While Yuta claimed that the recycling gain was roughly 3 for the 45 MHz sideband (alog 10441), I did an independent estimation of the power recycling gain.
I got a recycling gain of about 0.6 for the 9 MHz sideband based on the measured aboslute RF power on POPAIR_B at 18 MHz. Hmmm....
This estimation relies on the absolute power on the POPAIR_B and therefore it is less reliable than the ordinary unlocked-to-locked-comparison measurement. Note that the ring heater on ITMY was off when measured. Also, the detail of the estimation is attached.
- - - POPAIR_B_RF18 calibration:
According to alog 9845, the PD was calibrated to be 7803/(5.13 mW x 0.93 x 0.1) = 1.6e7 counts/W at 18 MHz. Since it gave 18000 counts when it was locked, this corresponds to
Pam@POPAIR_B = 18000 counts / 45 dB whitening gain / 1.6e7 counts/W = 6.2 uW at 18 MHz.
- - - Estimation of the recycling gain:
There are three mirrors which attenuate the 9 MHz sideband on its way to the POPAIR_B diode.
- PR2: T = 229 ppm
- M12 in HAM1: R = 90%
- BS on ISCT1: R = 50%
Then assuming the 18 MHz beatnote is only made of the 9 MHz sideband, we get an AM component of the light at the diode:
P_am@POPAIR_B = 2 x J1^2 x Pin x Gpr x T_PR2 x R_M12 x T_BS,
where Pin is the incident power on PRM, Gpr is the power recycling gain. If we assume that the modulation depth for 9 MHz is 0.17 (alog 9979) and Pin = 8.8 W x (Timc 80%) = 7.04 W, the power recycling gain Gpr should be
Gpr = 0.594
Update:
Actually I forgot to correct the responsivity for 1064 nm. The BBPD uses FFD-100 which has a responsivity of 0.4-ish and 0.15-ish at 980 nm and 1064 nm respectively. Because the calibration measurement was done for 980 nm, I should have corrected the counts/W by the ratio of the responsivity. This means that the POPAIR_B was detecting a bigger laser power than I estimated. The laser power at 18 MHz must have been 6.2 uW x (0.4 / 0.15) = 16.53 uW.
Therefore, the correct power recycling gain for 9 MHz is
Gpr = 0.594 x ( 0.4 / 0.15 ) = 1.584