I made a few changes in my calculations today, which changed the noise contribution of this photoelastic noise (coatTPE) to roughly half of the individual contribution from coating thermorefractive (coatTR). If this was true, it would significantly affect thermooptic optimization, although not totally destroying it. I admit there is an outcome bias in this statement, but this noise estimate fits very well with the noise floor measured by CTN lab.
Changes in the calculation:
I made two changes in total:
 I'm using original coefficients of thermal expansion for each layer instead of the "effective" coefficients used in calculations of thermooptic noise as per Evans et al. PRD 78, 102003 (2008)
 I removed the use of young's modulus and the crystal's elasticity tensor.
So now, the noise calculation is as follows:
 The temperature fluctuations cause isotropic strain fluctuations in the coating layers related through coefficient of thermal expansion
 The strain fluctuations cause changes in the refractive index of the layers through photoelastic tensor
In the last step above, I assumed isotropic bulk strain in the layers (which is expected for this cubic lattice), thus
 The product of the above two numbers give the coefficient of thermophotoelastic effect as:
I averaged this coefficient over all coating layers weighted by their thicknesses.
 The noise contribution comes same as coatTR term as they both are channels causing dn/dT.
Notes:
 The above calculation does not take into account any birefringence in the layers that could be caused by this effect. In fact, the cubic crystal symmetry of GaAs does not allow for birefringence to occur in usual formalism and the only way it could happen is due to a large strain in one direction breaking the symmetries. Thus, I would not call this noise "birefringence noise", but it is a credible noise source in it's own right.
 Note that the themooptic cancellation is only partially happening now, but the thermooptic noise is still much less than the simple quadrature sum of the noises. We can maybe check back our measurements in our previous paper if the measured photothermal transfer function allows this.
 Maybe this noise source is not perfectly coherent with coatTE and coatTR and needs to be added a bit differently.
About the plot:
 The trace marked "Coating ThermoOptic" is a coherently summed noise of coatTR, coatTE, and coatTPE.
 The trace marked "Coating Thermoelastic + Thermorefractive" is what we previously used to calculate as thermooptic noise.
 "Measured Beat" is the best measurement we made and is a median over 50 lowest noise measurements made in June of 2020.
 "Coating Brownian" trace is calculated using bulk loss angle value of 4.878e5 which was measured by Penn et al. in indirect measurement.
I think we need to regroup and discuss this further.
