A Spectrum analyzer for cavity locking

[kelly0303]

Hello! I apologize for this question not being very well defined by I am really confused by the topic and I am not even totally sure what to ask. Basically I have an optical cavity and I am trying to lock a laser to it. I have a commercial servo for that, but I still need to adjust the PID loop parameter (actually I have 2 integrators). While I know in theory (at a basic level) what a PID loop does, I have never implemented one. I talked to some people and they told me the best way to set it up is by looking at the signal transmitted out of the cavity using a spectrum analyzer and that will tell me what PID parameters to use. They gave me a quick explanation which I didn't really understand. I read a bit more, but most of the stuff online is highly theoretical, so I am still not sure what to do (but at least I know more of the terminology now). Can anyone help me have an idea of what to do or at least how to get started? Do I need to look at the signal while scanning the laser frequency, or after I lock it (which will be a flimsy lock, if any, until I find the right PID parameters)? What frequency range I am interested in on the spectrum analyzer (the cavity linewidth is about 100 kHz and the FSR is about 1 GHz, the scanning rate of the laser can be adjusted but it is about 1 kHz)? And how do I translate any information from the spectrum analyzer to PID parameters? Thank you!

 

[DaveE]

OK, first, IDK... but here's some thoughts about what I would do.

1) Ignore the D gain, set it to zero. Maybe forever, or at least until you are in the optimization phase. Then you can play with it and figure out it isn't very useful, or maybe it is, IDK. The derivative term is most useful for slow systems like motors. Your laser isn't slow.

2) Set the I gain low, but not necessarily zero at first.

3) Play with the P gain (and maybe I) and get the loop to lock. Once you have a feedback system that is working (i.e.locked), then you can adjust the gains to get better performance, however you define it.

4) At this point it is just another servo system and you can use normal tools like FRAs, step response, etc. to evaluate performance. There are a bunch of methods for tuning PID controllers out there, Ziegler-Nichols comes to mind. But I usually would measure bode plots and choose pole-zero placement as I wanted (Don't get me started on my "why is everything PID when it's just a compensator with poles and zeros" rant).

5) This is similar to PLLs where you have two regimes to operate in: scanning and locked. The feedback loop design is often in conflict here with excellent tracking performance making locking more difficult (eg. reduced capture range). That's a bit too complicated for this sort of reply, but... High I gain can be a problem for locking. More sophisticated designs can be non-linear, essentially switching to higher gains after locking. I'll plead ignorance on the effect of the D term on capture range, although if someone said it helped I wouldn't argue, that makes some intuitive sense to me.

 

[Twigg]

they told me the best way to set it up is by looking at the signal transmitted out of the cavity using a spectrum analyzer and that will tell me what PID parameters to use.

Are you side-locking or locking using modulation (PDH, lock-in, etc.)? If side-locking, that sounds right. As a rule of thumb, the signal you want to put on the spectrum analyzer is whatever signal normally goes into the PID servo. So, for example, if you were PDH locking, you would put the demodulated error signal into the spectrum analyzer (instead of transmission).

Also, I've found that a signal analyzer or vector network analyzer is more useful than a spectrum analyzer for this purpose, but I digress. I'd say DC to 10kHz should be plenty of bandwidth for most applications (see note at the end of this post for the exceptional cases where you care about higher frequencies).

To evaluate your locking performance, look at the error signal on the spectrum analyzer, and toggle between locking and unlocked states. When locking, you should see a significant reduction in the spectrum of the error signal. If your gains are too high or too low, you may see no reduction or even an amplification of the error signal noise spectrum.

What kind of commercial controller are you using? If it's a Vescent, you can find a representative plot of the controller's frequency response on the side of the enclosure. When you tune the settings, you are moving the corners of the frequency response (poles, in fancy EE speak). You can also increase the DC gain.

My advice is to start with just barely enough P and 1st stage I gain to lock to the peak. Then increase the I corners until you start to oscillate. The oscillations will look like a bump ("servo bump" is the usual jargon for this feature) at high frequencies in the error signal spectrum. Then turn up the P gain until the oscillation goes away, then increase the I gain some more. Do this until you are locked without oscillations with as much I gain as possible. If you have a little bit of servo bump left, that's fine. This procedure is engineered to maximize your gain at low frequencies, which is probably what you want. (The exceptions are cavities for timebase comparisons (like optical clock comparisons) or cavities for stabilizing the gate lasers in quantum computing. If either of these are your intended use case (I doubt because your linewidth is too broad), let us know in a reply.)