Vibrations in a bow-tie cavity

[kelly0303]

Hello! I am trying to build a bow tie cavity and it seems like I am dealing with a large amount of vibrations (I think!). When I scan the laser frequency over one cavity FSR (the cavity is not locked to anything), I see just one peak, which I think it means that I am at least mode matched. However the peak has a linewidth about 1000 larger than what I would expect and it also moves left and right a lot. If I connect the signal from the cavity through a low pass filter (<200 kHz), the peak still moves right and left, but it is as narrow as I would expect. The left and right motion frequency is on the order of 1-10 Hz (I can see it by eye in real time). What I think it happens is that I have some high frequency vibration which makes my cavity length move really fast and when I scan the laser I average over these different location of the cavity center, so what I see is basically a sum of these different narrow peaks, which looks in the end like a wide peak. Hence why this is gone when I use the low pass filter. On top of this I think I have a low frequency vibration (of quite large amplitude, maybe ~1 micron), that makes the peak move left and right, hence why I still see it even with the low pass filter in place. Does this make sense? And if so can someone advise me on what can the source of vibrations be or how can I try to figure it out? I do have some vibrational damping legs (viton), so I am a bit surprised that I still see the high frequency vibrations. Any advice is really appreciated!

 

[Twigg]

There's no way in heck that the broadening was caused by vibrations if it goes away with a 200kHz filter. That's waaay too fast for vibration. You likely have a laser issue or perhaps optical feedback. Are you using at least one Faraday isolator on your laser? That'd be my first guess.

Do you have access to a laser that you know is locked and has smaller linewidth than the laser you are probing the cavity with? You can verify that your czvity laser is working as intended by beating them together and seeing that the resulting sine wave has a stable frequency.

The 1-10Hz issue could very well be vibration. Sorbothane might help, or it might not. Trying to keep your optical setup as rigid as possible is best. You can also try poking things and seeing what optics are most sensitive as seen on the reflection signal.

What is your bowtie's finesse? That's an important factor when considering the scale of the problem.

 

[kelly0303]

There's no way in heck that the broadening was caused by vibrations if it goes away with a 200kHz filter. That's waaay too fast for vibration. You likely have a laser issue or perhaps optical feedback. Are you using at least one Faraday isolator on your laser? That'd be my first guess.

Do you have access to a laser that you know is locked and has smaller linewidth than the laser you are probing the cavity with? You can verify that your czvity laser is working as intended by beating them together and seeing that the resulting sine wave has a stable frequency.

The 1-10Hz issue could very well be vibration. Sorbothane might help, or it might not. Trying to keep your optical setup as rigid as possible is best. You can also try poking things and seeing what optics are most sensitive as seen on the reflection signal.

What is your bowtie's finesse? That's an important factor when considering the scale of the problem.

Thank you for your reply! The laser has a built-in Faraday isolator, but I am not sure what you mean by a second laser. I have just a cavity and a laser, and when I scan the laser frequency, the location of the peaks moves left and right, while being 1000 wider than expected. The cavity is free, not locked to anything and the laser I am using has a linewidth about 5-6 times smaller than the cavity. The finesse of the cavity is about 8000. But do you know why this linewidth effect disappears when I use the low-pass filter?

 

[Twigg]

An extra isolator never hurts. It's worth trying. The better you mode match your laser to the cavity, the better you end up mode matching the cavity retroreflected beam to the laser resonator. It's not uncommon that you need a second isolator in series with the first.

Are you looking at a transmission spectrum? Reflection? PDH?

Pictures of the spectra would be helpful if you can share them.

But do you know why this linewidth effect disappears when I use the low-pass filter?

On second thought, it's really strange that the lowpass filter appears to have an affect that cleans up the frequency domain (linewidth). If you're talking about a reflection or PDH spectrum, I would think that the lowpass wouldn't change anything in the frequency domain. If you had a single narrow peak that jittered around, then I would expect the lowpass to smooth it into a broad line.

