I did the same analysis as Antonio: https://nodus.ligo.caltech.edu:8081/PSL_Lab/1394

My recollection is that this was the justification for ordering the 36 and 37 MHz OCXOs.

Wow, nicely done!

For posterity, the design document is on the DCC: T1600071

The vendor report for the optics is here: Q1600019

I'm a little surprised at the finesse. The design value was 300. This should be set by the reflectivities of the flat mirrors, which are each supposed to be 99% ± 0.1% for p polarization.

/trunk/docs/algaas_ctn/sourceFiles/

Some necessities for implementing dual-quadrature RFAM suppression:

• Beam pickoffs:
  • Need to be in the forward-going direction of each beam.
  • Pickoff should be about 10% of incident power. With ~1 mW incident on each cavity, we then get about 100 µW on each RFAM monitor.
• Monitor PD:
  • Could be NF1811
  • Could be some in-house PD
• Electronics:
  • Need I&Q demodulator
• Voltage feedback:
  • Need to sum in dc/audio path into EOM drives along with rf

Compare with previous todo list.

To-do list (short term):

• Check health of PDH loops:
  • Check centering on RFPDs
  • Check slope and balancing of error signal
• Turn on chamber heating
• Re-establish beat
• Re-insert south EOAM

To-do list (medium term):

• Replace PBS/QWP reflection locking with Faraday isolators
  • Need two Faraday isolators with large apertures
  • Need four HWPs: one on each cavity input, one on each cavity output
• Fix power supply situation [Aidan already doing this]
• RFAM mitigation
• PMCs

To-do list (long term)

• Install crystal oscillators, retune RFPDs, retune EOMs
• Acromag

I reinstalled the old, underpowered unipolar HV supply that we used to use for the south cavity. Since Aidan is going to redo the power distribution anyway, there's no point in fussing with it now. The south cavity locks fine. The digital temperature offloading seems to be working as well. Light incident on each cavity is about 5 mW.

Pointing into both cavities has been recovered.

I could not get the PMC on the south path to lock, so I have just taken it out for now. Then I resteered through the BB EOM and resonant EOM and into the south cavity.

The north path did not require much resteering. North seems to lock OK, although I have not checked the health of the PDH loop. On south we need to install an HV supply before locking.

I reworked the beginning of the south optical path so that there are two steering mirrors before the beam goes into the FI.

Recall that previously we had no steering mirrors before the FI. Then in December, I just moved the FI sightly downstream, so that there was one mirror before the FI.

Today I added two steering mirrors  (Y1-1025-45P) in such a way that the total path length should be more or less unchanged. The first lens after the laser is now placed after the first steering mirror. (I tried to place it so that it has the same displacement from the laser head as it did previously.) The FI is placed after the second steering mirror, and it is immediately followed by a HWP.

Ideally we would maybe put down another HWP before the FI, since the steering mirrors are only HR for p-pol, and the beam on the first two steering mirrors is some combination of s-pol and p-pol (since we use a HWP + the FI to control the power after the FI).

After steering through the FI, the beam looks pretty round on the IR card. I don't see any spray or stray beams.

I tuned the pre-FI HWP so that there is now 20.4 mW transmitted through the FI. The power transmitted through the 21.6 MHz EOM (which is after the third steering mirror) is 19.6 mW. I also don't see any spray on transmission.

I reran multidiel_rt with the as-built coating structure. The penetration depth is x₀ = 560 nm. With A = 5.6 ppm absorption on each mirror, the absorption coefficient is therefore α = 0.05 cm⁻¹.

Penetration depth x₀ is defined via E(x)/E(0) = exp[−x/(2x₀)]. Absorption coefficient is defined as α = A/(2x₀), since the effective distance traveled through the coating is 2x₀. [I belive this is the same definition that Garrett uses.]

The script for this is in the paper directory of the svn, under source files.

On the south path, we have placed a HWP so that the transmitted beams can have their polarizations matched. It is on a 1" post and held down with a fork.

