1. INTRODUCTION
High power laser development is essential for various laser applications like high energy density physics (Hoffmann et al., 2005; Tahir et al., 2004), laboratory astrophysics (Gonzales et al., 2006), and basic issues of inertial fusion. Laser fusion requires very high energy/power output with a high repetition rate over 10 Hz (Atzeni & Meyer-Ter-Vehn, 2004; Nakai & Mima, 2004). However, the laser facilities NHELIX (Schaumann et al., 2005), PHELIX (Neumayer et al., 2005), PALS (Jungwirth, 2005), and the Vulcan Petawatt (Danson et al., 2005) are just some examples of laser systems that have limitations on the output power, and limitations on the repetition rate due to a thermal problem. To resolve the thermal problem in the solid-state laser system, many researchers have developed their own techniques. Among those techniques, the beam combination technique using stimulated Brillouin scattering phase conjugate mirrors (SBS-PCMs) as proposed by Kong et al. (1997, 2001) is the most promising, because the output energy of this laser system can be unlimitedly scaled-up by increasing the number of separate amplifiers. In addition, SBS-PCM gives the phase-conjugated wave (Zel'dovich et al., 1972) that can compensate for any optical distortions occurring in the amplifier chain for the best beam quality. Figure 1 shows the schematic diagram of the new beam combination technique as developed by the authors.
Scalable beam combination system with the wave-front dividing: PC; phase controller, AMP; amplifier, FR; Faraday rotator, WD1 and WD2; wave-front dividers, BE1 and BE2; beam expanders, PBS; polarizing beam splitter, QW; quarter wave plate.
Beam combination technique using SBS-PCM, which is to control the phases of the beams to be combined. SBS-PCM reflects the SBS wave within the random phase. For the phase controlling the beam combination with SBS-PCM, there are several different techniques developed. Among those techniques, the self-phase-controlling SBS-PCMs (SFC-SBS-PCM) as proposed by Kong et al. (2005b, 2005c, 2005d) is the most favorable, since it is applicable to the unlimited number of beams, and is the most simple among the techniques developed. By employing the phase control technique using a weak density modulation, we have stabilized the relative phase difference remarkably to the standard deviation of λ/36(0.028λ). Figure 2 shows the relative phase difference controlled by SFC-SBS-PCM (Lee et al., 2005a).
The relative phase difference selected from 220 interference patterns for the cases of both pump energies of 10 mJ (Ep1 ≅ Ep2 ≅ 10 mJ).
2. EXPERIMENT
Using the self-phase control technique, we have succeeded in controlling the phase of a SBS wave. However, the phase showed a long-term fluctuation due to the density fluctuation by the thermal convection of the liquid SBS medium, which is due to the absorption of the laser energy by the SBS medium.
Figure 3 shows the long-term fluctuation of the output energy and the phase difference of the two-beam combination system for 100 s for the case of Ep1,2 ≅ 10 mJ. Since the beam energy reflected by each SBS cell is almost constant (fluctuation of 1.89% and 1.98%, respectively), we can think that the long-term energy fluctuation is originated from the phase fluctuation by thermal convection of the SBS medium. We have stabilized this fluctuation by actively controlling the feedback mirror that was installed for the self-density modulation.
The long-term fluctuation of the output energy (arbitrary unit) and the phase difference of the two beam combination system without active control for 1000 s for the case of 10 mJ pump beam.
Figure 4 represents the experimental set-up for the long-term phase control of SBS-PCMs. A 1064 nm Nd:YAG oscillator with a bandwidth of ∼120 MHz was used for the pump. The pulse width was 8 ns and the repetition rate was 10 Hz. The output from the oscillator is divided into two beams by a polarizing beam splitter (PBS). Both beams are reflected by each SBS-PCM with the concave mirrors for controlling phase. We have used Fluorinert FC-75 as a SBS medium (Yoshida et al., 1997). The length of the SBS cell was 50 cm and the focal length of the concave mirror was −25 cm. Both reflected beams pass through PBS and are divided into two output signals by a wedge. The output beam passing through the quarter wave plate (QWP), experiences the phase changing by π/2. Therefore, the output energy measured by D1 (ID1) and the output energy with phase changed by π/2 measured by D2 (ID2) give us the following expressions,
where I1 and I2 is the energy of the SBS beam reflected by SBS cell 1 and cell 2, respectively, and Φ is the phase difference between the two SBS beams. Therefore, we can make the phase difference zero by maximizing the output energy ID1 or controlling the output signal ID2 as I1 + I2 using the feedback system. However, the output energy ID1 cannot be used as the feedback signal, since it is impossible to find the sign of the phase variation from the energy variation, cos Φ is the even function. On the other hand, the output energy ID2 can be used as the feedback signal, since the sign of the phase variation can be found from the energy variation, sine is the odd function. Therefore, the output signal with the phase changed by π/2 (ID2) is fed-back to the PZT controlling system of the feedback mirror, for compensating the density variation of the SBS medium.
