Error signal when locking a cavity

[kelly0303]

Hello! I am trying to lock a laser to a bow-tie cavity. I managed to align the cavity to a certain degree but when I lock it, the error signal looks as below. I do get a significant power enhancement (although about 10 times smaller than expected) and the lock is relatively stable, but the error signal looks nothing like what I would expect. I imagined it to be a flat-ish line, maybe moving up and down around zero, suggesting that the lock is decently good. But I am getting this signal with lots of peaks (again this is after I turn the lock on, not during the scan of the cavity). Has anyone seen this before? What should I do to get a well behaved error signal.

 

[Twigg]

First, a jargon thing: by error signal you mean the input to your locking servo, correct? Some people I know call the output of servo the error signal, and it gets confusing. (For the sake of clarity, I always call the output of the servo the "control signal."

Also, what's the vertical scale on that scope trace? I can't tell if those are 1mV peaks or 1V peaks.

If this is indeed the input to your servo, then you need to tune the gains on your servo. Here's how I do it:

1. Turn all the gains on your servo to the lowest values where the laser will stay locked. (Usually, you set I gain to 0 and P to minimum lock-able value.)
2. Turn up your P gain until you see parasitic oscillations in the error signal
3. Turn down the P gain just below the threshold for parasitic oscillations
4. Turn up the I gain until you see parasitic oscillations in the error signal
5. Turn down the I gain just below the threshold for parasitic oscillations
6. Repeat steps 2-5 until you can't turn up either P or I gain anymore without getting oscillations
7. Turn down the gains as necessary to get a stable lock

 

[kelly0303]

First, a jargon thing: by error signal you mean the input to your locking servo, correct? Some people I know call the output of servo the error signal, and it gets confusing. (For the sake of clarity, I always call the output of the servo the "control signal."

Also, what's the vertical scale on that scope trace? I can't tell if those are 1mV peaks or 1V peaks.

If this is indeed the input to your servo, then you need to tune the gains on your servo. Here's how I do it:

1. Turn all the gains on your servo to the lowest values where the laser will stay locked. (Usually, you set I gain to 0 and P to minimum lock-able value.)
2. Turn up your P gain until you see parasitic oscillations in the error signal
3. Turn down the P gain just below the threshold for parasitic oscillations
4. Turn up the I gain until you see parasitic oscillations in the error signal
5. Turn down the I gain just below the threshold for parasitic oscillations
6. Repeat steps 2-5 until you can't turn up either P or I gain anymore without getting oscillations
7. Turn down the gains as necessary to get a stable lock

Thanks for your reply! Yes, I am looking at the input (actually this input is passed through a 200 kHz low pass filter by default by the servo). The amplitude of the peaks is on the order of a few volts, and they get bigger, the better the lock (and by this I mean the power output from the cavity measured separately by a power meter). So I tried what you suggested, but I am not sure I can go beyond step 2. ANY lock I am able to make has these peaks (I am not sure if these are what you call parasitic oscillations). So there is no setup where I get a lock (even a bad one) with a nice, flat-ish signal on the oscilloscope. It's either this peak-like signal or no lock at all, regardless of the PID setup I use.

 

[Twigg]

Can you record what your error signal looks like unlocked when you manually tune the laser on resonance?

Also, can you lock the laser and show side-by-side the error signal and the control signal (output of the servo)? I suggest that on the scope settings you set triggering to the 60Hz AC setting (in auto acquisition). Triggering to a noisy signal just makes things more confusing. Also, in the future it's easier for folks to understand what's going on if you include the whole scope screen in your pictures.

What does the transmission photodiode signal look like while you are locked? It should be very flat and very large.

It will be more clear once you have those data, but my first impression is that either you are not actually locking (perhaps railing off to one side of the control voltage?) or your error signal is just so massive that your error signal oscillates at even the lowest gain settings. My money is on the first possibility.

If you can scan your laser and lock the servo at the same time (as shown in this post), then it's easy to tell (but some commercial lockboxes don't have this feature). Another way to tell is to look at the control signal when you engage the servo lock. If the control signal goes to the positive or negative maximum voltage (you'll have to look this up in the manual for your laser servo), then you know you are railing and not locking.

 

[kelly0303]

What does the transmission photodiode signal look like while you are locked? It should be very flat and very large.

Thank you for all these suggestions! I will try them tomorrow. One quick question about the above quoted thing you said. What do you mean by that? Isn't the signal I am showing above i.e. the input signal, the signal from the transmission photodiode (I am recording the signal by measuring the light transmitted out of the cavity)?

 

[Twigg]

Oh! Are you trying to side-lock to the transmission peak? (Sorry, I'm used to PDH locking.)

 

[kelly0303]

Oh! Are you trying to side-lock to the transmission peak? (Sorry, I'm used to PDH locking.)

Ah yes, sorry for not mentioning it. I am doing side-lock and the signal I am showing is directly from the transmission measured by the diode.

Also in case it helps (but I will show more pictures tomorrow), these peaks in the picture above, that I see when I am locked, are very similar to the peaks I see during scanning the laser frequency.

 

[Twigg]

What laser servo are you using? Is it commercial or homebrew?

 

[kelly0303]

What laser servo are you using? Is it commercial or homebrew?

I am using this model. Also, is there a way to attach a video here that is longer than 4 seconds? It would be a lot easier to show the oscilloscope before and after the lock, as well as the transitions between the 2 and the behavior when changing the PID settings.

 

[DaveE]

is there a way to attach a video here that is longer than 4 seconds?

Most people put them on YouTube and post the link to it.

 

[kelly0303]

Can you record what your error signal looks like unlocked when you manually tune the laser on resonance?