In the longer term, this should probably be replaced with the solid metal blocks that were used to hold the QWPs. If these blocks are reinstalled, the waveplate mount should be twisted slightly in yaw in order to reduce the amount of backscatter into the cavities.

Some tasks not included on the list:

• Temperature loops
  • Cavities
  • Can
  • PMC
• Noise candidates:
  • Scatter
  • RFAM
  • PDH loop noise

When Aidan and I turned on the south laser today, we found that the transmitted beam out of this Faraday was entirely crap. It was blindingly obvious on an IR card, and only 50 uW was making it to the input of the PMC. The rest was scattering at wide angles at the Faraday output port.

It is not clear to me how the pointing through the Faraday could have deteriorated, since it is on a solid metal mount and is only 10 cm from the output of the laser.

At any rate, I was able to "recover" the previous performance (i.e., crappy but workable) by placing the Faraday isolator slightly further down in the optical path. Before, the layout was:

Laser -> QWP -> HWP -> Faraday -> lens -> HWP -> steering mirror -> PMC EOM,

and the HWP angles were -1 deg and 167 deg, respectively.  Now the layout is

Laser -> QWP -> HWP -> lens -> steering mirror -> Faraday -> HWP -> PMC EOM,

and the HWP angles are 341 deg and 167 deg. The first HWP angle is chosen so that 20 mW is transmitted through the Faraday (the rest is dumped at the Faraday's various output ports). The second HWP angle is chosen to send s polarization through the PMC EOM. I then had to resteer through the PMC EOM and through the PMC. With 20 mW incident on the PMC, the transmission is 11 mW. Not great, but about the same as the previous situation.

I remark that the south optical path between the laser and the PMC should be reworked as soon as is feasible, because what I've done is a hack job to keep things moving. Either the Faraday mount needs to be remachined, or the optical path needs to be redesigned to allow for proper steering through the Faraday. Additionally, the table surface next to the laser mounts is noticeably warm to the touch, so I do not recommend trying to shim up the laser (as it may negatively impact the heatsinking).

I thought I had posted this several months ago, but I cannot find it now.

I believe this document explains how the "coating loss angle" ϕ_c (as measured in an optical experiment) is related to the true mechanical loss angles of the coating materials (as measured by a ringdown). In general they aren't the same, if I'm understanding the formalisms of Nakgawa and Hong correctly.

I believe the factor of π / F here is an error. It should instead be the transmission T. That lowers the absorption estimates to more like 5 ppm.

A manual for running the CTN experiment is attached. I'll update and expand as needed.

Yesterday I took some TFs and noise spectra on the south TTFSS with the loop open and the beam blocked. Relevant information:

• Gains were 800 common, 800 fast
• Excitations were injected into COM EXC
• The relevant test points I monitored were COM TP 4 (henceforth "com"), FAST OUT 2 (henceforth "fast"), and HV TP 4 (henceforth "HV").
• At each test point I took a TF with the excitation on, and a noise spectrum with the excitation off.
• I also took a TF from COM EXC to COM OUT 2, so that I can use the known gain of the first amplifier (−4 V/V) to refer everything to COM OUT 1.

Then using the noise spectra, I divided by the relevant TF to arrive at an input noise referred to COM OUT 1.

The results are attached. The low/high frequency upswings on the HV trace are due to the input noise of the SR785.

Since the common, fast, and HV traces all lie on top of each other, I interpret this to mean that the noise of all of them is dominated by sources occurring upstream of COM TP 4. So the TTFSS is limited by the noise of its input stages, with a spectrum (at COM OUT 1) of 25(5) nV/rtHz.

I also measured the slope of the south PDH error signal (with 3 mW incident, and with fresh mode-matching), and found a slope of 8.4 V/MHz, as measured at COM OUT 1. This gives a frequency noise of 3.0(6) mHz/rtHz, which is well below the current beat level.

