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Entry  Mon Aug 22 20:18:21 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise CTN_Thermo-Optic_Noise_Study.pdf
    Reply  Tue Aug 23 19:56:21 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise CTN_Thermo-Optic_Noise_Study.pdf
       Reply  Tue Aug 23 22:04:24 2022, awade, Summary, NoiseBudget, Birefringence noise in thermo-optic noise 
          Reply  Thu Aug 25 19:38:01 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise 
       Reply  Thu Aug 25 19:19:27 2022, Anchal, Summary, NoiseBudget, Looking at the measured and estimated photothermal transfer functions CTN_Photothermal_TF_with_TPE.pdfCTN_Thermo-Optic_Noise_Study.pdf
          Reply  Fri Aug 26 15:56:38 2022, Anchal, Summary, NoiseBudget, Checking with Martin Fejer's calculations CTN_Photothermal_TF_with_TPE.pdfCTN_Thermo-Optic_Noise_Study.pdf
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.

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).

Attachment 1: CTN_Photothermal_TF_with_TPE.pdf  38 kB  Uploaded Fri Aug 26 17:13:24 2022  | Hide | Hide all
CTN_Photothermal_TF_with_TPE.pdf
Attachment 2: CTN_Thermo-Optic_Noise_Study.pdf  42 kB  Uploaded Fri Aug 26 17:13:55 2022  | Hide | Hide all
CTN_Thermo-Optic_Noise_Study.pdf
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