Download New concept of laser fusion driver using Stimulated Brillouin

IFE laser driver using independent
phase control of stimulated Brillouin
scattering phase conjugate mirrors
by a self-generated density
modulation
Hong Jin Kong, Seong Ku Lee, and
Dong Won
KAIST
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New laser fusion driver with SBS beam combination
Wave-front
dividing
method
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Contents
1.
2.
3.
4.
5.
Motivation
Cross type amplifier with symmetric SBS-PCMs
Beam combination
Phase controlling of SBS-PCM wave
Pre-pulse technique for preserving the SBS pulse
shape
6. Conclusions
7. Future work
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Motivation
• LFE has the bottle neck in its laser driver with high rep.
rate over 10 Hz.
(NIF operates at 1 shot per several hours)
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New laser fusion driver
Using SBS beam combination
a. Scalable easily
b. Maintenance easy
c. High repetition rate over 10Hz
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Why bottleneck in lasers?
Cooling
Solid amp
High thermal load for cooling
Cooling
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How to solve the thermal load?
1.
LD pumping can reduce the thermal load.
2.
Ceramic crystals with high thermal conductivity can
reduce the thermal load.
3.
Fast ignition can reduce the driver energy.
But these technologies will not be able to realize the
practically useful fusion driver technology.
Beam combination using SBS-PCM can be one of the
promising technologies for the laser fusion driver.
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Beam combination
Phase distortion
Break up
Easy cooling
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Piston error
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How to solve the problems?
1. Phase distortions
By phase conjugation mirror
2. Piston errors
By phase locking / controlling the phase
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Phase conjugation mirror (PCM)
Conventional mirror
Phase conjugation
mirror
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Comparison of PCM to conventional mirror
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Types of PCMs
4w mixing
SBS
Medium
crystal
Any g, l, s, or p
Damage threshold
low
high
Size of the beam
Limited by the
crystal
No limitation
Complexity
complicated
most simple
Phase control
yes
No before this work
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Principles of SBS
Stimulated Brillouin scattering (SBS)
1. Scattering by acoustic phonon induced by laser
field
a.
Acoustic phonon = moving grating with the acoustic
velocity in the medium
2. Backward scattering ; high reflectivity
a.
b.
50% for 10mJ pumping
90 % for 100mJ pumping
3. Phase conjugated wave ; high fidelity over 90%
4. Frequency shift ; ~ 1GHz for liquid
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100
Reflectivity(%)
80
60
40
20
0
0
50
100
150
200
250
300
Laser input energy(mJ)
Reflectivity(%) / Breakdown(%)
Reflectivity and breakdown probability depending on
the laser mode of SBS-PCM with FC-75
100
80
60
40
20
Reflectivity
Breakdown
0
0
50
100
150
Laser Input Energy(mJ))
Single mode pumping
(Dn~120MHz, G=350MHz)
(No break down)
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Multi mode pumping
(Dn~30GHz, G=350MHz)
(Break down occurs)
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Cross-type amplifier with symmetric PCMs:
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Cross-type amplifier with symmetric PCMs:
1. Compensate the phase distortions such as birefringence,
thermal lensing effect, etc.
2. Perfect optical isolation possible
3. Insensitive to misalignment
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Beam combination using SBS-PCM for highly
repetitive high power and high energy laser
Proposed by H.J.Kong, Optical Review 4, 277-283(1997) and
Fusion Eng. & Design 44, 407-417(1999)
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Phase controlling of SBS wave
