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

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

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 mirror @ cryogenic T° Change beam mode and beam size Janyce Franc-ET meeting-Erice

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

Introduction to simulations Unless otherwise specified Reference : S. Hild et al. arXiv:0906.2655v2 [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

Janyce Franc-ET meeting-Erice Parameters values @ 10K COATING SUBSTRATE L 0.5 10-4 H 2 10-4 L (K-1) -0.25 10-6 H (K-1) 3.6 10-6 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 1.44876 nH 2.06 YL (Pa) 60 10-9 YH (Pa) 140 10-9 s (K-1) 4.85 10-10 σs 0.2205 s (W.m-1.K-1) 2325 Cs (J.K-1.Kg-1) 2.76 10-1 s (Kg.m-3) 2330 s 0.5 10-9 Ys (Pa) 162.4 10-9 L : Low index material H : High index material Janyce Franc-ET meeting-Erice

References for 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 arXiv:cond.mat/9912139v1 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 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

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

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

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

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

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

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

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

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: 0906.2655v2 [gr-qc] Janyce Franc-ET meeting-Erice