40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  PSL  Not logged in ELOG logo
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: 2613     Entry time: Tue Aug 23 19:56:21 2022     In reply to: 2612     Reply to this: 2614   2615
Author: Anchal 
Type: Summary 
Category: NoiseBudget 
Subject: Birefringence noise in thermo-optic noise 

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 thermo-refractive (coatTR). If this was true, it would significantly affect thermo-optic 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 thermo-optic 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
    \frac{\Delta \epsilon_{ii}}{\Delta T} = \alpha
  • The strain fluctuations cause changes in the refractive index of the layers through photoelastic tensor
    \Delta n = - \frac{1}{2}n^3(p_{11}\Delta \epsilon_{1} + p_{12}\Delta \epsilon_{2} + p_{13}\Delta \epsilon_{3}))) = - \frac{1}{2}n^3(p_{11} + 2 p_{12})\Delta \epsilon_{1}
    In the last step above, I assumed isotropic bulk strain in the layers (which is expected for this cubic lattice), thus
    \frac{\Delta n}{\Delta \epsilon_{ii} } = - \frac{1}{2}n^3(p_{11} + 2 p_{12})
  • The product of the above two numbers give the coefficient of thermo-photoelastic effect as:
    \frac{\Delta n}{\Delta T} = \frac{\Delta \epsilon_{ii}}{\Delta T}\frac{\Delta n}{\Delta \epsilon_{ii} } = - \frac{1}{2}\alpha n^3(p_{11} + 2 p_{12})
    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 themo-optic cancellation is only partially happening now, but the thermo-optic 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 Thermo-Optic" is a coherently summed noise of coatTR, coatTE, and coatTPE.
  • The trace marked "Coating Thermo-elastic + Thermo-refractive" is what we previously used to calculate as thermo-optic 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 4.878e-5 which was measured by Penn et al. in indirect measurement.

I think we need to regroup and discuss this further.

 

Attachment 1: CTN_Thermo-Optic_Noise_Study.pdf  39 kB  Uploaded Tue Aug 23 21:17:49 2022  | Hide | Hide all
CTN_Thermo-Optic_Noise_Study.pdf
ELOG V3.1.3-