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Entry  Thu Jan 10 10:39:27 2019, anchal, DailyProgress, NoiseBudget, New noise budget code is ready, but 
    Reply  Mon Aug 12 11:56:21 2019, anchal, DailyProgress, NoiseBudget, Adding specifics of discepancy 
       Reply  Tue Aug 13 11:59:56 2019, anchal, DailyProgress, NoiseBudget, Checking the differences between old and new noisebudget ComparisonOfOldandNewNoisebudget.pdfComparisonOfOldandNewNoisebudget.zip
          Reply  Tue Aug 13 17:05:53 2019, aaron, DailyProgress, NoiseBudget, Checking the differences between old and new noisebudget 
       Reply  Tue Sep 24 15:40:33 2019, anchal, DailyProgress, NoiseBudget, Adding specifics of discepancy 2 ComparisonEffReflectivities.pdf
          Reply  Tue Sep 24 17:11:13 2019, anchal, DailyProgress, NoiseBudget, Adding specifics of discepancy 2 (More) ComparisonEffReflectivitiesSignChange.pdf
             Reply  Tue Sep 24 19:39:06 2019, anchal, DailyProgress, NoiseBudget, Checking variation in estimated Coating Brownian Noise with Loss Angles VariationOfCoatingBrownianNoiseEstimate.pdfVariationOfCoatingBrownianNoiseEstimate.zip
                Reply  Fri Sep 27 16:40:49 2019, anchal, DailyProgress, NoiseBudget, Checking variation in estimated Coating Brownian Noise with Loss Angles Better Plots VariationOfCoatingBrownianNoiseEstimate.pdfVariationOfCoatingBrownianNoiseEstimate.zip
                   Reply  Mon Sep 30 11:14:41 2019, anchal, DailyProgress, NoiseBudget, Checking variation in estimated Coating Brownian Noise with Loss Angles 2D Plots VariationOfCoatingBrownianNoiseEstimate2.pdfVariationOfCoatingBrownianNoiseEstimate2.zip
                      Reply  Mon Sep 30 12:25:24 2019, rana, DailyProgress, NoiseBudget, Checking variation in estimated Coating Brownian Noise with Loss Angles 2D Plots 
                         Reply  Mon Sep 30 20:08:42 2019, anchal, DailyProgress, NoiseBudget, Checking variation in estimated Coating Brownian Noise with Beam Radius VariationOfCoatBrEstBeamRadius.pdfVariationOfCoatBrEstBeamRadius.zip
                            Reply  Tue Oct 1 13:46:49 2019, anchal, DailyProgress, NoiseBudget, Using bayesian inference to estimate loss Angles BayesianAnalysis.pdfBayesianAnalysis.zip
                            Reply  Wed Oct 2 15:13:27 2019, anchal, DailyProgress, NoiseBudget, Checking variation in estimated Coating Brownian Noise with Beam Radius VariationOfCoatBrEstBeamRadius.pdfVariationOfCoatBrEstBeamRadiusv2.zip
                               Reply  Wed Oct 23 13:21:12 2019, anchal, DailyProgress, NoiseBudget, Fixed all discrepancies. aLIGOComplexReflectivityVariationFig5.pdfaLIGOBreakDownThermalNoiseFig7.pdfaLIGOCoatingBrNoiseCalculations.zip
       Reply  Fri Jun 12 12:34:08 2020, anchal, DailyProgress, NoiseBudget, Resolving discrepancy #1 concretly 
Message ID: 2442     Entry time: Wed Oct 2 15:13:27 2019     In reply to: 2438     Reply to this: 2463
Author: anchal 
Type: DailyProgress 
Category: NoiseBudget 
Subject: Checking variation in estimated Coating Brownian Noise with Beam Radius 

I updated this calculation by adding curves for contribution through bulk loss angle and shear loss angle separately. Rana suspected that shear loss and bulk loss should behave differently with the change in beam radius on the mirrors. But apparently the Hong et al. calculations do not suggest that way. I checked this analytically too. The definitions of Eq. (96) of power spectral densities of coating thickness fluctuation of a particular layer due to Bulk or Shear loss angles have the same dependence on the effective area of the beam on the layer.

The only thing different between the final contribution from these different fluctuations is in the transfer functions mentioned in Table I from bulk and shear noise fields to layer thicknesses and surface height of coating-substrate interface. These are also plotted in a second curve to get an idea of these transfer functions.

Along with the effects of layer thickness and surface height changes to final mirror displacement (effective) via phase change of reflected light is given by parameters q^B and q^S as defined in Eq. (94). These are plotted in the third plot and show the real difference in contribution from bulk and shear. This is in stark contradiction with what Ian just told me. They believe that for a Gaussian pressure profile, the energy stored in shear strain is 3 times higher than that stored in bulk strain. For comparison with a figure of the paper (fig.7.), I plotted the square root of these transfer functions in the fourth plot. However, the paper plots these for Silica and Tantla, not AlGaAs.


My conclusion is that at least in Hong et al.'s treatment, the effect of beam area on the mirror is equal to both bulk and shear contributions (Eq. 96).

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