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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: 1191     Entry time: Wed Jun 5 22:25:28 2013     In reply to: 1183
Author: tara 
Type: Notes 
Category: NoiseBudget 
Subject: TO calculation review 

Since we have to review the calculation for Thermo-Optic noise (TO), I'll sketch an outline and some remarks here.

==TO noise overview==

To calculate TO noise, we have to calculate temperature fluctuations, then multiply by Thermoelastic (TE) and Thermorefractive (TR) coefficients to convert temperature fluctuation to displacement noise. Usually, in the frequency of interest, thermal length is much larger than coating thickness. Thermal fluctuations in coatings are uniform making the whole coatings expand/ contract uniformly. This assumption is important for cancellation between TE and TR. As TE effect comes from the whole coating thickness, while TR comes from only the first few layers (most of the power is reflected from these top layers). Modifying the first few layers can change TR effect significantly.

 ==Temperature fluctuations==

can be obtained from direct method (Levin 2008), by injecting heat with Gaussian beam profile. Example are done in Levin 2008, Evans etal 2008.

A few issues about these calculations:

  • heat flow in 1-D, under the assumption that temperature gradient is mostly in z direction coating thickness d << thermal length << beam radius. Where thermal length is ~ sqrt (  kappa/ (rho*C* 2pif) )  This is not true for AlGaAs coatings where kappa is ~ 60 W/mK which gives thermal length to be~ 2370 um  [sqrt (1Hz/f)], beam radius is ~ 200um.  Cerdonio 2001, and Mike Martin's thesis have the calculation in 3-D, however, heat diffusion in coatings is not taken into account.
  • Heat diffusion in coatings, is done in Fejer 2004, Somiya2009. (It is ignored in BGV1999/Liuthorne2000/cerdonio 2001)

At this point, I think Somiya paper is very good for us to look through. The calculation includes TE and TR. However, I don't quite get it yet. The calculation solve heat equation in 1-D, but has results for finite test mass. I need to spend more time on the paper.

 Heinert 2011, has calculation for TR in finite size substrate. I'm not sure how to connect the results to our setup yet. Plus, for our setup, the actual coatings will be ~ 8mm in diameter, with 1" diameter substrate, the boundary conditions will be non-trivial for us.

 ==TE +TR coefficients==

  [ coming soon]

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