Here are the new beam profiles after the faraday isolators. I am satisfied with the CCW profile, but the CW looks a bit crap. It is much more astigmatic, and I'm afraid that some diffractive effects near the output of the FI are tricking the fitting algorithm. We are going to re-profile the beam after the MMT, so we will verify that it is matched to the cavity mode and make adjustments if necessary.

[Alastair, Zach]

It seems like the consensus is that the best idea is to place the faraday isolators before the MMT. This way, we can use independent lenses to focus the beams into the FIs to avoid clipping and not have to deal with this additional constraint when designing the MMT and when adjusting the steering mirrors.

We played around with the layout this afternoon, and there just isn't enough room to fit both FIs and PDs (along with steering mirrors and lenses) side by side far enough upstream to leave room for modematching. We decided to rotate the AOM setup so that it folds back towards the laser instead of perpendicularly outward, as in the picture below.

The second picture shows that the FIs and PDs fit just fine with this newfound space.

[Alastair, Zach]

Our current idea is that clipping on the faraday isolator is resulting in disturbance of the error signal. The precise mechanism isn't quite understood yet, but there are several candidate theories. We have moved the FIs so that they are at the waists between the lenses of the mode-matching telescopes, and the beams going through them from the input sides (from the laser) are small enough that no clipping is evident as measured with a power meter.

The same can't be said of the beams returning from the cavity mirror. Moving the FIs to the MMT waists has highlighted the fact that the REFL beams do not seem to be of the same size as the input beams at this point, which indicates a problem with mode-matching.

Small changes to the MMT lens locations don't seem to do the trick, and since this is such a crucial aspect of our experiment (given the isolation method), it will probably pay to just redo the thing. Alastair had the idea of profiling the beam closer to where the lenses actually are/will be---instead of as farther upstream where we have done it in the past---and that way we can rule out anything weird going on in between. Since we have a fair amount of space at the right place on the table, we can also profile the beam after the lenses are in place by steering the beam to the unused area. This way we can actually verify that the beams have the right shape on the way into the cavity.

I moved the faraday for the CCW return path back into the middle of the MM telescope, where the waist is.  It turned out that the CW PD interfered with this, so I had to also move this back to the waist of the other MM telescope.   The beam wasn't quite at 4" through the telescope so I had to alter the height, which in turn un-aligned the beam for the CW input path.

I was able to get it looking like the input beam and the reflection beam were not clipping on the outside of the faraday.  Measuring the power that was being transmitted through the faraday into the cavity there was no measurable loss. However, when I looked at the beam rejected out the side (going to the PD) it was very weak.  I found that you could increase this by twisting the faraday slightly, however even then I was only able to get 1.26mW out of 1.56mW that was going in.  This is a serious disadvantage to this Faraday design!!!  You cannot see where any clipping is happening internally, even when the beam in is small at both sides, and there is no clipping on the outer apeture.  It would make life a lot easier if the input and output polarizers were separate.

Next I started aligning the beam back into the cavity again.  Of course we haven't touched the cavity mirrors so that is still aligned.  The CWW input beam had also become misaligned, though I have no explantion for this.  There were a few mirrors with screws that were not very tight, and I tightened them down.  Afterwards the CWW input beam was misaligned, so either something moved as I tightened it or I bumped an actuator.  After getting the beam vaguely aligned I then looked back at the faraday again.  Of course the return beam is now misaligned....  now I can't get more than 50% of the beam back through without clipping.

I think that this is going to require some iteration.  We'll need to just keep trying to keep the faraday aligned as we get the beam back into the cavity.

More mis-alignment tests to start with today.

I moved the faraday for the return CCW beam (the ingoing CW beam) an un-calibrated-small-amount to the side (about 1mm).  The transmission through the cavity gets worse (from 720mV down to 400mV DC on the trans PD).  The noise hump at low frequency gets worse by a factor of 2.

This test is really a precursor to trying to move the faraday back to where the waist is in the mode matching telescope in order to reduce the clipping.

Since we are wondering what effect pointing may have (in particular with respect to coupling into the cavity and through faradays and onto PDs  etc)  we decided to do a little deliberate misalignment to see if the noise was impacted at all.

Firstly we misaligned the beam into the cavity.  We used only the horizontal actuator on the last mirror before the cavity for the CCW beam.  Looking at the trans PD DC voltage we moved from the initial max transmission (with the plastic cover in place over the 2 input mirrors) to lower transmission by moving the actuator CW and then CCW.

The result is that at lower frequency the noise was slightly improved with misalignment.  The misalignmend in the CW and CCW directions produced strangely similar results in that we get a factor of a couple at low freq.  At frequencies around 1Hz and above the noise gets worse due to the box being removed.  We confirmed this was the cause by going back to the max transmission (now only 740mV) with the box off and seeing that the higher value stayed at around 1Hz.  Interestingly after this moving around the noise at max transmission was now a little better than when we started.