1. Interference between the beams at their boundaries
in beam combination gives spatial spiking if their
phases are not matched.
2. Phase difference between the beams should be less
than /4 for constructive interference at the
boundary of the combination not give spatial
spiking.
3. It is necessary to control the phases of the SBS
waves to match the phase difference between the
neighboring beams less than /4
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Previous works for phase locking
1. Overlapping the SBS focal points locks the phases of the beams.
2. Phase locking by back seeding the Stokes shifted beam, which
locks the phase of the PC wave.
Lens
SBS Cell
Seeding Beam
Polarizer
Faraday
Rotator
SBS Cell
SBS Cell
Beam
Splitter
Mirror
a) Overlap of two focal points
b) Back-seeding of Stokes wave
D.A.Rockwell and C.R.Giuliano, Opt. Lett. 11, 147 (1986)
T.R.Loree, et. al., Opt. Lett. 12, 178 (1987)
Impractical for many beams > 10
PC can be broken by back seeding beam
No PC anymore
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Proposed “Self-phase control”
1.
Feed back mirror > Counter propagating beams > standing wave > density modulation
2.
Standing density modulation locks the ignition position of the moving phonon
3.
This phonon locks the phase of the SBS wave.
4.
Phase controlling is possible by positioning the feed back mirror.
SBS Cell #1
SBS Cell#1
Lens
Concave Mirror
Concave Mirror
SBS Cell #2
SBS Cell #2
(a)Concentric type
(b) Confocal type
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Basic concept of a new phase control
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Theoretical backgrounds for phase control of SBS
SBS wave reflects from the density wave
  0  Cos((t  t0 )  ka ( z  z0 ))
And we should determine the initial position and time ,
z0 and t0, at which the density modulation occurs.
z0 is determined by the ignition position of the density
wave.
t0 is determined by the ignition time when the acoustic
grating occurs by the pumping pulse.
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LetLet
us us
assume
that that
assume
S p  A  Sin( pt  k p z   p ) (Pump wave)
SB  B  Sin( Bt  kB z  B ) (Stokes wave)
2
  C  S p  SB .
Then,   C  S p  S B
(Density modulation)
2
 C  [ A2 Sin 2 ( p t  k p z   p )  B 2 Sin 2 ( Bt  k B z  B )
(DC)
 A  B  Cos{( p   B )t  (k p  k B ) z  ( p  B )} (Fast osc.)
 A  B  Cos{( p   B )t  (k p  k B ) z  ( p  B.)} (Acoustic
wave)
If the acoustic wave is considered as   0  Cos(t  ka z,  a )
Thus,    p   B , ka  k p  k B ,and a   p  B
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If we assume that the acoustic wave is generated at t0 and z0, then the
acoustic wave has the form:
  0  Cos((t  t0 )  ka ( z  z0 ))
Then, the initial phase of the acoustic wave has the form:
a  t0  ka z0
, where t0 and z0 are the initial time and position when and where the
acoustic wave is ignited and generated. For fixing a, t0 and z0 must be
fixed.
The density modulation by the standing wave can fix the ignition position
z0 of the acoustic wave, assuming that the nodal points of the standing
wave act as an ignition position.
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Determination of z0
Nodal point of the standing wave
Da  2
a  t0  ka ( z0  ( p / 2)N)
 t0  ka z0  2 N, (N: interger)
, where we used the relation ka  k p  ks  2k p  4 /  p
z0 has the uncertainty of (p/2)N. But it does not affect
the accuracy of the phase.
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Determination of t0
Assume that the pump beam generates acoustic wave by its front
side of the energy:
Ec 
tC
 P(t )dt
0
,where Ec and P(t) are the critical energy for generating the
acoustic grating and the pump pulse profile, respectively.
tc is the time when the ignition occurs.
tc is determined by the pumping pulse energy and its profile.
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Let t0=tc. For fixing tc , the pump energy must be fixed.
 a =  t 0 – ka z0
The uncertainty of the phase with dz0=0, da can be expressed by
da  dtc

