I measured the slope of the error signal from ACAV and RCAV loop. The values are 0.11MHz/V for ACAV and 0.275 MHz/V for RCAV.

I also obtained the calibration for Vapplied to the laser's fast channel to frequency change to be 3.09 MHz/V.

This will be a note on how to measure error signal slope for PDH locking technique.

The slope of the error signal will allow us to project the noise from RFPD, or anything before the frequency discriminator to frequency noise.

The slope will also depend on the input power, modulation depth, so these are the parameters of the setup when I measured the data.

Power input to each cavity :1mW input

Modulation depth: 10V

Phase adj: 4.75 V.

We have two cavities, ACAV and RCAV, here I illustrate the plots from ACAV data only.

I scanned the laser by sending  triangular signal, 18V pk-pk (+/- 9V), 5Hz. to fast modulation input on the laser's controller.

I used the 35.5 MHz sideband peak to convert time on the oscilloscope to frequency change due to voltage applied.

fig1) screen on the oscilloscope, blue is error signal x 100 , green is voltage applied to scan the laser on the laser controller.

dT between the carrier and the sideband on the oscilloscope is 0.01059 - -0.05239 = 0.0630 [sec].

Thus the conversion is 35.5 MHz/0.0630 = 563.7 MHz/ sec. This will be used to convert the slope of the error signal from V/sec to V/Hz or Hz/V.

Note that we can also learn the calibration for applied V at fast channel to frequncy shift from green plot. dV = 6.3 - -5.2 = 11.5 V.

So the calibration for frequency shift due to the applied V is 35.5 MHz/11.5V =  is 3.09 MHz/V. 

Then, I measured the slope of the error signal, twice for different time spans on the scope, no big difference.

fig2) error signal from ACAV. The center slope in the plot is 5200 V/ sec. Use the calibration before to get

563.7 [MHz/sec] / 5200 [V/sec]= 0.11 [MHz/V] for ACAV.

The center slope for ACAV = 0.11 MHz/V (with x30 pre amp for RFPD signal)

                             for RCAV = 0.275 MHz/V (measured from mixer mon channel)

I checked the pk-pk  of the error signal to, the separation is

RCAV = 63.9 kHz

ACAV = 100.4 kHz 

which are supposed to be cavities' FWHM.