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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  
                                     Reply  Thu Oct 10 01:59:24 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis  
                                        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: 1320     Entry time: Sun Sep 1 18:38:37 2013     In reply to: 1315     Reply to this: 1322   1345
Author: tara 
Type: Notes 
Category: optic 
Subject: coating optimization for AlGaAs:error analysis 

I updated the optimization and error analysis. The error in optimized structure is comparable to that of a standard quarter wave length structure.

      After a discussion with Rana, Garrett, and Matt, I fixed the thermo-optic calculation, and the error analysis done in PSL:PSL:1315.  The modifications are

       1)  fix the TO calculation (Yamamoto TR correction): There is a modification for TR correction that is not in Evans etal 2008, paper. I contacted M. Evans to ask about the details of this correction which is done in GWINC.  

       2)  Try another optimized coatings with the correct TO calculation:  After the correction, I ran doAlGaAs.m code, cf PSL:1269  using fmincon function , to find another optimized structure. The result is shown below.

2013_09_01_opt_nbv2.png

above) layer structure in optical thickness, the .fig and .mat file are attached below. Note .mat file contains 54 layers, you need to add 1/4 cap to the first entry to calculate the noise budget.

  2013_09_01_opt_nb.png

above) noise budget of the optimized coating.

       3)  Repeat the error analysis : This time I used the following assumptions (from G Cole)

  • the error is not random among each layer
  • the error is constant in each layer type, ie all the layers from the same material (nH or nL) have the same percentage of error,
  • error from nH and nL have the same sign. If one is thicker, another one is thicker, but the magnitude are uncorrelated.
  • nH (GaAs) has better thickness control with 2sigma = 1percent, while nL(AlGaAs), has 2sigma = 2 percent.

error_dist.png

Fig1: Above, percentage of error distribution between the two materials used in the calculation. nH(red) has 2 sigma = 1% and nL(blue) has 2sigma=1%.The same error distributions are used for both optimized layers and QWL layers in comparion, see fig2.

The section below is the algorithm used to distribute the error, this one makes the error between the two materials to be the same sign. The whole code can be found on svn.

mu1 = 0;
sigma1 = 0.5;  % 2sigma is 1percent;
mu2 = 0;
sigma2 = 1;

run_num = 5e4; % how many test we want

errH = normrnd(mu1,sigma1,[run_num,1]);  %errH in percent unit
 
errL = normrnd(mu2,sigma2,[run_num,1]);  %errL in percent unit   
errL = abs(errL).*sign(errH);                        %make sure that errH and errL have the same sign

dOpt = xout;             % xout from doAlGaAs (optimized layer)
dOpt = [ 1/4 ; dOpt];    % got 54 layer no cap from doALGaAs, need to add the cap back

dOpt_e = zeros(length(dOpt),1);


  for ii = 1:run_num;

dOpt_e(1:2:end)= dOpt(1:2:end)*(1+ errH(ii)/100 );
dOpt_e(2:2:end)= dOpt(2:2:end)*(1+ errL(ii)/100 );

 

 

===Result==

This time I calculated the change in reflection phase (TOP left), the ratio between TO noise from the coatings with error and the coatings with no error(top right), transmission (bottom left), and ratio of BR noise ( bottom right). The result from the optimized coating(blue) is compared with the QWL coating (black).

 error_compare_opt0901v2.png

Fig2: Error analysis, in 5e4 run. Blue: from optimized coatings Black:from 55 QWL coatings, from 5x10^4 runs.

Reflection phase: The reflection phase can be away up to ~6 degree. The power at the surface will be ~Finesse/pi * Power input * sin^2 (6degree) ~ 50mW. Seems high, but this is about a regular power used in the lab.

Ratio of PSD TO/TO_0 : At worse, it seems the PSD TO noise will be ~ a factor of 10 higher than the design. However, this will be still lower than BR noise. I plotted only the error distribution for optimized coatings because for QWL coatings, the ratio will be about the same, since TO is dominated by TE.

Transmission: Most of the results are within 197-200 ppm. The optimized coating has transmission ~ 197ppm. The QWL with 55 layers has transmission ~100ppm.

Ratio of BR: not much change here.

 

Attachment 2: error_compare_opt0901v2.fig  29 kB
Attachment 6: 2013_09_01_opt_nbv2.fig  14 kB  Uploaded Mon Sep 2 19:24:56 2013
Attachment 7: 2013_09_01_200ppm_54v2.mat  625 Bytes  Uploaded Mon Sep 2 19:26:31 2013
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