 140. (17) McGraw, D. J.; Harris, J. M. Phys. Reu. A 1986, 34, 4829. (18) McGraw, D. J.; Michealson, J.; Harris, J. M. J. Chem. Phys. 1987, 86, 2536.
0022-3654/89/2093-0075$01.50/0
the spatial frequency present in the excitation interference pattern. Recently, the anharmonic thermal grating technique has been used to study the effects of photoisomerization on absorption saturation of a carbccyanine dye.19 Applications of the laser-induced thermal grating technique to detecting weak linear and nonlinear absorption is the subject of a recent review.20 Nonlinear processes as population saturation detected by four-wave mixing have been observed to give rise to higher order diffraction in atomic ~ a p o r s ~and l - ~in~l i q ~ i d s ? ~Discrimination -~~ between the anharmonic character of the grating and other contributions to higher order diffraction, from either cascading of diffracted orders or Raman-Nath behavior, was limited by the conditions of these experiments. This difficulty can be overcome by generating weakly modulated, “thick” volume gratings in the Bragg regime to avoid Raman-Nath diffraction behavior26and by probing the grating with weak nonresonant probe to eliminate cascading of diffracted orders.l7 Under these conditions, higher order diffraction can be assigned to spatial frequency harmonics in the thermal grating which arise uniquely from nonlinear excitation of sample molecules. Angular separation of diffraction from these higher order grating components provides a zerobackground signal responding only to nonlinear absorption even in the presence of a significant linear absorption. By measuring the excitation intensity dependence of several diffracted order, one can distinguish between mechanisms of nonlinear absorption -’~ such as due to multiphoton’s-’7 or saturated a b ~ o r p t i o n . ’ ~ In this paper, we report an application of laser-induced thermal gratings to a different nonlinear absorption process observed in all-trans-@-carotene. Based on experimental observations, a two-step absorption model is proposed to account for the nonlinear excitation behavior of this molecule. The intensity dependence of absorbed energy predicted by this model is sampled by excitation at an interference pattern which is spatially modulated at a single frequency. The resulting absorbed energy is expanded into the Fourier components of this spatial frequency, and the corresponding intensity of each diffraction order is predicted. ~~~~~~
~
(19) Zhu, X. R.; Harris, J. M. Chem. Phys. 1988, 124, 321. (20) Zhu, X. R.; Harris, J. M. Chem. Rev., manuscript in preparation. (21) Heer, C. V.; Griffenm, N. C. Opt. L e x 1979, 4, 239. (22) Tan-no, N ; Ohkawara, K.; Inaba, H. Phys. Reu. Lett. 1981,46, 1282. (23) Raj, R. K.; Gao, Q.F.; Bloch, D.; Ducloy, M. Opt. Commun. 1981, 51, 117. (24) Chang, T., Kim, H., Yu, H. Chem. Phys. Lett. 1984, 1 1 1 , 64 (25) Frueholz, R. P.; Gelbwachs, J. A. Appl. Opt. 1980, 19, 2735. (26) Gaylord, T. K.; Moharam, M. G. Appl. Opt 1981, 20, 3271.
0 1989 American Chemical Society
76 The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 Due to its essential, accessory functions in photosynthesis in green plants, 0-carotene is a biologically important natural product,27 the photophysics of which have been extensively s t ~ d i e d . ~Nevertheless, ~-~~ the photophysical and photochemical properties of @carotene are not fully understood, and uncertainties about its decay pathways and kinetic rates still exist. The extremely low fluorescence quantum yields (O) = 1, Z(tC0) = 0 k3alz
To(t)= ( a - b)ab [a(1 - e-bf) - b( 1 - e-a‘)]
where ulZs1= ( k , + k3)k4/(k3+ k4). For case (ii), So is given by
where d2ZS2 = k’,(k3 + k4)/k4.SIand Toare respectively related to Soand SIby the same equations as in case (i), given by eq 8b and eq 8c, respectively, while T I is given by Ti = (k3~’21/k4k’2)SI
(9b)
The total absorbed power (in units of the photon energy), for case (i), depends on the ground- and first excited-state populations according to P = Nu~ZSO+ N u ~ I S I (10) For case (ii), the absorbed power depends on the ground-state and trap-state populations where u2 and SIin eq 10 are replaced by d2and To.P i s the absorbed photon density due to the excitation intensity, 1,and the number density of solute molecules, N . If we assume that the radiationless quantum yields of the decay from SI and S, (or T I )both are nearly unity, the power transferred into heat then is proportional to the P in eq 10. This assumption is reasonable for @-carotenesince its fluorescence quantum yield is less than 10-5.28 The total absorption rate as a function of the excitation intensity in the steady-state approximation, for case (i), is then given by
(4a)
P=
NUll(l + 1 / 4 1 2 ) 1 + 1/41
(1 1)
+
where the ground-state population is given by So = 1 - To- SI, and
a,b = yz[(k1+ k3
+ k4 + all) f ( ( k , + k3 + uI1-
k4)’ 4u11k3)1/2]( 5 )
In the case of k4 being smaller than thermal grating decay rate, that is, k4 C lo5 s-I ZSl,Zs2, system approaches steady state can greatly exceed k4, as is evident from eq 5. In our experiments, the excitation pulse has a nearly Gaussian temporal profile Z ( t ) = (U/2 (T In 2)’/2to)exp(-tz/4 In 2t02),where U is the energy per unit area in the pulse and to = 67 ns. As the result, the steady-state approximation is valid in our experiments for system where k4 > 1.5 X lo7 s-l in the weak saturation limit. C. Photochemical Change. In the situation where the To population lives longer than the thermal grating decay time constant about 10 ks, that is k4 C l o 5 s-l