Also, can you lock the laser and show side-by-side the error signal and the control signal (output of the servo)? I suggest that on the scope settings you set triggering to the 60Hz AC setting (in auto acquisition). Triggering to a noisy signal just makes things more confusing. Also, in the future it's easier for folks to understand what's going on if you include the whole scope screen in your pictures.

What does the transmission photodiode signal look like while you are locked? It should be very flat and very large.

It will be more clear once you have those data, but my first impression is that either you are not actually locking (perhaps railing off to one side of the control voltage?) or your error signal is just so massive that your error signal oscillates at even the lowest gain settings. My money is on the first possibility.

If you can scan your laser and lock the servo at the same time (as shown in this post), then it's easy to tell (but some commercial lockboxes don't have this feature). Another way to tell is to look at the control signal when you engage the servo lock. If the control signal goes to the positive or negative maximum voltage (you'll have to look this up in the manual for your laser servo), then you know you are railing and not locking.

@Twigg I am attaching below some pics.

The first one show the scope screen in ramping more. The yellow is the signal from the photodiode, blue is the ramp itself and pink is the TTL ramp. The scale of the yellow is 50 mV (after placing a ND 1.0 filter on the photodiode) and the scale of blue is 1V.

The second one shows what happens right after I turn on the locking (without changing anything on the oscilloscope). The error signal (blue) is flat and has small oscillations, however it doesn't jump to the maximum voltage (that actually happens when the lock is lost i.e. when I don't measure a lot of power on the power meter anymore), but the input signal still has many peaks (they are now actually narrower than before as I aligned the cavity a bit better today).

Figure 3 and 4 show the beam spot measured on a CCD camera before and after the lock. The camera is definitely saturated, but a clear enhancement can be seen (on top of the one measured by the power meter).

I am also attaching my cavity setup. It's pretty straightforward. I am measuring everything (diode, power meter and CCD camera) in transmission mode.

Thanks a lot again for help and please let me know if I should provide more information.

 

[Twigg]

Sorry for the slow reply. This week hit me like a freight train.

Ok, you are most certainly locked.

There is definitely something wrong, as your transmission signal seems to fluctuate all the way to 0 while you are locked.

I am confused about the error signal trace (blue, in pic #2 of post #11) you sent. Shouldn't the error signal (blue trace) be the same as the transmission photodiode (yellow trace)? Or is the blue trace supposed to be the servo output (labeled "Servo Out" on the Vescent servo)? Sorry for doubting you, it's just really confusing why the yellow and blue don't look the same.

Can you elaborate the connections to and from the Vescent servo? Am I right that you connect the transmission photodiode into the "Error Input" port (bottom left of the front panel). Which of the ports is the blue trace?

 

[kelly0303]

Sorry for the slow reply. This week hit me like a freight train.

Ok, you are most certainly locked.

There is definitely something wrong, as your transmission signal seems to fluctuate all the way to 0 while you are locked.

I am confused about the error signal trace (blue, in pic #2 of post #11) you sent. Shouldn't the error signal (blue trace) be the same as the transmission photodiode (yellow trace)? Or is the blue trace supposed to be the servo output (labeled "Servo Out" on the Vescent servo)? Sorry for doubting you, it's just really confusing why the yellow and blue don't look the same.

Can you elaborate the connections to and from the Vescent servo? Am I right that you connect the transmission photodiode into the "Error Input" port (bottom left of the front panel). Which of the ports is the blue trace?

The blue line is indeed coming from "Servo Out" (I thought this is what you meant by "control signal").

In terms of the Vescent connections, it is like this: the photodiode signal goes to "Error Input". The "DC Error" output is the yellow line. The "Servo Out" is the blue line. The "Servo Output" goes to the laser. The "Ramp TTL" is the pink output.

 

[Twigg]

The blue line is indeed coming from "Servo Out" (I thought this is what you meant by "control signal").

Oh! Ok then that makes sense. In post #11 you called it the error signal and I got confused. Sorry about that.

Does the noise on the error signal get bigger or smaller when you increase the P gain (using the coarse gain knob)?

It bugs me that your servo doesn't even try to keep up with the noise on your error signal. That is strange. It could be that your high-frequency gain is too low (seems unlikely, but possible). To solve this, you could increase the corner frequencies for your first and/or second stage integrators (the knobs on the side of the Vescent box).

Do you have a network analyzer? If not, does your oscilloscope have an FFT function? I bring this up because looking at the FFT of your error signal makes adjusting corner frequencies much more intuitive.

 

[kelly0303]

Oh! Ok then that makes sense. In post #11 you called it the error signal and I got confused. Sorry about that.

Does the noise on the error signal get bigger or smaller when you increase the P gain (using the coarse gain knob)?

It bugs me that your servo doesn't even try to keep up with the noise on your error signal. That is strange. It could be that your high-frequency gain is too low (seems unlikely, but possible). To solve this, you could increase the corner frequencies for your first and/or second stage integrators (the knobs on the side of the Vescent box).

Do you have a network analyzer? If not, does your oscilloscope have an FFT function? I bring this up because looking at the FFT of your error signal makes adjusting corner frequencies much more intuitive.

The noise gets smaller when I increase the P gain, but also the power output gets smaller.

Actually the second integrator in my current setup is OFF. Honestly I didn't understand what it does and most of the resources I found online barely talked about it. Also we have another servo in our lab (might try that at a point), which has only one integrator, so I assumed the second one is maybe for fine tuning. I will try to play with that, too.

How exactly adjusting these corners work (i.e. how does it help)? Thank you!

 

[Twigg]

The noise gets smaller when I increase the P gain, but also the power output gets smaller.

Ok, that sounds like parasitic oscillation (overall gain too high) in some form or another.

Actually the second integrator in my current setup is OFF.

Totally reasonable. For what you're doing, you probably won't need it ever.

Honestly I didn't understand what it does and most of the resources I found online barely talked about it.

