Vibrations in building a cavity

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• Malamala

Malamala

Hello! I am trying to build an optical cavity and I am having some issues with vibrations. I attached below a plot of the acceleration in x, y and z as a function of time, when the accelerometer is placed on the optical plate (x is red, y is green and z is blue; I shifted them upwards for visualization purposes and the second image is just a zoomed in version of the first).

In my setup I have a plate made of aluminum (9.5 x 200 x 500 mm) that is attached to an optical table (not floated) at the 4 corners and on this plate I have the mirrors building the cavity. I initially thought that the vibrations are due to just motion in the room (or even on the table), but I added some sorbothane today and I saw no change in the vibrations.

I assume that the issue is of a different nature. I was thinking it might be the plate itself vibrating, but shouldn't in that case the vibrations be at the resonant modes of the table? My spectrum looks quite like a mess (the data is for some reason not taken at equal intervals, but I did a linear interpolation and took the FFT of that, and I saw no clear peak). I also see the effect of this vibration on the osciloscope when scanning the laser frequency, the peaks moving left and right on the scale of a second or so.

Does anyone know what can cause this kind of vibrations or how can I further investigate the cause? Thank you!

I attached below a plot of the acceleration in x, y and z as a function of time, when the accelerometer is placed on the optical plate
Which direction does the cavity span? Since it's a bowtie (per previous posts), we just need to know which plane its in (xy? xz? yz?) plus which direction the input beam goes in.

In my setup I have a plate made of aluminum (9.5 x 200 x 500 mm) that is attached to an optical table (not floated) at the 4 corners
How is it attached? Does the plate sit flat on the table or does it stand on supports (e.g., 1 inch pedestal posts)? If it stands on supports, how high is the plate off the table?

sorbothane today and I saw no change in the vibrations
This is highly unscientific on my part, but my personal experience is that sorbothane is overrated. But before you write it off as useless, check this next point:

Did you make sure that the accelerometer signal you see is above the noise floor? What is the noise floor for this accelerometer? It should be in the datasheet / manual somewhere.

I was thinking it might be the plate itself vibrating, but shouldn't in that case the vibrations be at the resonant modes of the table?
If the plate was bolted directly onto the table, then yes. If it's on supports, then it could have additional modes that the table doesn't have.

My spectrum looks quite like a mess (the data is for some reason not taken at equal intervals, but I did a linear interpolation and took the FFT of that, and I saw no clear peak).
For the issue of non-uniform sampling, try a Lomb-Scargle periodogram, aka least squares spectral analysis. Here's an implementation in Scipy and here's one in Matlab. I'm not 100% positive it's the right thing to do (since you signal isn't truly periodic), but it might be worth trying.

I also see the effect of this vibration on the osciloscope when scanning the laser frequency, the peaks moving left and right on the scale of a second or so.
I don't think this drift in the cavity is correlated with vibrations. The reason I say that is that your data clearly doesn't have much going on at the 1s timescale, it seems more active around 100ms. As mentioned before, when you're seeing frequency drifts at second timescales, thermal drifts are the usual suspect. Is your plate temperature controlled?

Also, on a related point, are the cavity mirrors each mounted independently to the plate or is there a mechanical spacer?

If you want to see whether or not the vibrations are a significant source of noise for you, try putting your laser frequency on the side of resonance and looking at your PDH signal while recording your accelerometer data. Then take a covariance between the acceleration and the PDH signal. If you get a statistically significant correlation, then you know it's vibrations.

On a more humorous note, I'm still jealous! Still haven't seen transmission on my high finesse cavity Back to lab I go

berkeman
the data is for some reason not taken at equal intervals
Why not? What are you using for the data acquisition setup?

I also see the effect of this vibration on the osciloscope when scanning the laser frequency, the peaks moving left and right on the scale of a second or so.
Also, this might be your laser's frequency drifting, not the cavity length drifting, since you mentioned earlier that this laser isn't frequency stabilized.

Edit: as in the center frequency of the frequency scan can drift

Which direction does the cavity span? Since it's a bowtie (per previous posts), we just need to know which plane its in (xy? xz? yz?) plus which direction the input beam goes in.
The cavity is in the xy plane. The laser comes from the x direction.

How is it attached? Does the plate sit flat on the table or does it stand on supports (e.g., 1 inch pedestal posts)? If it stands on supports, how high is the plate off the table?

It stands on 0.75 inch pedestals posts (these ones).