The experimental setup for the long term phase control of SBS-PCMs: M, mirror; PBS, polarizing beam splitter; FR, Faraday rotator; PM1&PM2, feedback mirror; PZT, piezoelectric transducer; W, wedge; P1&P2, polarizer; QWP, quarter wave plate; D1&D2, detector.
Figure 5 shows the output energy and phase difference of the two SBS beams controlled by this active controlling system. The result shows a 3.21% long-term energy stability and 0.009λ long-term phase stability of the two 10 mJ beam combination system. This system stabilizes the phase controlling system very well for a long time.
Experimental results for active control of the output energy (arbitrary unit) and the phase difference of two SBS beams (10 mJ pump beams).
The waveform of the SBS wave is known to be distorted by the SBS intrinsic process (Shen, 1984). The deformation of the SBS wave can cause the optical breakdown in the optical components, for it causes a temporal spike in the rising edge (Dane et al., 1992). We have found that the deformation is due to the effect of losing a front part of the pumping energy to create the acoustic Brillouin grating for the SBS process. And the authors expected it will be possible to keep the temporal waveform, if the acoustic grating is generated before the main-pulse enters the SBS interaction region by using the “pre-pulse technique.” In this technique, the incident wave is divided into two pulses, the pre- and the main-pulses, and the pre-pulse is sent to the SBS medium before the main-pulse with some delay in time. It has been shown successfully in a previous paper that the main-pulse shape can be well preserved by this method (Kong et al., 2005a).
The scheme of the proposed set-up is presented in Figure 6a. Pockels cell (PC) is used for adjusting the proper ratio of the pre- and the main-pulse energies, by adapting high voltage (HV), and HV applies to the PC for the passing time of the incoming pulse through the PC. The PC is in the off state when the pulse returns back. PBS2 and PBS3 reflect the S-polarization and pass the P-polarization. The incident wave is split into two paths after PBS3, path 1 (pre-pulse) and path 2 (main-pulse). The main-pulse cannot pass through path 1, similarly, pre-pulse cannot pass through path 2, and vice versa. The pre-pulse is initially S-polarized and reflected when it reaches PBS2 after the SBS process, because the PC is in the off state when the pulse returns back. The main-pulse which has initially a P-polarization follows the very similar process as the pre-pulse. So it takes the P-polarization to pass through PBS2. But in this experiment, we did not have the PC available, and the set-up of the experimental scheme as shown in Figure 6b for its alternative. We put HWP2 and the Faraday rotator (FR) (45 degree rotator), instead of the PC in this experiment. Figure 6b produces double pulses corresponding to the pre-pulse and the main-pulse. This problem will be resolved if we employ PC as shown in Figure 6a.
(a) The proposed system for preserving a temporal SBS pulse shape, and (b) the experimental set-up for this experiment: O, Nd3+:YAG Laser Oscillator; P, linear polarizer; HWPs, half wave plates; PBSs, polarizing beam splitters; ISO, Faraday isolator; FR, Faraday rotator; QWPs, quarter wave plates; PC, Pockels cell; Ms, full mirrors; W, wedge; L, convex lens (f = 15 cm); PDs, photo diodes; SBS cell (FC-75, 30 cm long).
Let us define Emain, Epre, and Tdelay as the energies of the main- and the pre-pulses, and the delay in time between the pre- and the main-pulses, respectively. Figure 7a shows the incident wave, and Figures 7b, 7c, and 7e correspond to the waveforms for delay times of 3 ns, 5 ns, 7 ns, and 10 ns, respectively, with the fixed values of Emain = 10 mJ and Epre = 5 mJ. For Tdelay = 5 ns, the waveform preservation is the best among these conditions.
