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Excitation Density (10 cm )

Fig. 13.41. Picosecond photoinduced absorption spectra of Cm film at t = 0 (5 ps resolution) and t = 2 ns (note change of scale by a factor of 5); the lines through the data points are to guide the eye. The inset shows the optical density (OD) spectrum and the photoluminescence (PL) emission band of the film. Horizontal arrows in the inset indicate energy separations between initial (PA,) and final (PA2) states in the photoinduced absorption spectrum [13.64].

Fig. 13.41. Picosecond photoinduced absorption spectra of Cm film at t = 0 (5 ps resolution) and t = 2 ns (note change of scale by a factor of 5); the lines through the data points are to guide the eye. The inset shows the optical density (OD) spectrum and the photoluminescence (PL) emission band of the film. Horizontal arrows in the inset indicate energy separations between initial (PA,) and final (PA2) states in the photoinduced absorption spectrum [13.64].

the induced photoabsorption band at 0.8 eV (see Fig. 13.41) was attributed to a transition from the singlet Sj exciton state to the LUMO+1 derived band, which is consistent with a tlg — tlu separation of ~1 eV that has been observed in many experiments (see §13.3.2). The broad maximum in the induced photoabsorption band at 1.8 eV corresponds to the next allowed optical transition to the LUMO+2 derived band, and this transition is much stronger than the transition to the LUMO+1 level [see Fig. 13.18(a)].

By identifying the long-lived excitations in the /lis range with triplet excitons and noting their strong temperature dependence, the two induced photoabsorption features with peaks at 1.1 and 1.8 eV are identified with excitations from the lowest triplet state to higher-lying neutral triplet states. Regarding the short-lived excitations, the two features at 0.8 and 2.0 eV are identified with charge polaron excitations because of their strong dependence on rf modulation frequency in ODMR experiments using both absorption [13.64] and emission [13.63] optical processes. Independent evidence for polaron formation is found in photoinduced EPR studies (see §16.2.3).

A few pump-probe studies of the electron dynamics of alkali metal-doped C60 have also been carried out [13.46,189]. The earliest experiments were reported for an uncharacterized RbxC60 film and yielded a sub-

picosecond relaxation time (0.6 ps) which is independent of temperature (10 < T < 300 K) and of laser pump intensity (<40 mJ/cm2, for 80 fs pulses at 620 nm or 2.0 eV) [13.46]. Subsequent pump-probe studies on well-characterized K3C60 and Rb3C60 films revealed the same relaxation time t for both materials, but r was found to be an order of magnitude faster in the alkali metal-doped compounds (~0.2 ps) relative to C60 for 50 fs pulses at 625 nm (1.98 eV), using very low power levels (~20 /iJ/cm2) [13.189], These fast relaxation times are consistent with the suppression of exciton behavior through metallic screening in the M3C60 compounds. By populating the excited states which are dipole-coupled to lower lying states, a more rapid return of the excited system to lower energy configurations can be realized.

13.7.2. Nonlinear Absorption Effects

Because of the high derealization of electrons on the shell of fullerenes and the relatively high isolation between molecules, fullerene-based materials are expected to exhibit large nonlinear optical effects such as third-order nonlinear optical susceptibility, comparable to those for v-conjugated organic polymers [13.190], Since the nonlinear polarizability for polymers depends on the fourth power of the length of the polymer chain, C70 would be expected to exhibit an even larger nonlinear response than C60 [13.191], in agreement with experiment. These nonlinear effects have been studied by degenerate four-wave mixing (DFWM) [13.191-195], third harmonic generation [13.196-199], and electric field-induced second harmonic generation [13.200], both in solution and in high-quality films. Since third harmonic generation and electric field-induced second harmonic generation are usually carried out above the absorption threshold, these techniques tend to be more surface sensitive because of the shorter optical skin depth. Therefore, more emphasis has been given in the literature to nonlinear studies using the DFWM technique.

In the DFWM experiment (see Fig. 20.4 for the geometry of the four light waves in the DFWM experiment), a polarization P, is induced in the sample by the interaction between three light waves and the electrons in the medium through the relation

where two light waves with electric field amplitudes Ey and E^ are incident at the same region on the sample and have equal and opposite wave vectors (see Fig. 20.4). The waves E; and E¿. from, for example, a He-Ne laser set up an interference grating which interacts with a third light beam E* coming from the back side of a transparent sample as shown in Fig. 20.4. A fourth beam (also shown in Fig. 20.4), resulting from this interaction with wave vector equal and opposite to that of E*, is detected, and the polarization vector P, in Eq. (13.20) corresponds to the fourth signal light beam. The tensor, which relates P, and the three interacting light waves E , Ea, and E*, is the third-order nonlinear susceptibility x)ju which is a fourth-rank tensor and the subscripts ijkl refer to the components of the vectors P,, Ej, Et, and Ej, each having independent x,y,z components. It can be shown that DFWM experiments measure the magnitude of the complex third-order nonlinear susceptibility xfjli* so that additional measurements are needed to determine the real and imaginary parts of xfjln as discussed below.

