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Message ID: 14054     Entry time: Wed Jul 11 18:13:19 2018     In reply to: 14044
 Author: keerthana Type: Summary Category: AUX Subject: Gouy Phase Measurements from AUX-Laser Scans

From the Measurement Jon made, FSR is 3.967 MHz and the Gouy phase is 52 degrees. From this, the length of the Y-arm cavity seems to be 37.78 m and the radius of curvature of the mirror seems to be 60.85 m.

$Guoy Phase = \cos^{-1} \sqrt{g1.g2}$

$\\ g = 1- \frac{L}{R}$

$L = \frac {c} {2*FSR}$

FSR = Free spectral Range

L = Lenth of the arm

R = Radius of curvature of the mirror (R1 =$\infty$  , R2= unknown)

Quote:

This note reports analysis of cavity scans made by directly sweeping the AUX laser carrier frequency (no sidebands). The measurement is made by sweeping the RF offset of the AUX-PSL phase-locked loop and demodulating the cavity reflection/transmission signal at the offset frequency.

# Y-Arm Scan

Due to the simplicity of its expected response, the Y-arm cavity was scanned first as a test of the AUX hardware and the sensitivity of the technique. Attachment 1 shows the measured cavity transmission with respect to RF drive signal.

The AUX laser launch setup is capable of injecting up to 9.3 mW into the AS port. This high-power measurement is shown by the black trace. The same measurement is repeated for a realistic SQZ injection power, 70 uW, indicated by the red curve. At low power, the technique still clearly resolves the FSR and six HOM resonances. From the identified mode resonance frequencies the following cavity parameters are directly extracted.

YARM Gautam V. Finesse Model Actual
FSR 3.966 MHz 3.967 MHz
Gouy phase 54.2 deg 52.0 deg

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