Determination of the Triplet State Lifetime of C 60 / Toluene Solution and C 60 Thin Films by Pump-probe Method

Excited state lifetimes of C 60 /toluene solution and C 60 films macromolecular were measured by pump-probe method. Relation between optical switching effect of material and pulse width of pumping field is briefly described. It is found that the faster switching speed of light is, the triplet state lifetime is shorter. A He-Ne laser, as a probe, passed through the sample in the pump-probe experiment. All-optical switching effect was realized. Changing the optical power of the pumping field, switching response of the sample and modulation depth were investigated. In certain experimental conditions, relation between transmission through the sample and response were measured by an oscilloscope. Triple state lifetime of the molecule is speculated. The result showed that C 60 /toluene solution and C 60 film have a fast response time. They would be utilized in some applications, such as optical switches, photonic devices.


Introduction
The nonlinearities of C 60 have been paid considerable attention for their promising use in the applications of photonic devices due to its unique opto-electronic properties, its reverse saturable absorption phenomenon was found by Guiliano and Hess [1].In recent years, the potential applications of RSA materials in optical limiting and switching have attracted more interests because of the growing needs for laser protection [2].RSA behaviours have been successively investigated in numerous materials.
The C 60 shows a strong and broad spectrum absorption induced in the visible domain.As an view of application, this makes C 60 an interesting candidate for optical power limiting purposes [3][4][5][6][7].On the other hand there exist a multitude of studies concerning the relaxation dynamics following a photo excitation of C 60 in liquid solutions and in thin films.In this paper, we compared with functionalized fullerene solutions, scattering contributions to the observed limiting performance, and possible limiting in the near infrared region, we got a clear picture of optical switching properties of liquid C 60 /toluene solution and solid C 60 thin films.

Experiment and Theory
The mechanism of optical switch of excited state absorption is that the molecules at excited states pumped by laser strongly absorbs photons at some wavelength, while the ground state absorption is very weak.So when the pump field stimulated the medium, the probe light is strongly absorbed, the output is in low state (in the closed state); on the contrary, when no pump exists, molecules in the ground state, probe light is not absorbed (or little absorbed), output in highly excited state (the switch turned on).
The experimental arrangement is shown in Figure 1.A doubled-frequency Nd: YAG laser with repetition rate of 10 Hz, at 532 nm, is employed to provide exciting pulse, and its pulse width is 10 ns.The laser beam first though the beam splitters 1 (BS1), part of the beam splitted was detected by detector D 1 , which is used as the trigger pulse for the oscilloscopes.The other part of the laser, which is used as the pump beam, passed through the beam splitters 2 (BS2), was focused on the sample by a lens (f = 300 mm).A He-Ne laser at 632.8 nm is used as the probe light.The probe beam first through the sam-ple, then focused by the lens, splitted by BS2.And at last the probe beam is detected by D 2 , then is recorded on a digital oscilloscope.
Figure 2 is the energy level diagram of C 60 molecules in the laser irradiation, the ground state molecule absorbs photon and transits to the first singlet excited state vibrational level S 1 , then rapidly relaxes through the intersystem crossing transition to the first excited triplet state T 1 , molecules of the excited state T 1 absorbs photon can transition to a higher excited level T n , then return to the energy levels of T 1 .Molecules of the level T 1 may have a longer lifetime, and can be back to the ground state in the form of non-radiative transition.
Considering the role of the pump light, the rate equations take the following: Boundary conditions: where N 0 , N S and N T represent the number densities of states S 0 , S 1 and T 1 , respectively.N is the total number density of the molecules,  L is the pump frequency, f(t) = exp[-c(t/t)] is described time function of pump pulse shape (c = 2) .Through the medium of the probe light can be expressed as:  ( ) ( ) ( ) Boundary conditions: ( , 0) where  T (p) is the absorption cross sections for the probe light of T 1 state.I po is the optical power density of incident to the sample surface for the detection.
The change of population along with time in the first triplet state are described by solving Equations ( 1) - (5).We obtain simulated transmission as shown in Figure 3.

Results and Discussion
The numerical result for the case of solutions is in good agreement with published results summarized in Table 1.
The data for  i of the C 60 /toluene is taken from Ref. [8][9][10],  S 1 and  T 1 is the S 1 and T 1 state absorption cross sections.The higher excited states S n and T n are assumed to have a very short lifetime [11][12][13] compared to our pulse duration, such that they can always be considered to be empty.Electrons relax back to the S 1 state almost immediately and the first excited triplet state T 1 is populated via intersystem crossing with a time constant  ST .The lifetime of the T 1 state  To of the investigated compounds have been reported previously and ranged between100 ns and 300 s.
In the pumping processing, the pumping field excites molecules at ground state to the excited states.The absorption of excited state leads to the decrease of probe field energy.When molecule returns to ground state from excited states.The absorption at excited states dispears.The probing power resumes the initial value.The time corresponding this process is considered as the lifetime of the excited state, which is equal to the closing time.We implemented similar measurement on C 60 toluene solutions in thin quartz cells.The result of the pump-probe experiment on C 60 /toluene solutions is shown in Figure 3(a).It is shown that the triplet state lifetime in our samples is 0.28 s.The parameters of interest are summarized in Table 1.The experimental results agree well with theoretical analyses.The output of the digital oscilloscope in our pump-probe experiment for a C 60 thin film is shown in Figure 3(b).The results show that the triplet state lifetime in the samples is 0.98 s.The numerical value of lifetime is between the two values of 100ns or 300 s [14].One difference in our experimental conditions is the fact that we used film as toluene solvent, which leading to a longer lifetime of these states.Under identical conditions, increasing the concentration and the thickness of the sample, the switching time is not changed and the contrast ratio is increased.These are essential characteristics of an RSA process involving a long-lived excited state.Our experimental method is well adapted to the determination of these important parameters by a purely optical method.

Conclusions
We studied the triplet state lifetime of C 60 /toluene solution and C 60 thin films.From the experimental results we conclude following conclusion: The lifetime of the excited state is about 0.28 s and 0.98 s of C 60 /toluene solution and C 60 thin films, respectively.The theoretical fits are in good agreement with experimental results.This is of advantage for RSA materials used as optical limiting.The absorption cross section of the excited state is larger than that of the ground state at both 532 nm and 632.8 nm.Furthermore, we showed with pump-probe experiments, that the T 1 state of C 60 decays exponentially with a time constant which depends on the vibrational excitation energy of the molecule.This also allowed us to find the unambiguous assignment of the number of absorbed photons associated with a specific lifetime.

Figure 2 .
Figure 2. The five-energy-level diagram showing optical excitation.

Figure 3 .
Figure 3. Transmission changes during a pump-probe experiment for a C 60 thin film.