Thermal noise reduction through LG modes Janyce Franc

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 2 nd ET General Meeting-ERICE 15 th October 2009 Janyce Franc-ET meeting-Erice 1

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 2

Thermal noise in 3 rd 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 mirror @ cryogenic T° -Change beam mode and beam size Janyce Franc-ET meeting-Erice 3

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 thermal noise for future GW detector. Janyce Franc-ET meeting-Erice 4

Introduction to simulations Unless otherwise specified Reference : S. Hild et al. ar. Xiv: 0906. 2655 v 2 [gr-qc] Coatings Standard : Si. O 2 -Ta 2 O 5 (HL)19 HLL : Transmission 4 ppm Substrate Silicon Temperature 10 K 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 LG 55 : w = a/5. 1 = 6. 1 cm LG 33 : w = a/4. 3 = 7. 2 cm LG 00 : w=a/2. 6 = 11. 9 cm Janyce Franc-ET meeting-Erice 5

Parameters values @ 10 K SUBSTRATE COATING L 0. 5 10 -4 H 2 10 -4 s (K-1) 4. 85 10 -10 σs 0. 2205 L (K-1) -0. 25 10 -6 s (W. m-1. K-1) 2325 H (K-1) 3. 6 10 -6 Cs (J. K-1. Kg-1) 2. 76 10 -1 σL 0. 159 s (Kg. m-3) 2330 σH 0. 23 s 0. 5 10 -9 L (W. m-1. K-1) 0. 13 H (W. m-1. K-1) 0. 4 Ys (Pa) 162. 4 10 -9 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 n. L 1. 44876 n. H 2. 06 YL (Pa) 60 10 -9 YH (Pa) 140 10 -9 L : Low index material H : High index material Janyce Franc-ET meeting-Erice 6

References formula For Infinite Mirrors with Gaussian Beam: 1. M. L. Gorodetsky Phys. Lett. A 372 (2008) 6813 -6822 Summary of all thermal noise formula 2. Cerdonio et al. Phys. Review D, 63, 082003 Description of substrate TE Noise without adiabatic assumption 3. Braginsky, Gorodetsky, Vyatchanin ar. Xiv: cond. mat/9912139 v 1 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) 244 -255 Gives details of calculation for Coating TE Noises sources Brownian Coating Brownian Substrate Thermoelastic Coating Thermoelastic Substrate INFINITE MIRRORS 4 4 4&1 4 1 & 4 (in progress) 1 & 4 & 5 (in progress) 4&2&3 Janyce Franc-ET meeting-Erice 7

Coating Brownian Noise Conclusions on Coat. Brownian Noise : -No difference between finite and infinite mirrors -LG 33 and LG 55 give the same results LG 0, 0/LG 3, 3 For finite mirror 1. 71 LG 0, 0/LG 3, 3 For infinite mirror 1. 61 NB: ‘Finite mirror’ is 62 cm diameter mirror Janyce Franc-ET meeting-Erice 8

Substrate Brownian Noise Conclusions on Sub. Brownian Noise : - No difference between finite and infinite mirrors for Gaussian Beam - TN decreases in finite mirror for LG 33 and LG 55 - A small advantage for LG 55 compare to LG 33 LG 0, 0/LG 3, 3 For finite mirror 1. 97 LG 0, 0/LG 3, 3 For infinite mirror 1. 39 Janyce Franc-ET meeting-Erice 9

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 10

Substrate Thermoelastic Noise Conclusions on Sub. TE Noise : - No difference between finite and infinite mirror - Advantage for LG 33 - Calculation for LG 55 is in progress LG 0, 0/LG 3, 3 For finite mirror 1. 13 to 1. 4 LG 0, 0/LG 3, 3 For infinite mirror 1. 13 to 1. 4 Janyce Franc-ET meeting-Erice 11

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

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=10 K BETTER RESULT FOR Ø=45 cm with LG 33 than Ø=62 cm with LG 00 Janyce Franc-ET meeting-Erice 13

Total Thermal Noise TARGET Thermal Noise for 2 nd generation GWD • Interferometer arms : 3 km • Temperature : 300 K • Large beams : 6. 7 cm (gaussian beam) Thermal Noise for 3 rd generation GWD • Long interferometer arms : 10 km • Temperature : 10 K • 2 cases : Ø=62 cm LG 00 & Ø= 45 cm LG 33 Low T° + High Mirror Size + LG 33 = Thermal noise Target confirmed Janyce Franc-ET meeting-Erice 14

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 - LG 33 mode appears as a good solution in order to decrease the total thermal noise (thermal noise reduced by 1. 71 for LG 33 compared to LG 00). - A study of LG 55 does not demonstrate a better result than LG 33. - Writing up of an ET note in progress - A proposition of ET design, using large dimension mirror and LG 33 mode, gives good sensitivity: Stefan Hild et al. ar. Xiv: 0906. 2655 v 2 [gr-qc] Janyce Franc-ET meeting-Erice 15