1. INTRODUCTION
For achieving a high power laser with a repetition rate over 10 Hz,
which is required for a laser fusion driver, several methods have been
widely investigated by many researchers such as a beam combination
technique, a diode pumped laser system with gas cooling, an electron beam
pumped gas laser, and a large sized ceramic Nd: YAG (Hogan et al., 1995; Kong
et al., 1997; Rockwell & Giuliano,
1986; Loree et al., 1987; Lu et al., 2002). Especially, the beam
combination method seems to be one of the most practical techniques for
this application (Kong et al., 1997;
Rockwell & Giuliano, 1986; Loree et al., 1987). The laser system using a
beam combination technique, in which a laser beam is divided into several
beams and recombined after separate amplification and does not need a
large gain medium. Hence, it can operate at a repetition rate exceeding 10
Hz regardless of the output energy and is easily adaptable to the modern
laser technology. Kong et al. (1997)
proposed a promising beam combination laser system using the stimulated
Brillouin scattering-phase conjugate mirrors (SBS-PCMs), whose output
energy can be unlimitedly scaled up by increasing the number of separate
amplifiers. In addition, the SBS-PCMs produce a phase conjugated wave to
compensate many kinds of optical distortions in the system, induced during
the amplification (Rockwell, 1988). In the beam
combination laser using SBS-PCMs; however, it is necessary to control the
phase of each beam reflected by the SBS-PCM to get the good beam
recombination. It has been known that the phase of the beam reflected by
SBS-PCM is inherently random (Loree et al.,
1987; Lu et al., 2002; Rockwell, 1988; Boyd et
al., 1990) because SBS starts from a noise in the SBS medium.
There have been several works to control or lock the phases of SBS wave,
and some of them are very successful (Rockwell &
Giuliano, 1986; Loree et al.,
1987). By overlapping the laser beams at one focal point, the
phases are almost locked (Rockwell & Giuliano,
1986). However, since all the beams must be focused at one point,
the energy scaling is limited, and the beams are not symmetrically focused
at the focal spot. The back seeding of the Stokes beam overcomes the above
drawbacks (Loree et al., 1987), but the
phase conjugation is incomplete if the injected Stokes beam is not
completely correlated. In this paper, we have proposed and demonstrated a
new phase control technique, wherein each beam is focused at separate
focal points without using any backward Stokes seed beams, and hence, the
energy scaling is not limited and the phase conjugation is not disturbed
at all. For getting a given output energy, we may simply install the
proper number of amplifier lines in parallel for beam combination, because
the whole system is alignment insensitive in this new laser systems.
2. PHASE CONTROL OF SBS WAVE BY
SELF-GENERATED DENSITY MODULATION
The acoustic wave, Brilluin grating, is simply represented as
propagating in the positive z direction, where
ρ(z,t), q, and Ω are the amplitude,
the wave vector, and the frequency of the acoustic wave, respectively. The
initial phase is given by φa =
qz0 − Ωt0, where
z0 and t0 are known to vary
randomly because the acoustic wave begins from a random acoustic noise
(Boyd et al., 1990). However, we have
found it is possible to decide z0 and
t0 by putting a mirror in the back of the SBS-PCM to
make a standing wave at the focus (Kong et
al., 2004). One of the standing wave is the candidate of the
ignition position z0, and t0 =
tc is determined by the pumping energy
Ep from the equation,
where Ec and P(t) are
the SBB threshold energy and the pumping pulse form, respectively, and
t0 = tc as described in
Kong et al. (2004).
Figures 1, 2, and
3 shows the theoretical values of the ignition
time (tc), phase uncertainty (Δφ),
and the relative phase difference uncertainty (ΔΦ) depending on
the pumping energy, respectively. It should be noted that Δφ is
inversely proportional to the pumping energy
Ep.
tc & dtc
/dEp as a function of the pump
energy.
Phase change of the SBS wave as a function of the pump energy
(ΔEp /Ep
= 1, 2 and 5%).
Change of the relative phase difference as a function of pump energy
for the cases of Ep1 =
0.5Ep2 and Ep1 =
0.999Ep2.
3. EXPERIMENTS ON THE PHASE CONTROLLING AND
LOCKING
We have measured the relative phase difference Φ =
φ1 − φ2 between two Stokes beams for
the case of the amplitude dividing. The experimental setup is shown
schematically in Figure 4. A Q-switched 1064 nm
Nd:YAG oscillator with a bandwidth of ∼ 120 MHz and ∼ 2% energy
stability was used for the pump. The pulse width was 7 to 8 ns and the
repetition rate was 10 Hz. The output from an oscillator is divided into
two sub-beams by a beam splitter (BS). Both beams then pass through the
separate wedges (W1 & W2) and are backward focused into each SBS-PCM.
The wedge reflects a part of the backward Stokes beam, which is overlapped
with that of the other Stokes beam, onto a CCD camera to get an
interference pattern of them. For stabilizing the phase by the
self-generated density modulation, the pump pulse is backward focused by a
concave mirror with R = 50 cm and reflectivity > 99%. The density
modulation is induced by the electrostriction in the SBS material,
especially at the focal area by the standing wave interference pattern at
the focal region. We used Fluorinert FC-75 as a SBS medium. The length of
a SBS cell of 50 cm is used in this experiment (Yoshida
et al., 1997).
Experimental setup for measuring the relative phase difference; HWP1
& HWP2; half wave plate; BS; beam splitter; M; mirror; W1 & W2;
wedges; P1; polarizer; PBS; polarization beam splitter; CM1 & CM2;
concave mirrors.