In most of the DFWM experiments that have been done thus far on fullerenes (both in solution and in films), the polarizations of all four beams have been the same, so that most of the measurements relate to the tensor component x^xx- A few measurements of x?yyx have also been made, when the pump and probe beams were cross polarized [13.195]. The cubic dependence of the DFWM signal on incident laser intensity verifies the third-order nonlinearity probed in the DFWM experiment as shown in Fig. 13.42. However, a wide range of magnitudes have been reported in the literature for Xxxxx, perhaps due to the sensitivity of this nonlinear coefficient to the presence of oxygen and the magnitude of the light intensity.

A frequently used wavelength for DFWM experiments in C60 and C70 has been 1.064 /im, where the optical absorption is negligibly small, and where resonant enhancement associated with a two-photon process may occur [13.191-194,201], A wide range of pulse widths (from the ns to fs range) have been used for nonlinear optics measurements, and the results obtained may be sensitive to the pulse widths because the contributions from the excited molecules become increasingly important as the pulse width increases.

Values of x^xxx are sensitive to laser excitation intensity and to pulse width. One estimate for the value of x'xxxx for C60 at 1.064 /¿m is ~60 times greater than for benzene for which xfxxx = 8.3 x 10~14 esu when each is normalized to the number of molecules [13.191,195]. When normalized to the number of carbon atoms per molecule, the magnitude for x(xxxx per carbon atom is within an order of magnitude equal to that for benzene. Evidence for a fifth-order nonlinear response has also been reported at higher laser excitation intensities for both C60 [13.187] and C70 (see Fig. 13.42) [13.195], The two-photon absorption, which is the dominant absorption process at 1.064 /¿m, is believed to be responsible for forming a two-photon excited-

Fig. 13.42. Diffracted beam intensity /4 in a 16.3 /¿m thick Cjq film as a function of the intensity of the three other beams (/i/2/3)1/3 measured in a degenerate four-wave mixing (DFWM) experiment. The data are presented on a log-log plot. All four beams /,, /2, /3, and /4 are polarized in the x direction. Solid and dashed lines refer to the cubic and fifth-order components of the signal intensity, respectively [13.195].

Fig. 13.42. Diffracted beam intensity /4 in a 16.3 /¿m thick Cjq film as a function of the intensity of the three other beams (/i/2/3)1/3 measured in a degenerate four-wave mixing (DFWM) experiment. The data are presented on a log-log plot. All four beams /,, /2, /3, and /4 are polarized in the x direction. Solid and dashed lines refer to the cubic and fifth-order components of the signal intensity, respectively [13.195].

INTENSITY (W/cm-)

state grating (see Fig. 20.4), thereby giving rise to a fifth-order contribution to the nonlinear response [13.195].

Increasing the photon energy into a regime of greater linear optical absorption leads to an enhanced nonlinear coefficient, as, for example, from XxL ~ 7 x 10"12 esu at 1064 nm (1.16 ev) to ~ 82 x 10 "12 esu at 675 nm (1.83 eV) to x?L ~ 380 x 10"12 esu at 597 nm (2.08 eV) [13.187], Although the reported magnitudes of \xxxx differ considerably from one group to another, there is general agreement regarding the dependence of x^xx on laser excitation frequency above the absorption edge [13.185,202], The variation in the magnitudes for xfxxx in the literature is large for both C60 and C70, with the variation of Xxxxx for similar nominal samples so large that it is difficult to distinguish between values of x(xxxx for fullerenes in solution or in films. Laser-induced phonon generation in DFWM experiments on Qo and C70 dissolved in toluene has also been reported for laser excitation at 532 nm using 20 ps pulses [13.202].

The linear and nonlinear optical parameters of C60 and C70 films at 1.064 fim have been compared. As shown in Table 13.10, an increase in linear absorption coefficient a is found with increasing fullerene mass, and this can be explained by the more stringent selection rules for dipole forbidden transitions at the absorption edge for the highest-

Table 13.10

Selected values of nonlinear optical coefficients for Qo and C70" [13.195,203],

Coefficient Cjo C70

"Here a and /3 are, respectively, the linear and nonlinear absorption coefficients and is the tensor which relates to the third-order nonlinear susceptibility. All data pertain to the laser wavelength of 1.064 /u.m.

symmetry C^ molecules. An increase is also found in the two-photon absorption coefficient /3 and in the nonlinear susceptibility Xxxxx for C70 relative to Q„ as shown in Table 13.10 [13.195,203], although similar values for \*yy* have been reported based on DFWM experiments [13.195],

From measurements of the two-photon absorption coefficient f3 and use of the relation [13.204]

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