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Entry  Mon Jul 29 22:30:34 2013, tara, Notes, optic, coating optimization for AlGaAs multilayer1.JPGmultilayer2.JPGopt1_2013_07_29.pngnb_opt1_2013_07_29.pngT1200003_refcav.png
    Reply  Wed Jul 31 00:31:39 2013, tara, Notes, optic, coating optimization for AlGaAs 
       Reply  Fri Aug 9 17:58:01 2013, tara, Notes, optic, coating optimization for AlGaAs TOoptimized_2013_08_09.pngTOoptimized_2013_08_09.figTO_opt_200ppm_layer.pngTO_opt_200ppm_layer.fig2013_08_09_TOopt_200ppm.mat
          Reply  Tue Aug 27 16:11:26 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis 8x
             Reply  Wed Aug 28 21:21:38 2013, tara, Notes, optic, GWINC for TO calculation: recap 
             Reply  Sun Sep 1 18:38:37 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis 7x
                Reply  Mon Sep 2 18:31:46 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis 
                   Reply  Wed Sep 18 21:55:11 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis opt_coatings.mat
                      Reply  Thu Sep 19 20:38:17 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis power_vs_mirror_size.png
                Reply  Fri Sep 20 19:26:45 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis error_check_params.pngerror_check_params.figerror_thick_params_compare.pngerror_thick_params_compare.fig
                   Reply  Fri Sep 20 21:19:29 2013, Matt A., Notes, optic, coating optimization for AlGaAs:error analysis 
                   Reply  Sat Sep 21 23:49:29 2013, rana, Notes, optic, coating optimization for AlGaAs:error analysis 
                      Reply  Sun Sep 22 00:27:09 2013, some random goon, Notes, optic, coating optimization for AlGaAs:error analysis 
                         Reply  Mon Sep 23 18:07:22 2013, rana, Notes, optic, coating optimization for AlGaAs:error analysis 
                            Reply  Mon Sep 23 18:50:05 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis compare_indices.pngcompare_indices.figcompare_indices.png
                               Reply  Thu Sep 26 23:25:40 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis  8x
                                  Reply  Thu Oct 3 10:34:32 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis  
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                                        Reply  Fri Oct 11 15:23:54 2013, tara, Notes, optic, coating optimization for AlGaAs:electric field in coating layer 6x
                                           Reply  Mon Oct 14 21:02:00 2013, tara, Notes, optic, coating optimization for AlGaAs:variation in x 
                                           Reply  Sun Oct 27 20:12:25 2013, tara, Notes, optic, photothermal noise in AlGaAs Int_cotings.pngInt_cotings.fig
                                              Reply  Wed Dec 18 21:05:28 2013, tara, Notes, optic, photothermal noise in AlGaAs: thickness resolution 8x
                                                 Reply  Sat May 17 22:01:28 2014, tara, Notes, optic, Coating TO opt for Adv LIGO: ETM 7x
                                                    Reply  Sun May 18 10:45:42 2014, tara, Notes, optic, Coating TO opt for Adv LIGO dOpt_ITM1.pngdOpt_ITM1.figAdvLIGO_AlGaAs.pngAdvLIGO_AlGaAs.fig
                                           Reply  Sat Jun 20 10:14:50 2015, Evan, Notes, optic, coating optimization for AlGaAs:electric field in coating layer Efieldtrans.pdf
Message ID: 1346     Entry time: Fri Sep 20 21:19:29 2013     In reply to: 1345
Author: Matt A. 
Type: Notes 
Category: optic 
Subject: coating optimization for AlGaAs:error analysis 

In our meeting, Eric mentioned that there might be some uncertainty in how the average coating properties are calculated.

To see how much it matters, I set the average properties to either that of the high-index (H) or low-index (L) material, and calculated the ratio of the new thermo-optic noise to the original calculation (TO'/TO) and the ratio of the new thermo-optic noise to the unchanged Brownian noise (TO'/Br) for Tara's optimized coating structure. The results are in the table below:

 

 

Change: TO'/TO TO'/Br
No Change 1 0.015
C_c = CH 0.99 0.014
C_c = CL 1.01 0.015
k_c = kH 1.12 0.016
k_c = kL 0.89 0.013
alphaBar_c = aH 358 5.17
alphaBar_c = aL 384 5.55
alphaBar_k = alphas 372 5.37
alphaBar_k_TR = alphas 3.12 0.045
alphaBar_c = alphaBar_kH 2.88 0.042
alphaBar_c = alphaBar_kL 2.047 0.030
alphaBar_k_TR = alphaBar_k 5.775 0.084
alphaBar_k = alphaBar_k_TR 145 2.096

 C = Heat Capacity/Volume, k = thermal conductivity, alpha/a = thermal expansion

alphaBar_c and alphaBar_k are more complicated, since they take into account the Poisson ratio and Young's modulus of the coating materials, and may be wildly different from the thermal expansion coefficient. alphaBar_c is an average of alphaBar_k values, and when I use "alphaBar_k = alphas", I'm indicating that alphaBar_k is an array, and I have replaced that array with an array of the corresponding thermal expansion coefficients. As we can see in the final four rows of the table, alphaBar_c has a much smaller affect if we use an alphaBar_k value with all its added moduli and ratios instead of just regular thermal expansion. alphaBar_k_TR is the array of values used in the "Yamamoto Correction" to calculate the appropriate alphaBar for the thremo-refractive noise.

This all indicates to me that while most of the averages won't have much effect on our cancellation, a mistake in the calculation of alphaBar_k will.

The difference between alphaB_k and alphaBar_k_TR (in the last two rows of the table) is also interesting. Kazuhiro Yamamoto tells us this equation is correct, and explains the correction here. It's apparently because there is no added strain in the substrate due to the change in the refractive index, while there is strain for the thermal expansion.

 

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