1. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 1 Properties of candidate materials for cryogenic mirrors D. Heinert, R. Nawrodt, C. Schwarz, P. Seidel Institute of Solid State Physics, University of Jena Kyoto, 18 th May 2010

2. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 2 I current detector parameters outline II improvement to 3rd generation challenges (thermal lensing, cooling) sensitivity possibilities of increasing sensitivity 2nd generation detectors way to 3rd generation noise sources substrate noise contributions III conclusion  impact on detector‘s working point  estimate resulting noise for ET

3. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 3 a) increase laser power b) decrease thermal noise (substrate and coating) Frequenz in Hz Planned detector sensitivities steps for 2nd to 3rd generation: 2nd generation detectors way to 3rd generation planned sensitivities thermal noise calculation thermal noise spectrum

4. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 4 Thermal noise processes Brownian noise Thermoelastic noise substratecoating [Braginsky 1999] [Liu, Thorne 2000] [Braginsky, Fejer et al. 2004] [Harry et al. 2002] 2nd generation detectors way to 3rd generation planned sensitivities thermal noise calculation thermal noise spectrum general result

5. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 5 Thermal noise for AdvLIGO thermal noise with minor influence on total sensitivity 2nd generation detectors way to 3rd generation planned sensitivities thermal noise calculation thermal noise spectrum [R. Adhikari]

6. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 6 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  optical instability of the interferometer strategies to solve the problem decreaseincrease thermal conductivity 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire

7. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 7 Why not just cool fused silica test masses? But: remember thermal noise expressions Decrease of thermal lensing I: decrease of beta  no thermal lensing fused silica show increasing loss for decreasing temperature  this even overcompensates benefit due to cooling [Nawrodt 2008] explanation: - defect energy distribution in amorphous solids (jumps of oxygen in the structure) 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire

8. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 8  crystalline samples (candidates: sapphire, silicon) Decrease of thermal lensing II: increasing thermal conductivity general temperature behaviour of thermal conductivity temperature 3 zones: a) phonon population b) defects c) phonon collisions 20…40 K  defects limit global maximum of thermal conductivity defects are - surface of the sample - lattice defects a) b) c) 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire

9. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 9 [Touloukian] Assumed numbers for thermal conductivity 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire our values (pure silicon with low defects)

10. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 10 change in thermal conductivity changes position of maximum for TE losses alpha is high in crystalline solids Consequences for thermoelastic noise Zener‘s model for thermoelastic damping  change of thermoelastic noise via FDT h 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire h=30 cm [Zener, 1937]

11. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 11 restriction of the detector‘s working point temperature, ideal: T=300 KT=20 K  coating Brownian dominates noise spectrum for low temperatures  hope for alternative reflection concepts (gratings, Khalili etalons, …) Rigorous noise calculation for silicon (Ø 50 cm x 30 cm, 111) 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire

12. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 12 Rigorous noise calculation for sapphire (Ø 50 cm x 30 cm, zcut) T=300 K T=20 K 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire bulk thermoelastic in the same order as coating Brownian for 20 K

13. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 13 Silicon vs. Sapphire monocrystalline silicon available in diameters up to 50 cm within the next 5 years change of wavelength to 1550 nm will increase Brownian coating noise moderately, but also decreases stray light by factor 4.5  silicon is presently the best choice for substrate material thermal noise requirements industrial background SiliconSapphire hardness  machinability optical absorption at 1064 nm good bad good bad good badmedium 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire

14. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 14 measurement for crystalline silicon (Ø 76.2 mm x 75 mm) Temperature dependene of mechanical loss of silicon  silicon maintains low losses at low temperatures  low Brownian noise further information: see talk of Ch. Schwarz 2nd generation detectors way to 3rd generation thermal lensing TE noise of crystals silicon vs. sapphire

15. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 15 Conclusions no fused silica due to high Brownian noise silicon as main candidate for substrate material with - availability of large geometries - big industry behind to achieve 3rd generation sensitivity we have to go cryogenic coating Brownian noise dominates below ca. 25 K  cool detector to 20 K due to high thermoelastic noise  change wavelength to 1550nm due to optical absorption achievable noise at 20 K: 2nd generation detectors way to 3rd generation

16. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 16 Rigorous noise calculation for silicon (Ø 50 cm x 30 cm, 111), T=20 K

17. Heinert et al.01.03.2010 Properties of candidate materials for cryogenic mirrors 17 Thermal noise opponents: silicon at 20 k vs. fused silica at 300 K silicon fused silica