I found that the beat above 100 Hz was about 10 times worse than before, with a 2 kHz hump similar to what I saw on the north cavity before I separated its BB and resonant EOMs.

I suspect this is some kind of effect involving light bouncing back and forth several times between the two EOMs.

To remedy this, I took out the post-PMC Faraday isolator and put the BB EOM in its place. This gives a longer path length between the EOMs. Then I realigned through the EOMs and took a beat. Now I've recovered the 0.03–0.05 Hz/rtHz level that I had yesterday morning.

I turned up the incident powers on the cavities to 3 mW, and then optimized the mode-matching. However, I do not seem to be able to push down the beat any further. So perhaps it is now limited by something else.

I tried reinserting the Faraday isolator between the two EOMs, but could not place it in such a way to get the beam to transmit through. Since it's not an essential component, I think I'm going to leave it out for the time being rather than undertake a huge realignment marathon.

I swept the south laser with a triangle wave and optimized the mode-matching as best I could using the periscope mirrors and the translation stages. I got to a visibility of 0.3, which stinks (the maximum is 0.7 with these birefringent coatings).

I took a beat spectrum (attached) and noticed that the noise around 0.1–1 kHz is improved. Indeed, by reducing the visibility south I find the beat gets worse.

I decided some more involved mode-matching (involving beam profiling and alm simulation) is needed.

Before setting up the beam profiler, I noticed that the beam entering the cavity does not appear Gaussian, as seen on an IR card.

The laser beam entering the first Faraday isolator appears to be 1–2 mm too low. It is clipping on the input aperture, and the transmitted beam looks like crap.

Neither the Faraday nor the laser itself have any alignment adjustment knobs. I therefore had to choose between two evils: shim up the laser mount (and thereby risk having to realign the entire optical path, as well as possibly reducing the heatsinking of the mount to the table) or reinsert the PMC and move the BB EOM.

I opted for the latter: I reinserted the PMC, removed the EOAM (+QWP+PBS), placed the resonant EOM where the EOAM used to be, and then placed the BB EOM where the resonant EOM used to be.

I will optimize the alignment through these components, check the polarization, and then take a new beat.

We've noticed for a while now that we cannot turn up the gain on the south TTFSS as high as on the north TTFSS, despite having similar optical power levels, similar mode-matching, etc. (See the OLTFs in ctn:1504.) The north gain can be set to 900/900 on the common/fast knobpots, but on south it's more like 600/600.

Because the BB EOM is placed before the PMC, I suspect the cavity pole of the PMC (1.8 MHz, measured in elog: in 2010) is giving us extra phase which prevents us from turning the loop gain up higher. Indeed, when I remove the PMC from the south optical path (and realign into the south cavity) I find I can turn the south TTFSS knobpots up to 800/800. A new OLTF is probably in order.

The easy thing to do for now is to leave the PMC out. The better thing is probably to move the BB EOM to come after the PMC. Since there's no room, this probably means putting the BB EOM where the resonant EOM currently is, put the resonant EOM where the EOAM currently is, and then put the EOAM elsewhere. The EOAM could just as well come before the PMC, since we're only attempting intensity stabilization well below the PMC cavity pole.

Background

Yesterday I think I narrowed down the source of the 2 kHz frequency noise hump: it is voltage noise from the TTFSS being injected into the broadband EOM.

With the north cavity unlocked (and the TTFSS set to "test"), I monitored the (undemodulated) RAM using the auxiliary 1811 and the HP4395A. There were clear, broad 600 Hz humps on either side of the 14.75 MHz carrier. It disappeared when I unplugged the drive to the broadband EOM.

Then I looked at various test points on the TTFSS HV board with the SR785. On the COM → EOM path, the TF shaping takes the COM noise and produces (what I think is) the same 600 Hz bump, which is then sent to the EOM. In the beat, the bump appears at 2 kHz because of the north TTFSS boost; with the boost off, it reverts to 600 Hz.