Next we put the mirror back to the max transmission, and put foil over the small path between box and vacuum system which was worrying Koji.  You can see the effect most clearly in the second pdf below.  The noise between 0.4Hz and 6Hz is improved by a reasonable amount.

The final test we did was to misalign the beam onto the CCW PD by a small amount.  It would have been nice to quantify this and to know where to put the beam back to, but the DC output is so noisy (really terrible) that it is just impossible.  I misaligned it gradually using the horizontal actuator on the mirror right before the lens that focuses the beam onto the PD.  I moved it until the cavity would not lock, and then came back just a little until it would lock again.  It is much further toward the edge of the PD now, though it was difficult to tell whether any of the beam was clipping on thed edge (at least I couldn't see any through the viewer).  As you can see in the last pdf below the spectrum is quite a bit worse.

So while this doesn't give us the answer, it perhaps gives some clues as to what is going on here.

I finished up by trying to realign the beam on the CCW PD.  Since the DC level is messy it is difficult to know what to use for this.  I used the viewer, and then swept the cavity and got the error signal up on the scope.  It seemed like the beam was already giving the full error signal, and that trying to move it around using the mirror before the lens didn't give any difference  to the height of the error signal until the beam got right off the edge of the PD (around 7 full turns of the actuator in either direction).  One last FFT showed that the noise is back down to the level it was at before I misaligned the beam on the PD.

PS:  I also notice that we don't have the vacuum system pumped down at the moment.  Clearly it's not making a great deal of difference, but I guess we should pump it back down again soon.

 For lack of a great way to look at the low-frequency noise in the REFL PDs (due to the noisy DC outputs described earlier), I went back to the old idea of using a pickoff from near the laser output to look at intensity noise. The setup is a little bit hacky, since I just shot the beam through the side of the box with no viewport, but I think it's fine for this measurement. I took the light that was being dumped from the initial PBS. It was strong enough that even through the box I still had to attenuate it using an OD(=2) filter.

The spectrum I saw had increasing noise at lower frequencies, as should be expected I suppose. It didn't look quite right to explain what we see in the gyro signal, but I it wasn't obvious enough to rule out. I built a simple ISS servo by feeding it into the digital system, subtracting an offset, putting it through a 100-Hz LPF and feeding the output to the power adjust on the laser controller. I was able to get ~200-300x suppression below 100 Hz without the loop becoming unstable. The loop had essentially no effect on either the gyro noise or the TRANS_DC spectrum, leading me to conclude that the excess noise is not from input power fluctuations. I guess this is somewhat of a relief, as I have no idea how that would cause the noise we're seeing anyway.

Here is a before/after plot of three signals: the gyro noise, the TRANS_DC signal, and the ISS PD signal. NOTE: The ISS PD signal units are arbitrary, so the fact that the open-loop noise is right with the other traces around a few Hz is meaningless. As in the last few entries, I have multiplied the TRANS_DC spectrum by a phenomenological factor of 10 to show that it has precisely the same shape as the gyro noise at low frequencies (that is less convincing in this plot due to less averaging and higher FFT BW, but look to old posts to be made a believer).

I did the same comparison as before using data from today, and the results are a little weird. The gyro noise is the same at low frequencies, and the DC_TRANS spectrum (when multiplied by 10) is also coincident at low frequencies. However, the high-frequency floor of the DC_TRANS spectrum today is higher than it was last night, and there is also a little bit of excess HF noise in the gyro spectrum. I am going to check what the dark noise of the TRANS PD is now.

I also took spectra of the DC outputs of the REFL PDs, and they don't share this low-frequency bump in the spectrum with the TRANS and gyro signals. This is above the ADC noise floor, but it could easily be the electronic noise of the DC output of the PD (which is very noisy for some reason). The point of this measurement was to verify that we saw power fluctuations on the REFL side in coincidence with the TRANS ones. Then, we would see if they were in or out of phase with the TRANS fluctuations to see if they were input power fluctuations or cavity coupling fluctuations. This would essentially give us the information we would get from setting up a pickoff PD near the laser to monitor input power fluctuations, plus a little more.

I will see if this is dark noise and then figure out a way to make a more precise measurement of the REFL fluctuations.

I confirmed with Hiro my suspicion that the situation described in the quote probably can't really be what's going on. As in the case of a regular fabry-perot cavity, the mirrors themselves define the mode and they must move for any rotation or translation of the mode to take place. So, pointing drift in the input beam can't cause a differential path length between the CCW and CW modes, though it would cause us to see AM at the output (like we do) as the coupling would go up and down.

I guess it's possible that the mirrors themselves can be twisting and causing the mode to wander, but I think geometry dictates that the effect would be the same for both directions.

