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

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

3. Timescales VIRGO/GEO/LIGO all plan ‘Advanced’ upgrades: uVIRGO (Benoit, yesterday) u2008/9 VIRGO + u2011 (?) Advanced VIRGO uLIGO u2008/9 (?) staged improvements u2010-13 Advanced LIGO uGEO u2008 ? GEO-HF – staged improvements u3 rd European detector (20??) uCommon theme for Advanced detectors is higher laser power (Benno) and new mirrors uWhat is the status of technologies related to low-thermal-noise mirrors? (Gregg will talk re: thermal loading effects)

4. Current mirrors uAll detectors currently use fused silica substrates with coatings formed from SiO 2 /Ta 2 O 5 uOptics in the detectors were installed several years ago uDesign curves for GEO, LIGO, VIRGO which we use were based on best models for thermal noise at that time uThe 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 uLevin: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 uPenn et al:loss in silica may be modelled as sum of surface, thermoelastic, and frequency dependent bulk losses – the latter improving towards low frequency uLevin, (Nakagawa, Crooks, Harry et al) Dissipation from dielectric mirror coatings is at a significant level

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

7. Substrates – fused silica uSemi-empirical model developed by Penn et al (Phys Rev Lett, Submitted) arXive:gr-qc/0507097 uC 1, C 2, C 3, C 4 are constants fitted to existing loss measurements, and dependent of the exact grade of silica used Mechanical loss in fused silica

8. Substrates – fused silica uPenn 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’’ uEmpirically we deduce that the manufacturing and processing of the different grades of silica is affecting the distribution of bond angles

9. Bulk loss uEmpirically it seems that Suprasil 311, 312 are the grades of silica with the lowest loss (SV not as low ??) uGood! -We tend to choose these for our optical needs uHowever 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) uUnderstanding this would perhaps allow us to lower loss even further

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

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

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

13. Coating studies uThermal noise from the dielectric mirror coatings applied to test masses is -essentially acceptable- for Adv. LIGO, (Adv. VIRGO ?) uHowever, reduction in coating noise translates directly to interferometer sensitivity uUnacceptable for any future detectors beyond Adv. LIGO uStudies 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 uFocussed initially on SiO 2 /Ta 2 O 5 coatings

14. Mechanical loss of multi-layer SiO 2 /Ta 2 O 5 coatings with varying proportions of SiO 2 and Ta 2 O 5

15. Silica and tantala mechanical loss results Assume for each material:  residual =  0 + f  f For silica:  residual = (1.2± 0.2) x 10 -4 + f(1.3 ± 0.5) x 10 -9 For tantala:  residual = (3.2 ± 0.1) x 10 -4 + f(1.8 ± 0.4) x 10 -9 y = 1.32E-09x + 1.16E-04 y = 1.78E-09x + 3.17E-04 0.E+00 5.E-05 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04 01020304050607080 Frequency [kHz] Loss Silica residual loss Tantala residual loss

16. Status uMeasured losses are dominated by intrinsic loss of the materials involved uTa 2 O 5 is mechanically lossier than SiO 2 uStudies carried out of loss of Ta 2 O 5 doped with TiO 2 - suggestion by LMA

17. Doping of Ta 2 O 5 with TiO 2 Loss Angle of SiO 2 /TiO 2 doped Ta 2 O 5 at 100 Hz Clear improvement with addition of titania Appears no strong correlation with amount of TiO 2 However exact concentrations of TiO 2 not known Results from Ian MacLaren in Glasgow now available 0102030405060 1.5 2 2.5 3 x 10 -4 Relative Concentration Loss Angle Small Coater Large Coater

18. Doping of Ta 2 O 5 with TiO 2 Loss Angle of SiO 2 /TiO 2 doped Ta 2 O 5 at 100 Hz Mechanism by which TiO 2 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 0102030405060 1.5 2 2.5 3 x 10 -4 Relative Concentration Loss Angle Small Coater Large Coater

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

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

21. Other approaches uPinto et al – studying algorithms to vary thickness and periodicity of coating layers uOptimise for desired reflectivity whilst minimising amount of Ta 2 O 5 present uUse ‘flat-topped’ laser beams to more efficiently average coating and substrate thermal noise?

22. Conclusions u2 nd generation of detectors will use fused silica optics uCoatings will be the limiting source of thermal noise in these ‘advanced detector’ test masses uTo go to 3 rd generation detectors we need better coatings – or maybe to cool?? uResults 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 3 rd generation detectors? uLimited by coating thermal noise/optical noise uPossibly considering cooling to reduce the coating noise uThermal noise is not the only issue for substrate and coating developments uOther substrate and coating issues; uThermal loading effects can be significant – see talk by Gregg uThe low thermal conductivity of silica may prove to make it unattractive for higher power operation uNecessitate switch to sapphire/silicon some other material??

24. Challenges for future detectors uFuture detectors may require higher levels of laser power uIn addition, further reductions in test mass and suspension thermal noise are required uPossible 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  /k th [Winkler et al., 1991].  = substrate expansion coefficient k th = substrate thermal conductivity Would like a substrate material for which  /k th is minimised

25. Mechanical dissipation - silicon uSilicon uBoth thermoelastic and intrinsic thermal noise may be reduced by cooling: Thermoelastic noise is proportional to  and should vanish at T ~120 K and ~18 K where  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 uSapphire ustudied in the US as part of Ad LIGO substrate downselect ustudied by colleagues in Japan for LCGT uLikely to have levels of intrinsic and thermoelastic dissipation similar to silicon (slightly lower) but without the nulls in expansion coefficient uCould be interesting, particularly at higher frequencies Sapphire piece used in spot polishing compensation demonstration; 25cm diameter sample (photo courtesy Goodrich).

27. 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 Coating Substrate l x y z 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 (cont d ) uDiffractive coatings: uTo 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. 3 rd generation detectors - a problem of size uTest masses of >50 kg are desirable uSilicon ingots of 450kg have been manufactured, but aspect ratio is not optimal uSapphire is available up to only ~40kg uUse composite test masses??, Bonded interfaces Separate mass segments Silicon ingot in growth furnace Cradle ? Segmented design? Pic. from D. Coyne

30. Conclusions cont ‘Analyse the recent developments in technologies foreseen for Advanced detectors to explore the path needed for a European 3 rd generation gravitational wave detector’ uStatus of substrate/coating technology for Advanced Detectors is in pretty good shape (silica + doped coatings) uLimited by coating thermal noise – but various approaches discussed here may help us uFor 3 rd 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