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 Mon Aug 22 20:18:21 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise Tue Aug 23 19:56:21 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise Tue Aug 23 22:04:24 2022, awade, Summary, NoiseBudget, Birefringence noise in thermo-optic noise Thu Aug 25 19:38:01 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise Thu Aug 25 19:19:27 2022, Anchal, Summary, NoiseBudget, Looking at the measured and estimated photothermal transfer functions Fri Aug 26 15:56:38 2022, Anchal, Summary, NoiseBudget, Checking with Martin Fejer's calculations
Message ID: 2617     Entry time: Fri Aug 26 15:56:38 2022     In reply to: 2615
 Author: Anchal Type: Summary Category: NoiseBudget Subject: Checking with Martin Fejer's calculations

Martin Fejer recently gave two talks in a coatings workshop where he showed calculations regarding the thermal photoelastic channel. I have not been able to under the logic behind some of the calculations yet, nevertheless, I used his formulas for our coatings to get an alternative idea of this noise coupling.

### Major difference

• Fejer argues that free body thermal expansion does not generate any strain, and it is only when the substrate is present to counteract with it, that such strain is generated.
• Hence, the calculation goes as: thermal expansion -> stress in presence of substrate -> strain -> photoelastic effect.
• So instead of the simple $-\frac{1}{2}n^3\alpha (p_{11} + 2p_{12})$ contribution for photoelastic tensor and thermal expansion that I take, the term is:
$\frac{1}{2}n^3(\alpha_s - \alpha_c)\left(p_{11} + p_{12}\left(1 - 2\frac{c_{12}}{c_{11}}\right )\right)$
• This gives an effective (averaged with layer thickness weighting) coefficient of thermal photoelasticity of 1.45e-5 K-1 instead of 4.30e-5 K-1 from my calculations. That's a reduction by a factor of roughly 3.