That is for some near-DC AM to be converted to AM of the 19-MHz beat frequency. The idea before was that jitter at 19 MHz would turn into a 19-MHz signal from misalignment into the AOM or via any other mechanism that turns jitter->AM (e.g., clipping). This looks like a DC error offset. Then, any low-frequency noise (e.g., slow pointing drift of the steering mirror on the way into the AOM, slow translation of some aperture relative to the beam) causes low-frequency AM of the 19 MHz signal, which looks like a time-varying error signal (noise). AM of the AM.

So, there is some 19 MHz oscillation set up by jitter->clipping or polarization->AM or some gremlin waving his hand steadily across the beam coming out of the laser at 19 MHz. Then, the amplitude envelope of this oscillation is modulated by some low-frequency noise source, and this is what looks like noise when demodulated by the PDH setup.

The question I'm wondering about now has nothing to do with envelope modulation of a 19 MHz signal. Instead, there could be low-frequency pointing noise on the way into the cavity. The cavity reflectivity looks like a real number close to 1 for the sidebands, independent of small angular misalignments. So, any existing 19-MHz signal is not amplitude modulated. The question is: how does this sort of thing become noise? I thought perhaps the eignenmodes of the cavity rotate with respect to each other since the beams are not being injected from symmetric points, and this could cause some relative length change that looks BIG in the gyro signal compared to what a common-mode length change would look like via FSR modulation. This could be why we don't see it in the primary (laser) actuation signal.

I think you raised the possibility that the same low-frequency pointing that causes us to see noise in the DC_TRANS signal could also produce RFAM via clipping or whatever, but in this case we would still see the noise with the cavity obstructed, which we do not.

In terms of a coupling mechanism, I'm wondering about this:  If the pointing of the carrier as it goes into the cavity is moving around at low frequency, then that's going to modulate the coupling into the cavity and give us some AM on the reflection PD  (I'm not talking about RFAM here, but low frequency AM as the coupling to the cavity wanders around).  This then causes the AOM to try to act, so we see noise superimposed on the reflection and transmitted beam.

It seems that whatever the cause, if we are seeing AM at low frequency in the transmitted beam then it is likely that we will also be seeing the exact same signal on our REFL PDs.

EDIT:  Zach pointed out to me that there needs to also be some phase shift between the carrier and sidebands for us to get an errors signal.  I think that I'm not clear now how we ever expected the RFAM to show up as noise.  Where is the phase shift there?

Since it looks like AM at the input side is not the root of our current low-frequency problem, we have been trying yet again to come up with new sources. Alastair had the idea that pointing noise of the beam going into the cavity might be causing us a problem in some not-yet-well-understood way (this was first discussed in the context of 19 MHz jitter from the EOM being converted to RFAM as it could be in the AOM, but the cavity should have very little response at 19 MHz with which to do this).

I decided to look at the low-frequency spectrum of the DC_TRANS signal to see if there was the same type of behavior as in the gyro spectrum. As it turns out, there is. Below is a plot of the two compared side-by-side (though I had to scale the DC_TRANS plot up by a factor of ~10 to get it to coincide). There is extremely good agreement in the shape of the curves, and I think we'll see that the HF floor of the DC_TRANS plot is just the noise floor of the (broadband wide-area Thorlabs) PD.

I can't say that I can think of any obvious coupling mechanism here. I think it's feasible that pointing drift of the input beam is causing the spatial eigenmodes of the cavity to wander differentially (i.e., the points at which the supported mode in one direction touches the mirrors all move horizontally across the mirrors a bit, making the whole square 'rotate'---this is dependent on the input beam and can thus happen independently in each direction). In this case, the cavity length would differ in the two directions, resulting in a gyro signal.

We need to do some more work to figure out what exactly is going on, but this is another data point that helps with the diagnosis. I think the next step is to look at the power at some pickoff point close to the laser to see if this is an input power drift or something caused by varying degree of coupling into the cavity (as from misalignment).

 Surely life at Caltech isn't that bad?

The ants are back again and it's only going to get worse over summer.

We have ant poison in the TCS lab. Feel free to use it.

 [Alastair, Zach]

Today we vented the chamber and obstructed the cavity internally to measure the open-loop noise on the PDs themselves. To account for noise in both PDs while still rejecting anything that was common-mode---things like laser noise that are suppressed by the primary loop and absent from the gyro signal---I took the demodulated outputs of the PDs (i.e. the open-loop error signals) and subtracted them with an SR560. I then relocked the cavity, measured the current gyro noise spectrum, and took OLTFs to obtain optical responses with which to calibrate the error signals into gyro noise. The noise is far too low to explain the excess LF gyro noise:

I also measured the error signal spectra individually. Both of them are at about the same level as the differential noise, so there isn't a huge common-mode component.