This is the case on both TTFSS boards, but it only leaked into the beat on the north cavity. So I suspected it was an issue with how the EOMs are aligned on the north path. On north, the BB EOM was immediately followed by the resonant PDH EOM; on south, between the BB EOM and PDH EOM there is a PMC, an FI, and some other optics.

Today's work

I moved the resonant EOM so that it follows the EOAM. After the post-EOAM PBS, I did the following:

• I set down a HWP, and then used a temporary PBS to ensure s-polarization of the beam.
• A few inches after the first HWP, I set down a second HWP and used a temporary PBS to ensure p-polarization of the beam.
• Between the HWPs, I placed the resonant EOM, screwed it down, and then aligned the beam through it.

Then I redid the mode-matching into the north cavity and measured the beat. I kept it locked for about 90 minutes and didn't see the 2 kHz hump appear, so I'm guessing this solved the issue.

To do

• Minimize RAM on north cavity
• RIN data is stale and needs to be retaken
• Need to fix a nominal operating power for beat PD (I pick 7 dBm, because we're using a ZRPD-1 phase detector)
• Marconi noise data is stale and needs to be retaken
• PLL readout data is stale and needs to be retaken
• Seismic data is stale and needs to be retaken

I added a 48 Ω kapton heater to the north resonant EOM. It's got 40 mA going through it right now; no loop yet.

I used the auxiliary 1811 as an out-of-loop RAM monitor. The RF from the 1811 is mixed with the PDH LO, and then low-passed at 1.9 MHz.

I'm not sure about the RAM calibration here. I took the raw spectrum (in V/rtHz), multiplied by 10^(4/20) (assuming 4 dB conversion loss in the mixer), then divided by the measured dc voltage (about 20 mV), then divided by 40 (because of the different dc/ac tranimpedances).

Anyway, the point is that the 200 Hz hump we see in the beat seems to be from the north RAM.

I've been unsure of how the EOAMs are affecting the state of the light impinging on the cavity.

So far we've been rotating the post-EOAM QWPs so as to maximize the strength of the amplitude modulation. I'm still not sure what this does. I'd like to instead fix the QWP at ±45° and then insert the EOAM, regardless of whether this introduces a DC power offset. At the very least this will give us a polarization state that we think we understand.

Since the straightforward tabletop optimizations (mode-matching, RAM minimization) have not been able to make the high-frequency excess beat noise disappear, perhaps it is time to undertake a more systematic study of the PDH loop noise and add these traces to the noise budget.

Here's my interpretation of the PDH block diagram for one of the two cavities.

I added a flipper mirror before the north EOAM, as well as a HWP before the resonant EOM (so that we can independently control the polarization entering the two EOMs). I optimized the RAM, but saw no improvement in the beat.

I went through the table today looking for ghost beams. Most were already dumped. For those that weren't, I put down a dump or an iris.

I again looked at TTFSS OUT2 with the cavities unlocked (i.e., the open-loop error signals) and found that the low-frequency seismic/scatter wall appears only on south. So I hunted around south for a while. I found a series of ghost beams reflecting off the EOAM input and hitting dangerously close to the EOM output aperture. So I moved the EOAM forward a few inches, then adjusted its kinematic mount to offset these beams a bit. The EOAM should be realigned, and we should check to make sure the ghost beams are not entering the EOM again.

With the increased space between the EOM and EOAM, I installed a flipper mirror that takes the beam to the 1811. Then I minimized the RAM (from –54 dBm to –72 dBm with 85 mV dc).

FM dev: 10 kHz

Averages: 10, 50, 100, 500

 In this noise budget I corrected the PDH shot noise level (incident power is 1 mW, visibility is 0.5).

I reinstalled the auxiliary 1811 on the input side of the table.

I tried to get the free-running noise of the north cavity by locking south and then using the PLL to read out the beat from the 1811. However, even on a FM deviation of 400 kHz / Vrms, I could not get the PLL to lock. So I suspect the free-running noise is just too high to use this method.