If you're actually talking about a transmission spectrum, something is very fishy. Your 50kHz-linewidth cavity should already be acting as a 50kHz lowpass filter on the transmission signal. A 200kHz lowpass filter should have a negligible effect. In this case, I would suspect electronic noise.

One final thought. Is it possible that you forgot to use a 50Ohm terminator on your photodiode signal and plugged it straight into a scope with high input impedance? That could result in your cavity signal being distorted. It could be that your lowpass filter has a 50ohm input impedance that fixed the impedance matching problem and made you think it was the filtering that helped. If you already thought of this, please ignore this suggestion.

 

[kelly0303]

An extra isolator never hurts. It's worth trying. The better you mode match your laser to the cavity, the better you end up mode matching the cavity retroreflected beam to the laser resonator. It's not uncommon that you need a second isolator in series with the first.

Are you looking at a transmission spectrum? Reflection? PDH?

Pictures of the spectra would be helpful if you can share them.On second thought, it's really strange that the lowpass filter appears to have an affect that cleans up the frequency domain (linewidth). If you're talking about a reflection or PDH spectrum, I would think that the lowpass wouldn't change anything in the frequency domain. If you had a single narrow peak that jittered around, then I would expect the lowpass to smooth it into a broad line.

If you're actually talking about a transmission spectrum, something is very fishy. Your 50kHz-linewidth cavity should already be acting as a 50kHz lowpass filter on the transmission signal. A 200kHz lowpass filter should have a negligible effect. In this case, I would suspect electronic noise.

One final thought. Is it possible that you forgot to use a 50Ohm terminator on your photodiode signal and plugged it straight into a scope with high input impedance? That could result in your cavity signal being distorted. It could be that your lowpass filter has a 50ohm input impedance that fixed the impedance matching problem and made you think it was the filtering that helped. If you already thought of this, please ignore this suggestion.

So the 50Ohm worked! Thanks a lot! Do you have any advice about the low vibration one? It seems like the amplitude is quite large, but I am not sure what can be the source.

Actually, just by doing some simple math i.e. using for the resonant frequency qc/L where q in my case is 1262867 (given that I am around 1064 nm for my laser) and L = 1.343691, the ~10MHz change in the location of the peak corresponds to a change in the length of the cavity of about 50 nm. This doesn't seem unrealistic, but also I am not sure how to prevent it, given that it is so small.

 

[Twigg]

I also get about 50nm.

I do have some vibrational damping legs (viton), so I am a bit surprised that I still see the high frequency vibrations.

10Hz is actually quite slow for vibrations. Vibrations can live anywhere inside the audio frequency range (1Hz - 10's of kHz). 10 Hz is probably below the natural cutoff frequency at which the viton mounts start damping out vibrations. See this guide for more info on solid vibration damping mounts.

You may want to research pneumatic vibration isolation if this 10 Hz is a serious issue. I believe pneumatic systems have lower cutoff frequencies since air is less stiff than rubber, but I'm no expert.

If you have lots of budget to throw around, active vibration cancellation is also a thing. Look up the company "Table Stable" for examples.

P.S.: Also, I realize in my last post I forgot that bowtie cavities are ring resonators and there is no PDH scheme. Sorry about that. I'm definitely more familiar with Fabry-Perot systems, but I'm happy to help where I can.

 

[kelly0303]

I also get about 50nm.10Hz is actually quite slow for vibrations. Vibrations can live anywhere inside the audio frequency range (1Hz - 10's of kHz). 10 Hz is probably below the natural cutoff frequency at which the viton mounts start damping out vibrations. See this guide for more info on solid vibration damping mounts.

You may want to research pneumatic vibration isolation if this 10 Hz is a serious issue. I believe pneumatic systems have lower cutoff frequencies since air is less stiff than rubber, but I'm no expert.

If you have lots of budget to throw around, active vibration cancellation is also a thing. Look up the company "Table Stable" for examples.

