1. Mirror thermal noises and its implications on the mirror design
Janyce Franc, Nazario Morgado, Raffaele Flaminio
Laboratoire des Matériaux Avancés-Lyon
Ronny Nawrodt, Iain Martin, Liam Cunningham, Alan Cumming, Sheila Rowan, James Hough
University of Glasgow
WP2 meeting – ERICE – 15th OCTOBER 2009
Janyce Franc-WG2-Erice

2. Janyce Franc-WG2-Erice
CONTENTS
INTRODUCTION
Objective and formula
PARAMETERS AND 300K
Different coatings
Total thermal noise in a HR mirror
PARAMETERS AND 10K
Substrates studies
Debate on the 18K temperature
Study on limiting thermal noise
PROPOSITION
ET-NOTE
ET-O21-O9 issue 2
Janyce Franc-WG2-Erice

3. Janyce Franc-WG2-Erice
Sources of Thermal Noises
Noises sources
Spectral Density
Brownian Coating
Brownian Substrate
Thermoelastic Coating
Thermoelastic Substrate
>>  c : possible adiabatic assumption
 <  c : impossible adiab. Assump.
Thermorefractive Coating
THERMO-OPTIC NOISE
(TE-TR compensation)
Voir ce qu’on dit sur ce transparent avec RAF
Janyce Franc-WG2-Erice

4. Janyce Franc-WG2-Erice
Substrates parameters at 300K
SiO2
Silicon
Sapphire 
5 10-9
10-8
2 10-9
 (kg.m-3)
2200
2330
3980
 (W.m-1.K-1)
1.38
145 33
C (J. K-1.Kg-1)
746
711
770
 (K-1)
 (dn/dT)
8 10-6
Y (GPa) 72
162.4
400 
0.17
0.22
0.235 n
1.45
3.453
1.75
Best 
Limiting factors
Janyce Franc-WG2-Erice

5. Janyce Franc-WG2-Erice
Coating parameters at 300K : low n materials
Higher Brownian
Noise
SiO2
Al2O3 
 (kg.m-3)
2200
3700
 (W.m-1.K-1)
0.5
3.3
C (J. K-1.Kg-1)
746
310
 (K-1)
 (dn/dT)
8 10-6
Y (GPa) 60
210 
0.17
0.22 n
1.45
1.63
SiO2
Al2O3 
 (kg.m-3)
2200
3700
 (W.m-1.K-1)
0.5
3.3
C (J. K-1.Kg-1)
746
310
 (K-1)
 (dn/dT)
8 10-6
Y (GPa) 60
210 
0.17
0.22 n
1.45
1.63
Higher TE
Noise
Thicker coating
Janyce Franc-WG2-Erice

6. Janyce Franc-WG2-Erice
Coating parameters at 300K : high n materials
TiTa2O5
TiO2
Nb2O5
ZrO2 
2 10-4
 (kg.m-3)
6425
4230
4590
6000
 (W.m-1.K-1)
0.6
0.45 1
1.09
C (J. K-1.Kg-1)
269
130
590 26
 (K-1)
 (dn/dT)
Y (GPa)
140
290 60
200 
0.23
0.28
0.2
0.27 n
2.06
2.3
2.32
2.15
TiTa2O5
TiO2
Nb2O5
ZrO2 
2 10-4
 (kg.m-3)
6425
4230
4590
6000
 (W.m-1.K-1)
0.6
0.45 1
1.09
C (J. K-1.Kg-1)
269
130
590 26
 (K-1)
 (dn/dT)
Y (GPa)
140
290 80
200 
0.23
0.28
0.2
0.27 n
2.06
2.3
2.32
2.15
Coating made
By evaporation
HIGH Brownian and
Thermo-optic Noise
Demander quel paramètre je mets : moyenne (ce qu’il y a là), la plus haute? La plus basse?
Janyce Franc-WG2-Erice

7. COMPARISON OF COATINGS AT 300K Unless otherwise specified
TOTAL THERMAL NOISES ON SIO2 SUBSTRATE
w=6 cm, T=4 ppm
Infinite mirror
Unless otherwise specified
SiO2-Ti:Ta2O5 coating offers the best result
SiO2-Nb2O5 is also a good candidate (but absorption slightly higher)
Refaire la simu en fonction de ce que dit RAF
Janyce Franc-WG2-Erice

8. COMPARISON OF SUBSTRATES AT 300 K
STANDARD COATING : SiO2-TiTa2O5 for 4 ppm transmission
TE noise limits
at low frequencies
Silica and sapphire substrates reach good sensitivity
Janyce Franc-WG2-Erice

