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Entry  Fri Dec 12 22:51:23 2008, Yoichi, Update, PSL, Reference cavity ring down measurement again RC-Ringdown.png
    Reply  Tue Dec 16 19:06:01 2008, Yoichi, Update, PSL, Reference cavity ring down repeated many times RC_Ringdown_Estimates.pngCavity_Pole_Histogram.png
Message ID: 1190     Entry time: Fri Dec 12 22:51:23 2008     Reply to this: 1191
Author: Yoichi 
Type: Update 
Category: PSL 
Subject: Reference cavity ring down measurement again 
Bob made new HV-cables with HV compatible coaxes. The coax cable is rated for 2kV, which was as high as Bob
could found. I used it with 3kV hoping it was ok.
I also put a series resistor to the pockels cell to tame down the ripples I saw in elog:1136.

Despite those efforts, I still observed large ringings.
I tried several resistor values (2.5k, 1k, 330ohm), and found that 330ohm gives a slightly better result.
(When the resistance is larger, the edge of the PBS Refl. becomes dull).
Since the shape of the ringing does not change at all even when the pulse voltage is lowered to less than 1kV,
I'm now suspicious of the DEI pulser.

Anyway, I estimated the cavity pole using the MATLAB's system identification toolbox again.
This time, I locked the reference cavity using only the PZT feedback, which makes the UGF about a few kHz.
So, within the time scale shown in the plot below, the servo does not have enough time to respond, thus the laser
frequency stays tuned with the cavity. This was necessary to avoid non-linear behavior of the transmitted power
caused by the servo disturbing the laser frequency. With this treatment, I was able to approximate the response of
the cavity with a simple linear model (one pole low-pass filter).

MATLAB estimated the cavity pole to be 47.5kHz.
The blue curve in the plot is the measured RC transmitted power.
The incident power to the cavity can be inferred from the inverse of the red curve (the PBS reflection power).
The brown curve is the response of the first order low-pass filter with fc=47.5kHz to the input power variation.
The blue and brown curves match well for the first 10usec. Even after that the phases match well.
So the estimated 47.5kHz is probably a reasonable number. I don't know yet how to estimate the error of this measurement.

According to http://www.ligo.caltech.edu/~ajw/PSLFRC.png the designed transmission of the reference cavity mirrors is 300ppm (i.e.
the round trip loss (RTL) is 600ppm).
This number yields fc=35kHz. In the same picture, it was stated that fc=38.74kHz (I guess this is a measured number at some point).
The current fc=47.5kHz means, the RTL has increased by 200ppm from the design and 150ppm from the time fc=38.74kHz was measured.
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