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Entry  Tue Apr 30 01:15:26 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
    Reply  Thu May 2 03:03:48 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
       Reply  Thu May 2 23:40:46 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 6x
          Reply  Mon May 6 03:11:44 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO RefCav_AlGaAs_TOnoise.png
             Reply  Mon May 6 17:08:25 2013, Matt A., Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
             Reply  Tue May 14 02:06:15 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
                Reply  Wed May 15 20:07:12 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO TO_compare_cap.pngTO_compare_cap.fig
                   Reply  Tue May 21 01:06:43 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
                      Reply  Wed May 22 00:04:48 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
                         Reply  Fri May 24 04:04:58 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 
                            Reply  Fri May 24 23:57:27 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO 6x
                               Reply  Wed Jun 5 22:25:28 2013, tara, Notes, NoiseBudget, TO calculation review 
                         Reply  Thu Jun 6 22:28:46 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO eighth.png
                            Reply  Tue Jun 11 00:45:48 2013, tara, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity sk2009nb.pngsk2009nb.fig
                               Reply  Tue Jun 11 16:46:52 2013, tara, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity getCoatBrownian2.m.zip
                               Reply  Wed Jun 12 01:34:27 2013, Koji, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity 
                                  Reply  Wed Jun 12 14:32:22 2013, not Koji, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity 
                                     Reply  Wed Jun 12 14:49:47 2013, Koji, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity 
                                        Reply  Fri Jun 14 02:36:22 2013, tara, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity 
                                           Reply  Tue Jun 18 11:53:17 2013, tara, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity spacer_br_8_edge.png
                            Reply  Mon Jul 15 10:55:40 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO alGaAsnb.pngalGaAsnb.fig
Message ID: 1178     Entry time: Tue May 21 01:06:43 2013     In reply to: 1177     Reply to this: 1180
Author: tara 
Type: Notes 
Category: NoiseBudget 
Subject: AlAs/GaAs layer structure optimized for TO 

I checked all the discrepancies in the calculations between GWINC and that of Cole. The issues are almost cleared, only the value of effective beta, (dn/dT) that still remains.

  The PSD of TO noise in [m^2/Hz] is given by Sx(f)= ST (f) x (dTE + dTR).  See Evans etal Phys Rev D 78, 102003.  Where:

  • ST (f) = Temperature fluctuation as sensed by a Gaussian beam
  • dTE = dx/dT, or rate of change of mirror position with respect to temperature change due to thermoelastic mechanism.
  • dTR = rate of change of mirror position with respect to temp change due to thermo-refractive mechanism

ST(f) can be calculated analytically, see BGV, Phys Lett A 271 , (2000) 303-307 eq9, this also assumes adiabatic approximation. In Mike Martin's thesis, the temp fluctuation is generalized  to all frequency (by contour integral, I'll show the details later). The parameters for calculating ST(f) are taken from that of substrate (in GWINC), but Cole's paper and Mike's thesis use that of the coatings. That makes Cole's result about a factor of 7 higher than that from GWINC. Matt and I discussed this with Mike, he thought that the calculation should use the substrate's properties since the thermal length in the frequency of interest is much larger than the coating thickness.

The issue with which parameters should be used might be a less serious problem if (dTE + dTR) can partially cancel out making the whole TO noise much smaller. Basically dTE is ~ alpha* coatings thickness, where alpha is the thermal expansion coefficient of the coatings. dTR is ~ beta_eff * lambda.  The calculations for dTE from GWINC and Cole are about the same (1.1 x 10^-10) [m/K], where the effective beta are different by about and order of magnitude. Cole reports the value of beta effective to be -5.5 x10^-10 , meanwhile GWINC gives me 0.5x10^-10.

This means that the TE and TR,as calculated from GWINC are more comparable, and the TO result is reduced significantly. While the TO result from Cole is mostly TR. I calculated the TR following the 1/4 stack approximation in Evans paper and got the same result as in Cole. I'm checking what happen in GWINC code for TR calculation.

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