( assuming dz0 =0)
dtc dEt
Et
dEt Et

, where Et   P (t )dt
0
Et is the total energy of the pump pulse.
For getting a good beam combination,
da, < /4 (/8).
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da < /4
10 ns
Pump energy Et vs. Critical time tc
P(t ) 
4 Et
a 3
t 2 exp[ (t / a) 2 ]
15
Pulse width ~10 ns (a=8.66)
Critical time (tc) (ns)
12
9
6
3
0
20
40
60
80
100
Pump enrgy (Et) (mJ)
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da < /4
dt c
Pump energy Et vs.
dE t
0
dtc/dEt
-1
-2
-3
-4
0
20
40
60
80
100
Pump energy (Et) (mJ)
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da < /4
Allowable fluctuation, dE t/Et (%)
 dt c

dEt
Pump energy fluctuation :
 Tolerance  
Et 
Et
 dEt 
1
12
10
8
6
4
Tolerance   / 8 ( / 4)
2
0
0
20
40
60
80
100
Pump energy (Et) (mJ)
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da < /4
19.2% energy fluctuation for 1000mJ
15.1% ~
500mJ
8.4% ~
100mJ
2.8% ~
10mJ
1.4% ~
5mJ
Energy Tolerance %
15
10
5
200
400 600
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Pump Energy mJ
800 1000
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da < /50(/100)
1.5% energy fluctuation for 1000mJ
1.2% ~
500mJ
0.67% ~
100mJ
0.22% ~
10mJ
0.11% ~
5mJ
Energy Tolerance %
1.5
1.25
1
0.75
0.5
0.25
200
400
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600
Pump Energy mJ
800 1000
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da < /50(/100)
3.4% energy fluctuation for 10J
2.7% energy fluctuation for 5J
3
2.5
2
1.5
1
0.5
Pump Energy mJ
Phase
derivative
fB
dt c
dE t
10000
2000
4000
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6000
8000
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Experimental setup for self-phase locking of two beams
(wavefront dividing)
W1
M1
L3
SBS Cell
CM1
SBS Cell
CM2
Faraday
Rotator
PBS
HWP2
Isolator
L1
L2
45 degree
Reflection
Coated Prism
L4
M2
W2
P1
HWP1
CCD
Camera
Nd:YAG Laser
M1&M2, mirror; W1&W2, wedge; L1&L2, cylindrical lens: L3&L4, focusing lens, CM1&CM2,
concave mirror; HWP1&HWP2, half wave-plate; P1, polarizer; PBS, polarization beam splitter
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Wave-front dividing
1. Requirements:
a. Phase accuracy : < /4 for constructive interference
b. Image relaying from the divider to the center of the
amplifier
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Average fluctuation ~ 0.3 
Normal case: No locking
180
135
Lens(f=250mm)
SBS Cell #2
90
Phase (degree)
SBS Cell #1(l=500mm)
45
0
-45
-90
-135
-180
0
50
100
150
Number of shot (A.U.)
Intensity profile of interference
Intensity profile of interference for 160 shots
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Average fluctuation ~ 0.165 
180
Concentric case
135
Phase (degree)
90
SBS Cell#1 (l=500mm)
45
0
-45
-90
-135
-180
0
50
100
150
200
Number of shot (A. U.)
Lens(f=250mm)
Concave Mirror
(R=300mm, uncoated)
SBS Cell #2
178/203 : success (88%)
Intensity profile of interference for 203 shots
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Average fluctuation ~ 0.135 
180
135
Confocal case
Phase (degree)
90
SBS Cell #1(l=500mm)
45
0
-45
-90
-135
-180
SBS Cell #2
0
50
100
150
200
Number of shot (A.U)
Concave Mirror
(R=500mm, 100%R)
228/238 : success (96%)
Intensity profile of interference for 238 shots
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Experimental setup
for amplitude dividing
Sd=41.85 fluctuation
9.4mJ & 4.66
mJ 
Average
~ 0.12
180
Pump energy: 9.4 mJ and 4.66 mJ
CCD
Phase(degree)
90
0
-90
SBS-PCM
BS2
-180
0
BS1
50
100
150
200
250
Number of shot
2
4
6
8
10
2
BS3
M
4
6
8
242/251 : success (96%)
10
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Average fluctuation
Sd=28.0 10.56mJ~0.08
and 10.55mJ
Experimental setup
for amplitude dividing
180
Pump energy:10.56 mJ and 10.55 mJ
CCD
Phase (degree)
90
0
-90
SBS-PCM
BS2
-180
0
50
100
150
200
250
Number of shot
BS1
2
4
6
8
10
2
BS3
4
M
6
256/256 : success (100%)
8
10
Intensity profile of interference for 256 shots
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Average fluctuation  0.09 
180
Two mirrors
135
Two mirrors
Phase(degree)
90
45
0
-45
Mirror1
-90
Mirror2
-135
-180
0
50
100
150
200
250
Number of Shot (A. U)
256 shots
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Comparison of control and mirror cases
Sd=28.0 10.56mJ and 10.55 mJ
180
180
Two mirrors
135
90
45
Phase (degree)
Phase(degree)
90
0
-45
0
-90
-90
-135
-180
-180
0
50
100
150
200
250
0
50
100
150
200
250
Number of shot
Number of Shot (A. U)
Mirror case
Controlling case
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Amplitude dividing
Requirements:
Phase accuracy: D < /25(/100)
for intensity fluctuation : DI/I  Sin2(D)>0.015
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Pre-pulse technique
Motivation:
