I've been working on this but still I am not quite done yet. However, here's a glimpse at the data I've taken

Measuring the photo-thermal response

I did this slightly differently from when I was doing this in the past: Instead of modulating and using the TPD signals on channel 1 and RedPitaya frequency control signal on channel 2 I instead recorded sweeps with the modulation source on channel 1 and alternatingly TPD signal or RedPitaya output on channel 2 to reject coherent noise at the sampling points.

• The transmission beat was used for this measurement, as the RedPitaya output is much less noisy at high frequencies due to the cavity filtering
• The nominal beat was ~450 MHz, which was mixed with a 480 MHz Marconi signal, and the difference 30 MHz was fed to the Red Pitaya
• The RP's control signal was calibrated using a second Marconi to replace the beat signal and stepping its frequency

The above plot (also Attachment #1) shows the photothermal response recorded for each path scaled to Hz per Watt of circulating cavity power. It looks like the absorption for the two paths is much closer than in the old cavities. Since we get the frequency modulation from the beat, I inverted the drive signal for one of the cavities so the measured responses would be in phase. Looking at the plot we should not use anything substantially over 1 kHz to fit the photothermal TF (for the individual paths). While this same measurement returned quite nice agreement with the model after fitting for absorption values, this is no longer the case (see attachment #2):

The fit minimizes the error in the complex plane (squared absolute value of the difference) and uesd only frequencies <1 kHz. The fit returns an absorption of ~0.75 ppm per mirror, however there is significant discrepancy throughout, even the slope at low frequencies is a bit off. The model uses only surface absorption and doesn't track the field strength in the layers yet, so I'm working to include that. It does already include bulk heating for modeling thermo-optic noise.

At high frequencies the amplitude modulation drives the PLL error point, which increasingly masks the photothermal effect, so I did the same trick from before, where I drive the amplitude modulation for the two paths out of phase wrt each other. Since the RedPitaya performs I and Q demodulation, I minimized the transfer function from modulation signal to amplitude estimate by adjusting the AOM bias of the two paths (At the locking points the lasers have slightly different output power, and the transmission beamsplitter is not perfectly 50/50). This suppresses the amplitude fluctuations of the beat note on the detector to first order.

To scale the dual modulation photothermal response to Hz/W I added the light powers in the two cavities, effectively treating them as a single cavity with ~double the circulating power.

I performed a series of sweeps of this dual photothermal response and used the IRIS routines to estimate measurement uncertainties (Attachment #4). Looking at the result, we might be able to use the sweep up to 20 kHz for fitting.