Fair enough, I couldn't find a good summary online either. The second integrator is to give the user the ability to suppress low frequency laser noise (1/f noise, aka "pink noise" aka "flicker noise") even more strongly than if you only had one integrator. Most laser applications only require a single integrator (and no differentiator), because most people don't care about excess noise at higher frequencies so long as the laser stays locked. The Vescent D2-125 is kind of like the Lamborghini of lockboxes, and it is a favorite in labs where frequency noise is crucial (e.g., trapped ion/atom quantum computing and optical atomic clocks). That being said, as you already pointed out, it's over-engineered and not simple to setup.

How exactly adjusting these corners work (i.e. how does it help)? Thank you!

The way you're supposed to fine-tune the second integrator and differentiator is to hook up your error signal to a oscilloscope or network analyzer and display the Fourier transform of your error signal. The amplitude of the Fourier transform indicates the magnitude of instability in your laser as a function of frequency. For example, if you used a PZT to modulate your laser at 10Hz, you would see a large peak in the FT of the error signal at 10Hz. If your laser drifts a lot due to thermal effects, you would expect to see a large component of your error signal FT at low frequencies (since thermal effects are slow), often following a 1/f dependence on frequency. To fine tune the D2-125 servo's many settings, you would adjust them until you make the FT of the error signal as small as possible over as large a frequency range as possible.

Look at the graph on the side of the D2-125 box. This shows the gain of the Vescent servo as a function of the Fourier frequency. When you adjust, for example, the first integrator knob on the side of the lockbox, you are moving the corner frequency labeled $\omega_I$. Likewise for $\omega_{PI}$ (2nd integrator) and $\omega_D$ (differentiator). Controlling the frequency of these corners allows you to distribute the gain of the servo over low- and high-frequency bands to best match the specifics of your laser noise spectrum. So you adjust the various settings until you optimize the FT of your error signal.

 

[kelly0303]

Ok, that sounds like parasitic oscillation (overall gain too high) in some form or another.Totally reasonable. For what you're doing, you probably won't need it ever.Fair enough, I couldn't find a good summary online either. The second integrator is to give the user the ability to suppress low frequency laser noise (1/f noise, aka "pink noise" aka "flicker noise") even more strongly than if you only had one integrator. Most laser applications only require a single integrator (and no differentiator), because most people don't care about excess noise at higher frequencies so long as the laser stays locked. The Vescent D2-125 is kind of like the Lamborghini of lockboxes, and it is a favorite in labs where frequency noise is crucial (e.g., trapped ion/atom quantum computing and optical atomic clocks). That being said, as you already pointed out, it's over-engineered and not simple to setup.The way you're supposed to fine-tune the second integrator and differentiator is to hook up your error signal to a oscilloscope or network analyzer and display the Fourier transform of your error signal. The amplitude of the Fourier transform indicates the magnitude of instability in your laser as a function of frequency. For example, if you used a PZT to modulate your laser at 10Hz, you would see a large peak in the FT of the error signal at 10Hz. If your laser drifts a lot due to thermal effects, you would expect to see a large component of your error signal FT at low frequencies (since thermal effects are slow), often following a 1/f dependence on frequency. To fine tune the D2-125 servo's many settings, you would adjust them until you make the FT of the error signal as small as possible over as large a frequency range as possible.

Look at the graph on the side of the D2-125 box. This shows the gain of the Vescent servo as a function of the Fourier frequency. When you adjust, for example, the first integrator knob on the side of the lockbox, you are moving the corner frequency labeled $\omega_I$. Likewise for $\omega_{PI}$ (2nd integrator) and $\omega_D$ (differentiator). Controlling the frequency of these corners allows you to distribute the gain of the servo over low- and high-frequency bands to best match the specifics of your laser noise spectrum. So you adjust the various settings until you optimize the FT of your error signal.

Thanks a lot for this explanation! Actually I am a bit confused about the second integrator, as on the Vescent diagram it appears to be bigger than the first one, but I keep it at zero while the first one is non-zero. How does that work? Also, in my case the differential one is also zero (the frequency i.e. $\omega_D$), so based on their diagram I would have no proportional gain, as that seems to be in between $\omega_{PI}$ and $\omega_D$, which are both zero. Am I reading that diagram wrong?

Ok, that sounds like parasitic oscillation (overall gain too high) in some form or another.

Is there something I can do about this? Reducing the gain does help but it also reduces the output power a lot.

 

[Twigg]

So when you turn the 2nd integrator off, you're not setting the corner to 0, you're removing that feature from the gain plot entirely. So if you turn off the 2nd integrator and the differentiator, what you have is a typical PI gain curve:

Edit: Whoops, I forgot to respond to your second question.

Ok, so if I understand you correctly, then (1) as you turn up the P gain the noise gets smaller and (2) as you turn up the P gain the output power increases to a maximum value and then gets smaller if you increase the P gain any further than that. However, even when you turn the P gain so high that your transmitted power gets smaller, your error signal noise still gets smaller? That part is very confusing to me.

If you put the P gain to the point where the transmitted power is maximum, what happens if you increase the first integrator gain?

Edit: In the sketch I drew, the x-axis should also be logarithmic scale (log f). My bad

 

[kelly0303]

So when you turn the 2nd integrator off, you're not setting the corner to 0, you're removing that feature from the gain plot entirely. So if you turn off the 2nd integrator and the differentiator, what you have is a typical PI gain curve:
View attachment 315931
Edit: Whoops, I forgot to respond to your second question.

Ok, so if I understand you correctly, then (1) as you turn up the P gain the noise gets smaller and (2) as you turn up the P gain the output power increases to a maximum value and then gets smaller if you increase the P gain any further than that. However, even when you turn the P gain so high that your transmitted power gets smaller, your error signal noise still gets smaller? That part is very confusing to me.

