A question was raised as to how much passive filtering we benefit from if we pick off the local oscillator beam for BHD from the PRC. I did some simplified modeling of this. For the expected range of arm cavity round trip losses (20-50 ppm), I think that the 40m CARM pole will be between 75-85 Hz. The corresponding recycling gain will be 40-50, with the current PRM. I assumed 1000 ppm loss inside the PRC. The net result is that, assuming the single pole coupled cavity response, we will get ~8-9 dB of filtering at ~200 Hz of the intensity noise of the input laser field to the interferometer if we pick the LO beam off from the PRC (e.g. PR2 transmission), instead of picking it off before.

The next questions are: (i) can we do a sufficiently good job of achieving the required RIN stability on the LO field for BHD without relying on the passive filtering action of the PRC? and (ii) is the benefit of the PRC filtering ruined in the process of routing the LO field from wherever the pickoff happens to the BHD setup?