Terra, Evan

We continued our examination of  EY body mode Q factors  and made a quick estimate of the resulting coating loss.

This time, we simultaneously rang up one of the butterfly modes and two of the drumhead modes during a 50 W lock and watched them ring down for about 45 minutes. The resulting Q factors are as follows, with the uncertainties determined by the χ² of the fit.

• Butterfly mode (6054 Hz): Q = 25.3(2.6)×10⁶
• First-order drumhead mode (8158 Hz): Q = 21.3(4.5)×10⁶
• Second-order drumhead mode, vertical (9830 Hz): Q = 46.9(5.9)×10⁶

Plots of the ringdowns, along with the fits, are attached. The script to generate the numbers and plots in this alog is also attached.

We have also used the rough FEA numbers given previously for the surface-to-bulk energy ratios to estimate the loss angles of the EY coating and substrate. We assume both losses are structural. The resulting posterior (assuming a log-uniform prior on each loss) is shown in the attached plot. The 1d marginalized loss estimates are as follows:

• Substrate loss: 1.56(39)×10⁻⁸
• Coating loss: 2.8(0.8)×10⁻⁴

Using the formula from Nakagawa et al., this implies a thermal noise of 8.1(8)×10⁻²¹ m/Hz^1/2 at 100 Hz, which is about 14 % higher than direct audio-band measurements on witness samples.

Future work:

• Remeasure these modes at a different interferometer power, to make sure the parametric gain is not affecting the measurement
• Measure the same modes on other test masses
• Use better FEA to extract the energy ratios
• Go beyond the Nakagawa approximation (coating has uniform loss, has material parameters identicaly to the substrate, and has no light penetration)