If you put the P gain to the point where the transmitted power is maximum, what happens if you increase the first integrator gain?

Edit: In the sketch I drew, the x-axis should also be logarithmic scale (log f). My bad

@Twigg sorry for the delayed reply. Actually as I turn up the P gain the noise get smaller, but the power gets smaller, too, it doesn't increase to a maximum. The maxium power is where the P-gain knob is at one of the lowest values (not the lowest, tho, as it loses lock there), if I increase it from there the noise is a bit reduced but the power, too.

Based on some of your suggestions I also replaced the damped legs with normal ones, such that the laser and the cavity feel the same vibrations and nothing changed. I also replaced one of the mirrors I am using (Layertech) with a Thorlabs one, with lower reflectivity, in the hope that maybe the issue is that the cavity linewidth is too narrow and this would make it bigger, but I got the same effect (but of course with much lower power output).

I am thinking to reduce the cavity length by a bit (it is about 1.2 meters long now) and see if things get better. Intuitively i expect that a small change in one of the mirrors would have a big impact on the alignment given that the cavity is not stabilized and so long, but I was hoping the servo would be able to solve that during lock.

To be honest everyone in my lab and even the technical support from Vescent told me they have never seen this effect before so I am kinda out of ideas as to what can cause it. Just for reference I am trying to do something similar to this. I don't need a beam spot size as big as theirs (2-3 mm is enough for me), I even went quite far from the stability edge just to see if things get better (they don't!) but even so I can't seem to make it work. On top of that they claim in the paper that in the bow tie setup with 2 curved and 2 flat mirrors (which is my setup, too), the system is quite insensitive to vibrations, and straightforward to lock, which is kinda frustrating give my experience with this cavity. Anyways, any further insight would be greatly apprecaited.

 

[DaveE]

Have you tried a different servo (controller) yet? Or tested the one you have. My gut feeling is that the controller just isn't doing what it should or what you want. You can adjust it for different gains, but did it actually do it?

 

[DaveE]

Can you just control the mirror position (voltage?) yourself, so you are the controller. Of course it will be very finicky, you'll need patience and a steady hand, but if you can (sort of) lock the cavity, a servo controller should also be able to.

 

[Twigg]

I'll write a longer reply when I have more time, but I want to second the suggestion to try a different servo other than the Vescent.

Do you happen to have another stabilized 1064 laser? I know it's unlikely, but if you do I would beat the two lasers on a photodiode so you can see the spectrum of your cavity lo ked laser in the RF beatnote. It's a really helpful diagnostic if you have the stable light to begin with.

Does the behavior of the Vescent lock change if you change the incident optical power? Maybe it's a thermal effect of the cavity?

 

[kelly0303]

I'll write a longer reply when I have more time, but I want to second the suggestion to try a different servo other than the Vescent.

Do you happen to have another stabilized 1064 laser? I know it's unlikely, but if you do I would beat the two lasers on a photodiode so you can see the spectrum of your cavity lo ked laser in the RF beatnote. It's a really helpful diagnostic if you have the stable light to begin with.

Does the behavior of the Vescent lock change if you change the incident optical power? Maybe it's a thermal effect of the cavity?

@Twigg @DaveE Thank you for your replies. I actually tried this servo, too, but with this one I was not able to get a lock at all (not even the one I got with Vescent where I see a significantly brighter spot, despite the power output looking so weird). I still haven't figured out what the issue is with this second servo. I don't think we have a second 1064 stabilized laser, but I will try to adjust the power more and see what happens. However the power I am using now is about 50 times smaller than what I aim to use once I am happy with the locking, and the mirrors are supposed to work properly at that, power, too, so I really hope it's not a thermal effect at this power already.

 

[DaveE]

Can you just control the mirror position (voltage?) yourself, so you are the controller. Of course it will be very finicky, you'll need patience and a steady hand, but if you can (sort of) lock the cavity, a servo controller should also be able to.

Or, in a similar vein, can you just input a ramp and then zoom your scope in on the good part? Is the cavity well behaved as the controller slowly sweeps through the resonance? Some adjustments may be needed to the ramp to stay in/near the resonance for long enough to see "good" behavior. But, my point is that if the controller can sweep through the resonance without all of that noise, then I see no reason why you couldn't lock to it with a good controller and the correct gain settings.

The common theme here is to see if the cavity works well open loop. If so, you have a problem with your electronic feedback system. If not, the electronics probably can't fix it.

 

[Tom.G]

Another possibility is that one of the actuators has a (mechanical?) problem; or even one of the mirrors may have an inhomogeneous coating.

Hopefully it is convenient to substitute them.

 

[DaveE]

Another possibility is that one of the actuators has a (mechanical?) problem; or even one of the mirrors may have an inhomogeneous coating.

Hopefully it is convenient to substitute them.

He's already tried different mirrors. But hysteresis could be a difficulty for the controller. That won't show up in the ramp mode. Maybe fixed by some sort of preload spring or such? I haven't seen this with mirror mounts since the MEs know to avoid it.

 

[kelly0303]

Or, in a similar vein, can you just input a ramp and then zoom your scope in on the good part? Is the cavity well behaved as the controller slowly sweeps through the resonance? Some adjustments may be needed to the ramp to stay in/near the resonance for long enough to see "good" behavior. But, my point is that if the controller can sweep through the resonance without all of that noise, then I see no reason why you couldn't lock to it with a good controller and the correct gain settings.

The common theme here is to see if the cavity works well open loop. If so, you have a problem with your electronic feedback system. If not, the electronics probably can't fix it.

@DaveE Thanks for this. What exactly do you mean by "Can you just control the mirror position yourself"?

