Dave O and Stefan B We measured the round trip gouy phase of the PRC using the same phase-locked sub-carrier that we used to measure the PRC length. We scanned the sub-carrier offset frequency over a full spectral range of the PRC (2.6 MHz) from 68.4 MHz - 72.4 MHz. We then monitored the amplitude and phase of the beat- note as measured by Refl-Air-B diode. Two plots are shown. The first shows the full sweep. Three tracs are shown. The blue trace is the transfer function for the full beat-note signal scanned over a full PRC FSR. The other two show the traces, when half the photo-diode is blocked and the sub-carrier is locked on either side of the main carrier. Unfortunately the interferometer lost lock half-way through both of these scans. The broader bumps show the resonance of the TEM01 modes. The second plot is the same trace zoomed in around this area. From this plot we can determnine that TEM01 modes resonate at 375kHz +/- 10 kHz off the main resonance and hence the round trip guoy phase for the PRC is 52 +/- 3 degrees.
I did some comparison of these results with some predictions from a Finesse model of the PRMI, and also compared with the results of the beam size measurements reported here
I attach plots with the predicted PRX Gouy phases over ITMX substrate lens power and PR2-PR3 distance offset.
The left-most solid diagonal line is the line that comes from the beam size measurements, and the right-most solid diagonal line is the one coming from the Gouy phase measurements (with two dashed lines representing the error bars there). The blue line is the expected ITMX substrate lens power (f=230km, 1/f~4.35uD).
It would help to know if the PD was covered left-right or top-bottom to know if you measured Gouy phase in x or y direction, but for now I just considered both possibilities.
One possible explanation for the larger measured Gouy phase than expected from the beam size measurements is if PRX and PRY were not ideally matched when the measurement was made. If ITMY was not heated enough to match ITMX, the PRC has a kind of "average" Gouy phase that is larger than the PRX Gouy phase on its own.
The contours of equal Gouy phase over the two varied parameters is the same as the contours of equal beam size, so there is still no chance to distinguish between ITMX substrate lens and PR2-PR3 offset (or PR3 Rc).