1. Backward SBS wave has a steep rising edge.
2. This can generate undesirable effects such as optical
breakdown, poor fidelity when entering next SBS cell.
Purpose:
Preserving a waveform of the backward SBS wave using a prepulse.
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Transmitted and spent for
generating an acoustic wave
Pulse shape of the pump and the SBS wave
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Experimental setup
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Waveform of the incident and reflected wave
(a) incident wave
(b) reflected wave
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<1> E(pre)=2mJ [E(main)=10mJ, delay time=5ns]
(a) with pre-pulse
(b) without pre-pulse
There is no significant difference between (a) and (b)
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<2> E(pre)=3mJ
(b) without pre-pulse
(a) with pre-pulse
(c) Comparison between (a) and (b)
(d) Comparison with incident wave
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<3> E(pre)=4mJ
(a) with pre-pulse
(b) without pre-pulse
(c) Comparison between (a) and (b)
(d) Comparison with incident wave
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<4> E(pre)=5mJ
(a)
(b)
(c)
(d)
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<5> E(pre)=5mJ at delay time=3ns, 5ns, 7ns, 10ns
(a) 3ns
(b) 5ns
(d)10ns
(c) 7ns
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Proposed pre-pulse system for preserving the wave
form of SBS wave
M1
QW1
Main pulse arm
PBS2
Pre-pulse arm
M2
SBS-PCM
QW2
HV
Pockels cell
10ns
Optical isolator
PBS1
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New laser fusion driver with SBS beam combination
Amplitude
dividing
method
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New laser fusion driver with SBS beam combination
Wave-front
dividing
method
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Comparison of WD (wavefront dividing) and
AD (amplitude dividing)
Spatial profile
Temporal fluctuation
Requirements
Large 45 rotator
(crystal)
Image relying
WD
AD
Depends on the phase
difference
Good
Good
Depends on the phase
fluctuation
D < /4
D < /100
No
Necessary
Necessary
No
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Summary
1.
2.
3.
4.
We have succeeded to control the phase of the SBS wave.
We have developed the necessary theoretical background the
phase control mechanism.
We have demonstrated the feasibility of the beam
combination using SBS-PCM.
We have proposed the next generation of the laser fusion
driver system with SBS beam combination.
2
4
6
8
10
2
4
6
8
10
No control
Phase control with WD
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Phase control with AD
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Conclusions
1. A cross type amplifier using SBS-PCM has many
advantages such as the alignment insensitiveness,
the stable beam pointing, and the perfect optical
isolation.
2. Pre-pulse technique is expected to suppress the
deformation of the SBS wave
3. Phase controlling of the SBS wave has been
successfully achieved by self density modulation.
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Future work
1. Demonstrate the phase controlling of the SBS wave
having the amplifiers
2. Stage I : Demonstrate 400J/10Hz system with 2 stage amplifier
system (4 X 100J@10Hz)
3. Stage II : Demonstrate 6kJ/10Hz system (64 X 100J@10Hz)
4. Stage III : Construct a single channel of laser fusion driver,
100kJ@10Hz (1024 X 100J@10Hz)
5. Stage IV : Construct a full laser fusion driver, > 500kJ@10Hz
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SBS for ultra-short pulse
1. The following techniques might be used for
SBS for the ultra-short pulse :
a. Pre-pulse for making the acoustic grating
b. Phase controlling by self density modulation
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Conditions for ultra-short pulse SBS
dE
EG 
G  Eth
dn
Phase locked
For single-mode-like (Dn < G),
For multi-mode-like (Dn > G, c/Dn > l),
Eth ~ 3mJ (FC75)
Eth ~ 3mJ (FC75)
G ~ 300MHz
G `‘~ 30GHz
Dnl ~ 3*1012Hz D~10nm@ =1um)
Dnl ~ 3*1012Hz D~10nm@ =1um)
El-pre-pulse > Eth (Dnl / DnB ) ~30J
El-pre-pulse > Eth (Dnl / DnB ) ~300mJ
El-main-pulse > 100J for 50% R (10mJ)
El-main-pulse > 3J for 75% R (30mJ)
500J for 80% R (50mJ)
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Principles of SBS
B
wL
ws
• Stimulated process of 3 waves, pumping, back scattered, and
acoustic waves; an incident laser beam of frequency L scatters from
the refractive index variation associated with a sound wave of
w
frequency B
• The two optical fields are governed by the Maxwell’s equations,
whereas the acoustic field is described by Navier-Stokes equation with
electrostrictive driving term:
 2 Ei n 2  2 Ei 4  2 Pi
 2
 2
,
2
2
2
z
c t
c t
2
2  

