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, 18th May 2010

2. 2nd generation detectors way to 3rd generation 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

3. planned sensitivities 2nd generation detectors thermal noise calculation way to 3rd generation thermal noise spectrum Planned detector sensitivities • steps for 2nd to 3rd • generation: a) increase laser power b) decrease thermal noise (substrate and coating) Frequenz in Hz

4. planned sensitivities 2nd generation detectors thermal noise calculation way to 3rd generation thermal noise spectrum Thermal noise processes coating substrate • Brownian noise [Liu, Thorne 2000] [Harry et al. 2002] general result • Thermoelastic noise [Braginsky 1999] [Braginsky, Fejer et al. 2004]

5. planned sensitivities 2nd generation detectors thermal noise calculation way to 3rd generation thermal noise spectrum Thermal noise for AdvLIGO [R. Adhikari] • thermal noise with minor influence on total sensitivity

6. thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire 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 decrease increase thermal conductivity

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

8. thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire 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 temperature 20…40 K • defects are • surface of the sample • lattice defects  crystalline samples (candidates: sapphire, silicon)

9. thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Assumed numbers for thermal conductivity [Touloukian] our values (pure silicon with low defects)

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

11. thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Rigorous noise calculation for silicon (Ø 50 cm x 30 cm, 111) T=300 K T=20 K • 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:

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

13. thermal lensing 2nd generation detectors TE noise of crystals way to 3rd generation silicon vs. sapphire Silicon vs. Sapphire Silicon Sapphire thermal noise requirements good good hardness  machinability good bad industrial background good bad optical absorption at 1064 nm bad medium • change of wavelength to 1550 nm will increase Brownian coating noise moderately, • 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

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

15. 2nd generation detectors way to 3rd generation 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: