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 Tue Jun 4 00:17:15 2019, gautam, Update, BHD, Preliminary BHD calculations Thu Jun 6 18:49:22 2019, gautam, Update, BHD, Preliminary BHD calculations Wed Jul 3 11:47:36 2019, gautam, Update, BHD, PRC filtering Wed Jul 31 09:41:12 2019, gautam, Update, BHD, OMC cavity geometry Wed Jul 31 17:57:35 2019, Koji, Update, BHD, OMC cavity geometry Fri Aug 23 10:01:14 2019, gautam, Update, BHD, OMC cavity geometry - some more modeling Tue Aug 6 15:52:06 2019, gautam, Update, BHD, Preliminary BHD calculations
Message ID: 14833     Entry time: Tue Aug 6 15:52:06 2019     In reply to: 14658
 Author: gautam Type: Update Category: BHD Subject: Preliminary BHD calculations

Summary:

The requirement on the phase noise on the direct backscatter from the OMC back into the SRM is that it be less than $10^{-5} \, \mathrm{rad/\sqrt{Hz}} \approx 10^{-12} \, \mathrm{m/\sqrt{Hz}}$ @ 100 Hz, for a safety factor (arbitrarily chosen) of 10 (= 20dB below unsqueezed vacuum). Assuming 5 optics between the OMC and SRM which contribute incoherently for a factor of sqrt(5), and assuming a total of 1 ppm of the LO power to be backscattered, we need the suspensions to be moving $< 5 \times 10^{-13} \, \mathrm{m/\sqrt{Hz}}$ @ 100 Hz. This seems possible to realize with single stage suspensions - I assume we get f^4 filtering from the pendulum at 100 Hz, and that there is an additional 80 dB attenuation (from the stack) of the assumed 1 micron/rtHz motion at 100 Hz, for an overall 160 dB attenutaiton, yielding 10^-14 m/rtHz at 100 Hz.

Details:

This is the same calculation as I had posted a couple of months ago (see elog that this is a reply to), except that Koji pointed out that the LO power is expected to dominate the (carrier) power incident on the OMC cavity(ies). So the more meaningful comparison to make is to have the x-axes of the plots denote the backscatter fraction, $\epsilon_{\mathrm{BS}}$ rather than the LO power. One subtlety is that because the phase of the scattered field is random, the displacement-noise induced phase noise could show up in the amplitude quadrature. I think that in these quadrature field amplitude units, the RIN and phase noise are directly comparable but I might have missed a factor of 2*pi. But in the worst case, if all the phase noise shows up in the amplitude quadrature, we end up being only ~10dB below unsqueezed vacuum (for 1 ppm backscatter).

For the requirement on the noise in the intensity quadrature - I think this is automatically satisfied because the RIN requirement on the incident LO field is in the mid 10^-9 1/rtHz regime.

 Attachment 1: OMCbackscatter.pdf  39 kB  Uploaded Tue Aug 6 17:24:10 2019
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