I'm checking the calculation for TE noise in substrate and spacer. I'm comparing the results from analytic calculation and simulation. The results still do not agree. Comsol gives a result ~ a factor of 4 lower than its analytical counterpart.

   Since the TE noise in substrate will be significant in AlAs/GaAs mirrors, the TE noise estimation should be correct. The TE calculation in substrate was done by (BGV, Liu and Thorne, and Cerdonio). The correction was noted in Numata 03 and Black 04 papers.  I think the calculation is well established because the calculations from all of the papers agree (with all corrections taken into account). So It will be nice if an FEA simulation predicts the similar result as well. 

   I followed the calculation done by Kessler etal paper where they calculated the Brownian noise in spacer. The mirror-spacer assembly is pushed by a static force with Gaussian profile, P = 2 F0 / (pi*w0^2) * exp(-2r^2/w0^2), where w0 is the spot radius = 182 um for 1.45" cavity with 0.5 mRoC mirrors, at r = w0, intensity drops by 1/e^2, F0 is the magnitude of the force (1N for my simulation) .

1.    I simulated 1/8 of the cavity which is cut by xy,yz, and zx planes.
2. Then I used COMSOL to calculated (gradient of expansion)^2,  (expansion = divergence of displacement in the body),
3. integrated over the calculated body. (get 4.18x10^-12)
4. Then multiplied by  8 to include all the sections of the cut cavity,
5. multiplied by 2 for double cavities,
6. divided by 2 for averaging the dissipated power over 1 period.
7. then followed the calculation given by Liu and Thorne. The result is still lower than the analytical model.

Note about COMSOL: I used extra fine mesh in a small volume where the beam hits the mirror, fine mesh in the rest of the substrate, and normal mesh in the spacer. This reduced the memory used in the calculation a lot and should not introduce a lot of error, since all the deformation will concentrate near the beam spot.