INTRODUCTION
Generally speaking, Gaussian-shaped pulse is produced by a laser in the time domain. However, flat-top pulse is preferred in some application fields such as laser material processing (laser welding and laser boring) (Cao et al., Reference Cao, Uschmann, Zamponi, Kampfer, Fuhrmann, Forster, Holl, Redmer, Toleikis, Tschentscher and Glenzer2007; Godwal et al., Reference Godwal, Taschuk, Lui, Tsui and Fedosejevs2008; Mulser & Schneider, Reference Mulser and Schneider2004), laser clinic medicine (excimer laser myopia therapy (Wieger et al., Reference Wieger, Strassl and Wintner2006), laser offset, detecting array laser radar, laser scanning, optical information processing, storage and record, etc (Laska et al., Reference Laska, Badziak, Boody, Gammino, Jungwirth, Krasa, Krousky, Parys, Pfeifer, Rohlena, Ryc, Skala, Torrisi, Ullschmied and Wolowski2007; Wolowski et al., Reference Wolowski, Badziak, Czarnecka, Parys, Pisarek, Rosinski, Turan and Yerci2007). Until recently, little research has been focused on flat-top pulse in the time domain compared with that in the space domain (Hoffnagle & Jefferson, Reference Hoffnagle and Jefferson2000; Lin & Wang, Reference Lin and Wang2000; Yen et al., Reference Yen, Huang, Liu and Lee1997). Kanabe et al. (Reference Kanabe, Nakatsuka, Kato and Yamanaka1986) has obtained a flat-top waveform in the time domain by a pulse stacking method, which is complex and costly for practical application.
The exploitation of stimulated Brillouin scattering (SBS) for phase conjugation and laser pulse compression has been extensively studied. However, these researches have been focused on the characteristics of the backscattered light rather than the transmitted light (Kong et al., Reference Kong, Lee and Lee2005a, Reference Kong, Lee and Lee2005b, Reference Kong, Yoon, Shin, Beak and Lee2006, Reference Kong, Yoon, Beak, Shin, Lee and Lee2007; Lontano et al., Reference Lontano, Passoni, Riconda, Tikhonchuk and Weber2006; Meister et al., Reference Meister, Riesbeck and Eichler2007; Wang, S.Y., et al., Reference Wang, Lu, Lin, Ding and Jiang2007; Wang, Y.L., et al., Reference Wang, Xu, Zhou, Chu and Fu2007; Yoshida et al., Reference Yoshida, Fujita, Nakatsuka, Ueda and Fujinoki2007; Hasi et al., Reference Hasi, Lu, Li and He2007a, Reference Hasi, Lu, Li, Ba and He2007b, Reference Hasi, Lu, Li and He2007c). When the incident light exceeds the SBS threshold, strong interaction occurs between the pump and the Stokes, resulting in a quick energy transfer from pump to Stokes in very short order. Therefore, optical limiting can be realized by adopting SBS for the transmitted light. Flat-top waveform in the time domain was obtained by double optical limiting based on SBS with pump wavelength at 1064 nm (Lu et al., Reference Lu, Hasi, Gong, Li and He2006), and by single SBS optical limiting with pump wavelength at 532 nm (Hasi et al., Reference Hasi, Lu, Liu, Li, Yin and He2008a). In this paper, a method of generating flat-top waveform in the time domain based on single SBS with pump wavelength at 1064 nm by choosing a medium with a short phonon lifetime is proposed.
The transmitted waveform after SBS process with a pump wavelength at 1064 nm has already been obtained (Lu et al., Reference Lu, Lu and Yang2003). The results demonstrate that the waveform based on SBS optical limiting features a sharp peak followed by a wide platform, which presents disadvantages to practical application of flat-top pulse. The sharp peak in the front of the transmitted waveform results from the relaxing time, which is required during the building of the phonon field. During this time, the pump still keeps high transmissivity and therefore the energy transfer from pump to Stokes is incomplete, thus leading to the appearance of the peak. According to the results shown by Lu et al. (Reference Lu, Lu and Yang2003, Reference Lu, Hasi, Gong, Li and He2006) and Hasi et al. (Reference Hasi, Lu, Liu, Li, Yin and He2008a), using a SBS medium with short phonon lifetime can lead to the advancement of building of an acoustic field and thorough energy transfer from pump to the Stokes, thereby eliminating the peak in front of the transmitted waveform. Since the phonon lifetime is in inverse proportion to the kinematic viscosity, flat-top waveform in the time-domain can be easily obtained by choosing a medium with a large kinematic viscosity.
