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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
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                            Reply  Tue Jun 11 00:45:48 2013, tara, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity sk2009nb.pngsk2009nb.fig
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                                        Reply  Fri Jun 14 02:36:22 2013, tara, Notes, NoiseBudget, noisebudget for 8" SiO2/Ta2O5 cavity 
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                            Reply  Mon Jul 15 10:55:40 2013, tara, Notes, NoiseBudget, AlAs/GaAs layer structure optimized for TO alGaAsnb.pngalGaAsnb.fig
Message ID: 1171     Entry time: Mon May 6 17:08:25 2013     In reply to: 1170
Author: Matt A. 
Type: Notes 
Category: NoiseBudget 
Subject: AlAs/GaAs layer structure optimized for TO 

I sent this to Tara in an email, but I thought I'd include it here for posterity:

 

 

So if you compare the low frequency and high frequency equations in the Cole paper, they're different by a factor of:

sqrt(pi)*r_G/r_T,

where r_G is the radius of the beam spot (r_G = w/sqrt(2)), and r_T is the thermal diffusion length (r_T = sqrt(kappa/(2*pi*C*f)). 


Plus, if you look at the definition of low and high frequency:

w^2*C*pi*f/kappa,

that is equal to (r_G/r_T)^2. After giving the low and high frequency thermo-optic equations, the cole paper cites Matt Evan's paper and a Braginski paper from 2000. In the conclusion to the Braginski paper, they mention that when the frequency is high, or the spot size is low, defined as r_G<r_T or r_G/r_T < 1, the adiabatic assumption that they use breaks down. Then, in Equation 9 of the Braginski paper, they indicate that the breakdown results in an error on the order of r_T/r_G. 


Going back to the Cole paper, it appears as though for the high frequencies, they've just adjusted the low frequency equation by the adiabatic breakdown error. What I still don't understand is where the extra factor of sqrt(pi) came from, and why it's the inverse of the adiabatic breakdown error. Some of it might be typo. I'll check with Garrett to see what he has to say about it. 

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