The diagnostics for the phase control of the Stokes beams is
straightforward. The interference pattern acquired by the CCD camera
yields the relative phase difference Φ = φ1 −
φ2 between the Stokes beams incident on the CCD, where
φ1 and φ2 denote the phases of two Stokes
beams, respectively. Therefore, we can quantitatively analyze the degree
of the phase stabilization by measuring the movement of the peaks. From
the interference pattern of every shot, the intensity profile of its
horizontal line is selected and stacked as shown in Figure 4. A peak position P is then
determined from the selected line. Since the relative phase difference
Φ between two beams fluctuates, the peak position P also
moves to the left or right with respect to a fixed point F. The
relative phase difference Φ can be expressed as
2π[ell ]/T, where [ell ] is the distance between F
and P and T is a spatial period of the interference
pattern.
4. RESULTS AND DISCUSSION
We have measured Φ for two specific cases of
Ep1 ≅ Ep2
and Ep1 ≅
0.5Ep2. Figure 5
shows the experimental results for the case of
Ep1 = 9.4 mJ and
Ep2 = 4.66 mJ. Each point in Figure 5a represents one of 256 laser pulses. Figure 5b shows the intensity profile of 256
horizontal lines selected from each interference pattern. It shows that
there is something missing for phase locking.
Figure 6 shows the experimental results for
the case of Ep1 = 10.56 mJ and
Ep2 = 10.55 mJ. The relative phase difference
between two SBS waves is smaller than λ/4 for every shot. Compared
to the previous results, the fluctuation of relative phase difference is
considerably reduced. The profile also represents that the relative phase
difference is stabilized quite a lot. The experimental results
qualitatively agree with the theoretical results in Figure 3. Consequently, we have shown that it is
possible to control and lock the relative phase difference by a
self-density modulation, provided that the energies of the two beams are
made similar.
(a) Relative phase difference for 256 laser pulses and
(b) Intensity profile of horizontal lines selected from 256
interference patterns for the case of Ep1 =
9.4 mJ and Ep2 = 4.66 mJ.
(a) Relative phase difference for 254 laser pulses and
(b) Intensity profile of horizontal lines selected from 254
interference patterns for the case of Ep1 =
10.56 mJ and Ep2 = 10.55 mJ.
5. PRE-PULSE TECHNIQUE FOR THE SBS WAVE
FORM
The wave form is deformed by the SBS reflection, due to the
consumption of the front part of the wave energy for the formation of the
acoustic grating formation and the extension of the interaction zone
during the pulse propagation. We have found it is possible to keep the
wave form by using the pre-pulse technique (Kong et
al., 2005). Figure 7a is the input
pulse, Figure 7b is the SBS wave without
pre-pulse, Figure 7c is the SBS wave with
pre-pulse, Figure 7d is the comparison of the
input pulse, and the SBS wave. From these experimental results, it is
clear that the pre-pulse technique is quite useful to preserve the pulse
shape.
The pulse shapes, (a); input wave, (b); SBS wave
without pre-pulse, (c): SBS wave with pre-pulse, and
(d); comparison of the input pulse and SBS wave with the
pre-pulse.
6. A NEWLY PROPOSED LASER FUSION
DRIVER
We have proposed two laser fusion drivers of amplitude dividing and
wave-front dividing schemes as shown in Figures 8a and
8b. With the phase controlling technique and the pre-pulse
technique described upper, we can produce huge output energy as we want by
scaling-up. The wave-front dividing scheme was proposed already by one of
the authors in 1997 (Kong et al.,
1997). Also these proposed laser systems are alignment insensitive
so that it is very easy to install or maintain the system because we may
just put the components in their position with the mechanical accuracy not
optical accuracy. Also this system requires low quality of the optical
components but the polarizing components, because the optical distortions
caused by the low quality optical components and during the amplifications
in the gain media can be compensated by this system automatically.
Schematic diagrams of the proposed laser fusion driver with SBS-PCM
beam combination; (a) amplitude dividing scheme and (b)
wave-front dividing scheme: PC; phase controller, PP1 and PP2; prepulsers,
AMP1 and AMP2; amplifiers, FR1 and FR2; faraday rotators, IR1 and IR2;
image relays, WD1 and WD2; wave-front dividers, BE1 and BE2; beam
expanders, PBS1; polarizing beam expanders, QW1 and QW2; quarter wave
plates, 45R; 45 degree rotator.
7. CONCLUSION
We have proposed a new phase control technique by a self-generated
density modulation in order to control the phase of the SBS waves, which
is required for the beam combination laser with SBS-PCMs. Theoretical
analysis shows that the phase fluctuation is inversely proportional to the
pump energy and is proportional to the pump energy fluctuation. By means
of the amplitude dividing, we have achieved that the relative phase
difference between two SBS waves can be made smaller than λ/4. We
expect that this phase control technique is very useful to develop a
practically useful laser fusion driver using the beam combination with
SBS-PCMs. Even if a large number of amplifiers should be installed in
parallel for huge energy/power output, it will be very easy to install
or maintain them because of their special characteristics such as the
compensation of the optical distortions by the phase conjugated mirrors
and the alignment insensitiveness by the cross type amplifier system with
the symmetrical SBS-PCMs.
ACKNOWLEDGMENTS
This work was supported by the KISTEP, the RRC at Dankook University,
and the IAEA, Austria, contract no. 11636/R2.
