INTRODUCTION
Stimulated Brillouin scattering (SBS) has been regarded as an effective way to recover beam front and can be exploited to improve beam quality. The SBS phase conjugation exhibits several advantages in terms of small frequency shift, simple configuration, high fidelity, and high energy reflectivity. Therefore, it has been a focus of theoretical and experimental investigation during the past several decades (Kong et al., Reference Kong, Yoon, Beak, Shin, Lee and Lee2007; Yoshida et al., Reference Yoshida, Fujita, Nakatsuka, Ueda and Fujinoki2007; Ostermeyer et al., Reference Ostermeyer, Kong, Kovalev, Harrison and Fotiadi2008; Bai et al., Reference Bai, Shi, Ouyang, Chen, Gong, Jing, Liu and Liu2008; Grofts et al., Reference Grofts, Damzen and Lamb1991; Wang et al., Reference Wang, Lu, Lin, Ding and Jiang2007, Reference Wang, Lu, He, Zheng and Zhao2009; Hasi et al., Reference Hasi, Lu, Li and He2007). A great deal of research has demonstrated medium is a crucial factor for improving the SBS performance (Yoshida et al., Reference Yoshida, Kmetik, Fujita, Nakatsuka, Yamanaka and Yoshida1997; Hasi et al., Reference Hasi, Lu, Gong, Liu, Li and He2008a; Park et al., Reference Park, Lim, Yoshida and Nakatsuka2006; Chalus & Diels, Reference Chalus and Diels2007; Gong et al., Reference Gong, Hasi, Lu, Dong, Lin, He, Zhao and Fan2009). In the previous investigations, SBS phase conjugation experiments are usually carried out in room temperature and the effect induced by temperature change is seldom considered. In reality, the medium temperature may be changed due to the absorption of pump light with a high power and repetition rate. Therefore, investigation on the effect of medium temperature upon SBS and SBS optical limiting is a meaningful issue (Hasi et al., Reference Hasi, Gong, Lu, Lin, He and Fan2008b, Reference Hasi, Lu, Gong, Li, Lin and He2008c).
In this paper, the effect of medium temperature upon characteristic of SBS and SBS optical limiting is investigated. The physical mechanism behind is analyzed theoretically and experimentally verified in Continuum's Nd: YAG Q-switched laser system using FC-72 as the SBS medium. The temperature affects the electrostrictive coefficient, refractive index, density and acoustic velocity of the medium weakly. In contrast, the kinematic viscosity, which is inversely proportional to the temperature, is related to gain coefficient and phonon lifetime, and thus greatly affects the SBS characteristics. Therefore, in the low temperature, the kinematic viscosity is usually high, which can lead to a small gain coefficient, and a short phonon lifetime. Therefore, the SBS characteristic can be changed by controlling the temperature to a great extent.
THEORY
The gain coefficient of medium can be expressed by (Park et al., Reference Park, Lim, Yoshida and Nakatsuka2006; Erokhin et al., Reference Erokhin, Kovalev and Faïzullov1986; Pohl & Kaiser, Reference Pohl and Kaiser1970)
where g is the gain coefficient, n is the refractive index, γ is the electrostriction coefficient, which is related to n by γ = (n 2−1)(n 2 + 2)/3, τ is the phonon lifetime, c is the light velocity in the vacuum, υ is the acoustic velocity, ρ is the density and λ is the wavelength of incident light.
The phonon lifetime τ of medium can be expressed by (Park et al., Reference Park, Lim, Yoshida and Nakatsuka2006; Erokhin et al., Reference Erokhin, Kovalev and Faïzullov1986)
where η denotes the kinematic viscosity. Eq. (2) shows that when the phonon lifetime τ is inversely proportional to the kinematic viscosity η.
Substituting Eq. (2) into Eq. (1), the gain coefficient g can be related to kinematic viscosity η by:
Eq. (3) shows that the gain coefficient is also inversely proportional to kinematic viscosity.
The temperature change has a little effect on the refractive index, density, and acoustic velocity. However, for the kinematic viscosity, it varies greatly with the temperature (Weaver, Patent (IPC8 Class: AF21V2900FI); Lagemann et al., Reference Lagemann, Woolf, Evans and Underwood1948; 3M Specialty Materials, 2000; Grassi & Testi, Reference Grassi and Testi2008), as shown in Figure 1.
Fig. 1. The kinematic viscosity of FC-72 versus medium temperature (3M Specialty Materials, 2000).
Table 1 lists the density and kinematic viscosity of SBS medium perfluoro-compound at 25°C and −54°C, respectively. The density of FC-72 increases from 1.68 g/cm3 at 25°C to 1.90 g/cm3 at −54°C, and the relative change is only 13%; however, the kinematic viscosity increases from 0.4 cSt at 25°C to 1.9 cSt at −54°C (3M Electronics Markets Materials Division, 2003).
