Direct Measurement of Thermo Optic Coefficients in Coatings

Direct Measurement of Thermo. Optic Coefficients in Coatings by Photothermal Spectroscopy Greg Ogin, Eric Black, Eric Gustafson, Ken Libbrecht Matt Abernathy Presenting LSC/VIRGO Conference, Rome, Italy, 10 September 2012 LIGO-G 1200935 1

The Ad. LIGO Noise Curve Source: Evans et al, LIGO-P 080071 -00 2

Thermo-optic Noise: TO = TE + TR • Thermo-Elastic (TE): Mirror’s surface expands into probe beam. By convention, negative dφ/d. T 3

Thermo-optic Noise: TO = TE + TR • Thermo-Refractive (TR): Coating layers deviate from λ/4 condition – due to both physical expansion and change in index of refraction. To first order, this manifests as a change in the phase of the reflected beam. E+ Quarter-wave stack: EE+ After expansion, index change: E 4

Photothermal Apparatus NPRO Test Mirror CO 2 Vacuum Chamber AOM λ/2 Beam Dump PBS λ/2 PZT Beam Dump Fringe Locking Electronics Data Acquisition Electronics 5

Mirror Under Test 6

Expected Signal: Canonical Form Substrate CTE 7

Expected Signal: Canonical Form Substrate CTE Coating properties (including coating CTE effects) 8

Sapphire Substrate Response Magnitude 9

Sapphire Substrate Response Phase 10

Silica Substrate Response Magnitude 11

Silica Substrate Response Magnitude +/- 20% 12

Recent Results: Silica Substrate 13

Combined TE/TR Results • QWL • Bragg 14

Gold coatings for pure TE measurements Challenge: 80% CO 2 absorption drops down to 0. 5% CO 2 absorption. 15

Much lower SNR Displacement (m) 10 -11 10 -12 16

Gold Coated “TE alone” Results • QWL • Bragg 17

Extracting Values For quarter-wavelength coatings For 1/8 -3/8 coatings For quarter-wavelength TE only (Cr? Chromium. ) For 1/8 -3/8 coatings TE only 18

The Measurement Matrix Which we invert to get… 19

The Parameter Estimation Matrix 20

Our Results… 21

Our Measurements of α Si. O 2 – Low Index • 2. 1 x 10 -6 K-1 – Cetinorgu et al, Applied Optics 48, 4536 (2009) • 5. 1 x 10 -7 K-1 – Crooks et al, CQG (2004) • 5. 5 x 10 -7 K-1 – Braginsky et al, Phys Lett A 312, 244 (2003) (5. 5 ± 1. 2)x 10 -6 K-1 • • Ta 2 O 5 – High Index + 4. 4 x 10 -6 K-1 – Cetinorgu et al, Applied Optics 48, 4536 (2009) + 3. 6 x 10 -6 K-1 – Crooks et al, CQG (2004) - 4. 4 x 10 -5 K-1 – MN Inci, J Phys D 37, 3151 (2004) + 5 x 10 -6 K-1 – Braginsky et al, ar. Xiv: grqc/0304100 v 1 (2003) (8. 9 ± 1. 8)x 10 -6 K-1 22

Our Measurements of β Si. O 2 – Low Index • 8 x 10 -6 K-1 – GWINC v 2 (“Braginsky”) (1. 9 ± 8. 0)x 10 -6 K-1 Ta 2 O 5 – High Index • 1. 21 x 10 -4 K-1 – MN Inci, J Phys D 37, 3151 (2004) • 6 x 10 -5 K-1 * – Gretarsson, LIGO-G 080151 -00 -Z (2008) *Assumes α (1. 2 ± 0. 4)x 10 -4 K-1 23

Ad. LIGO Baseline (GWINC v 3) 24

Ad. LIGO with Our Parameters Disclaimer: This Is Not an Ad. LIGO Prediction 25

Conclusions • Measuring these parameters is non-trivial, but we have demonstrated a technique, and reported initial results • We have the ability to measure exactly what Ad. LIGO needs • Thermo-optic noise, and these parameters in particular, could be critical and need further study for future generations of gravitational wave detectors 26

Future Directions • Characterize and reduce systematic errors • Perform measurements on Ad. LIGO coatings with Cr layers (or at the very least Ion Beam Sputtered coatings and Ti: Ta 2 O 5 coatings) • Look at measurements of other materials and geometries 27

Acknowledgements • • • Greg Ogin Ken Libbrecht, Eric Black Eric Gustafson Caltech LIGO-X, Akira Villar Family and friends LIGO and the NSF – Award PHY-0757058 28

Questions? 29

Supplimentary Slides follow 30

Measuring α: Cavity Assisted Photothermal Spectroscopy • Probe locked to cavity • Pump derived from probe laser chopped to cyclically heat cavity end mirror • Sensitivity to mirror expansion proportional to Finesse • Heating power in cavity proportional to Finesse • Sample coated with gold to enhance absorption Black et al, J Appl Phys 95, 7655 (2004) 31

Details of the two terms: • Thermo-Elastic: Negative phase • Thermo-Refractive: Positive phase Evans et al, Physical Review D 78, 102003 (2008) 32

Theory: Assumptions • The scale of periodic thermal disturbances (a “thermal wavelength”) is much smaller than our heating spot • The coating thickness is smaller than a thermal wavelength Together, these give us a 1 -D problem where thermal dynamics are all determined by the properties of the substrate. 33

Theory: Heat Equation Solutions • The heat equation becomes • With solutions 34

Theory: Boundary Condition • Our boundary condition gives C(ω) 35

Expected Signal A Coherent Sum of… 36

Expected Signal: Canonical Form 37

(Reminder) • Thermo-Elastic: Negative phase • Thermo-Refractive: Positive phase Evans et al, Physical Review D 78, 102003 (2008) 38

Expected Signal: Canonical Form 39

Expected Signal: Canonical Form 40

Expected Signal: Canonical Form 41

Expected Signal: Canonical Form 42

Recent Results: Sapphire Substrate Response Magnitude 43

Recent Results: Sapphire Substrate Response Phase 44

Recent Results: Sapphire Substrate Response Phase Wait, what? ! ? 45

Sapphire: Long Thermal Wavelength really means we have a 3 -D problem (axially symmetric), “plane thermal waves” don’t work 46

“Cerdonio”-type solution • Green’s function on the surface of a halfspace • Forced sinusoidally with a Gaussian profiled beam 47

Then all you have to do is… • Integrate • and again. 48

Thanks Mathematica 49

Thanks Mathematica 50