Thermal Compensation in Stable Recycling Cavity 21/03/2006 LSC Meeting 2006 UF LIGO Group Muzammil A. Arain

Thermal Compensation in Stable Recycling Cavity

21/03/2006LSC Meeting 2006

UF LIGO GroupMuzammil A. Arain

Table of Contents

Stable vs. Unstable Recycling Cavities Design of Stable Recycling Cavity- Review Thermal Compensation in Advanced LIGO

» Design Options» Substrate Compensation

– Negative dn/dT Approach

» Surface Compensation– Adaptive Mode Matching in Recycling Cavity– Compensation Scheme– Experimental Demonstration

» Reduced Beam Size Option

Summary

Advanced LIGO – arm cavities

U00V00W00

Arm Cavities:• Long and stable cavities• Uncertainties due to thermal lensing are probably small, thanks to TCS

TCS focuses on carrier:• Optimize beam size on test masses• Optimize interferometer contrast• Optimize mode matching(?)

U00V00W00

Adv. LIGOMarginally Stable Recycling Cavities

Marginally stable Recycling Cavities:

• All spatial modes of RF-sidebands resonant (current design: mode separation ≈ 4 kHz)• Major loss mechanism for sidebands in TEM00-mode

• Loss of up to 30%-50%• (Also for signal sidebands!)

• Impact on LSC and ASC

U00V00W00

Adv. LIGOStable Recycling Cavities

Stable Recycling Cavities:

• Only fundamental mode of RF-sidebands resonant• Higher order modes suppressed• Strongly reduces losses of TEM00-mode• (Better performance for signal sidebands) • Expect improved LSC, ASC, and even Bull’s eye (mode matching) signals • Interferometer will be much easier to understand and debug

Power Recycling CavityCold State

Parameter Unit Value

MC Waist mm 2.113

MC Waist Loc.-PR1 m 2.0

PR1 ROC m -128.895

PR1 - PR2 m 16.655

PR2 ROC m 1.524

Beam Size @ PR2 mm 3.567

PR2 – PR3 m 16.655

PR3 ROC m 31.384

Beam Size @ PR3 cm 7.23

PR3 –ITM m 24.995

Beam Size @ ITM cm 7.10

ITM ROC m 2037.5

Mode Matching - 1.0

ITMx

PR3

ITMy

PR2

PR1

From MC

Hot Operation @ 120 W

6 cm Beam Size and 0.5 ppm Loss in ITM

110 km Thermal Lens at Surface

6.8 km Thermal Lens in Substrate

Thermal Lensing in ITM

Surface Deformation (64.76 km Thermal Lens, 12 th Degree Polynomial Fit to H-Vinet Theory)

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0x 10

-8

Radial Distance (m)

Su

rfa

ce D

efo

rma

tion

(m

)

Thermal Lensing in ITM

Substrate Contribution

Coating Contribution

Total Thermal Lensing

Thermal Lensing in Substrate

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-7

-6

-5

-4

-3

-2

-1

0x 10

-7

Radial Distance (m)

The

rmal

Abe

rrat

ions

(m)

Substrate Contribution (23 km)

Coating Contribution (4.93 km)

Total Thermal Lensing (4.09 km)

Thermal Aberrations (12 th Degree Polynomial Fit to H-Vinet Theory)

Optimized Thermal ROC Estimation

x

wo

R(z) R1

s(x)

E1(x,z)E2(x,z)

)(),(

14/1

1

22

),(

12),(

zRi

Azwx

opt

opteAzw

zxE

211

22 )(42

)()(

14/1

2)(

12),( x

xsi

Ri

zRi

zwx

ezw

zxE

optAiR

izR

izw

x

ezw

zxE4

2

)()(

14/1

31

22

)(

12),(

Calculate Overlap Integral b/w E2 and E3 and maximize itw.r.t. the ROC of thermal lens to get the optimal value

The Solution

)(

2

14

)2

(22

22

123

2

)(1

2N

2n

N

2n

2

22

2

22

2

22

2

2

22

2

42

zAAni

AAnAAnAA

zI

opt

n

nn

N

nn

nn

N

nn

nn

N

nn

nn

n

nn

optopt

An analytical solution is difficult however a numerical solution can be obtained. The curve is a parabola like shape and the vertex gives you the optimal value.

