I minimized the RFAM by aligning the 35.5 MHz EOM and remeasured the RIN coupling coefficient.
The upper limit is 5 [Hz/uW (fluctuation of input power = RIN x Pin) ]@ 10 Hz
(This entry is approved by Kiwamu and is written in his style)Tue May 10 19:20:22 2011
As pointed out in the LIGO-X meeting that my setup might suffer a lot from RFAM, so I came back to:
The power input was 1mW as usual.
The frequency of Vmod is 10Hz. The amplitude of Vmod to EAOM for amplitude modulation was varied from 2 to 10 Vpkpk. Common/Fast gain was 500/900. I had to reduce it so the signal is not too large. I measured the spectrum of FASTMON and tried to observe the peak at 10Hz with 12.5 mHz linewidth. The background level was ~10mV.
I do this to determine what is the maximum driving voltage where the effect from RFAM is still small compared to the background.
Drive Vpkpk FASTMON peak(Vrms/rtHz)
2 ~comparable to BG level ~ 10mV/rtHz
[ 1. aligning EOM ]
I picked up the beam after EOM on RCAV path and sent it to a PD (Thorlabs PDA10A.) There were 35.5 MHz pick up on the table, so I had to choose where the peak from pickup was minimum. Then I adjusted the half wave plate before the EOM and EOM's pitch/yaw position to minimize the peak.
[ 2. determine max Vmod ]
Although we want to modulate the power as small as possible to have a good linear approximation, we also need the signal to be large enough to be able to see the effect. However, the alignment of the EOM is not perfect, there will be RFAM effect adds into the signal. If the modulation is too large, the RFAM will mask the real signal. I need to determine what is the maximum Vmod I can use without having the RFAM effect excited above the background.
To see the effect of RFAM, I kept the setup similar to what I did with RIN coupling coefficient measurement, but without locking the cavity, and the laser frequency off from the resonance. This will tell us how much "fake signal" is produced by RFAM.
When the cavity is not locked, all the carrier and sidebands will be incident on the RFPD. The signal should be flat (beat between the carrier and both sidebands cancel each another,) and after it is demodulated by 35.5 MHz from LO, the level should be zero. However, if the amplitude is modulated at 35.5 MHz due to misalignment of the EOM, this will appear as DC signal at the error point. Hence, any power modulation at f0 (for this case, 10 Hz) will multiply up the error signal and cause offset fluctuation and slope change at f0. Slope change is not a problem, but the offset is. It will change the point where the laser will be locked, as the error signal moves up and down. Thus the system will interpret it as frequency noise of the laser and try to fight against it. This will appear as a peak in the FASTOUT spectrum at the modulation frequency, f0.
I measured the spectrum of FASTOUT (MIXER OUT is another option) to see the effect of RFAM
[ 3. remeasure RIN coupling coefficient ]
So I used 2Vpkpk drive, locked the cavity, and measured FASTMON again to see if I can measured the RIN coupling or not. The gain was set back to optimum value (common = 970 fast= 900.) However, there was no observable peak at 10Hz from FASTMON signal. It was quite flat ~100 uVrms/rtHz.
I made sure that the amplitude was really modulated by checking RCTRANSPD. It had a 5.37 Vrms/rtHz peak at 10Hz with 200mV DC level. Therefore, the laser noise is higher than the thermo-optic effect at this modulation level. I cannot increase modulation depth because the RFAM will mask the signal.
If I use this number to calculate the coupling coefficient, (flat level of FASTOUT, and peak from RCTRANSPD)
it will be ~ 8 [Hz/ uW of fluctuation of the input power into the cavity] still larger than 1[Hz/uW] as measured at 40m, but it's getting smaller than the last entry (60 [Hz/uW] of input power)
I still can change the power input, but I think the RFAM will scale up by the same amount and mask the signal again. I'll try that later.
Let's check what does this value give us in the noise budget @10Hz. The input power is 1mW, RIN = 10^-4. Frequency noise will be
8 [Hz/uW] x 1000 [uW] x 10^-4 [RIN] = 0.8 [Hz/rtHz] which is higher than coating noise (10 [mHz/rtHz]@10Hz) So we still cannot ignore the effect.
I tried 16 mW input power, there was signal from RFAM when I measured FASTOUT with unlocked cavity, the peak was 46 m[Vrms/rtHz] above 10m[Vrms/rtHz] background. Vmod = 1Vpkpk.
When I lock the cavity and measure the coupling:
FASTMON peak = 278.6 uVrms/rtHz
RCTRANSPD peak = 30.82 mV, DC level = 2.57 V, Pin = 16mW. Linewidth = 12.5mHz.
Common/Fast gain = 480/906
Use the calculation from here.
The upper limit for coupling coeffiicient is ~ 5 [Hz/uW]. It is only the upper limit because RFAM effect is still present.