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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: 1345     Entry time: Fri Sep 20 19:26:45 2013     In reply to: 1320     Reply to this: 1346   1347
Author: tara 
Type: Notes 
Category: optic 
Subject: coating optimization for AlGaAs:error analysis 

I'm using Matt's code to do error analysis for AlGaAs coatings. This time I vary materials' parameters and compare the thermo optic noise, reflected phase and transmission. There is no alarming parameter that will be critical in TO optimization, but the values of refractive indices will change the transmission considerably.

Eric, Matt and I discussed about this to make sure that even with the errors in some parameters, the optimization will still work.

Parameters in calculation and one sigma estimated from Matt

% Coating stuff
betaL = 1.7924e-4 +/- 0.07e-4; %dn/dT
betaH = 3.66e-4  +/-0.07e-4 ;
CL = 1.6982e6   +/- 5%  ; % Heat Capacity per volume
CH = 1.754445e6   +/- 5%;
kL = 69.8672   +/- 5%   ; % Thermal Conductivity
kH = 55           +/- 5%;
alphaL = 5.2424e-6 +/- 5%; % Thermal expansion
alphaH = (5.73e-6 ) +/- 5%;
sigmaL = 0.32      +/- 10%; % Poisson Ratio
sigmaH = 0.32     +/- 10% ;
EL = 100e9    +/-20e9; % Young's modulus
EH = 100e9    +/-20e9;
nH = 3.51  +/-0.03   ; % Index of refraction
nL = 3.0     +/-0.03 ;

 

* Note: when I change nH and nL value, I keep the physical thickness of the layers constant. This is done under the assumption that the manufacturing process controls the physical thickness. The optical thickness in the calculation will be changed, as the actual dOpt = physical thickness * actual n / lambda.  And averaged values of coatings will depend on physical thickness.

 This is fixed in Line 120-180

== Effect on TO cancellation from each parameters==

 First, I calculate the TO cancellation when one of the parameter changes. Some parameters, for examples, Poisson ratios, Young's moduli, are chosen to be the same for both AlAs and GaAs. In this test, I vary only one of them individually, to see which parameters are important. The numbers indicate the ratio between the PSD of TO noise with change in the parameter and the optimized TO noise . Not the standard deviation of the parameters.

params +sigma -sigma Note
BetaL 1.02 1.12  
BetaH 1.03 1.15  
Young L 8.0 1.77  A
Young H 8.3 1.8  A
Young HL 28.3 4.7  B
       
alpha L 1.54 1.2  
alpha H 1.19 1.53  
kappa L 0.979 1.023  
kappa H 0.975 1.028  
CL 0.99 1.0143  
CH 0.99 1.0137  
sigmaL   20.6  C
sigmaH   21.7  C
sigmaHL   84.14  B
nH 1.168 1.004  
nL 11.15 6.507

 

 

  • A) + value for Young modulus is 142 Gpa, and - value is 83 Gpa, the value in the section below is 100 +/- 20 GPa
  • B) Young's moduli and Poisson's ratios for the two materials are the same value in the calculation, Young HL row calculate the TO noise when both materials have the same value of Young's modulus, while YoungH and Young L row calculate the TO noise under the assumption that only nH material or nL material has different Young's mod.
  • C) + value for Poisson is the nominal value, and - value is 0.024  the value in the section below is 0.32 +/- 10%

 Turns out that the change in Young's moduli and Poisson's ratios are quite important.

==Effect on TO cancellation, from all paramerters==

 Then, I calculate the TO noise when all parameters vary in Gaussian distribution, similar to what I did before,all parameters are uncorrelated. The histograms from 1000 runs are shown below.

error_check_params.png

  1. Top, ratio of PSD of TO noise at 100Hz. The cancellation should still work well.
  2. Bottom left, reflected phase. It is still close to 180 degree.
  3. Bottom fight, transmission. The design is 200ppm, the result spread out in a big range from  10-500ppm.

I'll try more run overnight. Each run takes about 1 second.

== combined effect from errors in layer thickness and material parameters==

Since the comparison does not need to calculate the thermal fluctuations and finite size correction all the time, I cut that calculation out and save some computation time.  Now I compare errors from

  1. Error in both layer thickness and materials parameters (red)
  2. Error in layer thickness only (green)
  3. Error in materials parameters only (blue)
  4.  Error in refractive indices only (cyan)

Each simulation contains 5e4 runs.   The Transmission varies a lot depending on the material parameters ( mostly refractive indices,  see the cyan plot).

error_thick_params_compare.png

The cancellation seems still ok. Most of the time it will not be 10 times larger than the optimized one. Only the transmission that seems to be a problem, but this is highly depends on refractive indices. It's weird that the error makes the mean of the transmission smaller.

Attachment 2: error_check_params.fig  11 kB  Uploaded Fri Sep 20 23:48:01 2013
Attachment 4: error_thick_params_compare.fig  40 kB  Uploaded Sat Sep 21 02:54:03 2013
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