We did cavity scan measurement yesterday. Keeping Xarm locked to Green, we shifted the offset of frequency-locking between IR and Green, then got some resonant peaks.
The measurements was carried out twice. Before the second measurement we increased the modulation depth of f1: 10dB --> 15dB.
##Information
Sweep Speed: 100 Hz/s
modulation frequency f1 = 16.875150 MHz
modulation frequency f2 = 45.000400 MHz
FSR = c/(2*3km) ~ 49.965 kHz
round trip Gouy phase separation ~ 4.376 rad (<=> ~34.80 kHz)
We identified some peaks as following way of consideration:
1. A higher mode appear at 34.8kHz after a lower mode.
2. (f1 = 337FSR + 36.807kHz.) Sideband peaks of f1 appear 36.8kHz (or 13.2kHz) distant from 00-peaks.
3. (f2 = 900FSR + 31.531kHz.) Sideband peaks of f2 appear 31.5kHz (or 17.5kHz) distant from 00-peaks.
4. We took a movie of beam shape during the measurement. So unknown peaks may be identified using it. (But not yet checked it.)
From this result you can obtain cavity properties:
1. Finesse, from fitting with Lorentzian. (Not yet tried)
2. Arm length, by FSR
3. Gouy phase
##Arm length
We obtained FSR by using sideband peaks and it was 49.96554(4) kHz.
(Of course you can find FSR by measuring the distance between 00-peaks and it was 49.95(5) kHz, which has more errors.)
Therefore the Xarm length was calculated as 2999.992(3) m.
##Gouy phase
round-trip Gouy phase is given as (Gouy = 2*arccos(sqrt(g_front*g_end)), g=1-armlength/RoC).
Measured round-trip Gouy phase = 4.37570(1) rad.
