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Entry  Mon Nov 12 22:56:10 2012, tara, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate cavity_TE_v2.png
    Reply  Tue Nov 13 01:56:24 2012, tara, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate 
       Reply  Wed Nov 14 00:25:48 2012, tara, Notes, NoiseBudget, ฺBrownian noise in spacer and substrate IMG_1975.jpg
       Reply  Wed Nov 14 19:46:47 2012, tara, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate substrateTE_compare.pngTE_cavity_v2.mph
          Reply  Tue Nov 20 11:50:29 2012, rana, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate 
             Reply  Wed Nov 21 20:16:55 2012, rana, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate 
                Reply  Mon Nov 26 15:36:46 2012, rana, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate 
                   Reply  Tue Nov 27 05:30:03 2012, rana, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate 
          Reply  Tue Nov 27 05:38:01 2012, tara, Notes, NoiseBudget, Thermoelastic noise in spacer and substrate TE_Brownian_compare2.pngTE_Brownian_compare2.fig
Message ID: 1083     Entry time: Tue Nov 27 05:38:01 2012     In reply to: 1076
Author: tara 
Type: Notes 
Category: NoiseBudget 
Subject: Thermoelastic noise in spacer and substrate 

 I calculated brownian noise in AlAs/GaAs coatings, brownian noise and thermoelastic noise in fused silica substrate for different beam sizes. From the plot, we can see that a smaller spotsize might be better for us.

     This is a quick study to see the how spotsize on a mirror affects Brownian noise and thermoelastic noise in coatings and substrate. The radii of the beam (where the beam intensity drops by 1/e^2) used in the calculation are 91, 182, 364 um. Loss in coatings is 10^-5, loss in substrate is 10^-7. Note for 1.45" cavity with 0.5m RoC mirrors, the beam radius is 182 um.

TE_Brownian_compare2.png

Reminders:

  • The plot is shown in displacement noise, not frequency noise from cavity.
  • The psd (m^2/Hz) of coating Brownian noise is proportional to 1/w^2 (w is the beam radius)
  • The psd of substrate Brownian is proportional to 1/w
  • The psd of substrate thermoelastic is proportional to 1/w^3 ,at high frequency where adiabatic assumption valids. But at low frequency, when heat diffusive flow rate is comparable to the beam radii, TE noise is reduced from that of adiabatic assumption.

The Brownian noise in the coatings is more comparable to TE noise in substrate with smaller beam size although the crossing between the two noises are at higher frequency. So it should be able to see the total noise from both effects. However, to get smaller beamsize, we probably have to use even shorter cavities, or smaller RoC mirrros. So it might not be practical for us.. Nevertheless, going to smaller beam size should  be a good idea.

Note:

  • for 1.45" long cavity, no choices of RoC give w = 92 um,
  • for mirror with RoC = 0.5m, cavity length of 0.1 inch(2.5 mm) gives w = 92 um
  • I think I made a mistake in the proposal since Brownian noise in substrate was higher than coatings' noise. I double checked it for this calculation and Brownian noise in substrate is always lower than coating brownian.

 

Attachment 2: TE_Brownian_compare2.fig  156 kB
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