Mirrors for Advanced Interferometer – substrate and coating requirements

1. Mirrors for Advanced Interferometer – substrate and coating requirements S.Rowan ESF workshop Perugia 20-23rd September 2005

2. Reminder of motivation Analyse the recent developments in technologies foreseen for Advanced detectors to explore the path needed for a European 3rd generation gravitational wave detector • Consider here: technology status of some aspects of the detector mirrors and coatings • Thermal noise from mirrors and coatings forms an important limit to design sensitivities at most sensitive point in mid-frequency band Coated fused silica mirror ~18cm diameter

3. Timescales VIRGO/GEO/LIGO all plan ‘Advanced’ upgrades: • VIRGO (Benoit, yesterday) • 2008/9 VIRGO + • 2011 (?) Advanced VIRGO • LIGO • 2008/9 (?) staged improvements • 2010-13 Advanced LIGO • GEO • 2008 ? GEO-HF – staged improvements • 3rd European detector (20??) • Common theme for Advanced detectors is higher laser power (Benno) and new mirrors • What is the status of technologies related to low-thermal-noise mirrors? (Gregg will talk re: thermal loading effects)

4. Current mirrors • All detectors currently use fused silica substrates with coatings formed from SiO2/Ta2O5 • Optics in the detectors were installed several years ago • Design curves for GEO, LIGO, VIRGO which we use were based on best models for thermal noise at that time • The same optics are still installed but our models for the thermal noise have changed a lot LIGO fused silica mirror (10kg) in suspension cradle

5. Three significant changes • Levin: for mirrors with inhomogeneous loss we should not simply add incoherently the noise from the thermally excited modes of a mirror – loss from a volume close to the laser beam dominates • Penn et al: loss in silica may be modelled as sum of surface, thermoelastic, and frequency dependent bulk losses – the latter improving towards low frequency • Levin, (Nakagawa, Crooks, Harry et al) Dissipation from dielectric mirror coatings is at a significant level

6. Substrates - Fused silica • Two big vendors used – Corning (LIGO) , Heraeus (LIGO, VIRGO, GEO) • Each vendor makes a number of different optical grades • Empirical measurements suggest: • Heraeus fused silica has lower mechanical loss than Corning • The various Heraeus Suprasil grades have different loss from one another

7. Substrates – fused silica • Semi-empirical model developed by Penn et al (Phys Rev Lett, Submitted) arXive:gr-qc/0507097 Mechanical loss in fused silica • C1, C2, C3, C4 are constants fitted to existing loss measurements, and dependent of the exact grade of silica used

8. Substrates – fused silica • Penn et al point out: ’’The internal friction of very pure fused silica is associated with strained Si-O-Si bonds, where the energy of the bond has minima at two different bond angles, forming an asymmetric double-well potential. Redistribution of the bond angles in response to an applied strain leads to mechanical dissipation’’ • Empirically we deduce that the manufacturing and processing of the different grades of silica is affecting the distribution of bond angles

9. Bulk loss • Empirically it seems that Suprasil 311, 312 are the grades of silica with the lowest loss (SV not as low ??) • Good! -We tend to choose these for our optical needs • However we don’t yet understand in detail what processing (annealing/cooling/ temps/rates geometry etc) optimises the mechanical loss (eg why is Corning silica not as good as Heraeus..?) (Penn et al actively researching this area) • Understanding this would perhaps allow us to lower loss even further

10. Surface loss • Empirically, measurements are consistent with the existence of a surface loss ‘limit’ • Annealing samples allows them to approach this, but dissipation then reaches a lower ‘limit’ • The source(s) of dissipation for this surface layer are not unambiguously determined (microcracks, polishing damage – what about flame annealled samples??)