This is highly unscientific on my part, but my personal experience is that sorbothane is overrated. But before you write it off as useless, check this next point:

Did you make sure that the accelerometer signal you see is above the noise floor? What is the noise floor for this accelerometer? It should be in the datasheet / manual somewhere.
I am not sure about sorbothane. Someone suggested me to try using it, but I have no experience with it myself. I will check the noise floor for it. Actually (@berkeman) I used my phone accelerometer to measure this, hence why the issues with the data (I am waiting for a better one to arrive but it will take a bit, so I wanted to get an idea of what is going one before). The main issue (as mentioned in my previous post, too) is that the peaks are oscillating left and right, so something is changing in time. Might not be the cavity itself, tho.

If the plate was bolted directly onto the table, then yes. If it's on supports, then it could have additional modes that the table doesn't have.
Sorry, I meant to say that I would expect to see oscillations at the resonant frequency of the plate, not the table. I ran a basic modal simulation in Inventor, and the resonant modes (assuming the plate is fixed at the 4 location as in the lab) are all above 100 Hz.

I don't think this drift in the cavity is correlated with vibrations. The reason I say that is that your data clearly doesn't have much going on at the 1s timescale, it seems more active around 100ms. As mentioned before, when you're seeing frequency drifts at second timescales, thermal drifts are the usual suspect. Is your plate temperature controlled?
The plate is not thermally controlled. Should I probably aim for a different material, other than aluminum (maybe invar)?

Also, on a related point, are the cavity mirrors each mounted independently to the plate or is there a mechanical spacer?
They are all mounted independently using these mounts.

It stands on 0.75 inch pedestals posts
That's pretty short, which is good

I am not sure about sorbothane. Someone suggested me to try using it, but I have no experience with it myself.
A good way to test it out is to use a controlled vibration source. Measure the accelerometer spectrum with the sorbothane and without it. A good way to make a vibration source with known amplitude is to take a motor and stick an eccentric load on its shaft. It won't need to be a powerful motor (actually it gets pretty darn sketchy with more motor power), 1/8hp or less should be fine. Low speeds are also preferable, and you'll want an enclosure around the motor to protect you and protect the optics in case it literally rattles itself to pieces. Alternatively, you can drop a large ball bearing from a fixed height, but this could leave divots on your optics table. Maybe tightly bolt a sacrificial steel plate to the table and drop the bear on that? Get creative! There's a lot of ways to do this.

The plate is not thermally controlled. Should I probably aim for a different material, other than aluminum (maybe invar)?
It really depends on your application. I know you mentioned in a different post that you intend to lock your 1064 diode laser to this cavity for maximum power, I'm just not sure whether thermal stability of the cavity matters for that or not. I think (?) it's not a big issue? Unless the drifts are pushing you back and forth over a mode hop of the laser, then that'd be annoying.

In fact, because your cavity lacks a mechanical spacer and instead relies on independent kinematic mounts, I'm going to go out on a limb and say that thermal drifts were probably considered and determined to not be an important factor for your application.

If you want to reduce thermal fluctuations, the first step is enclosing the cavity as best you can. 2 inches of foam insulates way better than 2 inches of air gap, because in convection cooling the more distance you have to generate a convection cycle the more heat transfer occurs. If you put your cavity in as small as possible an enclosure, you can limit thermal drifts. You could just get a sheet metal electronics enclosure, line it with some foam for extra insulation, drill some holes for the laser beam, and place it upside down over the cavity. Spray adhesive works well for foam. This might be overkill, I dunno, but it can be tried out in 15 minutes if you have the parts

That's pretty short, which is good

A good way to test it out is to use a controlled vibration source. Measure the accelerometer spectrum with the sorbothane and without it. A good way to make a vibration source with known amplitude is to take a motor and stick an eccentric load on its shaft. It won't need to be a powerful motor (actually it gets pretty darn sketchy with more motor power), 1/8hp or less should be fine. Low speeds are also preferable, and you'll want an enclosure around the motor to protect you and protect the optics in case it literally rattles itself to pieces. Alternatively, you can drop a large ball bearing from a fixed height, but this could leave divots on your optics table. Maybe tightly bolt a sacrificial steel plate to the table and drop the bear on that? Get creative! There's a lot of ways to do this.

It really depends on your application. I know you mentioned in a different post that you intend to lock your 1064 diode laser to this cavity for maximum power, I'm just not sure whether thermal stability of the cavity matters for that or not. I think (?) it's not a big issue? Unless the drifts are pushing you back and forth over a mode hop of the laser, then that'd be annoying.

In fact, because your cavity lacks a mechanical spacer and instead relies on independent kinematic mounts, I'm going to go out on a limb and say that thermal drifts were probably considered and determined to not be an important factor for your application.