2)(for Only Valid xAxs opt

Solution: Numerical Integration

dxeezw

AIxAxsi

zwx opt

)(

12)(

2

12

2 4)(4

)(

22/1

Various Approximations for ITM

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-2.5

-2

-1.5

-1

-0.5

0x 10

-7

Radial Distance (m)

Th

erm

al A

be

rra

tion

(m

)

Data12th Degree Pol. Fit12th Degree Quad8th Degree QuadExact Solution

Overlap Integral (1-D)

60 70 80 90 100 110 120 130 140 15099.82

99.84

99.86

99.88

99.9

99.92

99.94

99.96

99.98

100

100.02

Modelled Thermal Radius of Curvature (km)

Po

we

r in

fun

da

me

nta

l ga

uss

ian

mo

de

(%

)

Various Approximations for Substrate

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0x 10

-6

Radial Distance (m)

Th

erm

al A

be

rra

tion

(m

)

Ddata

12th Deg. Poly. Fit

12th Deg. Quad

8th Deg. Quad

Exact Spolution

Overlap Integral (1-D)

2 3 4 5 6 7 8 965

70

75

80

85

90

95

100

Modelled Thermal Radius of Curvature (km)

Po

we

r in

fun

da

me

nta

l ga

uss

ian

mo

de

(%

)

Comparison of ROC Change Estimation

Thermal Lens in Substrate

Thermal Lens in ITM

Method Thermal

ROC(Km) Losses

% A2 of 12th Pol. 4.091 37.43 A2 of 8th Pol. 4.890 21.29 Exact Sol. 6.42 10.52

Method

Thermal ROC(Km)

ROCcold (m)

Cold Beam Size (cm)

Losses %

A2 of 12th Pol. 64.768 2012.46 9.29 0.48 A2 of 8th Pol. 77.013 2022.45 8.04 0.23 Exact Sol. 110.10 2038.54 7.05 0.06

Hot Operation @ 120 W




Com. Plate

?No

15% Losses in

RC

End?

Yes

Adaptive Mode Matching

No96% Mode Matching

End ?Yes

Ring HeaterOn ITMs

Adaptive TelescopeOn PR2 and PR3

RH & Adaptive Telescope

Option 3Option2Option1

Advantages:1. 100% Mode Match2. No Differential Effects

Disadvantage1. Relatively large power2. Induced Noise

Choose an Option

-ve dn/dt Material Plate

Annular Heatingon Plates

Ring Heating on Plates

Advantages:1. 100% Mode Match2. Insensitive Optics3. Non-power-related

mismatchDisadvantage

1. Only Common Mode Corr

Diff. through RHCommon through PR2 & PR3

Advantages:1. 100% Mode Match2. Low RH Power3. Low Noise Induction

1. Reduce Beam Sizes to 5.5 cm → Higher Noise2. Move Telescope intoarms → Space

Restrictions

Other Options

Compensation Plate for Substrate Compensation

Annular & Ring Heater Compensation

Refractive Index is decreasing at the center

Probe Beam Constant Power

Annular Heating Beam

Plate acts as a diverging lens

Annular Heating

+ve dn/dT Plate(Fused Silica)



Ring HeatersIncreasing Electrical Power


Ring Heating

+ve dn/dT Plate(Fused Silica)

dT

dn

L

Ln

)1(

Increasing Value

Negative dn/dT CompensationConstant temperature, Uniform refractive index

Probe Beam (1064 nm)Low power

Normal Divergence

Negative dn/DT plate

Probe Beam (1064 nm)Increasing Power


Plate acts as a simple glass plate



Heating Beam

dT

dn

L

Ln

)1(


Passive Compensation

Active Compensation

Increasing Value

Active Compensation Requirements:

» CO2 laser system for surface heating

» Availability in Large Size

» Purity/homogeneity

Advantages:» Works without any doubt, trick is use

same beam size as ITM

» Requires very low power (< 2W)

» Highly Efficient/Adaptive

Disadvantages:» New material

» A lot of Data and tests needed

» Requires coating on both surfaces

Option 1: Negative dn/dT

Passive Compensation Requirements:

» Availability in Large Size» Purity/homogeneity» Exact Size absorption values

Advantages:» No laser needed» Highly Efficient» Analogous to compensation in

Faraday Rotator Disadvantages:

» New material» A lot of Data and tests needed» Less Adaptive» Requires coating on both sides

Combination of Two is essential due to substrate heating at 1064 nm

Does such a material Exists ??