G


t 2
 t
i  1, 2

2 2
       f ,

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Principles of SBS
Basic equations
 e q B2
2



(
G

2
i

)

i
G



A
A
. (for an acoustic wave)
B
B
B
B
1
2
t
4
t 2
 ew
n A1
A1

i
A2
(for Incident wave)
c t
z
2nc 0
 ew
n A2
A2

i
  A1
(for Stokes wave)
c t
z
2nc 0
If we consider three waves in the form
E1 ( z, t )  A1 ( z, t )ei ( k1 z  w1t )  c.c.,
(Incident wave)
E2 ( z, t )  A2 ( z, t )ei (  k 2 z  w2 t )  c.c.,
(Stokes wave)
 ( z, t )  0   ( z, t )ei(qB z  B t )  c.c.,
(Acoustic wave)
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Principles of SBS
Steady state SBS
Ai / t  0, i  1, 2
dI1
  g B I 2 I1
dz
dI 2
  g B I1 I 2
dz
1.00
reflectivity, R
0.75
,where gB is SBS gain
0.50
0.25
0.00
0
SBS generator
2
6
8
10
G/Gth
I1 (0)
G  I1 (0) g B L
I1 ( z )
I 2 ( z)
Z=0
4
Z=L
R  1
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1
(for G >> Gth )
G / Gth
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Principles of SBS
Phase conjugation by SBS
E0 (r, t)  E0ˆ ei ( k0 r w0t )  c.c.,
(Incident wave)
 
~ 
Ec ( r , t)  E0ˆ ei (  k 0  r w 0 t )  c.c..
(Phase conjugate wave)
Thus, the phase conjugation is in fact equivalent to time reversal:
~ 
~ 
Ec ( r, t)  E0 ( r, - t)
is replaced by E0 , hence the wavefront is reversed.
i) E
0