If you want to reduce thermal fluctuations, the first step is enclosing the cavity as best you can. 2 inches of foam insulates way better than 2 inches of air gap, because in convection cooling the more distance you have to generate a convection cycle the more heat transfer occurs. If you put your cavity in as small as possible an enclosure, you can limit thermal drifts. You could just get a sheet metal electronics enclosure, line it with some foam for extra insulation, drill some holes for the laser beam, and place it upside down over the cavity. Spray adhesive works well for foam. This might be overkill, I dunno, but it can be tried out in 15 minutes if you have the parts
@Twigg I am back to the cavity after a break, sorry for replying so late. I have a quick question. So I have these vibrations left and right and also quite big variations in the height of the peaks (without touching the cavity). Meanwhile I placed the cavity on vibrational damping legs and the laser company said that this amount of vibrations shouldn't be from the thermal servo of the laser. I will go back to further debugging on Monday, but I was wondering if this can be from the mode matching. The locations and heights of the peaks corresponding to different modes are different, so if the mode that matches the cavity changes, I would have the left right motion (as the central frequency would be different) and also a change in the height of the peaks, as the given mode would be amplified differently (for example when I actually match the laser I would have a much higher power output than in the other modes). Could all these vibrations be only from the mode matching issues? Thank you!

Hmmmm, if you added the vibrational damping legs to the cavity and the amount of drift in the modes didn't change, then you can safely rule out vibrations.

By the way, can you remind me, what is the amount of drift you see in MHz?

Your hypothesis is a good one. The first thing that comes to mind for me is thermal lensing. This is what happens when a high power laser causes one of the optics to heat up, thermally expand, and that expansion causes a change in the focal length of that optic. If you want to test this, I would try and get a thermal camera. If you don't have one in the lab, try borrowing one from whoever does HVAC maintenance for your building. Just ask nicely and be respectful to their tool! If you see that your mirrors are significantly above ambient, that's a sign. To fix the issue, you want to find mirrors with either a suitable substrate with a lower coefficient of thermal expansion or a mirror coating with lower absorption at your operating wavelength. I like this hypothesis because it still acts at the thermal timescale (1s drifts are perfectly plausible) and it explains the motions you describe.

My next suggestion for you is the pointing of the beam going into the cavity. How is the laser head mounted? If you can attenuate the beam power enough, try recording the beam position on a camera, and looking for drifts. A change in the beam profile also would cause cavity fluctuations.

Hmmmm, if you added the vibrational damping legs to the cavity and the amount of drift in the modes didn't change, then you can safely rule out vibrations.

By the way, can you remind me, what is the amount of drift you see in MHz?

Your hypothesis is a good one. The first thing that comes to mind for me is thermal lensing. This is what happens when a high power laser causes one of the optics to heat up, thermally expand, and that expansion causes a change in the focal length of that optic. If you want to test this, I would try and get a thermal camera. If you don't have one in the lab, try borrowing one from whoever does HVAC maintenance for your building. Just ask nicely and be respectful to their tool! If you see that your mirrors are significantly above ambient, that's a sign. To fix the issue, you want to find mirrors with either a suitable substrate with a lower coefficient of thermal expansion or a mirror coating with lower absorption at your operating wavelength. I like this hypothesis because it still acts at the thermal timescale (1s drifts are perfectly plausible) and it explains the motions you describe.

My next suggestion for you is the pointing of the beam going into the cavity. How is the laser head mounted? If you can attenuate the beam power enough, try recording the beam position on a camera, and looking for drifts. A change in the beam profile also would cause cavity fluctuations.
Thanks a lot! The amplitude of this left-right motion is about 50MHz. The power I am using is currently 0.5 W, I will look into what you suggested.

One things I just realized (taking a break might have been helpful after all), is that I am very close to the stability edge of the cavity, so close that I might not even be inside the stability region. Just for reference, the stability region is when I have ##0 \le g_1g_2 \le 1##, where ##g_1=1-\frac{d_1+2d_2}{R}## and ##g_2=1-\frac{d_3}{R}##, where ##d_3## is the distance between the curved mirrors, ##d_1## is the distance between the plane mirrors, ##d_2## the diagonal distance between curved and plane mirrors and ##R## is the radius of curvature of the curved mirrors. In my case, in theory, ##d_3 = 0.2506##m and ##R=0.25##m. This means I am in the stability region, but for ##d_3<0.25## I would go outside, as ##g_2## would become negative. But the difference between the 2 cases is 0.6 mm, which might be below the machine precision of the holes made for the mirror mounts (which tbh I don't know what it is). If I have some error in the curvature of the mirrors, too, I can just be outside the stability region. Could this be the cause of my problems? I am still a bit confused, as I would imagine that if I am outside the stability region, I shouldn't see any peaks at all (the light would escape the cavity almost instantaneously, without having time to build up power). Given that I do see peaks, I am not sure if I am outside the stability region. Maybe I am just at the boundary and small vibrations can take me out and in hence why all these variations? What do you think?