Also the peaks are not very nice if you zoom in enough (I can post a video on Monday). Not sure if I mentioned in this thread or a previous one, but the cavity is not stabilized, so the mirrors will have some vibrations, hence the peak will not always be in the same position relative to the ramp. However the goal was to make the laser follow the cavity length using the servo (I just need a large power enhancement inside the cavity, I don't care about the actual frequency that gets amplified), so I hoped that the vibrations wouldn't be a problem once the laser is locked to the cavity.

As I mentioned before this is the first time I am building a cavity so it might also be that I am just doing something stupid that everyone assumes I am doing right. Overall the cavity doesn't seem to be special relative to many others cavities I read about (e.g. the finesse is about 10000, which is not at all big relative to what you can find in the literature), so I am really puzzled about why I see so strange effects.

 

[Twigg]

As I mentioned before this is the first time I am building a cavity so it might also be that I am just doing something stupid that everyone assumes I am doing right. Overall the cavity doesn't seem to be special relative to many others cavities I read about (e.g. the finesse is about 10000, which is not at all big relative to what you can find in the literature), so I am really puzzled about why I see so strange effects.

I work on optical cavities a lot, and I can say that me and my coworkers all agree that cavities are just hard and troubleshooting them can feel like you're going in circles. It's not a reflection on your abilities. Cavities are just scheming little gremlins.

Another possibility is that one of the actuators has a (mechanical?) problem; or even one of the mirrors may have an inhomogeneous coating.

It's a little hard to understand why that would cause the transmitted optical power to continually decrease as the proportional gain is turned up.

The common theme here is to see if the cavity works well open loop. If so, you have a problem with your electronic feedback system. If not, the electronics probably can't fix it.

If the resonance is well-behaved/stable enough that you can be a human servo, I would also second this suggestion.

@Twigg sorry for the delayed reply. Actually as I turn up the P gain the noise get smaller, but the power gets smaller, too, it doesn't increase to a maximum. The maxium power is where the P-gain knob is at one of the lowest values (not the lowest, tho, as it loses lock there), if I increase it from there the noise is a bit reduced but the power, too.

Because the optical power seems to depend on prop gain, the problem ought to be something to do with the servo.

One possibility is that you don't have enough gain at low frequencies (integral gain) and are locking at an offset to the locking setpoint, which happens to put the laser closer to resonance than your setpoint. This is a little hard to describe in words. Suppose you set the servo to lock to the blue (higher frequency) side of your transmission peak. If your integral gain is low and if your cavity frequency is drifting redder (lower resonant frequency over time), then you could lock your laser at an offset frequency redder than the side of the fringe where your setpoint was. This would mean your laser would settle closer to resonance than your locking setpoint, and so the beam would be brighter. As you turn up the prop gain, the servo would clamp down harder and the laser would get closer to the setpoint (and farther from resonance), so the optical power would go down. The power would keep going down until you got near the setpoint and then it should not change anymore. This isn't a bug, it's just the servo locking to a setpoint that is not the maximum of cavity transmission.

If this is the case, you should be able to tell by looking at the "DC Error" port of the Vescent D2-125. When you lock at low gain (where you get higher power), is the error signal 0 volts? What about when you turn up the prop gain? If my hypothesis is right, then you should see a non-zero voltage on the error signal at low gain, and that should get smaller and smaller and go to zero as you turn up the prop gain.

I hope that helps!

 

[kelly0303]

I work on optical cavities a lot, and I can say that me and my coworkers all agree that cavities are just hard and troubleshooting them can feel like you're going in circles. It's not a reflection on your abilities. Cavities are just scheming little gremlins.It's a little hard to understand why that would cause the transmitted optical power to continually decrease as the proportional gain is turned up.If the resonance is well-behaved/stable enough that you can be a human servo, I would also second this suggestion.Because the optical power seems to depend on prop gain, the problem ought to be something to do with the servo.

One possibility is that you don't have enough gain at low frequencies (integral gain) and are locking at an offset to the locking setpoint, which happens to put the laser closer to resonance than your setpoint. This is a little hard to describe in words. Suppose you set the servo to lock to the blue (higher frequency) side of your transmission peak. If your integral gain is low and if your cavity frequency is drifting redder (lower resonant frequency over time), then you could lock your laser at an offset frequency redder than the side of the fringe where your setpoint was. This would mean your laser would settle closer to resonance than your locking setpoint, and so the beam would be brighter. As you turn up the prop gain, the servo would clamp down harder and the laser would get closer to the setpoint (and farther from resonance), so the optical power would go down. The power would keep going down until you got near the setpoint and then it should not change anymore. This isn't a bug, it's just the servo locking to a setpoint that is not the maximum of cavity transmission.

If this is the case, you should be able to tell by looking at the "DC Error" port of the Vescent D2-125. When you lock at low gain (where you get higher power), is the error signal 0 volts? What about when you turn up the prop gain? If my hypothesis is right, then you should see a non-zero voltage on the error signal at low gain, and that should get smaller and smaller and go to zero as you turn up the prop gain.

I hope that helps!

It is actually quite difficult to estimate the magnitude of the error signal. It usually kinda stays still, and then it suddenly makes huge jumps up and down (to the limits of the voltage it can go to), then stays stable a bit more and so on (I am talking about the voltage going from the servo to the laser). It is difficult to say if it is more stable with higher gain than lower gain, given that it does this behavior in either case. Also, I am attaching again the signal I see when I am locked. The ramp is 500 Hz, so each horizontal yellow line is 1ms, so these peaks seems to come and go every 50 $\mu s$ or so. This is definitely not consistent with the behavior of the error signal (it definitely stays almost still for much longer than that), or with the oscillations of the peaks during ramping, which is on the order of a few Hz. I have no idea how these peaks are created during lock.

