Summary: The PMC's FWHM was measured to be 3.8 MHz.

- Motivation

We are characterizing the PMC loop TF. We needed to measure the cavity's FWHM in order to know the cutoff frequency of the cavity.
This number will be used in the Simulink model to simulate the TF of PMC.

- Method

The length of the PZT was scanned, while the PDH error signal was also recorded.

The time span between the maximum and minimum peaks of the error signal was measured in order to obtain the width of the cavity resonance. The time-to-frequency conversion [second to Hz] will give us the FWHM. The conversion between the time and the frequency was obtained by looking at the zero crossings of the error signal which are separated by the modulation frequency.

- Measurement setup

• A function generator provides a triangular waveform at 200 Hz, 10V pk-pk, which is split by a T connector. One goes to an oscilloscope for trigger, another goes to EXT DC channel on PMC card.
   
• The signal going to EXT DC ch is used for scanning the PMC.
   
• The sideband is 21.5 MHz away from the carrier.
   
• Another ch on the oscilloscope is connected to MIX OUT ch on PMC card.
  This measures the error signal after the mixer.

- Result

• The time span between the carrier and the sideband: 768 us.

• The sideband frequency: 21.5 MHz

• ==> the conversion factor: 21.5 MHz/ 768 us = 28 GHz/s

• The time span between pk-pk of the error signal at the carrier resonance: 136 us
   
• ==> The FWHM is 136 us x 27.5 GHz/sec = 3.8 MHz

- Discussion

1) The cavity pole frequency is obtained from the measured FWHM. It is FWHM/2 = 2 MHz.
FSR is  c/Lroundtrip = c/(0.42m) = 714 MHz.
Thus we can compute the finesse F = FSR/FWHM = 188.

2) Another way to measure the FWHM is by measuring the transmission peak of the transmitted light while scanning the cavity. I’ll try this and see if two results agree.

Many thanks to Koji for useful discussion on the measurement and how to improve elog quality.