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