As far as I can tell, we still haven't found the source of the blasted LF junk.

[Alastair, Zach]

Over the past couple days (in between overhauling malfunctioning PDs), we have been trying to hunt down the excess low-frequency noise. Last week, with Koji's help, we essentially ruled out the possibility of scattered light noise from the transmitted end of the gyro by intentionally reflecting varying amounts of light back into the cavity and observing NO DIFFERENCE in the low-frequency spectrum.

AM from the EOM still seems to be the most likely suspect, and we continue to find ways in which it could couple. Yesterday, we think we traced the crazy AM level modulation that I mentioned in my last post to the iris we are using to isolate the proper beam out of the AOM setup. The double-1st order (desired) and single-1st order (undesired) beams are extremely difficult to isolate from one another, so we had to use a very small aperture that we think was coupling EOM jitter into AM quite strongly. We moved the iris down the beam path closer to the waist(s) and were able to get better isolation with a larger aperture. The drift in AM level now seems absent.

While the AM levels in the CCW and CW beams (as measured on the RF analyzer) are not simultaneously minimized at the same pre-EOM HWP angle, there is no longer a large-angle discrepancy; the difference is <1 degree and the noise in both beams can now be kept fairly low at some compromise angle. I have set up a PDA255 in each path immediately before the cavity to monitor them both simultaneously. By adjusting the HWP before the EOM and fine-tuning the EOM orientation, I was able to get the AM peaks in both beams to be <10 ppm relative to the carrier.

After re-locking the gyro, I saw NO IMPROVEMENT in the low-frequency noise yet again. I replaced the PDA255s and tried looking at the LF noise directly after demodulation. I saw some excess noise above the broadband floor below about 1 Hz, which is roughly where the excess gyro noise begins. Upon deliberately de-tuning the HWP so that the RF peaks were >20x higher, however, I saw NO NOTICEABLE CHANGE in the audio spectrum. Looking at the peaks in the RF spectrum more closely, I discovered that the linewidths are below 1 Hz, suggesting that this may not be the source after all.

I suggest that we vent the chamber and obstruct the cavity so that we can run the same tests with the REFL PDs themselves. Then, we can use the noise we measure in the error signal to easily and accurately estimate the contribution to the NB.

 I got around to doing the EOM AM/PM measurement, and the results aren't fantastic.

PM:

I already measured this the other day, but we've done some switching stuff around since then so I did it again. 

• Carrier: 780 mV
• SB: 11.4 mV
• Γ ~ 2*sqrt(11.4/780) = 0.24 rads (this agrees with the other day's measurement)

AM:

This is where it gets messy. I measured this in two places: after the BS in the CCW path, and after the AOM in the CW path. It was measured by putting the signal from a PDA255 directly into the RF analyzer and measuring the peak (in V) at 19 MHz. The DC level of the light for all measurements was 3.00 V.

CCW:

The first thing I noticed was that the peak was not minimized at the same HWP angle that made the beam have exactly S polarization. Rather, it was best about 5 degrees off.

Even at this minimal point, the peak fluctuated in amplitude from ~10 uV to 180 uV with a period of 1-2 minutes. You could literally sit there without touching it and watch it go up and down before your eyes. WTF?

Rotating the beam to exactly S made the peak climb to 500 uV!

CW: 

This was even worse than the other direction. I had to turn it 17 degrees away from S in order to minimize the peak at ~50 uV. Putting it at S made it ~1.3 mV!

It didn't seem to oscillate as wildly as the CCW beam at the minimal point.

I think the most alarming thing is that the AM in both beams cannot be simultaneously minimized. This explains why we always see junk at low frequencies, I think: minimizing the peak for the CCW beam just ensures that there's more junk in the CW direction.

Need to figure out what gives.

I tuned up our first TRANS PD, S/N 03, that Alastair was working on with the J-Laser tonight. Here is the TF:

As before for the REFL diodes, I measured the output node of the diode with a probe so that I could tune the readout notch to 100 MHz. I had to change C2 to 33 pF to get 100 MHz in range with the tunable cap (C4), which I changed to a 1.5-50 pF one. Here is a full-span plot and a zoom around the notch:

I think it looks ratty at high frequencies because we are starting to see interference effects from the O(1 m) length cables.

 To aid my memory, the new values for the 100MHz notch

• C2=82pF
• C4=11.8pF(1.5-15pF tunable)
• L3=27nH

 So here is the outline of the Trans PD component choice:

1) Shot noise:  at 3mW the shot noise limit is ~3e-11A.

2) The transimpedance is entirely set by the component choices we make for the inductor/capacitor pair in the readout notch, since the diode capacitance and resistance are fixed.

3) We want to make sure we're well away from railing the opamp.  We want approx 0.3V output max, which is a transimpedance of 100.  This includes the gain of 10 from the opamp stage.