Another issue I forgot to mention: theoretically I expect the cavity linewidth to be ~30 kHz. However, when scanning the cavity, and looking at individual peaks, the linewidth seems to be almost 1 MHz (I estimated this by eye). Of course part of this is also the exponential decay of each peak, so I am not sure how much is the true linewidth and how much is the exponential decay, but either way it seems much larger than expected, even if the cavity seems quite well aligned.

EDIT: Someone in my lab managed to make the other servo I mentioned work and get a lock to the cavity (same alignment as before) and the result is basically exactly the same. Similar power output when locked and many peaks in the signal to the diode instead of a constant power output. I guess at least this shows that the issue is with the cavity not with the servo (right?), but still no idea what it can be.

 

[Twigg]

Another issue I forgot to mention: theoretically I expect the cavity linewidth to be ~30 kHz. However, when scanning the cavity, and looking at individual peaks, the linewidth seems to be almost 1 MHz (I estimated this by eye). Of course part of this is also the exponential decay of each peak, so I am not sure how much is the true linewidth and how much is the exponential decay, but either way it seems much larger than expected, even if the cavity seems quite well aligned.

This is very suspicious. If I were you, I would spend some time to confirm your linewidth measurement before anything else. A broader-than-expected linewidth could very likely mean that you have dirt on your cavity mirrors. Dirt scatters light from the cavity mode into random, uncoupled modes, so it behaves similarly to excess transmission loss (increases linewidth) except that the lost power doesn't actually transmit through the cavity (so your transmission contrast is lower than if you just had less reflective mirrors). Dirt also creates noise when it gets really bad (I couldn't give you a number, it's just from my experience). In my case, the cavity I work on (>200000 finesse when clean) loses about a factor of 2 in finesse for every week or so it spends out of vacuum. Because your finesse is much lower, yours should be more forgiving.

To put some rough numbers on this: If your beam is 1mm in diameter when it reflects off each mirror and you have a spec of dust that is 10 microns in radius on one your mirrors, then this spec of dust will scatter a fraction of your intracavity power equal to $\frac{\pi \times (10\mathrm{\mu m})^2}{\pi \times (0.5\mathrm{mm})^2} = \frac{1}{2500}$. In other words, your finesse will be limited to 2500. For context, a human hair is usually 50-100 microns thick. A 10 micron radius particle ought to be clearly visible on a benchtop microscope at the high magnification settings, so you could try looking at your cavity mirrors under a microscope.

I don't have any experience working on cavities that aren't in vacuum and with similar finesse to yours, so I couldn't tell you how concerned you should be. Maybe someone else on the forums has?

Also, I'm confused by your estimated linewidth. If your cavity linewidth is 30kHz (when clean) and your finesse is 10,000, then your FSR ought to be 3GHz. If that's true, then your total cavity path length should be 10cm, but it looks waaay longer in the pictures in post #11?

It is actually quite difficult to estimate the magnitude of the error signal. It usually kinda stays still, and then it suddenly makes huge jumps up and down (to the limits of the voltage it can go to), then stays stable a bit more and so on (I am talking about the voltage going from the servo to the laser). It is difficult to say if it is more stable with higher gain than lower gain, given that it does this behavior in either case. Also, I am attaching again the signal I see when I am locked. The ramp is 500 Hz, so each horizontal yellow line is 1ms, so these peaks seems to come and go every 50 μs or so. This is definitely not consistent with the behavior of the error signal (it definitely stays almost still for much longer than that), or with the oscillations of the peaks during ramping, which is on the order of a few Hz. I have no idea how these peaks are created during lock.

Do you know the modulation port's scaling factor for your diode laser? Multiply that number by 20V (output voltage range of the D2-125 lockbox) and that's your servo's locking range (but if your laser controller has a smaller input voltage range than the D2-125's +/-10V, use that voltage instead). I would look at your transmission peak while scanning and see what the typical range of frequency noise is. How does that frequency noise compare to the locking range?

Edit: If you do try to look at your mirrors under a microscope, it can be a bit tricky to focus on the surface of the mirror because there shouldn't be anything to focus on when you look at a clean mirror. I usually keep a cheap dirty mirror around of the same thickness as your cavity mirrors, and I focus the microscope on the dirt on the cheap mirror. Then I swap the dirty mirror with the optic I actually want to look at (i.e., your cavity mirror), and it should be pretty nearly focused. Alternatively, if you have a really fancy optical microscope, dark-field imaging is the way to go! It makes examining optics really, really easy!

 

[kelly0303]

This is very suspicious. If I were you, I would spend some time to confirm your linewidth measurement before anything else. A broader-than-expected linewidth could very likely mean that you have dirt on your cavity mirrors. Dirt scatters light from the cavity mode into random, uncoupled modes, so it behaves similarly to excess transmission loss (increases linewidth) except that the lost power doesn't actually transmit through the cavity (so your transmission contrast is lower than if you just had less reflective mirrors). Dirt also creates noise when it gets really bad (I couldn't give you a number, it's just from my experience). In my case, the cavity I work on (>200000 finesse when clean) loses about a factor of 2 in finesse for every week or so it spends out of vacuum. Because your finesse is much lower, yours should be more forgiving.

To put some rough numbers on this: If your beam is 1mm in diameter when it reflects off each mirror and you have a spec of dust that is 10 microns in radius on one your mirrors, then this spec of dust will scatter a fraction of your intracavity power equal to $\frac{\pi \times (10\mathrm{\mu m})^2}{\pi \times (0.5\mathrm{mm})^2} = \frac{1}{2500}$. In other words, your finesse will be limited to 2500. For context, a human hair is usually 50-100 microns thick. A 10 micron radius particle ought to be clearly visible on a benchtop microscope at the high magnification settings, so you could try looking at your cavity mirrors under a microscope.

I don't have any experience working on cavities that aren't in vacuum and with similar finesse to yours, so I couldn't tell you how concerned you should be. Maybe someone else on the forums has?