P.S.: Also, I realize in my last post I forgot that bowtie cavities are ring resonators and there is no PDH scheme. Sorry about that. I'm definitely more familiar with Fabry-Perot systems, but I'm happy to help where I can.

@Twigg I spent some more time on this cavity and I am still having issues but I tried a few things. After I added the 50 Ohm resistance the peaks are now about as narrow as I would expect from calculations (around 50 kHz - the laser has a linewidth of 5 kHz). Also they seem to not move a lot left and right. However the amplitude of the peaks during ramping changes a lot (by a factor or 2 even more) over very short periods of time (below one second). I looked at the beam profile outside of the cavity, and it seems to be TEM00 without any other modes present (at least not intense enough for my camera). Also the beam diameter seems to be about the size I would expect from calculations. However the intensity of the spot of the camera changes a lot (corresponding to the change in the peaks height I assume). All this happened when I was scanning the laser frequency, while the cavity was free (the cavity is not locked). Today I added a piezo to one of the mirrors and I applied the ramp to the piezo while the laser frequency didn't change (the laser frequency it's supposed to be super stable - I would need to check the exact numbers). However, the result was basically the same as before. Everything is as predicted by calculations, but the peaks heights change a lot. I expected that using a piezo would at least reduce the issue. Also, if it is due to vibrations, I am not sure I understand why the height of the peaks changes so much. If the length of the cavity changes due to vibrations, I would imagine that the location of the peaks to change, not the height. Do you have any idea of what is going on? Or at least a way to try to figure out what is going on? Thank you!

 

[Twigg]

Just to clarify, you are seeing a variation in the peak height of the power transmitted as seen on a photodiode (or camera), from one frequency scan to the next? What frequency are you scanning the laser at?

The camera is not a great tool for this, because it is updating with some frame rate which may alias with the frequency at which you scan the laser. However, if you see the effect on a photodiode, then you know it's real.

Vibrations sounds likely. You are right that vibrations of the cavity mirrors should cause both peak height fluctuations and shifts of the resonance. However, you could also have vibrations upstream of the cavity that cause fluctuations in the coupling of the incident beam. You could verify this by putting your camera (or even better, a quadrant photodiode) in front of the cavity (temporarily, just to see how much the beam position fluctuates).

Another possibility is absorption of the enhanced cavity field by the air. (Check the absorption of H2O at 1064nm.) When you scan the laser with a positive sloping ramp, is the linewidth any different than for a negative sloping ramp? That effect (thermal self-locking) is the signature of absorption in a cavity. This asymmetry is more prominent at higher power and the two linewidths should become more equal at low power.

 

[Fred Wright]

I am certainly no expert, so take my observation with a grain of salt, but I suspect that the variation of amplitude are caused by back scattering in the ring cavity. Unfortunately, back scatter is unavoidable due to imperfections in the cavity mirrors.

 

[kelly0303]

@Twigg @Fred Wright thank you for your replies. Just to clarify, I am using a photodiode to see the power transmitted (peaks) and a camera to see the spatial modes. So I decided to put my diode before the cavity and I noticed that I have a weird signal at around 500 Hz and it seems like it is not from the laser. When I blocked the laser, the oscillation was still there (see attached picture). Do you know what that can be from?

 

[Twigg]

Maybe try using a different power supply with that photodiode? It could be a ripple on the bias voltage caused by a faulty power supply.

 

[kelly0303]

Maybe try using a different power supply with that photodiode? It could be a ripple on the bias voltage caused by a faulty power supply.

So I tried a different diode, with a smaller area, and I see the same effect, just reduced magnitude. Then I realized that if I turn off the light in my lab, the effect is significantly reduced. So it seems to be from that, although not totally sure why. But I assume that wouldn't affect the lock. Could it just be that I am simply not yet well aligned? Maybe I am in a sort of local maxima where I do get some amplification, but it is not the ideal alignment point.

 

[Twigg]

Oh right. Your overhead LED lights are probably being dimmed by pulse width modulation at a switching speed of 500Hz, causing them to flicker imperceptibly.