11. Substrates – fused silica • Status of current models and experiments suggest substrate thermal noise could be ~10 times lower (or more?) than old design sensitivities - good news!! • Maybe we can lower it even further – however…. • Coatings – now are a dominant source of thermal noise

12. Consider an ‘Advanced LIGO-Like’ design • Coating thermal noise is expected to be the dominant noise source at mid frequencies for advanced interferometer designs Penn et al

13. Coating studies • Thermal noise from the dielectric mirror coatings applied to test masses is -essentially acceptable- for Adv. LIGO, (Adv. VIRGO ?) • However, reduction in coating noise translates directly to interferometer sensitivity • Unacceptable for any future detectors beyond Adv. LIGO • Studies carried out with coatings from number of vendors (MLD, Waveprecision, REO, LMA Lyon) to study the mechanical dissipation of ion-beam-sputtered dielectric coatings via loss measurements • Focussed initially on SiO2/Ta2O5 coatings

14. 5.0E-04 4.5E-04 4.0E-04 3.5E-04 3.0E-04 Loss 2.5E-04 2.0E-04 1.5E-04 lambda/4 silica, lambda/4 tantala 1.0E-04 lambda/8 tantala, 3lambda/8 silica 3lambda/8 tantala, lambda/8 silica 5.0E-05 0.0E+00 0 10 20 30 40 50 60 70 80 Frequency [kHz] Mechanical loss of multi-layer SiO2/Ta2O5 coatings with varying proportions of SiO2 and Ta2O5

15. Silica and tantala mechanical loss results 5.E-04 y = 1.78E-09x + 3.17E-04 5.E-04 Assume for each material:fresidual = f0 + fff 4.E-04 4.E-04 3.E-04 Loss 3.E-04 2.E-04 Silica residual loss 2.E-04 Tantala residual loss y = 1.32E-09x + 1.16E-04 1.E-04 5.E-05 0.E+00 0 10 20 30 40 50 60 70 80 Frequency [kHz] For tantala: fresidual = (3.2 ± 0.1) x 10-4 + f(1.8 ± 0.4) x 10-9 For silica: fresidual = (1.2± 0.2) x 10-4 + f(1.3 ± 0.5) x 10-9

16. Status • Measured losses are dominated by intrinsic loss of the materials involved • Ta2O5 is mechanically lossier than SiO2 • Studies carried out of loss of Ta2O5 doped with TiO2 - suggestion by LMA

17. Doping of Ta2O5 with TiO2 Loss Angle of SiO2 /TiO2 doped Ta2O5 at 100 Hz • Clear improvement with addition of titania • Appears no strong correlation with amount of TiO2 • However exact concentrations of TiO2 not known • Results from Ian MacLaren in Glasgow now available -4 x 10 3 Small Coater Large Coater 2.5 Loss Angle 2 1.5 0 10 20 30 40 50 60 Relative Concentration

18. Doping of Ta2O5 with TiO2 • Mechanism by which TiO2 reduces dissipation not yet known • (Helping prevent movement of oxygen vacancies..??) • Recent measurements by Black et al (Caltech) confirm reduction in thermal noise from doped coatings Loss Angle of SiO2 /TiO2 doped Ta2O5 at 100 Hz -4 x 10 3 Small Coater Large Coater 2.5 Loss Angle 2 1.5 0 10 20 30 40 50 60 Relative Concentration

19. Importance of material properties • NB to get previous loss results needed to know the Young’s modulus of the individual coating materials • Previous results use ‘best estimates’ of properties (– these are typically not well known for ion-beam-sputtered coatings) • I. Wygant et al (Stanford) measured the acoustic impedance of witness multi-layer samples using an ultrasonic reflection technique • If coating density is known then this allows Young’s modulus to be found • However it has proved difficult to extract precise properties of the individual materials from measurements of multi-layers

20. Material properties – next steps • Studies of some single layers of materials would be very valuable • Study loss, Young’s modulus and density (may have to study as a function of thickness) • These would then help inform our analysis of multi-layer coatings • Necessary both to quantify our loss measurements and thermal noise calculations

21. Other approaches • Pinto et al – studying algorithms to vary thickness and periodicity of coating layers • Optimise for desired reflectivity whilst minimising amount of Ta2O5 present • Use ‘flat-topped’ laser beams to more efficiently average coating and substrate thermal noise?