Table 1. The density and kinematic viscosity of SBS medium at different temperature
Since the gain coefficient and phonon lifetime are both related to the kinematic viscosity, the temperature change will greatly affect the two parameters. In the low temperature, the gain coefficient and phonon lifetime are small. Increasing the temperature will lead to the increase in the gain coefficient and phonon lifetime.
EXPERIMENT
The experimental setup is shown in Figure 2. Continuum's Nd: YAG Q-switched laser outputs single mode s-polarized light with line-width 90 MHz, which becomes p-polarized after passing the 1/2 wave plate, and then circular polarized after passing the 1/4 wave plate. The SBS system comprises a generator cell and a focus lens L1 (f = 30 cm). The pump light is focused into a generator cell to produce Stokes light. Polarizer P together with a 1/4 wave plate forms a light isolator, preventing the backward SBS light from entering YAG oscillator. The Stokes light becomes s-polarized after passing the 1/4 wave plate, and is reflected by polarizer P. The pump energy can be adjusted through a 1/2 wave plate. The energy of pump pulse, Stokes pulse, and transmitted pulse are measured with energy meter OPHIR. The pulse shape is detected with PIN photodiode, and recorded with digital oscilloscope TDS684A.
Fig. 2. Experimental setup.
The output wavelength of Continuum's Nd: YAG Q-switched laser is 1064 nm, with a repetition rate of 1 Hz, pulse width 8 ns, and divergence angle 0.45 mrad. FC-72 is adopted as the SBS medium. The medium temperature is altered by resistance heating films and semiconductor-refrigerating chips. Table 2 lists the parameters of some SBS media. In order to eliminate the water droplet formed on the cell window plate due to the temperature difference between air and medium at low temperature, SBS cell with double window plates is designed, as shown in Figure 3. The interspace between the two window plates is vacuum-pumped; therefore no water droplet can be formed while the light can propagate freely.
Fig. 3. SBS cell with double window plates, the cell length is 60 cm and inside diameter is 5 cm.
Table 2. The SBS parameters of some media at room temperature
Figure 4 provides the dependence of SBS energy reflectivity on the medium temperature for fixed pump energy. The reflectivity scales is almost linearly with the temperature. This is because small kinematic viscosity due to a high temperature can lead to a large gain coefficient, thus enhancing the energy coupling efficiency between the pump and Stokes (Boyd & Rzazewski, Reference Boyd and Rzazewski1990). Therefore, a proper choose of temperature increase can lead to improved SBS energy reflectivity. For the output energy of SBS optical limiting, it will turn high at a low temperature (Hasi et al., Reference Hasi, Lu, Fu, Lu, Gong, Lin and He2009).
Fig. 4. The dependence of SBS reflectivity on medium temperature as pump energy fixed at 40 mJ.
Figure 5 shows the transmitted waveforms of SBS optical limiting at different temperatures. The top of the transmitted pulse is almost a platform at 8°C, while a peak appeared at 15°C. This can be explained as follows: at a high temperature, kinematic viscosity is small and leads to a long phonon lifetime; thus the energy transfer is incomplete and the peak appears. In contrast, at a low temperature, the phonon lifetime is comparatively short and the complete energy transfer can lead to the generation of flat-top waveform (Hasi et al., Reference Hasi, Lu, Liu, Li, Yin and He2008d). Therefore, a low temperature is preferred to be chose for the generation of flat-top pulse in time domain.
Fig. 5. (a) Pump waveform and transmitted waveforms of SBS at different temperature (b) 8°C, and (c) 15°C, respectively.
CONCLUSIONS
The effect of medium temperature upon characteristic of SBS and SBS optical limiting is investigated. The physical mechanism behind is analyzed theoretically and experimentally verified in Continuum's Nd: YAG Q-switched laser system using FC-72 as the SBS medium. The temperature affects the electrostrictive coefficient, refractive index, density and acoustic velocity of the medium weakly. In contrast, the kinematic viscosity, which is inversely proportional to the temperature, is related to gain coefficient and phonon lifetime, and thus greatly affects the SBS characteristics. Therefore, in the low temperature, the kinematic viscosity is usually high, which can lead to a small gain coefficient and a short phonon lifetime. Therefore, the SBS characteristic can be changed by controlling the temperature to a great extent.
ACKNOWLEDGEMENTS
This work is supported by National Natural Science Foundation of China (Grant Nos. 60778019, 60878005), the Program for New Century Excellent Talents in University (Grant No. NCET-08-0173), and the Program of Excellent Team in Harbin Institute of Technology.