Also, I'm confused by your estimated linewidth. If your cavity linewidth is 30kHz (when clean) and your finesse is 10,000, then your FSR ought to be 3GHz. If that's true, then your total cavity path length should be 10cm, but it looks waaay longer in the pictures in post #11?Do you know the modulation port's scaling factor for your diode laser? Multiply that number by 20V (output voltage range of the D2-125 lockbox) and that's your servo's locking range (but if your laser controller has a smaller input voltage range than the D2-125's +/-10V, use that voltage instead). I would look at your transmission peak while scanning and see what the typical range of frequency noise is. How does that frequency noise compare to the locking range?

Edit: If you do try to look at your mirrors under a microscope, it can be a bit tricky to focus on the surface of the mirror because there shouldn't be anything to focus on when you look at a clean mirror. I usually keep a cheap dirty mirror around of the same thickness as your cavity mirrors, and I focus the microscope on the dirt on the cheap mirror. Then I swap the dirty mirror with the optic I actually want to look at (i.e., your cavity mirror), and it should be pretty nearly focused. Alternatively, if you have a really fancy optical microscope, dark-field imaging is the way to go! It makes examining optics really, really easy!

Thank you for the reply again! Isn't the formula for the linewidth: $\frac{c}{FL}$, where F is the finesse and L the cavity length (about 1 meter in my case). So I would get $\frac{3\times 10^8}{10^4} = 3\times 10^4$ i.e. 30 kHz?

Do you know the modulation port's scaling factor for your diode laser? Multiply that number by 20V (output voltage range of the D2-125 lockbox) and that's your servo's locking range (but if your laser controller has a smaller input voltage range than the D2-125's +/-10V, use that voltage instead). I would look at your transmission peak while scanning and see what the typical range of frequency noise is. How does that frequency noise compare to the locking range?

The laser changes by 100 MHz per applied V. Is that what you mean by scaling factor? My laser can only accept between -4 and 4 V as input so I am using a voltage divider (when using the Vescent servo) and I am usually only applying between -3 and 3 V, so I am covering at most 600 MHz (but usually I do much lower, just to see one peak per ramp). What exactly do you mean by frequency noise? The peak sometimes moves left and right quite a lot (more than 100 MHz), probably due to mechanical vibration (as that motion is quite slow). Do you mean some noise on top of that?

EDIT: I will have to look around for a microscope, but I did clean the mirrors in the past without a visible change in the linewidth. I also completely changed the mirrors from 0.5 to 1 inch (I thought it might be some diffraction losses issue) and I got similar results, so I doubt the linewidth issue (assuming I did the math right) is from the cleanliness of the mirrors (at least not only from that).

 

[Twigg]

Thank you for the reply again! Isn't the formula for the linewidth: cFL, where F is the finesse and L the cavity length (about 1 meter in my case). So I would get 3×108104=3×104 i.e. 30 kHz?

Yep, sorry. I just suck at math apparently

The laser changes by 100 MHz per applied V. Is that what you mean by scaling factor?

Yep, that's what I meant.

What exactly do you mean by frequency noise? The peak sometimes moves left and right quite a lot (more than 100 MHz), probably due to mechanical vibration (as that motion is quite slow).

That's exactly what I meant by frequency noise: side-to-side motion of the transmission peak when you scan the laser.

The peak sometimes moves left and right quite a lot (more than 100 MHz), probably due to mechanical vibration (as that motion is quite slow).

That's quite a lot. Sorry if you mentioned this before now. This thread's gotten a little long and it's hard to remember everything.

I have one more suggestion that would be easy to fix, and if it's not that then I think you're in for a long slog trying to decouple your cavity from the environment.

The potential easy fix is optical feedback. Do you have an optical isolator between your laser head and your optical cavity? I know I asked you about this once before, but I don't remember the context and I don't see an isolator in the picture in post #11. Even if you have an optical isolator already there, I would check that it has >40dB isolation (to measure isolation, just flip the isolator in reverse without rolling it and measure it's "transmission", which should be very very small). If your isolator doesn't give you 40dB of isolation (check the datasheet/manual), then just use two of them in series. Also, if it's not too much hassle, I would make sure that the isolator is the first thing the beams sees out of the laser enclosure. I would put it before the rail-mounted optics you have. When you align to a cavity, you are aligning the cavity-reflected beam exactly overlapped with the incident laser beam, so the optical feedback will be absolutely brutal if it's not sufficiently isolated. Optical feedback is one of those nonlinear things that can easily confuse the heck out of a simple PID servo and cause all kinds of pathological behavior, even at the 100MHz level.

If it's not optical feedback, then it will be tricky in your situation to determine exactly which environmental variables (temperature, pressure, vibrations, air currents, etc.) are responsible for your cavity frequency noise. The reason it will be tricky is that your cavity is very well coupled to the environment (open to air currents, no thermal insulation or temperature servo control, highly vibration sensitive kinematic mounts and no vibration isolation other than the optical table legs). I would recommend at least trying to cover up and insulate the space around the cavity and perhaps adding a thermistor and temperature servo to the baseplate. For vibrations, there's really no substitute for active vibration isolation. If you have large vibrations at the 1 second or 100 millisecond level, viton legs and other passive vibration isolation techniques are absolutely useless. Active vibration platforms can give you a 1Hz corner frequency. To put this in perspective, to get a 1 Hz corner frequency with passive isolation, you'd need a 10 meter long pendulum or 5 meter long viton post of 1" diameter (which cause horrendous problems with your horizontal vibrations). If you do decide to go with active vibration isolation, I would recommend putting the laser head and the cavity both on one breadboard and put that breadboard on the AVI system. That way your cavity alignment won't drift as the AVI legs settle over time (same issue you saw with the viton legs).