4) We are well below any noise level that could be of concern for us in transmission readout.

Since we are well above the noise level we care about in transmission, I've chosen the values to make sure the opamp isn't railing at 3mW input power.  This does mean we will be dominated by voltage noise in the opamp.

Based on this I picked the value of L (which had to be a value we have, 27nH) to give the nearest transimpedance to 10V/A which I checked in Matlab (see attached Matlab graph).  I then checked the model in LISO, and get the correct transimpedance for the full circuit including the opamp.  As you can see the noise is now dominated by voltage noise in the LMH6624, simply because we have such low optical gain.  It seems like the LMH6624 is not the nicest way to do this if we ever want to use more power than 3mW....  the minimum gain of 10 is causing us to reduce the gain at the point where we really want it - the input.

The noise level from this at 100MHz is 1e-10A/rt(Hz), which corresponds to a frequency noise of 3e-9 Hz / rt(Hz) at 0.1Hz.  The equivalent rotation noise is then 1e-15 rads / rt(Hz) at 0.1Hz

 I mentioned in the last post that I had measured the AM in the CCW beam after the beam splitter using a PDA255. I saw that the noise spectrum was flat well above where we see the excess low-frequency noise, so I ruled it out as the cause. What I didn't do is the same thing for the CW direction. I had a hunch today that AM could be generated by jitter of the input beam into the AOM caused by the EOM (Rana said that jitter was one source of EOM->AM coupling).

I put a PDA255 in the CW path after the AOM double-pass, stuck the signal into the demod setup, and---lo and behold---I saw low-frequency noise with just about the same shape we're seeing in the gyro signal:

I decided to try putting separate EOMs in each path. This was extremely messy for a few reasons:

• sheer lack of space: not only did I need room for the EOMs, but also for several waveplates to rotate the beam to S and then back to P into the faradays.
• inability to put in focusing lenses to get the beam through the crystal without fudging the whole modematching setup.
• only having one multi-axis EOM mount---one direction had to use one of the old fixed brass mounts, and I had to use what little parameter space I had to work with before the beam goes through the faraday isolator to do it.

Anyway, I found a way to do it that sort-of-kinda-maybe fit:

I split the power from the FG to the EOMs and realigned the beams into the cavity. Needless to say, the setup was far from optimal. Anyway, I decided to lock the cavity and PLL and see if I saw any improvement. There was none; in fact, the noise was worse. I then realized that I had forgotten to put the top on the box. I replaced it, and the noise went down a bit, but still slightly higher than before. I THEN realized that I didn't have the auxiliary box around the CCW injection steering mirrors. I replaced it, and the noise level was at just about where it was before. See below:

It is obvious that the sensitivity is suffering au cause d'the shitty way I put it together. I don't think we're seeing oscillator noise in the middle band since the PLL signal looks no better than the AOM signal (see previous post). I think it may be worth trying to do a better job at setting up the twin-EOM scheme, but there are two things that have me on the fence:

1. Doing this right essentially means redesigning the optical layout altogether. There are too may waveplates to count at the moment, and I'm certain that with a few minutes' thought we can come up with a better layout. We will absolutely need another multi-axis EOM mount to avoid over-constraining the beam path, and we don't have one. I think Frank and Dmass have one, so perhaps we can snag theirs and order another one, but this is time and money. The bright side to this is that we will be replacing the cavity optics either way, and it might be "therapeutic" to rebuild the IO anyway.
2. This is the tricky one: why do we see an equal improvement in both signals with the replacement of the box cover? No one ordered that, so to speak; the model predicts that IO noise should be suppressed by the CW loop gain, so the PLL should always look better than the AOM in bands where we're limited by IO noise. It could be that the AOM loop has $&#@all gain with my piss-poor attempt, but I think it's unlikely that we've lost over 60 dB of gain, even in this state.

I'll see what kind of loop diagnostics I can do in this limp-mode, and otherwise we'll just have to take a leap of faith that things will look better once we've reconfigured. If not, it will be the same amount of work again just to bring it back to the single-EOM setup. In the meantime, I'll try to think more about how the IO noise could couple to the PLL unsuppressed.

http://nodus.ligo.caltech.edu:8080/TCS_Lab/135

It does seem to suggest that the source of the low frequency noise is something that is not unique to either the transmission or reflection readout (ie not the MZ phase noise or PLL phase noise), and is not something that should be suppressed by the loop gain (like input optics noise or AOM oscillator phase noise) in the transmission readout.

EDIT: I should have mentioned that rotating the polarization before the EOM in order to minimize the error signal offset did not have a noticeable effect on the bulk of the low frequency noise. It did, however, make the coherent-looking peaks from 100-600 mHz go away, though I have no materials to support this.

