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
Janyce Franc-WG2-Erice CONTENTS INTRODUCTION Objective and formula PARAMETERS AND SIMULATIONS @ 300K Different coatings Total thermal noise in a HR mirror PARAMETERS AND SIMULATIONS @ 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
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
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) 0.51 10-6 2.54 10-6 5.1 10-6 (dn/dT) 8 10-6 5.15 10-6 1.3 10-5 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
Janyce Franc-WG2-Erice Coating parameters at 300K : low n materials Higher Brownian Noise SiO2 Al2O3 0.5 10-4 2.4 10-4 (kg.m-3) 2200 3700 (W.m-1.K-1) 0.5 3.3 C (J. K-1.Kg-1) 746 310 (K-1) 0.51 10-6 8.4 10-6 (dn/dT) 8 10-6 1.3 10-6 Y (GPa) 60 210 0.17 0.22 n 1.45 1.63 SiO2 Al2O3 0.5 10-4 2.4 10-4 (kg.m-3) 2200 3700 (W.m-1.K-1) 0.5 3.3 C (J. K-1.Kg-1) 746 310 (K-1) 0.51 10-6 8.4 10-6 (dn/dT) 8 10-6 1.3 10-6 Y (GPa) 60 210 0.17 0.22 n 1.45 1.63 Higher TE Noise Thicker coating Janyce Franc-WG2-Erice
Janyce Franc-WG2-Erice Coating parameters at 300K : high n materials TiTa2O5 TiO2 Nb2O5 ZrO2 2 10-4 6.3 10-3 4.6 10-4 5.9 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) 3.6 10-6 0.5 10-6 5.8 10-6 10.3 10-6 (dn/dT) 14 10-6 -1.8 10-4 1.43 10-5 10 10-5 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 6.3 10-3 4.6 10-4 5.9 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) 3.6 10-6 0.5 10-6 5.8 10-6 10.3 10-6 (dn/dT) 14 10-6 -1.8 10-4 1.43 10-5 10 10-5 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
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
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
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) -0.25 10-6 4.85 10-10 5.3 10-10 (dn/dT) 1.01 10-6 5.8 10-6 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) -0.25 10-6 4.85 10-10 5.3 10-10 (dn/dT) 1.01 10-6 5.8 10-6 9 10-8 Y (GPa) 71.2 162.4 464 0.159 0.2205 0.23 n 1.449 3.45 1.75 Unsuitable @ 10K Janyce Franc-WG2-Erice
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
SILICON SUBSTRATE AT LOW TEMPERATURE TOTAL THERMAL NOISES SUBSTRATE HIGH SENSITIVITY VARIATIONS vs TEMPERATURES!! Janyce Franc-WG2-Erice
Debate around 18K 18K 10K I. Martin et al. Class. Quantum Grav. 25 (2008) 055005 Janyce Franc-WG2-Erice
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
Janyce Franc-WG2-Erice Coating Parameters @ 10K SiO2 thin film Ti:Ta2O5 thin film Silicon substrate 5 10-4 3.8 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 3.17 @ 50K 0.276 (K-1) -0.25 10-6 3.6 10-6 4.85 10-10 (dn/dT) 1.01 10-6 14 10-6 5.8 10-6 Y (GPa) 60 140 162.4 0.159 0.21 0.2205 n 1.44876 @ 30K 2.05 3.45 @ 30K Janyce Franc-WG2-Erice
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 =3.6 10-6 =14 10-6 Unless otherwise specified Janyce Franc-WG2-Erice
Impact of thermal coefficients on thermal noises =25 10-4 (K-1) =6 10-5 (K-1) Thermal expansion coefficient limits sensitivity if value 20 times larger than value @ 300 K Thermo refractive coefficient limits sensitivity if value 200 times superior to value @ 300 K Janyce Franc-WG2-Erice
CONCLUSION on and parameters THERMAL EXPANSION COEFFICIENT 1.Thermal expansion coefficient should attain 6 10-5 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 25 10-4 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 (1.01 10-6 @ 30K), Silicon (5.8 10-6 @ 30K). Coating Thermoelastic and Thermorefractive noise not likely to be a problem at cryogenic temperature: Brownian noise is the limit Janyce Franc-WG2-Erice
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
PROPOSITION: Cryogenic mirror reference design SILICON SUBSTRATE+ DIAMETER : 45cm + THICKNESS : 30 cm + STANDARD COATING FINITE MIRROR Janyce Franc-WG2-Erice
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