ii)
kc  k0 , hence the direction of propagation is reversed.
iii)The polarization vector of the outgoing wave is the complex conjugate of ˆ
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Principles of SBS
An example of phase conjugation by SBS
CCD
camera
SBS-PCM
PBS
Mask
QW
SBS-cell
Lens (FC-75)
Optical isolator
SBS-PCM
Ordinary Mirror
Nd:YAG Laser
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Principles of SBS
Three physical regimes of relevance to SBS
1. Narrow band case (single mode) : Dn < G
2. Broad band case (multi mode) : Dn > G, c/Dn > l
}
3. Broad band case (multi mode) : Dn > G, c/Dn < l
High gain
Low gain
Dn: Pumping laser line-width
G: Brillouin line-width
tp= 1/ G: Acoustic phonon life time
l: Geometrical interaction length ( ~ Rayleigh length)
c: Light velocity
c/Dn: coherence length
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Principles of SBS
Experimental setup for reflectivity measurement
M
ND
Calorimeter
PBS
BS
Lens(f=15cm)
/4
SBS-PCM
Isolator
Pol
PD
/2
Nd:YAG Laser
Experimental setup for the measurement of the SBS reflectivity; /2, half wave plate; Pol,
polarizer; M, mirror; ND, neutral density filter; /4, quarter wave plate; PBS, polarizing
beam splitter; BS, beam splitter; PD, photodiode
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LSRL
Principles of SBS
Properties for liquids
( λ = 1μm)
(MHz)
gB (cm/GW)
n2 (10-22 m2/V2)
Pc (MW)
Eb (mJ)
Carbon tetrachloride (CCl4)
528
3.8
5.9
0.4
2
Fluorinert FC-75
350
4.5-5
0.33
7.1
6
Aceton
119
15.8
8.6
0.28
1.5
Carbon disulfide (CS2)
50
68
122
0.02
<0.5
Liquid
G, Brillouin linewidth; gB, SBS gain; n2, nonlinear refractive index;
PC; critical power of the self-focusing; Eb, breakdown threshold.
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LSRL
Principles of SBS
Characteristics of some liquids
Gain Factor
Substances
CS2
Aceton
n-Hexane
Toluene
CCl4
Methanol
Benzene
H2O
Cylohexane
FC-72
FC-75
Frequency shift
(MHz)
5850
4600
5910
4390
4250
6470
5690
5550
1100
1340
Linewidth
(spont.)
(MHz)
52.3
224
222
579
520
250
289
317
774
270
350
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Calculated
(max)
(cm/MW)
0.197
0.017
0.027
0.013
0.0084
0.013
0.024
0.0066
0.007
Measured
(max)
(cm/MW)
0.13
0.020
0.026
0.013
0.006
0.013
0.018
0.0048
0.0068
0.006
0.005
LSRL
Compensation of birefringence
Compensation of birefringence
Double-pass + Faraday rotator + SBS-PCM
can compensate the optical birefringence.
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LSRL
Compensation of birefringence
Measuring the depolarization for 1-pass amplification
Laser beam
P
Amp
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A
CCD
LSRL
Compensation of birefringence
Depolarization for 1-pass amp
6.96 mJ
10.2 mJ
20 mJ
29.9 mJ
39.9 mJ
50 mJ
60.6 mJ
89.3 mJ
119 mJ
152 mJ
200 mJ
284 mJ
4.5
Depolarization Ratio(%)
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
5
10
15
20
25
30
Input Energy(J)
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LSRL
Compensation of birefringence
Leak beam patterns for 1-pass amp
depending the pumping energy
(a) Input beam
(b) No pumping
(c) 3.4 J
(d) 9.4 J
(e) 18.4 J
(f) 33.8 J
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LSRL
Compensation of birefringence
Experimental set-up for measuring the depolarization for
(double pass amp) + FR/QW + SBS-PCM
CCD
PBS PBS
Laser beam
PBS
FR
Amp
FR / QW
SBS-PCM
QW
Type 1
Type 2
Type 3
Type 4
FR
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LSRL
Compensation of birefringence
Birefringence of the gain medium
r'


r
r
eir
o 
 cos 
G
, R
i 
  sin 
0 e 
G '  RGR 1
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sin  
cos  
LSRL
Compensation of birefringence
Theoretical calculation for 4 types of doube pass amp
Japanese Journal of Applied Physics - Part 2 : Letters, Vol. 34, P. 994 - 996, 1995.
eir
1  1 1
1 1 i 
F
 1 1 , Q 
i 1 , G  
2
2


0
Type 1
o 
 cos 
,
R


  sin 
ei 

sin  
cos  
 Ex 
i (cos   i sin  )2 (e2ir  e2i ) 
1
1 1 
 E   QRGR RGR Q     

2i
2ir
0
2
(
e

e
)
y




 
 Ex 
i 8sin  cos  (eir  ei ) (cos 2  eir  sin 2  ei ) 
1
1 1 
Type 2    RGR QQRGR    

i 2
i 2
ir
ir
E
0
2

(
e

e
)

(
e

e
)
cos(4

)
y




 
Type 3
 Ex 

cos(2 ) (e2ir  e2i )
1  
1
1

FRGR
RGR
F

E 

0  2ir
2i
2i
2i
  e  e   (e   e r )sin(2 ) 
 y
E 
1 
Type 4  x   RGR 1FFRGR 1    2 eir i
0
 Ey 
0
1 
 
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LSRL
Compensation of birefringence
Depolarization Ratio(%)
Depolarization for (double pass amp) + FR + SBS-PCM
7
5.1mJ
10 mJ
30.3 mJ
50.4 mJ
102.5 mJ
156 mJ
198.5 mj
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
Pumping Energy(J)
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LSRL
Compensation of birefringence
Depolarization for (double pass amp) + QW + SBS-PCM
Depolarization Ratio(%)
7
33.3 mJ
50.5 mJ
102 mJ
148 mJ
202 mJ
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
Pumping Energy(J)
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LSRL