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High Optical Power Cavity with an Internal Sapphire Substrate
—Thermal lensing, thermal compensation & three modes interactions
Chunnong Zhao
for
ACIGA
Contents
• Strong thermal lensing observation• Closed loop thermal lensing control• Observation of beam astigmatism in
high power cavity• Opto-acoustic parametric interactions
Gingin High Power Facility cavity setup
PRM(M1)
100W
ETMITM(M2)
800kW1kW
ETM
ITM
Fused silica compensation plate
1kW
ITM(M2)
ETM(M1)
4W
CCD
Mode matching telescope
Filter
•Substrate of the input mirror inside the cavity !
•Creates a strong thermal lens to simulate PRC in advanced detectors
Strong Thermal Lensing
Observation and compensation (PRL 16 June 2006)
Thermal Lensing and Thermal Compensation
heat
heat
Compensation Plate + Heating ring
Closed Loop Thermal Lensing Control
CCD
LaserITM
1kW
CP
ETM
4W
Heating wire
Power Suppl
y
Controller
Thermal lensing control Demonstrated
The beam distortion due to thermal lensing
• non-quadratic thermal lensing• thermal stress birefringence • inhomogeneous absorption in the test mass
• Sapphire is known to have high inhomogeneity• Gingin test mass
– No detailed absorption map– At centre ~50ppm/cm (Measured in Caltech, agrees with
average thermal lensing measured in Gingin)
• Analysis of several other samples to get “typical absorption” in sapphire samples
Average absorption across sapphire samples
UWA 1 UWA 2
Caltech 1 Caltech 2
Absorption measured at at Laboratoire des Matériaux Avancés (LMA)
Example of absorption along the thickness of a sample (Caltech 1)
0
20
40
60
80
100
120
140
-130.0 -110.0 -90.0 -70.0 -50.0 -30.0 -10.0x (mm)
Ab
s (p
pm
)
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120 140
1. UWA1 (at 50mm from centre)
2. UWA2 (at -50mm from centre)
3. UWA2 (at 50mm)
4. UWA2 (at -50mm)
5. Caltech1(at centre)
6. Caltech1 (at 50mm)
7. Caltech1 (at -50mm)
8. Caltech2 (at centr)
9. Caltech2 (at 50mm)
10. Caltech2 (at -50mm)
11. 65ppm/cm (uniform)
12. 30 ppm/cm (uniform)
Ab
sorp
tion
pp
m
Thickness mm
5
7
6
8910
11
12
Integrated absorption along the thickness of test masses
Uniform absorption—∫A(x)dx vs. thickness Should be a straight line
Integrated absorption along the thickness of test masses
(enlarged)
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60
Abs
orpt
ion
ppm
Thickness mm
1 2345
6
78
3
910
11
12
51ppm/cm, 50mm
30ppm/cm
65ppm/cm
Between 30-65ppm/cm
Beam size vs circulating power at Gingin HOPF
14
15
16
17
18
19
0 200 400 600 800 1000 1200
Circulating power (W)
Bea
m d
iam
eter
(m
m)
0 0.1 0.2 0.3 0.4 0.5 0.6
Absorbed Power@50ppm/cm (W)
Long axis
short axis
Simulated@50ppm/cm
Astigmatism due to birefringence(simulated sapphire with uniform absorption)
0.94
0.95
0.96
0.97
0.98
0.99
1
0 0.2 0.4 0.6
Absorbed Power (W)
Wai
st X
/ W
aist
Y
Uniform absorption will still result in power dependent astigmatism due to stress birefringence
0.89
0.9
0.91
0.92
0.93
0.94
0.95
0 200 400 600 800 1000 1200
Circulating Power (W)
Wa
ist
X /
Wa
ist
Y E
xp
eri
me
nta
l
0.97
0.98
0.99
1
1.01
1.02
1.03
0 0.1 0.2 0.3 0.4 0.5 0.6
Absorbed Power@50ppm/cm (W)
Wa
ist X
/Wa
ist Y
sim
ula
tion
Experiment
Uniform (50ppm/cm)
• There is an initial systematic astigmatism• The power dependent astigmatism did not differ
much from that due to uniform absorption
Astigmatism vs Circulating Power
Opto-Acoustic Parametric Oscillation
m
0
a =0 +m
m
0
1 =0 -m
Anti Stokes process— absorption of phonons
Stokes process—emission of phonons
• Some test mass ultrasonic acoustic modes heated(amplified)
• OAPO gain must be kept below acoustic oscillation threshold
• Significant number of modes likely to be excited above
threshold in Advanced interferometers.
• OAPO interaction observed at Gingin.
Instability Condition
1)/1
(2
~2
121
112
Q
McL
PQR
m
m
Parametric gain[1]
[1] V. B. Braginsky, S.E. Strigin, S.P. Vyatchanin, Phys. Lett. A, 305, 111, (2002)
m 101
21110 11arccos
R
L
R
Lnpmk
L
c
Changing mirror radius of curvature will change the cavity mode gap
Demonstration of thermal tuning of high order optical frequencies
•Heat the compensation plate•Change the equivalent RoC•Change the cavity mode
spacing
Transmitted beam size Mode spacing between TEM00 and LG01
Three mode interaction at low power level
• Excite the target acoustic mode electrostatically• Observe the high order mode resonance as the
HOM resonance frequency is thermally tuned
0 5 10 15 20 25 30 35
Heating Power
Op
tical
sig
nal
Experimental Setup
CCD
LaserITM
CP
ETM
Heating wire
84.8 kHz oscillator
Capacitor actuator
Spectrum Analyzer
yxQPD
Fundamental mode
High order mode
Lock-in
Mechanical mode and optical mode overlap
50 100 150 200 250 300
50
100
150
200
250
300 20 40 60 80 100 120 140
20
40
60
80
100
120
140
Mechanical mode84.8kHz
Optical mode
Three modes interaction observationat Gingin HOPF
Amplitude of optical modes beating signal at 84.8kHz vs. time of heating (RoC change)
g factor ~ 0.98
1.4 1.5 1.6 1.7 1.8 1.9 2
x 105
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
-4
Cavity mode spacing (Hz)
Hig
h or
der
mod
e am
plitu
de (
a.u.
)
MeasurementFitted data
Conclusions
• Feedback control of thermal lensing demonstrated
• Sapphire test mass inhomogeneity effect marginally detectable
• First demonstration of opto-acoustic parametric interactions between the cavity fundamental mode, the cavity high order mode and the test mass acoustic mode (basic physics of parametric instability).
UWAChunnong ZhaoLi Ju Jerome DegallaixYaohui FanDavid BlairZewu YanSlawek GrasPablo Barriga
ANUBram Slagmolen David McClelland
U. AdelaidePeter VeitchJesper Munch David HoskenAidan Brook U. FloridaDavid Reitze
CaltechGariLynn Billingsley
Participants
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