Transcript D. Heinert
Properties of candidate materials for cryogenic mirrors Properties of candidate materials for cryogenic mirrors D. Heinert, R. Nawrodt, C. Schwarz, P. Seidel Institute of Solid State Physics, University of Jena Kyoto, 18th May 2010 Heinert et al. 01.03.2010 1 2nd generation detectors way to 3rd generation Properties of candidate materials for cryogenic mirrors outline I current detector parameters • sensitivity • noise sources II improvement to 3rd generation • possibilities of increasing sensitivity • challenges (thermal lensing, cooling) • substrate noise contributions impact on detector‘s working point estimate resulting noise for ET III conclusion Heinert et al. 01.03.2010 2 planned sensitivities 2nd generation detectors thermal noise calculation way to 3rd generation thermal noise spectrum Properties of candidate materials for cryogenic mirrors 3 Planned detector sensitivities • steps for 2nd to 3rd generation: a) increase laser power b) decrease thermal noise (substrate and coating) Heinert et al. 01.03.2010 planned sensitivities 2nd generation detectors thermal noise calculation way to 3rd generation thermal noise spectrum Properties of candidate materials for cryogenic mirrors 4 Thermal noise processes substrate coating • Brownian noise S ITM X 2k BT 1 2 ( f , T ) 3/ 2 substrate( f , T ) f wY Sx ( f ,T ) [Liu, Thorne 2000] 2k BT d Y ' Y || 2 2 f w Y Y Y' [Harry et al. 2002] general result • Thermoelastic noise S ITM TE S x ( ) ~ T 4k BT 1 ( f ,T ) 5 / 2 2 C 2 f 2 w3 2 2 ~2 8k BT 2 d S CF 2 1 s g ( ) STE ( f , T ) 2 2 f w CS 2 [Braginsky 1999] Heinert et al. [Braginsky, Fejer et al. 2004] 01.03.2010 planned sensitivities 2nd generation detectors thermal noise calculation way to 3rd generation thermal noise spectrum Properties of candidate materials for cryogenic mirrors Thermal noise for AdvLIGO [R. Adhikari] • thermal noise with minor influence on total sensitivity Heinert et al. 01.03.2010 5 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors Task 1: Reducing photon shot noise • requires increase of laser power in the interferometer increase of optically absorbed power in the test mass • change of refractive index variation of wave front effect of thermal lensing of transmissive parts • fused silica with high dn 14 10 6 K 1 dT optical instability of the interferometer • strategies to solve the problem decrease increase thermal conductivity Heinert et al. 01.03.2010 6 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 7 Decrease of thermal lensing I: decrease of beta • Why not just cool fused silica test masses? 0 n(T ) T const , dn T 0 0 dT no thermal lensing • But: remember thermal noise expressions [Nawrodt 2008] S x ( ) ~ T 1E-3 this even overcompensates benefit due to cooling explanation: - defect energy distribution in amorphous solids (jumps of oxygen in the structure) mechanical loss • fused silica show increasing loss for decreasing temperature 1E-4 1E-5 1E-6 1E-7 0 50 100 150 200 temperature T [K] Heinert et al. 01.03.2010 250 300 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 8 Decrease of thermal lensing II: increasing thermal conductivity • general temperature behaviour of thermal conductivity b) 3 zones: a) phonon population b) defects c) phonon collisions a) c) defects limit global maximum of thermal conductivity 20…40 K • defects are - surface of the sample - lattice defects temperature crystalline samples (candidates: sapphire, silicon) Heinert et al. 01.03.2010 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 9 Assumed numbers for thermal conductivity our values (pure silicon with low defects) Heinert et al. [Touloukian] 01.03.2010 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 10 Consequences for thermoelastic noise • Zener‘s model for thermoelastic damping change of thermoelastic noise via FDT ET0 2 h 2 C ~ , 2 C 1 2 2 h • alpha is high in crystalline solids [Zener, 1937] • change in thermal conductivity changes position of maximum for TE losses 2 10 fused silica -2 1 10 0 -3 10 fmax [Hz] fmax [Hz] silicon h=30 cm 10 10 -1 10 -4 10 -2 10 -3 -5 10 0 50 100 150 200 250 300 10 0 50 100 150 T [K] T [K] Heinert et al. 01.03.2010 200 250 300 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 11 Rigorous noise calculation for silicon (Ø 50 cm x 30 cm, 111) 10 10 10 T=300 K -18 10 bulk Brownian bulk TE coating Brownian coating TE coating TR total -20 thermal noise [m/ Hz] thermal noise [m/ Hz] 10 -22 -24 10 0 10 1 2 10 frequency [Hz] 10 3 10 4 10 10 10 T=20 K -18 bulk Brownian bulk TE coating Brownian coating TE coating TR total -20 -22 -24 10 0 10 1 2 10 frequency [Hz] 10 3 coating Brownian dominates noise spectrum for low temperatures hope for alternative reflection concepts (gratings, Khalili etalons, …) • restriction of the detector‘s working point temperature, ideal:T 18 K 0 Heinert et al. 01.03.2010 10 4 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 12 Rigorous noise calculation for sapphire (Ø 50 cm x 30 cm, zcut) T=300 K 10 10 10 -18 10 bulk Brownian bulk TE coating Brownian coating TE coating TR total -20 thermal noise [m/ Hz] thermal noise [m/ Hz] 10 T=20 K -22 -24 10 0 10 1 2 10 frequency [Hz] 10 3 10 4 10 10 10 -18 bulk Brownian bulk TE coating Brownian coating TE coating TR total -20 -22 -24 10 0 10 1 2 10 frequency [Hz] • bulk thermoelastic in the same order as coating Brownian for 20 K Heinert et al. 01.03.2010 10 3 10 4 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 13 Silicon vs. Sapphire Silicon Sapphire thermal noise requirements good good hardness machinability good bad industrial background good bad bad medium optical absorption at 1064 nm • change of wavelength to 1550 nm will increase Brownian coating noise moderately, 4 but also decreases stray light by factor 4.5 ( ) • monocrystalline silicon available in diameters up to 50 cm within the next 5 years silicon is presently the best choice for substrate material Heinert et al. 01.03.2010 thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Properties of candidate materials for cryogenic mirrors 14 Temperature dependene of mechanical loss of silicon • measurement for crystalline silicon (Ø 76.2 mm x 75 mm) -7 10 mechanical loss 111 100 silicon maintains low losses at low temperatures S x ( ) ~ T -8 10 low Brownian noise • further information: see talk of Ch. Schwarz -9 10 0 50 100 150 200 250 300 temperature [K] Heinert et al. 01.03.2010 2nd generation detectors way to 3rd generation Properties of candidate materials for cryogenic mirrors 15 Conclusions • to achieve 3rd generation sensitivity we have to go cryogenic • no fused silica due to high Brownian noise • silicon as main candidate for substrate material with - availability of large geometries - big industry behind cool detector to 20 K due to high thermoelastic noise change wavelength to 1550nm due to optical absorption • coating Brownian noise dominates below ca. 25 K • achievable noise at 20 K: S x (100 Hz ) 11022 Heinert et al. m Hz 01.03.2010