I also used this aux 1811 to optimize the PDH EOM alignments. I saw no change in the beat spectrum after doing this. I would like to demodulate the 1811 signal using the PDH LO, but this will require some reconfiguration of the RF distribution.

Here is the beat measurement from Thursday, with the ISS loops on and the table floated.

I've fudged the photothermal noise slightly by just using twice the south cavity's PT measurement, rather than south and north. I need to take RIN data from north, and then I can add south + north PT.

We turned on both ISS loops today.

Here is an in-loop characterization of the south RIN with and without the ISS.

I didn't like the EOAM situation, so I rotated the post-EOAM QWP from 302° to 285°. With no voltage applied to the EOAM, this gives 6 mW of p and 6 mW of s. This may not be the true optimal setting, but the previous 2 mW / 9 mW situation seems too weird to be right. For commissioning the ISS I suspect we'll have to redo this EOAM setup to make sure the polarizations are behaving as we think.

The results are attached. I'm still seeing discrepancies at the points where the TFs are stitched together. Maybe it's because I'm using the SR785's auto source adjust feature.

I took a swept-sine measurement of the photothermal TF just as Tara and I did for the north cavity. To get a better measurement, I made some configuration changes:

• I turned the power incident on the south cavity up to 8.5 mW by adjusting the post-laser HWP from 318° to 286°.
• I placed an OD2.0 in front of the beat PD to prevent RF saturation.

Settings/values:

• The beat was at 13.8 MHz.
• The PLL Marconi was on 50 kHz FM deviation, and the SR560 gain was 100 V/V.
• South transmission PD was 460(5) mV dc.
• South transmission power (directly out of vacuum chamber) was 2.20(5) mW dc.

The results are attached. I'm not sure why there's a discrepancy around 200 Hz between the two traces. Below 100 Hz the measurement looks relatively clean.

The light rejected out of the post-EOAM PBS is only 2 mW (compared with 9 mW transmitted), which makes me suspicious that the post-EOAM QWP is not rotated properly, or else the input polarization into the EOAM is wrong. We should check this before redoing this measurement.

As with the north cavity, I find that an absorption of 6 ppm is needed make the measured curve lie on top of the theory curve.

For the time being, I have left the input power at 8 mW in case we want to take this again tomorrow. There's currently a dump upstream of the PMC to block the beam.

We locked the south cavity using the north TTFSS. 200 kHz oscillation is still present, so whatever this is probably doesn't reside in the TTFSS box.

Tara and I also took cavity pole measurements using the EOAM and two PDA10CSs, one placed before the cavity (monitoring the light rejected from the post-EOAM PBS) and one after the cavity (on the ISS breadboard). The HP4395A was used to drive the EOAM, and we then took the transfer function which takes the pre-cavity PD voltage to the transmission PD voltage. I will fit these later, but the poles appear to be consistent with the values tabulated in ctn:1475.

Last night, I looked at the TTFSS OUT2 on the spectrum analyzer, with the cavity unlocked and the laser PZT and broadband EOM unplugged. I believe this should give the demodulated spectrum of the RAM.

For north, the spectrum was white. For south, the spectrum was white down to 10 Hz, and below 10 Hz there was an apparent scattering shelf that rose several orders of magnitude above the white spectrum.

Tara and I went through the south path and placed an OD0.3 ND filter between various optics. We tried twisting one of the mode-matching lenses to reduce the scatter shelf, but it didn't seem to work.

This morning I went through the south path again with an OD0.5 filter, and eventually focused on the lens right after the FI. I found that I could greatly reduce the height of the scattering shelf (relative to the height of the white noise) by placing the filter downstream of lens, but not upstream of it. So I twisted this lens slightly, re-modematched into the cavity (minimal adjustment was required), and I found that the scatter shelf was reduced to less than 1 order of magnitude above the white noise.

Then I took a beat spectrum (carrier at 11.5 MHz, seems stable). The scatter shelf in the beat is not reduced by much, so I'll have to think about where to look next.