Also, by placing a PDA255 after the initial beam splitter and demodulating it at the sideband frequency, I observed that the RFAM noise is flat well above the frequencies where we see the excess noise. This isn't purest way to rule it out, but I think it is convincing: if the noise we see at low frequencies is from RFAM, we would see it extending to higher frequencies.

 Below are the (delayed) results of Friday's oscillator noise measurements, calibrated to gyro units and plotted alongside the gyro noise. The traces are:

1. Gyro noise from AOM actuation
2. Gyro noise from PLL actuation
3. Two marconis with f_carr = 100 MHz and dev = 100 kHz/V beating together, with the beatnote fed back to one and the other's dev input shorted. This is divided by sqrt(2) to estimate the noise from the PLL oscillator alone in gyro mode. It agrees pretty well with (2) in the region we think is dominated by oscillator noise.
4. Two marconis with f_carr = 50 MHz and dev = 100 kHz/V beating together, with the beatnote fed back to one and the other's dev input shorted. This is multiplied by sqrt(2) (i.e., 2/sqrt(2)) to estimate the noise from the AOM actuator alone in gyro mode, taking into account the double pass. This agrees pretty well with (1) in the region we think is dominated by oscillator noise
5. This isn't really an oscillator phase noise measurement. It is the feeback signal to the PLL oscillator with the modulation on the AOM off (i.e., no gyro signal). This is significant in that, since it is roughly equal to the estimated PLL oscillator noise at low frequency, it rules out the possibility that the excess LF noise comes from phase noise in the output MZ. Therefore, the excess noise must be noise imparted on the CW light by the secondary loop. This helps narrow things down.

I measured eight of the 45P mirrors from the 40m.  The transmission doesn't look as high as we realistically need it to be.  They were: 57ppm, 38ppm, 46ppm, 36ppm, 48ppm, 64ppm, 34ppm, 55ppm, with some ~10ppm error.

Using combinations of these mirrors the best we could do is a transmission through the cavity of 20% with losses at 40% and a contrast defect of 0.22, the rest being lost in transmission through the turning mirrors.

We are starting to get quotes back in for coating runs.  It seems that they may not be able to get exactly the transmission we want, but instead will have +- 30ppm.  It may be that we want to be a bit cautious in our transmission choice since 100ppm -30 would end up with a transmission much lower than we want.  If we go for a higher transmission in the first place then we reduce that risk but may get a slightly lower finesse, for example 130ppm would give a finesse of 15k instead of 18k for 100ppm.  The extra upside is that we get a better contrast defect (0.12).  

The C_d is never going to be zero since the input and output mirrors will have very similar transmissivity.

I've put in requests for quotes to a number of companies now for 100ppm coatings.  I also checked through our history of measured transmissions, and notices that these mirrors have some that are very close to what we want.  The Y145P 2" mirrors that I previously measured seem to have much higher transmission for 45S than the ones in the Mott measurements.  I'm going to go across and dig these out again so we can repeat the measurement.

 [Alastair, Koji, Zach]

As we discussed doing, we removed the PBS that was used to split the power between beams and put a 50/50 power splitter in its place:

The thinking was that doing this would minimize the AM coupling from polarization rotation in the EOM. After realigning the entire experiment, we observed no improvement in the low-frequency noise spectrum (compare with this post):

It does seem like there is a reduction from 10 mHz to 100 mHz, but it is tough to tell whether or not this is meaningful given the FFT bandwidth. There remains the possibility of true AM from the EOM itself, though it seems unlikely that it would be stronger than that from the rotation. I suppose we should measure it either way.

Another not-extremely-likely case is that the phase noise from the two oscillators is the same below 1 Hz. This means that their absolute noise levels (V/rHz) would have to be different by a factor of two to accommodate the fact that the AOM oscillator noise couples in twice as strongly from the double-pass. Since the phase noise tends to go up with carrier frequency, and since the AOM carrier is half that of the PLL, this isn't out of the question. We are planning to beat our two Marconis together to see if the low-frequency noise is enough to explain the gyro noise. Frank and Tara's data suggest that it stays fairly flat at lower frequencies, but they don't have a measurement at the low frequencies we're concerned with.

 The polarization going into the EOM was off by 90 degrees. This must have happened when I was minimizing the DC offset at some point (since there is a minimum whenever we are aligned with either of the crystal's axes, but of course the phase modulation is minimal here). I fixed it and we now have reasonable sidebands:

The carrier peak is at ~11 V, the sidebands are at ~176 mV. Using the 1st order bessel approximation, the modulation depth is

Γ = 2 sqrt(0.176/11) = 0.25 rads        this is about what we want.

