THEORY

In order to improve the optical limiting performance based on SBS, the SBS output is further optically limited by a suspension with a lower threshold. We first define two parameters to characterize the SBS optical limiting: (1) the input energy threshold, which is defined to be the energy value above which the output energy does not increase linearly with input energy. (2) the clamped output energy, which is defined to be the output energy at which the input energy is just above the input energy threshold (Vincent, Reference Vincent2001; Mansour et al., Reference Mansour, Soileau and Stryland1992). In the case of a low pump energy, only the SBS optical limiting works. However, as the pump energy increases, the suspension limiting process can be activated if the transmitted power of SBS exceeds the threshold of carbon nanotube/HT-270 optical limiting. Therefore, this hybrid optical limiting approach has an improved performance compared with that based on single SBS in terms of the output energy.

The input energy threshold of SBS optical limiting is determined by the system's exponential gain coefficient G, which is denoted by (Boyd & Rzazewski, Reference Boyd and Rzazewski1990):

(1)

where g is the Brillouin gain coefficient, I is the input power density, and L is the effective interaction length. The system exponential gain coefficient G can be controlled by adjusting g, I, and L. The value of g can be changed by choosing a different medium, while I and L can be altered by adopting lens with different focal lengths. Therefore, the input energy threshold of SBS optical limiting is controllable. If a high threshold of SBS optical limiting is preferred, a medium with small gain coefficient and lens with a long focal length can be utilized. Whereas, a medium with large gain coefficient and lens with a short focal length can be adopted in order to decrease the input energy threshold. So the threshold of SBS can be kept lower than that of suspension.

The carbon nanotube, which rolled up like a hollow cylinder, consists of multiple layers of grapheme sheets. The structure of the carbon nanotube is either a single-wall or a multi-wall depending on the number of the grapheme sheet. The carbon nanotube has been recognized as a good material for broadband optical limiting (Vivien et al., Reference Vivien, Anglaret, Riehl, Hache, Bacou, Andrieux, Lafonta, Journet, Goze, Brunet and Bernier2000; Sun et al., Reference Sun, Yu, Xu, Hor and Ji1998; Chen et al., Reference Chen, Wu, Sun, Lin, Ji and Tan1999; Zhang et al., Reference Zhang, Zhang, Yuan, Sun, Xu and Zhu2005a). The optical limiting property of a carbon nanotube mainly results from its nonlinear scattering during which the laser pulse leads to vaporization and ionization of the carbon nanotube and the generation of the microplasma. The microplasma strongly scatters the incident light, leading to a decrease in the transmitted light energy. At the same time, the carbon nanotube transfers energy to the surrounding liquid and leads to the formation of micron-scale bubble, which in return scatters the incident light and thus further enhances the performance of optical limiting (Durand & Grolier-Mazza, Reference Durand and Grolier-Mazza1998; Zhou et al., Reference Zhou, Tian and Wu2007). The threshold of the suspension can be controlled by adjusting the concentration and focal length of the lens (Luo et al., Reference Luo, Wang, Zhang, Luo and Liu2006). If a high input energy threshold of suspension optical limiting is preferred, a medium with low concentration and lens with a long focal length can be utilized. In contrast, a medium with high concentration and lens with a short focal length can be adopted in order to decrease the input energy threshold.

According to the SBS optical limiting model and the carbon nanotube/HT-270 nonlinear absorption model given (Lu et al., Reference Lu, Lu and Yang2003; Zhang et al., Reference Zhang, Niu, He and Yu2005b), we numerically simulate the curves of output energy of optical limiting based on single SBS and hybrid optical limiting approach and the simulation results are shown in Figure 1. The parameters used in the simulation are as follows: the incident wavelength is 532 nm with a repetition of 1 Hz; the pulse duration is 8 ns with a divergence angle of 0.45 mrad. The medium of the SBS cell is FC-72. The SBS cell length is 40 cm and the focal length of the lens for it is 15 cm. The SBS parameters of media FC-72 and HT-270 are listed in Table 1 (Yoshida et al., Reference Yoshida, Kmetik, Fujita, Nakatsuka, Yamanaka and Yoshida1997; Hasi et al., Reference Hasi, Lu, Gong, Liu, Li and He2008d). The cuvette filled with suspension has a length of 3 mm and the focal lengths of lens for it is 20 cm. When the pump energy is low, output energy of optical limiting based on hybrid optical limiting approach shows similar performance with that based on single SBS. However, when the pump energy is high and the suspension optical limiting works, the output energy based on hybrid optical limiting approach shows nearly a plateau, demonstrating much better the optical limiting performance.

Fig. 1. The simulation result of the dependence of output energy on the input energy based on single SBS optical limiting and hybrid optical limiting.

Table 1. SBS parameters of FC-72 and HT-270

EXPERIMENT

The experimental setup is shown in Figure 2. The Continuum's Nd: YAG seed-injected laser outputs s-polarized light, which becomes p-polarized after passing the 1/2 wave plate and circular polarized after passing the 1/4 wave plate and then injected into the SBS cell. The SBS system is composed of lens 1 and SBS cell. A polarizer P together with a 1/4 wave plate forms a light isolator, preventing backward SBS light from entering the YAG oscillator. The Stokes light becomes s-polarized after passing the 1/4 wave plate, and is reflected by polarizer P. The divergence beam after the SBS optical limiting becomes parallel after passing the lens 2, and then is focused into the cuvette filled with suspension by the lens 3. The divergence beam after the cuvette becomes parallel after passing the lens 4. The pump pulse energy is altered by adjusting the 1/2 wave plate in the experiment. The energies of incident and transmitted pulse, and Stokes pulse are measured with energy meter OPHIR. Waveforms are detected by PIN photodiode and recorded by oscilloscope TDS684.

Fig. 2. Experimental setup.

The procedure in preparing the carbon nanotube/HT-270 suspension is as follows: first, 20 mg single-wall carbon nanotube is mixed with 50 ml HT-270; second, the mixture is oscillated for 24 h in the ultrasonic oscillator; finally the mixture is filtered by a filter with an aperture of 1.2 µm (Hasi et al., Reference Hasi, Lu, He, Wang and Liu2004). Figure 3 gives the experimental curves of output energy versus input energy based on SBS optical limiting and hybrid optical limiting, which agree well with the simulation results. It can be seen that only the SBS optical limiting works in the case of a low pump energy. However, as the pump energy increases, the suspension limiting process can be activated. Therefore, the output energy based on hybrid optical limiting shows much better performance compared with that based on single SBS.

Fig. 3. The dependence of output energy on the input power density based on single SBS optical limiting and hybrid optical limiting.