If you put the photodiode back on the cavity transmission and if you turn off the lights, how is the peak amplitude? More stable?

 

[kelly0303]

@Twigg it doesn't seem to be any major change with light off either. I was thinking, given that the cavity I am building is quite close to the stability edge (the distance between the 2 curve mirrors is close to the value of the radius of curvature of the mirrors), the transverse alignment might be very important. I am not totally sure how to quantify that (the formulas I found are usually for stability assuming the mirrors are at the ideal angles), but the mounts I am using have an angular resolution of 11 mrad/revolution. Could it be that I am close to the right cavity alignment, but given the quite bad resolution of the mount (I am adjusting them by hand) I am not able to improve further than this? Maybe using motorized mounts (with a resolution of 0.5 $\mu$rad/0.1 V) would help? Could this be an explanation for the behavior I am seeing?

In general I am still confused (again this is the first time I am aligning a cavity) about whether when I am not properly aligned, should I just see stable peaks, but with low intensity, or should I expect to see what I am seeing?

 

[Twigg]

Alignment shouldn't be the issue. A poorly coupled cavity should still have transmission peaks that are steady in time. It is possible that because youre on the edge of stability, your cavity might be extra picky about alignment, but it shouldn't cause amplitude jitter.

Motorized mounts won't solve your amplitude jitter.

If you want to know how well aligned you are, try to measure the amplitude of the other TEM modes. You want the ratio of TEM00 to higher order modes as large as possible.

In general I am still confused (again this is the first time I am aligning a cavity) about whether when I am not properly aligned, should I just see stable peaks, but with low intensity, or should I expect to see what I am seeing?

Yes, you should see stable peaks with lower intensity AFAIK. The timescale of these changes is way too slow to be intrinsic dynamics of the cavity. The cavity should reach a steady state after a time $\tau = \frac{1}{\Gamma}$ where $\Gamma$ is the cavity linewidth. For you, that ought to be much, much faster than the rate at which you modulate/scan the laser.

What's your transmission contrast (transmitted power divided by input power) like?

My first guess is still that the issue lies with your input beam. Did you try looking for fluctuations in the beam position on a camera before the cavity?

 

[kelly0303]

Alignment shouldn't be the issue. A poorly coupled cavity should still have transmission peaks that are steady in time. It is possible that because youre on the edge of stability, your cavity might be extra picky about alignment, but it shouldn't cause amplitude jitter.

Motorized mounts won't solve your amplitude jitter.

If you want to know how well aligned you are, try to measure the amplitude of the other TEM modes. You want the ratio of TEM00 to higher order modes as large as possible.
Yes, you should see stable peaks with lower intensity AFAIK. The timescale of these changes is way too slow to be intrinsic dynamics of the cavity. The cavity should reach a steady state after a time $\tau = \frac{1}{\Gamma}$ where $\Gamma$ is the cavity linewidth. For you, that ought to be much, much faster than the rate at which you modulate/scan the laser.

What's your transmission contrast (transmitted power divided by input power) like?

My first guess is still that the issue lies with your input beam. Did you try looking for fluctuations in the beam position on a camera before the cavity?

I am attaching below a plot of the center of the input beam (with a diameter of about 1 mm) taken over a period of 2 minutes. It seems like the center changes by about 1-2 microns. The center is obtained by fitting a 2D gaussian to the beam profile, however due to some internal interference on the CCD camera, there is some interference pattern on top of that, so I am not even 100% sure if this change in the center is real or just some fitting issues.

 

[Twigg]

In that case, its definitely not caused by fluctuations in input beam pointing.

If it is backscatter, as @Fred Wright suggested, then it would be a significant amount of light in the counterpropagating mode, comparable to what you see in transmission (since you're able to see a factor of 2 change).

You can look for backscatter with a 50:50 nonpolarizining beamsplitter placed in front of the cavity. Half of the backscattered light should come out on one side of the beamsplitter, on the opposite side that the incident light gets reflected. Sorry I know that's not terribly clear without a diagram.