Potassium Bromide, Initial Choice

Normally used in IR Spectrometers

Available in large sizes

Crystalline in nature

Soluble in water

Important Properties (KBr): n = 1.5441 @ 1064 nm (dn/dT-(n-1)t = -17.43×10-6 /0C

Absorption = 0.002 cm-1

Kt = 4.816 W m-1 K-1 @ 319K

Important Properties (Fused Silica): n = 1.4497 @ 1064 nm dn/dT = 8.7×10-6 /0C t = 5.5 ×10-7 /0C

Absorption = 2 ×10-6 cm-1

Kt = 1.37 W m-1 K-1

A Typical Example6.42 km Thermal Lens in Substrate

Crystal Thickness = 2.05 mm Coating Absorption = 2.0 W Uncompensated Losses = 11% After Compensation = 0.001%

-20 -15 -10 -5 0 5 10 15 20-7

-6

-5

-4

-3

-2

-1

0

1x 10

-7

Radial Distance (cm)

Abe

rrat

ions

(m

)

CompensatedUncompensatedCompensation

Other Options for Compensation

Option 2: Ring Heaters General Comments

» Easy to control electrical power» Sensitive to geometry» Requires relatively high power» Compensating a lens of 6.8 km

in substrate might be too much for ring heaters

» Increases the temperature

Further Considerations for Experts

Annular Heating General Comments

» Established technique» Probably will require less power

as compared to Ring Heaters» Silica can be used as

compensation plates» No new material is required» Still needs an extra laser and

related control like negative dn/dT

» Less efficient than negative dn/dT method

Surface Thermal Lensing

1. Highly variable due to coating variations2. Differential Variations can be severe3. Changes the mode in the arm cavity and mode matching can decrease to 96% without correction4. Can cause contrast defects


Ring HeaterOn ITMs

Adaptive TelescopeOn PR2 and PR3


Advantages:1. 100% Mode Match2. No Differential Effects

Disadvantage1. Relatively large power2. Induced Noise

Advantages:1. 100% Mode Match2. Insensitive Optics3. Non-power-related

mismatchDisadvantage

1. Only Common Mode Corr



Recall:

Procedure1. Use RH on ITMs to keep the ROC on both ITMs same. 2. Use Adaptive correction on PR2 and PR3.

Assumptions1. We have selected a base value of 0.5 ppm as coating

absorption2. Any deviation more than this, has to be corrected by RH.

(Probably requires very low power). 3. If absorption is low, we have to apply some correction in

the hot case.

Proposed Scheme

Compensation Scheme for Adaptive Mode Matching – Hot Case

From MC

ITMx

PR3

ITMy

PR2

PR1

COMx

COMy

CO2 Laser Beam

CO2 Laser Beam

Optional RH

Optional RH

RH

RH

Parameter Unit Hot Value

MC Waist mm 2.113


PR1 ROC m -128.895

PR1 - PR2 m 16.655

PR2 ROC m 1.783


PR2 – PR3 m 16.655

PR3 ROC m 31.1217


PR3 –ITM m 24.995


ITM ROC m 2076.0

Mode Matching - 1.0

PR2 and PR3 ROC designed for hot value with 110 km thermal lens at ITM surface(i.e., 0.5 ppm, ITM ROC 2076 m)

Compensation Scheme for Adaptive Mode Matching- Cold Case

From MC

ITMx

PR3

ITMy

PR2

PR1

COMx

COMy

CO2 Laser Beam

RH

Correction @ PR2 m 10.49

Correction @ PR3 Km 3.72



Parameter Unit Value

MC Waist mm 2.113


PR1 ROC m -128.895

PR1 - PR2 m 16.655

PR2 ROC m 1.524


PR2 – PR3 m 16.655

PR3 ROC m 31.384


PR3 –ITM m 24.995


ITM ROC m 2037.5

Mode Matching - 1.0

Plate Heating

Details of Adaptive CorrectionPR Cavity Designed for Hot Case

Correction @ PR2

» Requires a 10 m converging lens at 3.5 mm as we move from hot to cold case

» Easily achievable by using CO2 heating

» Experimental demonstration in progress

Correction @ PR3

» Requires a 3.4 km diverging lens at 7.1 cm beam size as we move from cold to hot case

» Proposed locations are substrate of PR3 or separate plate before beam splitter

» No higher order losses in the hot state

» 10% higher order losses in the cold state

» Cold state losses can be decreased by using CO2 beam of larger size

Substrate Lens Heating

BS

Experimental Demonstration

0.85

0.9

0.95

1

Bac

k F

ocal

Dis

tanc

e (m

)

0 0.5 1 1.5 2 2.5 3 3.50

10

20

30

40

50

60

Heating Beam Power (W)

The

rmal

Len

s F

ocal

Len

gth

(m)

1 cm Thick Fused Silica Plate

HR

Coa

ting

@

1 m

icro

n 1 cm CO2 Heating Beam

1.8 mm Probe Beam

Summary Solid Line is H-V Theory Dots are experimental data 10 m focal length lens at 1.2 W of

surface heating at 1.8 mm probe beam and 1.0 cm heating beam

Problems/Concerns

CO2 beam power stability ‘Beam Walking’ Problem Beam Pointing Stability Geometrical Considerations

