Direct Measurement of Thermo Optic Coefficients in Coatings
- Slides: 50
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
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