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 contribution for photoelastic tensor and thermal expansion that I take, the term is:
  
• 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.

Updates

• Attached is the photothermal transfer function calculated with TPE contribution as calculated by Fejer. This makes the situation bit more messy on what to trust.
• I updated the noise budget with two new noise traces, the thermo-photoelastic contribution as calculated by Fejer and the total thermo-optic noise as calculated by Fejer.

I just received more calculation notes of Fejer (through Yuta) which I'll study and try to make more sense of this calculation. It also contains the calculations of sough-after birefringence noise.. But in his presentation as well, he stated that birefringence noise is not sourced through termperature fluctuations and is not part of thermo-optic noise (something I didn't understand again).