In this paper, the transmitted waveform based on SBS optical limiting is numerically simulated with a SBS medium having short phonon lifetime. In the experiment performed in the Nd: YAG laser, FC-72, and HT-270, which differ significantly in the phonon lifetime, were used as the SBS media. Both the simulation and experimental results indicate that, when choosing a medium with long phonon lifetime, there is a peak in front and a platform thereafter, while the top is almost a platform when choosing a medium with short phonon lifetime. The generation of flat-top waveform in the time domain based on SBS optical limiting may pave the way for some applications.
THEORY
According to the SBS model given by Lu et al. (Reference Lu, Lu and Yang2003), the transmitted waveforms are numerically simulated when the phonon lifetime is 1.0 ns and 0.1 ns, respectively, as shown in Figure 1. The other parameters in the simulation are as follows: the pump wavelength is 1064 nm, the pump pulse has a repetition of 1 Hz, a pulse width of 15 ns, pump energy of 50 mJ and divergence angle of 0.45 mrad, the cell length is 60 cm, focal length is 10 cm, gain coefficient of medium is 6 cm/GW, and absorption coefficient is 10−3 cm−1.
Fig. 1. The numerical simulation of pulse shape based on SBS. (a) pump pulse, (b) transmitted pulse choosing medium with 1.0 ns phonon lifetime, (c) transmitted pulse choosing medium with 0.1 ns phonon lifetime.
It can be seen from Figure 1 that there is a peak in the front and a platform thereafter when choosing a medium with 1.0 ns phonon lifetime, while the transmitted pulse is almost a platform when the phonon lifetime is 0.1 ns. When the front edge of pump pulse entering the medium, the power is not strong enough to produce SBS, so the front edge is transmitted completely and the transmitted pulse tracks the pump pulse with great fidelity, showing a quasi-Gauss profile in the front edge. When the pump power exceeds the SBS threshold, strong SBS process takes place and the pump energy quickly transfers to the Stokes, therefore the transmitted pulse keeps a platform. In the SBS process, the building of phonon field demands some relaxing time, during which the pump transmits linearly in the medium. Therefore, the peak appears easily when choosing a medium with long relaxing time. The relaxing time is closely related to the phonon lifetime. Short phonon lifetime will lead to a short relaxing time and thus complete energy transfer from pump to Stokes, therefore facilitating the generation of flat-top waveform.
The phonon lifetime can be expressed as follows (Park et al., Reference Park, Lim, Yoshida and Nakatsuka2006):
where λ is the pump wavelength and η is the kinematics viscosity. According to Eq. (1), the phonon lifetime is in inverse proportion to the kinematics viscosity for a fixed pump wavelength. The viscosity varies greatly (more than several or dozens of times) among different liquid media and contributes mostly to the difference in the phonon lifetime. The kinematic viscosity is decided by the relative molecular weight. The medium with a great relative molecular weight is accompanied by a big interaction force between molecules and thus a large kinematic viscosity. A series of perfluoro-compound media with short phonon lifetime and low absorption have been reported (Hasi et al., Reference Hasi, Lu, Gong, Liu, Li and He2008b).
The gain coefficient is proportional to the phonon lifetime, as is expressed by Erokhin et al. (Reference Erokhin, Kovalev and Faizullov1986)
where g, γ, n, c, υ, ρ, and λ are the gain coefficient, electrostriction coefficient, refractive index, light velocity in the vacuum, acoustic velocity, density of the medium and pump wavelength, respectively. It can be seen from Eq. (2) that the medium with short phonon lifetime has small gain coefficient, which can enhance the output energy based on SBS optical limiting. The output energy of SBS optical limiting is decided by system exponential gain coefficient (G = gIL, G is the system exponential gain coefficient, g is the gain coefficient of the medium, L is the effective interaction length, and I is the pump power density) (Boyd & Rzazewski, Reference Boyd and Rzazewski1990). Large system gain coefficient can lead to low output energy of SBS optical limiting. Thus, short phonon lifetime can facilitate the generation of flat-top waveform and enhance the output energy simultaneously.