 

[kelly0303]

Yep, sorry. I just suck at math apparently Yep, that's what I meant.That's exactly what I meant by frequency noise: side-to-side motion of the transmission peak when you scan the laser.That's quite a lot. Sorry if you mentioned this before now. This thread's gotten a little long and it's hard to remember everything.

I have one more suggestion that would be easy to fix, and if it's not that then I think you're in for a long slog trying to decouple your cavity from the environment.

The potential easy fix is optical feedback. Do you have an optical isolator between your laser head and your optical cavity? I know I asked you about this once before, but I don't remember the context and I don't see an isolator in the picture in post #11. Even if you have an optical isolator already there, I would check that it has >40dB isolation (to measure isolation, just flip the isolator in reverse without rolling it and measure it's "transmission", which should be very very small). If your isolator doesn't give you 40dB of isolation (check the datasheet/manual), then just use two of them in series. Also, if it's not too much hassle, I would make sure that the isolator is the first thing the beams sees out of the laser enclosure. I would put it before the rail-mounted optics you have. When you align to a cavity, you are aligning the cavity-reflected beam exactly overlapped with the incident laser beam, so the optical feedback will be absolutely brutal if it's not sufficiently isolated. Optical feedback is one of those nonlinear things that can easily confuse the heck out of a simple PID servo and cause all kinds of pathological behavior, even at the 100MHz level.

If it's not optical feedback, then it will be tricky in your situation to determine exactly which environmental variables (temperature, pressure, vibrations, air currents, etc.) are responsible for your cavity frequency noise. The reason it will be tricky is that your cavity is very well coupled to the environment (open to air currents, no thermal insulation or temperature servo control, highly vibration sensitive kinematic mounts and no vibration isolation other than the optical table legs). I would recommend at least trying to cover up and insulate the space around the cavity and perhaps adding a thermistor and temperature servo to the baseplate. For vibrations, there's really no substitute for active vibration isolation. If you have large vibrations at the 1 second or 100 millisecond level, viton legs and other passive vibration isolation techniques are absolutely useless. Active vibration platforms can give you a 1Hz corner frequency. To put this in perspective, to get a 1 Hz corner frequency with passive isolation, you'd need a 10 meter long pendulum or 5 meter long viton post of 1" diameter (which cause horrendous problems with your horizontal vibrations). If you do decide to go with active vibration isolation, I would recommend putting the laser head and the cavity both on one breadboard and put that breadboard on the AVI system. That way your cavity alignment won't drift as the AVI legs settle over time (same issue you saw with the viton legs).

The laser head has an optical feedback included, but I will check what isolation it has. However, as the cavity is bow-tie, shouldn't most (if not all) of the reflected power leave the input coupler at an angle and hence not return to the laser head?

I totally agree that all these other sources might be an issue, but shouldn't the servo be able to account for such small effects? For example the large motion of the peak I mentioned from left to right, has large amplitudes, but it is not really periodic. Usually the peak is quite stable (has very small left-right oscillations), then suddenly it moves a lot to left and right then comes back. This happens maybe once per second (but doesn't seem very regular). Should the servo easily account for the small variations and maybe lose lock during this large one, hence I would see a constant power output for 1 second then a drop then re-lock again for a second and so on? In general I would have expected that any mechanical or thermal vibrations would be very slow (which is what I see during ramping), but when I lock the cavity, these peaks appear once every 50 $\mu s$ or so, which would imply that the laser loses lock that often. A mechanical vibration shouldn't be able to produce that effect, no? It almost looks like the laser lock tries to perform a lock, overshoots, then try again and overshoots and so on, so it basically moves back and forth over a given peak. But if that was the case, I imagine that reducing the P-gain would solve the issue, which is not the case.

 

[Tom.G]

Another wild guess here, just from the troubleshooting aspect.

What do the error signal and the drive signal look like open-loop, that is with either
1) the Laser control signal set with a fixed external voltage

or​

2) the Laser turned off/blocked and a DC, battery, powered incandescent lamp illiminating the detector? A cheap LED flashlight may be adequate if it doesn't have any electronics in it; a lense may be needed to get enough power density on the sensor.

That should help determine if it is a servo loop tuning problem, faulty electronics, or perhaps outside interference (either mechanical, electrical, or possibly acoustic [air conditioning with an ultrasonic whistle ]).

 

[Twigg]

However, as the cavity is bow-tie, shouldn't most (if not all) of the reflected power leave the input coupler at an angle and hence not return to the laser head?

You're right about the reflection being at an angle. I forgot about that quirk of bowtie cavities.

I totally agree that all these other sources might be an issue, but shouldn't the servo be able to account for such small effects?

Looking back at post #11 again, I noticed the timescale of your noise events is really fast (roughly 10 microseconds), so I think you're right. This is way too fast to be environmental fluctuations. Sorry for not noticing that sooner.

The problem could very well be electronic noise. After all, with the humongous 100MHz/V scaling factor on the laser modulation port, it only takes 10mV to push you off a 1MHz line (if you line is actually 30kHz, then it only takes a mere 300 microvolts). Because electronic noise can be very fast, it's possible that your servo can't keep up. I'm curious what will happen if you engage the differentiator on your D2-125 and set the corner frequency to about 10kHz or 20kHz or somewhere around there. Alternatively, you could try adding a 10 or 20kHz lowpass filter between your photodiode and your servo. (Using the battery-powered photodiode was a good choice!). Another possibility is that the origin of your noise could be from ground loops (remember, your oscilloscope is a connection to ground).

If it's not electronic, then it could be vibrations in the upper audio band. Does your lock get messed up if you start talking or clapping your hands near the cavity?

The differentiator should help regardless if the noise is electronic or vibrational. But the lowpass filter should only help if the noise is electronic and from your photodiode.