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MIF (General)
yuta.michimura - 3:03 Friday 13 February 2026 (36340) Print this report
Comment to PRX and PRY power recycling measurements (36242)

[Haoyu, Yuta]

Haoyu pointed out that my calculation of finesse for PRX/Y was wrong.
I was doing pi*sqrt(rp*0.5*0.5*rloss)/(1-rp*0.5*0.5*rloss), but I had to do pi*sqrt(rp*0.5*0.5*rloss)/(1-rp*0.5*0.5*rloss).
This gives PRX/PRY finesse of 3.71(14) with optical loss of 13(5)%.

This changes the linewidth I used to calibrate the PRC length by twice, so the effect is non-negligible.
Updated values will be

Estimated f2 detuning of PRC    0.0599+/-0.0033 MHz
f2 sideband PRG for PRX    0.0244+/-0.0017
f2 sideband PRG for PRY    0.0200+/-0.0014
Average PRC length      66.540+/-0.005

So the measured PRCL is shorter from the design (66.591 m) by 5.1(5) cm.
If we are to keep the current f2 modulation frequency (44.9946924104 MHz), PRCL needs to be longered by 8.9(5) cm.
Note that f2 sideband PRG written above does not mean that f2 sideband power is enhanced by this amount. This is only relevant for POP90 calibration.

Using these values, the calibration factor for POP90 sqrt(I^2+Q^2)/Pin will be 1.88(9).
This gives the following (see attached).

f2 sideband PRG for PRFPMI 2.44+/-0.12
f2 sideband loss in PRC for PRFPMI 29.7+/-0.9 %

This loss includes the losses from f2 detuning.
Schnupp asymmetry of las = 3.36(1) m (klog #14575) gives f2 reflectivity for Michelson (with no losses from the arms) of rmi**2 = cos(2*f2/(2*pi)*las/c)**2 = 0.97445(15).
This gives f2 PRG of PRGmax = 36.62(4), if PRC length is perfectly matched with f2.
The finesse for PRC with no losses is given by Fprc = pi*sqrt(rp*rmi)/(1-rp*rmi) = 24.25(6).
Since the FSR for PRC using the measured value above 66.540(5) m is FSRprc = 2.25272(17) MHz, HWHM of PRC without losses is HWHMprc = FSRprc/Fprc = 0.024230(34) MHz.
Using the measured f2 detuning above of det = 0.0599(33) MHz, f2 sideband PRG with detuning, without losses will be PRGdetuned = PRGmax/(1+(det/HWHMprc)**2) = 3.41(32).
To explain measured f2 PRG in PRFPMI of 2.44(12), additional 12.6-16.1% loss is necessary. This is consistent with loss measurements in PRX and PRY.

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