22. Conclusions • 2nd generation of detectors will use fused silica optics • Coatings will be the limiting source of thermal noise in these ‘advanced detector’ test masses • To go to 3rd generation detectors we need better coatings– or maybe to cool?? • Results from Yamamoto et al suggest coating loss angle does not decrease significantly with lowering T but still gain in reducing thermal noise

23. Where does this leave us for 3rd generation detectors? • Limited by coating thermal noise/optical noise • Possibly considering cooling to reduce the coating noise • Thermal noise is not the only issue for substrate and coating developments • Other substrate and coating issues; • Thermal loading effects can be significant – see talk by Gregg • The low thermal conductivity of silica may prove to make it unattractive for higher power operation • Necessitate switch to sapphire/silicon some other material??

24. Challenges for future detectors • Future detectors may require higher levels of laser power • In addition, further reductions in test mass and suspension thermal noise are required • Possible materials meeting these requirements are sapphire or silicon – are there others??? • Mirror substrates must sustain high thermal loads and maintain optical figure • Deformation of mirror surface is proportional to a/kth [Winkler et al., 1991]. a = substrate expansion coefficient kth = substrate thermal conductivity • Would like a substrate material for which a/kth is minimised

25. Mechanical dissipation - silicon • Silicon • Both thermoelastic and intrinsic thermal noise may be reduced by cooling: • Thermoelastic noise is proportional to a and should vanish at T ~120 K and ~18 K where a tends to zero • Intrinsic thermal noise exhibits two peaks at similar temperatures • Silicon may allow significant thermal noise improvements at low temperatures but material properties need further study Calculated intrinsic thermal and thermoelastic noise @ 10 Hz in a single silicon test mass, sensed with a laser beam of radius ~ 6 cm

26. Mechanical dissipation - sapphire • Sapphire • studied in the US as part of Ad LIGO substrate downselect • studied by colleagues in Japan for LCGT • Likely to have levels of intrinsic and thermoelastic dissipation similar to silicon (slightly lower) but without the nulls in expansion coefficient • Could be interesting, particularly at higher frequencies Sapphire piece used in spot polishing compensation demonstration; 25cm diameter sample (photo courtesy Goodrich).

27. Coating z x y l Substrate Mechanical dissipation from coatings • Potential sources of loss : • Dissipation intrinsic to the coating materials (defects, vacancies etc?) • Thermoelastic damping(see Fejer et al, Phys Rev D, Braginsky,PLA)resulting from the different thermal and elastic properties of the coating and substrate • In both cases resulting thermal noise level depends on relative thermal and elastic properties of coating and substrate • It follows that the optimum coating for a fused silica or sapphire mass may not be the ideal choice for a silicon mass

28. Mechanical dissipation in coatings (contd) • Diffractive coatings: • To use silicon as a diffractive optic, either: • a diffraction grating can be etched on to the surface of the test mass onto which a coating is applied (Institute for Applied Optics, University of Jena); or • the test mass can be coated, and a diffraction grating etched into the coating surface (Lawrence Livermore National Laboratories). • The mechanical dissipation associated with such coatings (room and cryo) needs investigated

29. 3rd generation detectors - a problem of size • Test masses of >50 kg are desirable • Silicon ingots of 450kg have been manufactured, but aspect ratio is not optimal • Sapphire is available up to only ~40kg • Use composite test masses??, Cradle ? Segmented design? Silicon ingot in growth furnace Bonded interfaces Pic. from D. Coyne Separate mass segments

30. Conclusions cont ‘Analyse the recent developments in technologies foreseen for Advanced detectors to explore the path needed for a European 3rd generation gravitational wave detector’ • Status of substrate/coating technology for Advanced Detectors is in pretty good shape (silica + doped coatings) • Limited by coating thermal noise – but various approaches discussed here may help us • For 3rd generation detectors cooling and/or a change of substrate material is likely to be needed – really need to work hard on how to beat coating thermal noise