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 then circular polarized after passing the 1/4 wave plate. The SBS system comprises a generator cell and a focus lens 1. The pump light is focused into the generator cell to produce Stokes light. 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 energy of pump, output light, and Stokes are measured with energy meter ED200. The pulse shape is detected with PIN photodiode, and recorded by digital oscillograph TDS684A.
Fig. 2. Experimental setup.
The experimental parameters are identical to those in the simulation. The parameters of FC-72 and HT-270 are listed in Table 1. Figures 3b and 3C provide the output waveforms of FC-72 and HT-270 in the time domain based on SBS optical limiting. It can be seen from Figure 3 that there is a peak in front and a platform thereafter with FC-72. However, the output pulse waveform is a platform with medium HT-270. These results agree well with the simulations. FC-72 has comparatively long phonon lifetime, so the acoustic field builds slowly and the pump energy transfer is incomplete, leading to the appearance of the peak. However, the phonon lifetime of HT-270 is short and the building of acoustic field advances, therefore the energy transfer is thorough, leading to the appearance of the platform in the waveform.
Fig. 3. Experimental pulse waveforms. (a) pump waveform, (b) transmitted pulse with medium FC-72, (c) transmitted pulse with medium HT-270.
Table 1. The SBS parameters of FC-72 and HT-270 (Park et al., Reference Park, Lim, Yoshida and Nakatsuka2006; Yoshida et al., Reference Yoshida, Kmetik, Fujita, Nakatsuka, Yamanaka and Yoshida1997)
The experimental results have also shown that small peak appears in the front edge for comparatively low pump energy while small peak appears in the back edge for comparatively high pump energy (Hasi et al., Reference Hasi, Lu, Liu, Li, Yin and He2008a). This is because that for low pump energy, when the front edge of pump pulse enters the medium, the power is not strong enough to produce SBS and the front edge is transmitted completely. Therefore, the Stokes pulse interacts with the back edge of the pump pulse, resulting in the appearance of a peak in the front edge. For high pump energy, the base of front edge of pump pulse is strong enough to produce SBS, therefore, the Stokes pulse interacts with the front edge more intensely compared with the back edge of pump pulse, leading to the appearance of a peak in the back edge. Nevertheless, this problem can be solved by altering the focal length of lens: when pump energy is low, a lens with a short focal length can be adopted; correspondingly, a lens with a long focal length can be adopted when pump energy is high. The impact of the focal length on the generation of the flat-top pulse can be explained as follows: when the pump energy is low, high pump power density owing to the short focal length results in the advancement of SBS process, thus eliminating the peak in the front edge and producing a flat-top pulse; when the pump energy is high, low pump power density owing to the long focal length results in the delay of SBS process, thus eliminating the peak in the back and producing a flat-top pulse as well. However, it is impossible to obtain flat-top waveform when choosing a medium with long phonon lifetime, even in the case of higher pump energy than 50 mJ.
CONCLUSIONS
A method of generating flat-top waveform in the time-domain based on SBS choosing a medium with short phonon lifetime is proposed. The building of acoustic field is slow when the medium has long phonon lifetime; therefore the energy transfer of the pump front edge is incomplete and a peak appears before the platform. However, when the phonon lifetime is short, the building of acoustic field advances and the energy transfer becomes thorough; therefore the SBS optical limiting waveform in the time domain is almost a platform. Medium with short phonon lifetime will facilitate the generation of flat-top waveform. The generation of flat-top waveform in the time domain based on SBS optical limiting may have some promising applications.
ACKNOWLEDGEMENTS
This work is supported by National Natural Science Foundation of China (Grant No. 60778019, 10476009, 20771030), the China Postdoctoral Science Foundation (Grant No. 20060390795) and the Program of Excellent Team in Harbin Institute of Technology.
