We checked the half wave cap solution for  minimizing TO noise. WIth a half wave cap of nl, the TO noise is smaller by ~ a factor of 2 in Hz^2/Hz unit.

Matt and I checked the  calculate the TO noise for a half wave cap solution. The noise goes down by a factor of 2. 

A few issues that we still have to investigate:

• A thin layer of nh: we talked to Mike, he said that to prevent the oxidation that occurs on GaAs layer (nL), a thin layer of AlGaAs(nH) has to be applied on top. We are not sure how thick the layer will be, we should ask G Cole, so that we can estimated the effect before hand.
• The TO noise with  half wave cap may already be lower than substrate thermoelastic (TE) noise. I'm checking the TE calculation and find out that the value for thermal expansion of fused silica is 3.9e-7 in Gwinc, but 5.5e-7 elsewhere (add sources). If it is really 5.5e-7, this will be higher than the current TO noise already. I'll look into it.
• A factor of 2 : This comes from double sided PSD or either 2 mirrors. I'll change that to our standard here (1-sided PSD, with single mirror).
•  The cancellation might change for different numbers of doublet. Since we plan to have ~ 100-200 ppm, the actual TO noise may be different than this calculation (2ppm). I try using 56 layers (1/2 lambda cap of nL included) which give us 100ppm, and TO noise is below coating brownian from DC to 200 Hz. This is a pretty good result which should be expected. Since we reduce the number of doublet, the effect from TE becomes smaller, (still larger than TR). Thus the different between the two (the total TO noise) is smaller.
  
• Different cap thickness may bring down TO noise more than half wave cap does. I just try the cap with 0.1 wavelength of nL (for 40 doublet stack), and TO noise goes down by another factor of 2. This might apply for 56 stack as well. I'll check.