9. Janyce Franc-WG2-Erice
Substrates parameters at 10K
SiO2
Silicon
Sapphire 
10-3
10-9
4 10-9
 (kg.m-3)
2220
2331
3997
 (W.m-1.K-1)
0.4
2330
800
C (J. K-1.Kg-1) 3
0.276
0.0934
 (K-1)
 (dn/dT)
9 10-8
Y (GPa)
71.2
162.4
464 
0.159
0.2205
0.23 n
1.449
3.45
1.75
SiO2
Silicon
Sapphire 
10-3
10-9
4 10-9
 (kg.m-3)
2220
2331
3997
 (W.m-1.K-1)
0.4
2330
800
C (J. K-1.Kg-1) 3
0.276
0.0934
 (K-1)
 (dn/dT)
9 10-8
Y (GPa)
71.2
162.4
464 
0.159
0.2205
0.23 n
1.449
3.45
1.75
10K
Janyce Franc-WG2-Erice

10. THERMAL NOISE OF DIFFERENT SUBSTRATES Unless otherwise specified
w=6 cm
Infinite mirror
Unless otherwise specified
SiO2 is unsuitable at 10K
Silicon and sapphire have the same tendency
With an advantage for silicon substrate
Janyce Franc-WG2-Erice

11. SILICON SUBSTRATE AT LOW TEMPERATURE
TOTAL THERMAL NOISES SUBSTRATE
HIGH SENSITIVITY VARIATIONS vs TEMPERATURES!!
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12. Debate around 18K
18K
10K
I. Martin et al. Class. Quantum Grav. 25 (2008)
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13. Simulation at 18K and assumption of =0(K-1)
Higher Brownian Noise
No thermoelastic substrate noise but
High Brownian Coating Noise
No particular interest in working at 18K (unless coatings get much better)
Janyce Franc-WG2-Erice

14. Janyce Franc-WG2-Erice
Coating 10K
SiO2 thin film
Ti:Ta2O5 thin film
Silicon substrate 
5 10-4
10-9
 (kg.m-3)
2200
6425
2331
 (W.m-1.K-1)
0.13
0.4
(taken at room T°)
2330
C (J. K-1.Kg-1) 4
50K
0.276
 (K-1)
 (dn/dT)
Y (GPa) 60
140
162.4 
0.159
0.21
0.2205 n
30K
2.05
30K
Janyce Franc-WG2-Erice

15. Unless otherwise specified
Study of the unknown parameters of Ta2O5 film
T=10K
Substrate : Si
w=8.65 cm (Ø: 45 cm)
Infinite MIRROR model = =
Unless otherwise specified
Janyce Franc-WG2-Erice

16. Impact of thermal coefficients on thermal noises
= (K-1)
= (K-1)
Thermal expansion coefficient limits sensitivity if value 20 times larger than 300 K
Thermo refractive coefficient limits sensitivity if value 200 times superior to 300 K
Janyce Franc-WG2-Erice

17. CONCLUSION on  and  parameters
THERMAL EXPANSION COEFFICIENT
1.Thermal expansion coefficient should attain to disturb the tendency of thermal noise
2. Values at room T° for thin film that we can find in the litterature stayed around 10-6.
At low temperature only substrate values are known and they still decrease.
THERMO OPTIC COEFFICIENT
1.Thermo refractive coefficient should attain to overtake the curve of brownian noise = Not reasonable !
2. Indeed, the values at room and low temperatures that we can find in the litterature stayed also around 10-6 or tends to decrease at cryogenic temperature. For example : Silica ( K), Silicon (5.8 30K).
Coating Thermoelastic and Thermorefractive noise not likely to be a problem
at cryogenic temperature: Brownian noise is the limit
Janyce Franc-WG2-Erice

18. Mirror reference design for ET (cold case)
Substrate material: several arguments in favor of silicon.
Good mechanical properties
Good transmission
Can rely on microelectronics industry investment to get larger pieces
Dimension
Microelectronics industry objective: 45 cm wafer by 2012
Reasonable reference solution: 45 cm diameter, 30 cm thick mirror (avoid thin mirror solution)
Weight ~110 kg (~x3 Advanced detectors): sufficient for pendulum thermal noise?
Coating
Keep present materials as reference solution: Ti:Ta2O5 / SiO2
Spectrophotometer measurements show good transparency at 1.5 mm (no absorption bands). But absorption need to be precisely measured
Alternatives: Nb2O5 and/or Gratings
Janyce Franc-WG2-Erice

19. PROPOSITION: Cryogenic mirror reference design
SILICON SUBSTRATE+ DIAMETER : 45cm + THICKNESS : 30 cm + STANDARD COATING
FINITE MIRROR
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20. Janyce Franc-WG2-Erice
Conclusion
At 300K : Silica substrate and Ti:Ta2O5/SiO2 coating the best solution so far
Other coatings deserve more studies (e.g. Nb2O5)
- At cryogenic temperature
Several coating thermal parameters unknown but detailed study shows small impact on total noise
Coating brownian noise remains the limit
Sapphire and Silicon gives similar results
No significant interest to operate at 18K. The coating loss angles are larger.
Silicon mirror (Ø=45 cm + h=30cm) + T° of 10K + Standard coating gives already promising result. Could be the first reference solution for cold mirror.
Janyce Franc-WG2-Erice