I spent some time tonight measuring the free-running laser beat noise in various ways. Recall that, as of yesterday, I had tried setting up a couple analog PLLs to no avail and I didn't trust the spectrum I was getting from the Zurich PLL. So, I wanted to measure it another way to see if I could corroborate.

First, eye candy:

Now, an explanation of the various measurements.

I-Q demodulation method

This is a method I have used with some success in measuring the Marconi noise in its quietest state (with no modulation and therefore no means of feedback---see ATF:1877). It is done in the following way:

1. Split the beat PD output and send it to the RF input of two mixers (I used level-7 ZAD-1-1s), using equal path lengths.
2. Set Marconi to a frequency close to the beat (~50 MHz in this case) and an amplitude of +10 dBm
3. Split the Marconi output, send one splitter output to each mixer from (1), but with 90º rotation between them.
4. The outputs of the mixers are now at the difference frequency between the beat and the Marconi, but maintain their I-Q separation. (This is the reason for using the Marconi rather than beating the lasers at a lower frequency in the first place---the I-Q separation is maintained regardless of the differential laser drift, and it also only requires a short cable length.)
5. Acquire both I and Q signals and perform the I-Q analysis:
   1. Normalize the signals and atan2(I,Q) to get phi, then unwrap(phi) to get continuous phase evolution vs time
   2. diff(detrend(phi))/diff(t)/2/pi to get instantaneous frequency as a function of time
   3. pwelch

The main complication here is that, as you can see in the plot, the high-frequency RMS of the beat is several tens of kHz, which means you still have to sample at a high rate to get what you need. The best acquisition scheme I could think of was the Zurich box, which can do 460 kS/s. Still, to take meaningful data, I had to very carefully tune the laser beat to the Marconi LO and then quickly engage acquisition before the (wildly fluctuating) IF signals drifted above the Nyquist frequency (around one second of data was used to make this trace).

That said, the result doesn't look that crazy, and in fact it agrees very well with the DFD measurement that was carried out in a completely different way (see below).

Delay-line frequency discriminator (DFD) method

This is the usual scheme where one mixes a signal with a time-delayed version of itself to create dispersion. What I did:

1. Split the PD signal
2. Using one splitter output, find the appropriate combination of attenuators and amplifiers needed to obtain a LO-worthy +7-dBm signal (I needed -7 dB and then ~+25 from a ZFL-500-LN) and send it to a mixer LO input via a long (several-meter) cable.
3. Send the other output to the mixer RF input via a short cable (attenuate if necessary---wasn't in my case).
4. Verify that the DC level of the IF output varies sinusoidally with the beat frequency
5. Null the output and measure the frequency resolution. I measured 5.5 nV/Hz.
6. Amplify with SR560 and measure spectrum on spectrum analyzer
7. Divide spectrum by SR560 gain and the number in (5) to get frequency noise

This method worked swimmingly and reproduced exactly the result I found using the I-Q scheme. The noise floor (cyan in the plot) was measured by sending a quiet Marconi sine wave of the same amplitude and frequency as the beat through the pipeline.

Zurich PLL method

This method is incredibly straightforward. Simply plug the beat (ensuring it's < 1 V_rms and under 50 MHz) into the Zurich box and lock the internal PLL by pressing "ON" on the screen. Route the PLL control signal to one of the front panel outputs and choose the scale factor in V/Hz. I chose the same number as I measured for the DFD (including the SR560 gain) for ease of comparison on the spectrum analyzer.

Results

• All methods agree below ~50 Hz 
• The I-Q and DFD methods agree everywhere, but they are higher than the PLL result by ~2 from 50 Hz to around 10 kHz, above which they re-converge somewhat
• All traces (save for the PLL in a narrow band from ~50-500 Hz) are higher than those on the spec sheets sent with the laser (shown in black on the plot---note that the West laser is everywhere noisier than the East one).

I'm not sure what to believe. One would think the Zurich PLL is the most trustworthy, but a) I still am bothered by the time-domain behavior I see in the PLL control signal when I adjust the laser beat while watching it, and b) I've generated two nearly identical spectra that differ from it using completely different schemes from measurement to FFT.

All that said, I think the excess noise (and thanks to Dmass for saving me time by pointing this out) is just coming from the ThorLabs drivers, so this should be redone when we have our low-noise ones.