40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 Coating Ring-down Measurement Lab elog Not logged in
Message ID: 373     Entry time: Fri Jul 21 14:55:02 2017
 Author: Gabriele Type: General Category: Measurements Subject: Shear and bulk losses in annealed tantala

I repeated the analysis for bulk and shear losses described in an early elog entry, with the same coating, but after annealing at 500C for 9 hours.

The COMSOL model is the same as before, so the dilution factors are the same, except that this time I could measure a few more modes at high frequency:

As in the previous analysis, I fitted four different models:
1) one single loss angle for both bulk and shear, constant in frequency
2) one single loss angle for both bulk and shear, linear in frequency
3) separate bulk and shear loss angles, constant
4) separate bulk and shear loss angles, linear in frequency

The data strongly favor the last model: two loss angles for shear and bulk, linearly dependent on frequency (Bayes factor -22.7 for the second best model, which is the frequency dependent single loss angle).

The results are below.

## Single constant loss angle

$\phi = (3.95 \pm 0.08) \times 10^{-4} \mbox{ rad}$

## Single loss angle, linearly dependent on frequency

$\phi = (3.69 \pm 0.17) \times 10^{-4} + \frac{f-1 kHz}{1 kHz} (4.6 \pm 0.3)\times 10^{-6} \mbox{ rad}$

## Bulk and shear loss angles, constant

$\begin{array}{l} \phi_{shear} = (3.4 \pm 0.5) \times 10^{-4} \mbox{ rad} \\ \phi_{bulk} = (7.3 \pm 3.3) \times 10^{-4} \mbox{ rad} \\ \end{array}$

## Bulk and shear loss angles, linearly dependent on frequency

$\begin{array}{l} \phi_{shear} = (3.58 \pm 0.15) \times 10^{-4} + \frac{f - 1 kHz}{1 kHz} (6.1 \pm 2.4) \times 10^{-6} \mbox{ rad} \\ \phi_{bulk} = (4.5 \pm 1.2) \times 10^{-4} + \frac{f - 1 kHz}{1 kHz} (-7 \pm 16) \times 10^{-6} \mbox{ rad} \\ \end{array}$

 Attachment 7: postannealing_linear_bulk_shear.png  34 kB
ELOG V3.1.3-