The beat is currently at 450 kHz. So I've changed the setpoint on the chamber temperature from 31.200 °C to 31.300 °C. We'll see if this pushes the beat to a higher frequency.

Edit: actually I decided to leave the chamber temperature alone and instead adjust the north cavity heater again. With a DVM, I measured the initial heater voltage as 10.64 V. I turned the power supply knob ever so slightly to get 10.60 V instead.

Some minor maintenance/improvements to the optical setup:

• We replaced the existing lens before the beat PD (RoC = 51.5 mm) with a slightly faster lens (RoC = 38 mm) in order to reduce the spot size on the diode.
• Tara improved the clamping of mode-matching lenses before the south cavity (they weren't tightened down enough before)

Tara and I took another photothermal TF of the north cavity today. Relevant parameters:

• Power incident on cavity: 10 mW (up from the usual 1 mW)
• Beat frequency: 1.2 MHz, drifting to 650 kHz (we are hoping it will swing through 0 Hz overnight and settle above a few megahertz by tomorrow)
• DC voltage on north ISS PD: 2.39(5) V
• DC power transmitted through cavity: 3.77(2) mW
• PLL actuation coefficient: 50 kHz_pk / 1 V_rms
• PLL UGF: 80 kHz (measured)
• EOAM drive: 5 Vpp from 20 kHz to 300 Hz, then 3 Vpp from 300 Hz to 0.2 Hz

In the attached data I have already converted the raw data (in V/V) into hertz of beat frequency per watt of circulating power. For this I use the conversion factor (50 kHz / 2^1/2 V) × (2.39 V / 3.77 mW) × π / F, with F = 16 700. Since the TF (again) appears to be junk above 1 kHz, I haven't bothered undoing the CLTF of the PLL.

The attached plot shows the expected photothermal TF in terms of hertz of beat frequency per watt of absorbed power per mirror. Therefore, the scaling factor that makes our measurement (given in hertz per watt of circulating power) overlap with the expected TF (given in hertz per watt of absorbed power per mirror) should be the average absorption of each mirror. I find that this scaling factor is 6 ppm, which seems surprisingly low, especially given our earlier finding that we have at least 120 ppm of scatter + absorption loss. So I will double check for missing factors of 2, 4, π, etc.

At any rate, the shape of the measured transfer function appears to be in good agreement with the expectation up to 100 Hz. If we believe that the coating/substrate photothermal crossover happens around 10 Hz, and we believe our measurement from 10 Hz to 100 Hz, then this seems to indicate that the thermo-optic cancellation has been somewhat successful.

Acutally it does look like it's a 50 Ω loading issue. I find that when 50 Ω inline terminators are added to OUT1 and OUT2, the measured OLTF is reduced by a factor of 1.6. This explains the discrepancy between the SR785 and HP4395 measurements. I've attached the corrected OLTF plots, along with plots of a vector fit, and the expected residual frequency noise [assuming a free-running NPRO noise of 10⁴ Hz/Hz^1/2 × (1 Hz / f)].

South UGF is at 200 kHz with almost no phase margin. We need to fix this.

Tara and I took an SR785 measurement of the north photothermal transfer function.

Clearly there's something wrong with the measurement above 1 kHz.

With the cavities locked, Tara and I took OLTFs of the PDH loops.

Below 100 kHz, we used the SR785 with a 70.7 mVpk excitation. Above 30 kHz, we used the HP4395A with a 22.4 mVrms excitation (these are the "HF" traces on the attached plot).

Before taking these TFs, we turned the loop gains up as high as possible without making the loops saturate.

• For north, the gains were 900 common and 900 fast, and the incident power was 1.26(5) mW.
• For south, the gains were 632 common and 770 fast, and the incident power was 1.05(2) mW.

We injected the excitation on common EXC. We then measured the TF which takes common OUT2 to common OUT1. This is almost the OLTF of the loop, except for an AD829 between OUT2 and OUT1 which has a gain of −4 V/V.