Oh! I just realized, for the hypothesis of thermal lensing, I forgot to recommend the easiest test of them all! Try turning down the power. If your peaks drift less, it was thermal lensing.

Edit: I don't know where your lasing threshold is, but if you try it at 100mW and still see 50MHz drifting on a 1s timescale, you can forget about thermal lensing.

Edit edit: Alternatively, if your lasing threshold prohibits you from going to 100mW, try going to higher power. For example, if you go to 5W 2.5W and see 5x as much noise (so 250MHz on the 1s timescale), then you know it was thermal lensing.

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Oh! I just realized, for the hypothesis of thermal lensing, I forgot to recommend the easiest test of them all! Try turning down the power. If your peaks drift less, it was thermal lensing.

Edit: I don't know where your lasing threshold is, but if you try it at 100mW and still see 50MHz drifting on a 1s timescale, you can forget about thermal lensing.

Edit edit: Alternatively, if your lasing threshold prohibits you from going to 100mW, try going to higher power. For example, if you go to 5W 2.5W and see 5x as much noise (so 250MHz on the 1s timescale), then you know it was thermal lensing.
That's a good idea, thank you! I can adjust the power over quite a big range, so that should help. Do you have any insight about this stability region I mentioned above?

My gut feeling is that if you're still seeing lots of modes on the oscilloscope, then it's probably not resonator stability?

What I can do is give you some advice for getting a better measurement of ##d_3##, but it's a lot of work. 2-4 hours maybe? Most of it just solving trigonometry problems.

This is going to be a lot easier to show you how to do than to explain. Funnily enough, I happen to have a couple of 1" posts on hand so I took a picture of how you'd do the measurement:

This is going to be the most convenient way for you to take measurements of the distance between mirrors with a typical 12" caliper set.

The next piece of information you need is the distance between the center of the mounting post and the front face of the mirror. I can tell you by looking at the cad drawing from the mirror mount you linked that the distance from the mounting hole (the center axis of the post underneath) to the mirror face is 0.5inch. The issue is that the mirrors are at an angle to the measurements you are taking, so you need to do some ray optics to get the angle of all the mirrors. If you have those angles, then you can do some trigonometry and find the exact offset between the measurement I showed above (distance between insides of the mounting posts) and the true distance between mirrors.

My gut feeling is that if you're still seeing lots of modes on the oscilloscope, then it's probably not resonator stability?

What I can do is give you some advice for getting a better measurement of ##d_3##, but it's a lot of work. 2-4 hours maybe? Most of it just solving trigonometry problems.

This is going to be a lot easier to show you how to do than to explain. Funnily enough, I happen to have a couple of 1" posts on hand so I took a picture of how you'd do the measurement:
View attachment 289334
This is going to be the most convenient way for you to take measurements of the distance between mirrors with a typical 12" caliper set.

The next piece of information you need is the distance between the center of the mounting post and the front face of the mirror. I can tell you by looking at the cad drawing from the mirror mount you linked that the distance from the mounting hole (the center axis of the post underneath) to the mirror face is 0.5inch. The issue is that the mirrors are at an angle to the measurements you are taking, so you need to do some ray optics to get the angle of all the mirrors. If you have those angles, then you can do some trigonometry and find the exact offset between the measurement I showed above (distance between insides of the mounting posts) and the true distance between mirrors.
Thanks a lot for this! I actually have the math of it ready already (I used it when designing the holes for the mounts), so I should be able to calculate ##d_3##. One thing I am not sure about is the angle of the mirrors. In theory I know what it should be. But most probably that is different in practice (i don't know by how much). Do you know how I can measure that?

But tbh, I am more worried about the radius of curvature of the mirrors than the ##d_3##. The error quoted on the radius is 1.25 mm, which is double the amount needed to take me out of the stability region (that might be a conservative estimate, but it is still quite big). I just realized that this weekend, and actually I am a bit curious why am I getting peaks at all (of course it might happen that both mirrors have the right size).

In general, if I am outside the stability region should I see no power transmitted at all (what I see is about 2 orders of magnitude smaller than what I expect, tho)?