This is almost certainly what is happening---I guess I assumed that was the case. We can trim the offset that develops away by making slight changes to the HWP before the EOM, counteracting the rotation that happens in the modulator. I have seen lots of setups with PBSs after modulators, so I didn't foresee it being a problem when we designed it in the first place.

I guess we could use a power splitter instead of the PBS, then put a waveplate directly after it in the AOM path (before the second PBS that directs the beam to the AOM). Using the waveplate, we could make small changes to the power that gets sent into the AOM (vs straight through the 2nd PBS into a beam dump) to finely balance the power without having a maximal linear coupling from the polarization rotation in the EOM.

 To estimate the RAM before the measurement, we can use the following logic:

The cavity has a linewidth of ~100 kHz. According to the Gyro Doc the gyro signal df ~ omega / lambda, where omega is the rotation rate. Since the noise now is ~10^-5 rad/s, this is equivalent to ~10 Hz/rHz of frequency noise at 0.1 Hz.

This would require a AM/PM ratio of ~(10 Hz / 100 kHz) ~10^-4 at 0.1 Hz. Its easily possible; I have seen things of this size.

Another possibility is that our setup has been made especially sensitive to this by the PBS after the modulator. The RAM typically gets made by unwanted polarization rotation. If we have tuned a waveplate to split the power after the EOM 50/50, it means that we are also in the configuration where the polarization -> AM conversion is maximized. We can reduce this by trying to do a polarization insensitive split or by having separate EOMs in the two paths.

To verify that its a polarization to AM conversion, you ought to adjust the waveplate to put minimize the power in one path and measure the RAM in the other one. Then you ought to be quadratically sensitive to the angle.

Here is the current gyro noise spectrum, as computed from both the AOM and PLL control signals:

It is not any better than before, but there is one important thing going on here: the noise in the PLL signal is lower than that in the AOM signal between ~1-100 Hz. The noise in this band is dominated by oscillator phase noise (from the AOM driver or from the PLL LO, depending on the signal). This marks the first time that we can verifiably show that some noise in the locking loops is suppressed in the transmission readout. This has been predicted by our noise model for quite some time, but we haven't really been able to demonstrate it yet.

In fact, it's been there ever since we rebuilt the gyro, but I had forgotten a factor of two in the AOM calibration due to the double-pass. If you look at some older plots, you can see that the noise at high frequencies differed between the two signals by just enough to make the mid-frequency noise look the same (while even making the AOM noise look BETTER than the PLL noise at low frequencies).

I'm pretty confident that what we see now is correct. The noise above ~200 Hz is well described by the "spillover" noise, so the only mystery that remains is the excess low-frequency noise. It appears to be exactly the same in both loops, so this isn't something that is being suppressed by the CW loop gain. This has been verified by watching the LF noise as we turn the CW boosts on and off.

The main suspect at the moment is the RFAM drift we see as a modulation of the primary-loop error signal offset, so this will be our next focus. I will soon have a quantitative analysis of the AM/PM levels we are getting from the EOM, and drifts with time therein.

http://www.youtube.com/watch?v=IRzcoRFkpBQ

http://www.youtube.com/watch?v=hHN20qP0HCY

 The right way to choose the component values is to write down the correct cost function which you are trying to minimize. Since its a straightforward kind of circuit you can analytically construct the Jacobian.

The LMH6624 has a dynamic range which is larger than the what you can achieve with with the light (i.e. signal/shotnoise).

I didn't explain that properly in the last post.  We had set up the PD with a low gain because we need to keep the signal low enough for the mixer.  After putting it together and measuring the transfer function we noticed that there was a large peak at high frequency as Zach mentioned in this post.  Today I went back and remeasured it after removing the 200MHz notch, and then started increasing the gain to see if it would go away.  That is the reason why I have plotted the three different gains.

Definitely we need to keep the gain at >=10.  The issue now is whether we need to reduce the gain somehow (ie reduce the transimpedance using a smaller inductor, or finding a low gain opamp).  Any views?

There is no case in which you can run the MAX4107 or LMH with less gain than the minimum gain of the datasheet. If you look at the time series of the PD with low gain its probably oscillating like crazy.

From the datasheet's Bode plots, you can see how the phase margin is for low gains: bad news.

I thought about it, but only because of the rainbow font. And the plz.

so plz do not mess with the instruments attached to the setup

(don't even think about it)

After some major software issues (trial license had expired ) i re-installed everything.
Also characterized the first bunch of 3mm EG&G diodes from PK, so that i can have the not awesome ones for destruction.

Current device being tested  is #1136, 20W and 2ms pulse duration.
Taking measurements of impedance, dark current, dark noise etc. every 100 pulses.
Also taking pictures after every single pulse, 1000ms delay between pulses.

Yes.  Jokes on you fool!

Is this an April Fools joke?