The waveforms of the reflected wave for the delay times: (a) Incident wave, (b) 3 ns, (c) 5 ns, (d) 7 ns, and (e) 10 ns.
It has been shown that the pre-pulse technique is quite powerful for preserving the SBS waves. This system can be applied to the beam combination laser system using SBS-PCM.
It is a well-known fact that the pulse width should be longer than the phonon life-time of the SBS medium for the SBS. In addition, we propose a new idea for the fast ignition laser operating at the high repetition rate over 10 Hz by this technique. This self-phase controlling technique can be applied to the ultra-fast pulsed laser system whose pulse width is much lower than the phonon life-time of the SBS medium, by (1) applying this technique in the chirping stage in the OPCPA stage or (2) applying the pre-pulse technique.
For the first method, we can apply this technique in the chirping stage of OPCPA. For the single-mode pumping regime of the SBS (Lee et al., 2005b), the line-width of the pumping laser, Δν, is shorter than the Brillouin gain width of the SBS medium, Γ. Let the threshold of the SBS of the medium be Eth. If the line-width of the chirped pulse is Δνl, we can consider the laser spectrum with a bandwidth of Γ as a single mode composition. Then, the energy of this composition should be larger than Eth for SBS. Therefore, the total pumping energy should be larger than Eth (Δνl /Γ), which is the threshold of the chirped pulse. For the FC-75 SBS medium, Eth = 3 mJ and Γ = 300 MHz. Assuming the spectral width of the chirped pulse as Δλ ∼ 10 nm at λ = 1 μm for the pulse-width (τl = 300 fs), then Δνl ∼ 3 × 1012 Hz . The threshold of this chirped pulse is 30 J. For the reflectivity of 50%, we need 100 J pumping energy. For the reflectivity of 80%, we need 500 J pumping energy. For the multi-mode regime (Δν > Γ), we can expect the threshold energy to be 3 mJ, and the energy for the reflectivity of 75% to be 30 mJ.
For the pre-pulse technique (Kong et al., 2005a), the pre-pulse can generate the Brillouin grating, the main-pulse can be reflected by this pre-existing acoustic grating, and can give the SBS wave. We can apply this idea to the ultra-short pulse laser system also. The pre-pulse might generate the acoustic grating during the phonon life-time after the excitation occurred, even if it is much shorter than the phonon life-time. Therefore, we can expect that the main-pulse can interact with the pre-existing grating for the SBS process, if we inject the pre-pulse to generate the acoustic grating (Brillouin grating) prior to the main-pulse.
3. CONCLUSION
Using the self-phase control technique, we have succeeded in stabilizing the phases of the SBS waves remarkably to the standard deviation of λ/36 (0.028λ). However, SBS phase shows a severe long-term fluctuation due to the density fluctuation by the thermal convection of the liquid SBS medium. Therefore, we stabilized this fluctuation by the active controlling system of the feedback mirror for compensating the density variation of the SBS medium. This system stabilizes the phase controlling system very well for a long period of time at the standard deviation of 0.009λ. This long-term stabilization technique will be useful for the ultra-high power/energy laser operating at high repetition rate, and can be realized for the laser fusion energy. The pre-pulse technique for preserving the pulse shape is very important for the beam combination system that has serial SBS-PCMs, for the rising edge of the SBS wave becomes steeper and steeper every time it experience the SBS reflection. This steep rising edge is dangerous for the optical damage, and this pulse preserving is very important. Together with the pre-pulse technique, this self-phase controlling system can be applied to the real laser fusion driver.
In addition, this self-phase controlling technique can be applied to the ultra-fast pulsed laser system whose pulse width is much lower than the phonon life-time of the SBS medium, by (1) applying this technique in the chirping stage in the OPCPA stage or (2) applying the pre-pulse technique. In the chirping stage, the pulse width should be longer than the phonon life-time of the SBS medium for this technique. For the pre-pulse technique, the pre-pulse can generate the Brillouin grating and the main-pulse can have the SBS process by this pre-existing acoustic grating and can give the SBS wave.