-0.2

0

0.2

0.4

0.6

0.8

1

1 401 801 1201 1601 2001 2401 2801 3201 3601

Time Seconds

Bea

m D

isp

lace

men

t at

1 m

in (

mm

)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Hea

tin

g B

eam

Po

wer

(W

)

X Axis Deviation

Y-Axis Deviation

Power

Inherently ‘Athermal’ Cavity

Reduce the Beam Size

Increase the ROC

Reduced beam Size Operation

4

6

8

10

12

14

16

18

20

2000.0 2020.0 2040.0 2060.0 2080.0 2100.0 2120.0 2140.0 2160.0 2180.0 2200.0

ROC (m)

wE

TM

=

wE

TM

(c

m)

-1.000

-0.975

-0.950

-0.925

-0.900

-0.875

-0.850

-0.825

-0.800

g F

ac

tor

Beam Radius

g factor

(2076, 6.0, -0.929)120 W Mode

No Correction Required Thermally Stable No differential problems

Increased Noise Reduces Sensitivity Deviates from 6.0 cm magical beam

size value ??

Can we operate here ???

Thermally Insensitive Operation at Reduced Beam Size

2050 2075 2100 2125 2150 2175 2200 2225 22500.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Hot ROC of ITM (m)

Mo

de

Mis

ma

tch

fro

m C

old

to H

ot C

on

diti

on

4.5

5

5.5

6

6.5

7

7.5

8

8.5

Bea

m S

ize

in b

oth

Col

d an

d H

ot C

ondi

tions

(cm

)

X: 2137Y: 5.691

Hot ROC = 2137 m, Cold ROC = 2096.27m Beam Size = 5.7 cm No Correction Required More Stable

Arbitrary Limit of 99% Mode Matching

Thermal Noise Considerations

Thermoelastic Noise Comparision (120 W Case)

0.0E+00

5.0E-24

1.0E-23

1.5E-23

2.0E-23

2.5E-23

3.0E-23

3.5E-23

4.0E-23

4.5E-23

5.0E-23

1.0 4.0 15.8 63.1 251.2 1000.0

Frequency (Hz)

No

ise

(√

Hz)

Total

Thermoelastic

Thermal

1. Thermoelastic noise scales as 1/(beam size)3/2 , not thermal noise

2. Thermoelastic noise is a minor contributor to the total thermal noise

3. Total Noise does not scale as 1/(beam size)3/2 of beam size

Comparison of Thermoelastic Noise

Thermoelastic Noise Comparision (120W Case)

0.0E+00

1.0E-23

2.0E-23

3.0E-23

4.0E-23

5.0E-23

6.0E-23

1.0 4.0 15.8 63.1 251.2 1000.0

Frequency (Hz)

No

ise

(√

Hz)

1.0362

1.0364

1.0366

1.0368

1.0370

1.0372

1.0374

1.0376

1.0378

1.0380

5.7 cm

6.0 cm

N5.69/N6.0

Comparison of Total Noise

Total Noise Comparision (120W Case)

0.0E+00

2.0E-24

4.0E-24

6.0E-24

8.0E-24

1.0E-23

1.2E-23

1.4E-23

1.6E-23

1.8E-23

2.0E-23

1.0 4.0 15.8 63.1 251.2 1000.0

Frequency (Hz)

No

ise

(√

Hz)

0.970

0.980

0.990

1.000

1.010

1.020

1.030

1.040

1.050

Total Noise at 6 cm

Total Noise at 5.7 cm

Ratio

Maximum hit of 4.5 % at 64 Hz

Is it acceptable??

Familiar Bench Noise Curve

5.7 cm Beam Size Details: Finesse: 1238.07 Power Recycling Factor: 16.83 Power on beam splitter: 2019.75 NS Binary Inspiral range: 126.24 Mpc Stochastic signal sensitivity: 6.836e-

009/h^2

6.0 cm Beam Size Details: Finesse: 1238.07 Power Recycling Factor: 16.83 Power on beam splitter: 2019.75 NS Binary Inspiral range: 130.61 Mpc Stochastic signal sensitivity: 6.682e-

009/h^2

Hardly any difference in Log Scale

Can we sacrifice a little sensitivity ??

100

101

102

103

10-25

10-24

10-23

10-22

10-21

10-20

10-19

f / Hz

h(f)

/ H

z1/2

quant.Int. thermalSusp. thermalResidual GasTotal noise

Summary/Recommendations




Com. Plate

?

Yes



Option 3



1. Reduce Beam Sizes to 5.7 cm → Higher Noise

-ve dn/dt Material Plate

RecommendationSuggestionsComments

Documents

Thermal Compensation in Stable Recycling Cavity 21/03/2006 LSC Meeting 2006 UF LIGO Group Muzammil A. Arain