Here are some new plots of the 100MHz transmission PD.  I removed the 200MHz notch that I had put in (since we don't need it), and saw that the resonance at high frequency looked pretty bad.  I wanted to check if this was because of the low gain we were using (datasheet says that it is stable for gain>=10), so I retook the TF and then changed the gain up to 3 and then 10 by changing R5 to 100 and then 453.

The gain3 is an improvement, but there's still some nastiness at high freqency.  The gain 10 plot looks pretty clean though.  Compared to the liso model (which I have set to gain 10, and have changed the diode capacitance down to 100pF) the gain seems to be a lot higher than we should be getting.  I've gone over the calibration a few times and don't see any errors.  I've also checked the values in liso and they seem correct too.  This is not great since we really don't want to have such a high gain in the first place.

We should probably see if there is a low gain version of the LMH6624 that we can use in its place.

EDIT:

I should also mention that I did take into account the difference in the laser power on the two PDs.  The 1611 had 1.16mW on it, and our PD had 0.47mW on it.

 I reinstalled the REFL PDs and relocked the gyro. I am going to have to wait for a brief pause in Frank's measurements tomorrow to tune the EOM circuit; it is running in broadband now. After everything is back in place I will take the new loop TFs, etc.

Attached again

i tried to open the liso file but it seems to be empty

 [Alastair, Zach]

Alastair finished building our first TRANS PD (S/N 03), and we tuned it and took a transfer function with the Jenne Laser:

Not sure quite what's happening up at 277 MHz. The gain at the readout frequency (100 MHz) is a bit higher than what is predicted by the model, but that's probably because Alastair used 200 pF as the diode capacitance, whereas it's closer to 100 pF with the 5V bias. 200 pF puts the diode pole (RC = ~10 ohm * 200 pF) at ~80 MHz, but it's probably more like 160 MHz, explaining the extra gain.

We also retuned the REFL PDs to have their readout and 2f rejection frequencies at 19 & 38 MHz, respectively. They match up quite nicely, save for some difference in the diode capacitance:

I still need to re-tune the EOM resonant circuit, which I will have to sneak in during a break in Frank's diode demolition derby tomorrow. Otherwise, we're ready to get the gyro gyroing again.

I'm in the middle of stuffing the first Trans_PD at the moment.  I'm using the following values for the resonant notches:

• AC coupling
  • L6=6.8uH
• 100MHz notch
  • C2=22pF
  • C4=9pF(1.5-15pF tunable)
  • L3=82nH
• 200MHz notch
  • C10=6.3pF(1.5-15pF tunable)
  • L2=100uH

You can compare these values to Zach's 33MHz diodes in this post.  The lower inductance of L3 gives a lower transimpedance and I've set the gain of the opamp to 2.

I have some concerns that we don't want to much gain for these PDs.  A total transimpedance of 30dB V/A means that 20mW of laser power becomes about 7dBm at the output of the PD.  If we're using a level 13 mixer then that seems about right.  If we want to increase the power at all then we will need to attenuate the output of the PD.

LISO file is attached

I updated arbcav to include more functionality. Now, in addition to giving you the transmission/reflection spectrum of the cavity you tell it to build, it will also calculate the HOM structure (carrier and sideband) for linear, triangular, and quadrangular cavities, taking astigmatism from arbitrary angles of incidence into account. You have the option of whether or not to include RoC for the mirrors. If you don't, it will just spit out the T/R spectrum as before; if you do, it will give the HOM info. You can also choose whether or not to give it a modulation frequency, and if you don't it will only plot the carrier HOMs.

I've updated the copy on the SVN (link above).

Below is the output of the function for our cavity. With the new length of 3 m (for FSR = 100 MHz), it looks like f_mod = 19 MHz is the best bet.

I have made the HOM plot such that higher orders correspond to lighter shades (as well as shorter lines) to aid in identifying the stronger modes.

I guess that this is a transfer function between the source out of an RF analyzer and the RF output of the New Focus 1811 PD (which goes up to 125 MHz). If so, It looks like the EOM is nicely free of mechanical resonances in the band we care about, Nice job, Thorlabs.

Here is the RFAM measurement redone.  First plot is the full spectrum from DC to 100MHz.  Second plot is put together from multiple scans to give higher resolution in the area of interest.  We used the same setup as before, but with an 1811  instead of the PDA255 to improve bandwidth.  The steps in the plot at 15MHz and 25MHz are the points where the scans have been joined.

Thanks for adding that Joe.

I've changed the description in the ATF wiki to include restarting the front-end in the MEDM screen, and I've added a description about how to get the channel status from daqd using telnet, since that's a handy thing to be able to double check.

At Rana's suggestion, the GYRO_MAIN medm screen background is now linked to the C2:DAQ-FB0_ATF_STATUS epics channel, so that the whole screen turns a horrible pink/red colour if this channel goes to anything other zero.