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Message ID: 717     Entry time: Tue Jul 22 22:11:58 2008
Author: Yoichi 
Type: Update 
Category: LSC 
Subject: X-arm g factor measurement 
Alberto, Yoichi

We measured the g factor of the X-arm by slightly shifting the 166MHz sideband frequency:

We first locked the X-arm to TEM00 mode. Then misaligned the ETMX in yaw a little bit until the transmitted power is a half of the normal value.
In this way, we can expect that TEM01 mode will be resonated in the arm if a sideband with a suitable frequency is introduced.
To add such a sideband, we used the 166MHz EOM. According to John's calculation (ELog entry 690), the TEM01 mode of the 166MHz upper sideband is only about 100kHz away from the resonance. So by changing the 166MHz modulation frequency, we should be able to see the 166MHz upper sideband resonating in the X-arm.
We used the 166MHz PD at the AS to find the resonance.
When we modulated the 166MHz RF frequency by +/- 100kHz, we could see spikes in the AS166_I signal.
Then we fine tuned the RF frequency slowly by hand to find the exact resonant frequency. At that time, the X-arm PDH servo was oscillating at ~480Hz.
So the resonance was determined by maximizing this signal in the AS166_I.
The 166MHz signal was originally at 165.977195 MHz. I found the resonance around 165.985MHz. It is surprisingly close to the original modulation frequency (only 7.3kHz away). This number yields the g factor of 0.626 and the transverse mode interval of 0.285*FSR. I used the arm length of 38.5750m in this calculation. Because of the 480Hz oscillation, it was difficult to precisely determine the resonant frequency. We will try this again tomorrow after mitigating the oscillation.
Although the resonance of the 166MHz upper sideband is located at a lower frequency in John's prediction, we found a resonance at a higher frequency.
This can be interpreted as the discrepancy between the actual g-factor and the designed g-factor.

To confirm what we saw was really an arm cavity resonance, we will try to do the same thing with the arm cavities all mis-aligned.
(We expect no signal in this configuration.)

Appendix: the expected signal from AS166 port when the 166MHz upper sideband passes by a resonance of the arm cavity.
Since the carrier is resonating in the cavity and kept there by the PDH feedback using 33MHz sideband, its phase is virtually fixed at the AS166 port. The lower sideband's phase also does not change much because it is off resonance. The upper sideband get a large phase change when approaching to the resonance. This effectively rotates the modulation angle of the 166MHz sidebands, which was orthogonal to the carrier when off resonance (i.e. phase modulation), to create 166MHz amplitude modulation. Because the sideband axis is rotated, the signal should appear both in I and Q phases.
ELOG V3.1.3-