Currently I'm not sure how to explain the magnitude discrepancy between the SR785 and HP4395 measurements. Both OUT1 and OUT2 have a 50 Ω output impedance, so I would expect the impedance difference between the SR785 and HP4395 would cancel out in this measurement.

The first attachment shows the photothermal TFs which take absorbed power (in watts) to the mirror displacement (in meters) as sensed by our 215-µm beam. Since last night, I've fixed the coating TE part and committed the updated ipynb to the SVN.

The second attachment shows the noise budget, with the photothermal shot noise contribution.

Beat frequency drifted to 61 MHz over the course of a few hours. We need to wait for the cavity temperatures to settle.

I improved the mode-matching a little bit on the south cavity; it's about 50% (the theoretical max is 71%). The south lenses are now on translation stages.

I've attached a beat spectrum. Nothing is floated, RAM is not optimized, etc.; this is just a rough indicator of where things stand.

Here is what I think should happen next, in rough order of importance:

1. Float chamber
2. Measure RIN
3. Measure photothermal TF (I also need to recheck my photothermal code — I don't believe the coating TE part)
4. Put photothermal noise on noise budget
5. Reduce RAM.
6. Measure residual frequency noise.
7. Measure PLL noise. Use ATF DAQ and make spectral histogram.
8. Measure seismic noise (with Guralp or T240), with table floated and unfloated. Use ATF DAQ and make spectral histogram.

Tara added some more juice to the north cavity heater last night. Now we can lock both cavities to TEM₀₀ and get a beat within the bandwidth of the 1811.

• North laser slow: 5.020 V
• South laser slow: 0.722 V
• Beat frequency: 49.3 MHz

With this setup, I find that a sub-100-MHz beat occurs for north slow at 5.015 V and south slow at 0.725 V. This south slow voltage corresponds to a south cavity TEM₀₀ mode, but the nearest north slow voltage is at 5.298 V.

On Koji's suggestion, I set up a second 1811 to monitor the beat on the input side of the cavities, so that we can see what the lasers are doing independent of the cavity resonances. For each path, I am using the s-polarized light that is rejected from a PBS, so that we don't need to add extra optics to the beam paths.

For example, for south slow at 1.206 V and north slow at 5.565 V, I get a 69 MHz beat (with both cavities unlocked).

We should use this in conjunction with the cavity locking optics to figure out what the correct axial cavity modes are, and whether the cavities need any temperature adjustment.

Searched around over various axial modes in order to find a beat.

I fiddled a bit with the output QWPs in order to get the polarizations to match. Because of the birefringent coatings, light transmitted through the cavity is not circular, and the polarization state will depend on which of the two modes we lock to. In case, the original QWP angles were 202° for north and 19° for south.

Same data and same isolation model as for the silica/tantala noise budget. Since we have new table legs, we should retake this data (and make a spectral histogram).

The resonance frequencies of the stack are given as 10 Hz and 35 Hz in the noise budget. Are these for the old stack? I recall that with the new stack we measured resonances at 3, 7, and 10 Hz.

Also I want to double check the sequence of interpolation steps we've used on the silica/tantala noise budget. There are some seismic peaks and silica/tantala beat peaks that almost (but don't quite) match up in frequency, and I wonder whether this is an artifact of the interpolation.

Tara has found south transmission on camera. I steered the transmitted beams onto the beat PD and then made the k-vectors as parallel as I could as seen on an IR card.

The DC voltage on the PD is okay (ca. 50 mV from each beam), but I cannot see a beat note on the AC path using the HP4395. Tara will give a temperature kick which hopefully will bring the beat note within the range of the 1811.

I predict (via alm) that the spot size on the diode (z = 991 mm) is 79 µm in the current configuration.

Beat breadboard is slid back into place. North transmission appears on north camera. Still need to do south transmission.

Ignoring for the time being the issue of offsets in the PDH error signal, here's my prediction for the new PDH shot noise level, assuming a visibility of 0.92 × 0.7 = 0.64 and an incident power of 2 mW.

