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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: 1194     Entry time: Tue Jun 11 16:46:52 2013     In reply to: 1193
Author: tara 
Type: Notes 
Category: NoiseBudget 
Subject: noisebudget for 8" SiO2/Ta2O5 cavity 

note about the calculation for coating Brownian noise in a finite size mirror .

==Coatings Parameters==

Young's modulus, Poisson's ratio, and loss angle are taken from the volume averaged value of the coatings (Yavg = d/ ( d1/Y1 + d2/Y2) , sigma avg = 1/2 (sigma1+sigma2 ). These are used for "perpendicular" direction in Harry2002 formula.

Loss angles

  • SiO2 loss angle  = 1e-4
  • Ta2O5 loss angle = 2.3e-4
  • coatings loss = 1.32e-4

Young's moduli

  • SiO2 Young's modulus = 72e9  Pa
  • Ta2O5                         =140e9  Pa
  • Coatings Young's modulus = 93e9 Pa

Coatings structure

  • 1/2 lambda cap of SiO2
  • 26 layers
  • 300 ppm transmission

 ==calculation codes==

  • I got the file for finding zeroes of the bessel function from Matlab exchange.
  • The code for calculating Br noise is attached below.
  • For the finite size bdy condition, the solutions include all the besselj function of all orders (m=1 to inf). I used m from 1 to 55 in the calculation since it converged quite fast after that.
  • For the integration to calculate all the elastic energy, I used Riemann sum, with stepsize of ~0.15 um. The result does not change much (less than 3%) if I go from 0.8*a to a where a is the radius of the mirror. This is important to note because our coatings do not cover the whole surface of the mirror. There is an annulus edge with ~3mm width for optical contact area. The result means that the elastic energy is still localized in the spot area.

 ==Implication to AdvLIGO coatings==

As noted in SK2009, the estimated values for half infinite and finite size analyses are about the same (~2.5% difference) (I have not verified this). Then, the result from GWINC using Harry2002 formula is still accurate.

==note/comments==

  • The calculation in SK2009 uses an overall loss angle of the coatings, while calculation in Harry2002 separates the elastic energy in two directions,parallel and perpendicular to the surface, and also loss angles in the associated directions.  I use the perpendicular average under the assumption that most energy/deformation occurs in that direction.
  • The result matches the measurement quite well. This reassures us that other noises introduced by the setup (i.e. noise in optical bonding/ noise from supporting structure/ thermoelastic/ brownian noise in the spacer) are not higher than coating thermal noise.

 

Attachment 1: getCoatBrownian2.m.zip  1 kB  Uploaded Tue Jun 11 19:16:19 2013
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