Thermal Noise in Advanced LIGO Core Optics Gregory

Thermal Noise in Advanced LIGO Core Optics Gregory Harry and COC Working Group Massachusetts Institute of Technology - Technical Plenary Session March 17 -20, 2003 LSC Meeting - Livingston, LA LIGO-G 030036 -00 -R 1

Outline • Sensitivity impact • Coating thermal noise • Relevance for material downselect • Silica annealing • Sapphire status • Modeling (analytical and FEA) • Direct thermal noise measurements LIGO-G 030036 -00 -R 2

Significance for sensitivity BNS Range 120 Mpc LIGO-G 030036 -00 -R BNS Range 200 Mpc 3

Coating thermal noise Status • Tantala/silica coating studied on silica - fcoat = 2. 8 +/- 0. 7 10 -4 (in modal Q measurements) - tantala dominates loss • Various other materials tried - niobia/silica, tantala/alumina, alumina/silica - none have consistently improved loss • Some work on sapphire substrates • Figure of merit developed d fcoat ( Ypar/Ysub + Ysub/Yperp) LIGO-G 030036 -00 -R 4

Coating thermal noise Recent results • Special coating developed at SMA/Virgo - tantala doped to reduce stress in coating - fcoat = 2. 8 10 -4 undoped tantala/silica - fcoat = 1. 8 +/- 0. 1 10 -4 MIT - fcoat = 1. 5 +/- 0. 7 10 -4 Glasgow - Young's modulus and optical absorption unchanged • Annealed alumina/silica sample measured - 2. 1 +/- 0. 6 10 -4 Glasgow - results pending at Syracuse • Coated sapphire next (Glasgow) LIGO-G 030036 -00 -R 5

Coating thermal noise Future plans • New material being developed at SMA/Virgo - index similar to tantala - Young's modulus similar to silica - working to get optical absorption down • Further work with doped tantala/silica • Correlate loss with coating stress • Explore effects of annealing • Measure coating thermal noise directly LIGO-G 030036 -00 -R 6

Material downselect Substrate loss BNS Range vs Q for Ycoat = 100 GPa and fcoat = 1 X 10 -5 LIGO-G 030036 -00 -R 7

Material downselect Coating loss BNS Range Ycoat = 70 GPa LIGO-G 030036 -00 -R Coating f BNS Range Ycoat = 200 GPa Coating f 8

Material downselect Coating Young's modulus BNS Range with fcoat = 1 X 10 -5 Coating Young's modulus LIGO-G 030036 -00 -R BNS Range with fcoat = 5 X 10 -5 Coating Young's modulus 9

Substrate thermal noise Silica status • Empirical understanding of silica loss is developing • Lossy surface layer limits Q • Annealing can dramatically increase Q • High Q in polished sample - 54 106 • High Q in flame drawn sample - 200 106 • See silica discussion Thursday afternoon LIGO-G 030036 -00 -R 10

Substrate thermal noise Sapphire status • • Thermal noise dominated by thermoelastic damping Modal Q's typically about 200 106 (S. Rowan, V. Mitrofanov, et al) • • Q's span 65 to 400 106 (K. Numata, P. Willems, et al) Low frequency dependence to loss unknown Anisotropy of loss not well understood See talk by G. Billingsley LIGO-G 030036 -00 -R 11

Substrate thermal noise Recent Q results on sapphire Two 40 kg samples measured for Q at Caltech by Phil Willems, 6 modes each - white (“good”) sapphire two degenerate modes show high Q Q 1 = 200 106 Sets limit on 6 Q 2 = 180 10 anisotropy of loss } - pink (“not”) sapphire shows high Q of 260 106 LIGO-G 030036 -00 -R 1/Q vs mode for both samples • Results fit two parameter model for single bulk f and surface (barrel) f very well 12

Other loss sources Bonding and charging • Silicate bonding to silica suspension • Bonded silica samples measured for Q at Glasgow and Syracuse using different geometries • Loss very high in bond region (f ~ 100 - 10 -2) • Calculations indicate will not effect thermal noise in advanced LIGO (Syracuse sample bonded in Glasgow) • Charging of optics • Modeling and Q measurements suggest will not limit thermal noise • Could be a source of other noise sources • May need more study LIGO-G 030036 -00 -R 13

Thermal noise modeling Analytical models we have • Non-modal, direct thermal noise calculation (Yu. Levin) Better Paradigm than modal Q for thermal noise • Finite sized, uncoated mirrors (Liu and Thorne, Bondu et al) • Infinite sized, coated mirrors (Nakagawa / Gretarsson et al) • Anisotropic coatings (assuming isotropic layers) fcoat+ = Ycoat / d (d 1 f 1 / Y 1 + d 2 f 2 / Y 2 ) • Thermoelastic damping in coatings (M. Fejer, S. Rowan) - sets limit on how low coating loss can be - creates preferential matching of coatings and substrates - see talk by Sheila Rowan later on Thursday LIGO-G 030036 -00 -R 14

Thermal noise modeling Models we need • Finite sized, coated mirrors N. Nakagawa is thinking about this problem FEA models indicate thermal noise goes down • Multiple coatings on substrate have secondary coating below first coating mechanical impedance matching one coating with low absorption, one with low loss no one is thinking about this problem • Anisotropic substrate used for sapphire, may not be necessary • Inhomogeneous loss distribution probably better done by finite element analysis (FEA) • (Coating thermal noise with Mexican hat beam) not strictly necessary LIGO-G 030036 -00 -R 15

Thermal noise modeling Finite element analysis Code we have OCEAN - coating, bonding, and surface loss Q (D. Crooks, et al) invaluable for coating and bonding loss efforts I-DEAS – inhomogeneous, anisotropic modal Q, and thermal noise (D. Coyne) good agreement with Nakagawa theory, being used for initial LIGO TAMA - inhomogeneous thermal noise (K. Numata, K. Yamamoto, et al) shows thermal noise lower than Nakagawa theory for finite mirrors What we need A sharable version of TAMA code Further development of most codes LIGO-G 030036 -00 -R 16

Direct measurement of thermal noise Thermal Noise Interferometer (Caltech) • Designed to measure thermal noise in silica and sapphire • Silica mirrors in place • Sapphire mirrors on hand • Measured noise close to Coating thermal noise tantala/silica coating thermal noise • Development ongoing • See TNI Technical Advisory Committee session from Tuesday LIGO-G 030036 -00 -R 17

Direct measurement of thermal noise University of Tokyo experiments • K. Numata thesis experiment • Measure Brownian and thermoelastic • BK 7 glass for Brownian, f independent • Ca. F 2 for thermoelastic, good agreement with theory • Trying to measure coating noise • K. Yamamoto thesis experiment • Examined nonhomogeneous loss • Good agreement with Levin LIGO-G 030036 -00 -R

Thermal noise prospectus What we need to do from here • Reduce coating thermal noise to acceptable level • Determine if high Q can be obtained in large, polished silica optics • Continue to study sapphire • Further development of theories to turn Q’s into thermal noise predictions • Confirm thermal noise predictions with direct measurements 19

Conclusions • Thermal noise is a crucial problem in advanced LIGO • Coating thermal noise reduction is proceeding • Material downselect depends on many factors • Silica and sapphire both are possible choices • Work remains on thermal noise modeling • Direct thermal noise measurements are beginning to provide input LIGO-G 030036 -00 -R 20