Lately I've been trying to calculate the corrections to the recycling cavity lengths that would compensate for the phase that the sidebands will pick up from the arms in the upgraded interferometer.

To do that calculation , I tried two quite different ways, although equivalent in principle. They both use the optickle model of the 40m, but the calculation is made differently.

In the first way, I looked directly at the phases of the field: phase of [input field] / [reflected field], phase of [input field at PRM] / [transmitted field at SRM].

In the second way I looked at the demodulation phases of the LSC signals.

The first way is much simpler, especially from a computational point of view. It is the first I tried several weeks ago, but then I had abandoned because back then I thought it wasn't the correct way.

Anyway, both ways gave me the same results for the PRC length.
For the SRC length, the first way has given me a clear outcome. On the other hand, the second way has produced a less clear result.

According to these results, these would be the proposed adjustements to the cavity lengths:
dl(PRC) = -0.0266 m; dl(SRC) = 0.0612 m

I) 1st Way
a) case of arms ideal length (33.86 m)

b) case arm length = 38.40 m

PRC

  zoom ->

SRC

zoom ->

II) 2nd Way
a) case of arms ideal length (33.86 m)

b) case arm length = 38.40 m