1. Thermal noise reduction through LG modes
Janyce Franc, Raffaele Flaminio, Massimo Galimberti
Laboratoire des Matériaux Avancés-LYON
Simon Chelkowski, Andreas Freise
University of Birmingham
Stefan Hild
University of Glasgow
2nd ET General Meeting-ERICE
15th October 2009
Janyce Franc-ET meeting-Erice

2. Janyce Franc-ET meeting-Erice
Contents
Introduction
Motivations
Objectives
Laguerre-Gauss advantages
Simulations
References and Parameters
Influence of LG mode on Brownian and TE Noises
LG modes and different substrates
LG modes and different mirror sizes
Conclusion and future work
Janyce Franc-ET meeting-Erice

3. Thermal noise in 3rd generation of GWD
All these thermal noise sources are at least at some frequencies above the ET target
The ideas to reduce thermal noise :
Arm lengths
New coating materials
Cooling cryogenic T°
Change beam mode and beam size
Janyce Franc-ET meeting-Erice

4. Motivation for using LG modes
Advantages : Best power distribution on the mirror surface
Lower Thermal Noise
Lower Thermal Lensing
The idea is to prove the efficiency of the combination of cryogenic temperature and the use of Laguerre-Gauss modes to decrease the thermal noise for future GW detector.
Janyce Franc-ET meeting-Erice

5. Introduction to simulations Unless otherwise specified
Reference : S. Hild et al. arXiv: v2 [gr-qc]
Coatings
Standard : SiO2-Ta2O5
(HL)19HLL : Transmission 4 ppm
Substrate
Silicon
Temperature
10K
Mirror dimension
2 cases considered :
Infinite mirror
Finite mirror : Ø : 62 cm, h : 30 cm
Beam dimensions
Ratio insuring 1 ppm diffraction losses versus order of the LG mode
LG55 : w = a/5.1 = 6.1 cm
LG33 : w = a/4.3 = 7.2 cm
LG00 : w=a/2.6 = 11.9 cm
Janyce Franc-ET meeting-Erice

6. Janyce Franc-ET meeting-Erice
Parameters 10K
COATING
SUBSTRATE L H
2 10-4
L (K-1)
H (K-1) σL
0.159 σH
0.23
L (W.m-1.K-1)
0.13
H (W.m-1.K-1)
0.4
CL (J.K-1.Kg-1) 4
CH (J.K-1.Kg-1)
3.17
L (Kg.m-3)
2200
H (Kg.m-3)
6850 nL nH
2.06
YL (Pa)
YH (Pa)
s (K-1) σs
0.2205
s (W.m-1.K-1)
2325
Cs (J.K-1.Kg-1)
s (Kg.m-3)
2330 s
Ys (Pa)
L : Low index material
H : High index material
Janyce Franc-ET meeting-Erice

7. References for formula
For Infinite Mirrors with Gaussian Beam:
1. M. L. Gorodetsky Phys. Lett. A 372 (2008)
Summary of all thermal noise formula
2. Cerdonio et al. Phys. Review D, 63,
Description of substrate TE Noise without adiabatic assumption
3. Braginsky, Gorodetsky, Vyatchanin arXiv:cond.mat/ v1 1999
Helpful to determine substrate TE Noise without adiabatic assumption applicable to higher LG modes
For Finite Mirrors with LG modes:
4. B. Mours et al CQG 23 (2006), J.-Y.Vinet : Living Rev. Relativity 12,  (2009)
Provides all formula for finite/infinite mirrors and for gaussian and LG beams
5. V.B. Braginsky, S.P. Vyatchanin, physics letter A 312 (2003)
Gives details of calculation for Coating TE Noise.
Noises sources
INFINITE MIRRORS
FINITE MIRRORS
Brownian Coating 4
Brownian Substrate
4 & 1
Thermoelastic Coating
1 & 4 (in progress)
1 & 4 & 5 (in progress)
Thermoelastic Substrate
4 & 2
4 & 2 & 3
Janyce Franc-ET meeting-Erice

8. Coating Brownian Noise
Conclusions on Coat. Brownian Noise :
-No difference between finite and infinite mirrors
-LG33 and LG55 give the same results
LG0,0/LG3,3
For finite mirror
1.71
For infinite mirror
1.61
NB: ‘Finite mirror’ is 62 cm diameter mirror
Janyce Franc-ET meeting-Erice

9. Substrate Brownian Noise
Conclusions on Sub. Brownian Noise :
- No difference between finite and infinite mirrors for Gaussian Beam
- TN decreases in finite mirror for LG33 and LG55
- A small advantage for LG55 compare to LG33
LG0,0/LG3,3
For finite mirror
1.97
For infinite mirror
1.39
Janyce Franc-ET meeting-Erice

10. Coating Thermoelastic Noise
Work in progress and in discussion with Jean-Yves Vinet
Some problems have been identified in comparing formula from
different references
Janyce Franc-ET meeting-Erice

11. Substrate Thermoelastic Noise
Conclusions on Sub. TE Noise :
- No difference between finite and infinite mirror
- Advantage for LG33
- Calculation for LG55 is in progress
LG0,0/LG3,3
For finite mirror
1.13 to 1.4
For infinite mirror
Janyce Franc-ET meeting-Erice

12. Substrates Comparison
Study of two limiting Noises : Coating and Substrate Brownian Noise
Coating Brownian Noise
Substrate Brownian Noise
Finite Mirror
Ø=62 cm
h=30cm
COATING BROWNIAN NOISE
ADVANTAGE SAPPHIRE
SUBSTRATE BROWNIAN NOISE
ADVANTAGE SILICON
Janyce Franc-ET meeting-Erice

13. Total Thermal noise in Interferometer
Mirror sizes effects : Diameter dependency
For 1 ppm diff. losses
Ø=35 cm
w=6.7 cm
Ø=45 cm
w=8.7 cm
Ø=62 cm
w=11.9 cm
Silicon substrate
Arm = 10 km
T=10K
HORS SUJET?
BETTER RESULT FOR Ø=45cm with LG33 than Ø=62cm with LG00
Janyce Franc-ET meeting-Erice

14. Total Thermal Noise TARGET
Thermal Noise for 2nd generation GWD
Interferometer arms : 3 km
Temperature : 300K
Large beams : 6.7 cm (gaussian beam)
Thermal Noise for 3rd generation GWD
Long interferometer arms : 10 km
Temperature : 10K
2 cases : Ø=62 cm LG00 & Ø= 45 cm LG33
Low T° + High Mirror Size + LG33 = Thermal noise Target confirmed
Janyce Franc-ET meeting-Erice

15. Conclusion and future work
- Impact of different thermal noises depends on the considered LG modes but the main results does not change: coating Brownian noise remains the limit
- LG33 mode appears as a good solution in order to decrease the total thermal noise (thermal noise reduced by 1.71 for LG33 compared to LG00).
- A study of LG55 does not demonstrate a better result than LG33.
- Writing up of an ET note in progress
- A proposition of ET design, using large dimension mirror and LG33 mode, gives good sensitivity: Stefan Hild et al. arXiv: v2 [gr-qc]
Janyce Franc-ET meeting-Erice