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 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).