So our beat will be slightly worse around 1 kHz, but we aren't completely hosed by the shot noise. I'd think the true solution here is to find (or buy) two large-aperture Faraday isolators to replace the PBS+QWP setup (according to alm, the spot size in this region is about 1.1 mm). E.g., we might consider a large-aperture ThorLabs isolator.

 Here's what I expect to happen given

• perfect mode-matching,
• critical coupling with 150 ppm transmissivity for each mirror,
• p/s mode splitting of 2.0 MHz, and
• perfect demod phase.

It seems to match up qualitatively with the measurement. In particular, it does not appear possible to exceed 70% visibility for each mode.

I moved both lens mounts back by 1″, then adjusted the Vernier knobs and periscope mirrors to try to maximize the visibility as seen on north REFL DC.

The best I am able to do so far is a visibility of v = 1 − 0.57(1) V / 1.74(1) V = 0.672(6).

Current configuration:

• Target waist: 180 µm, z = 0 mm
• Lens 1: 140 mm focal length, z = −711 mm (24″ from center of vacuum chamber + 4″ through periscope)
• Lens 2: 84 mm focal length, z = −991 mm (11″ further behind lens 1)
• Seed waist = ??

Since we know we were mode-matched fairly well into the 180 µm waist of the silica/tantala cavity (>93% visibility), I asked alm to propagate this waist backward through the lenses in order to find a seed waist. It reports a waist of 161 µm at z = −1373 mm.

I asked alm for a new configuration using the same two lenses. The best configuration (mode overlap = 1) is as follows:

• Seed waist: 161 µm at z = −1373 mm
• Lens 1: 140 mm focal length, z = −743 mm
• Lens 2: 84 mm focal length, z = −1023 mm
• Target waist: 215 µm, z = 0 mm

So we should move lens 1 back by 32 mm (=1.3″), and move lens 2 back by the same amount.

North PZT sweep: 10 Vpp triangle wave, 3 Hz

North slow control voltage: 3.6805 V

Actuation on north broadband EOM removed

Phase tuning needed, mode-matching needed

Find TNC-SMA converters

I've implemented the TO calculation following Evans et al. (2008), along with the so-called Yamamoto correction for the CTE.

These changes are on the SVN.

To do:

• Finish implementing true TO calculation
• Add photothermal (requires RIN data)
• Add seismic (requires seismic data, seismic stack TF data)

We put on the CF gasket and closed the transmission side of the chamber. Now we are pumping down.

Tara did some work last night to ensure that the window reflections on the input side of the chamber are not overlapping with the cavity reflections. The south window reflection appears to be clipping on the bottom periscope mirror, but we can fix this later.

Next steps:

• Mode matching (including adjustment of the input lenses)
• Locking
• Realignment of transmission optics
• Re-establishing beat

I swept the south NPRO PZT with a 2 Vpp, 5 Hz triangle wave and watched the transmission of the south cavity using a PDA100A. I saved three such transmission sweeps from the oscilloscope, and then performed Lorentzian fits on each of them in order to get the cavity pole.

From the Lorentzian fits along with the 4.4(2) MHz/V calibration found earlier [and FSR = 4070(30) MHz], I find the following:

• Lower resonance: cavity pole of 135(3) kHz, corresponding to a finesse of 15100(340). This gives the total round-trip loss as 417(10) ppm.
• Upper resonance: cavity pole of 139(9) kHz, corresponding to a finesse of 14600(1000). This gives the total round-trip loss as 429(28) ppm.

I temporarily removed the QWP immediately before the periscope. Then I added a HWP directly in front of the vacuum chamber window.

While sweeping the laser across the south TEM₀₀ resonances, I monitored the peak voltage of each resonance.

For this particular HWP mount, rotating the mount to 23(1) degrees produces s polarization, in the sense that placing this HWP between two PBSs causes the second PBS to reflect 100% of the beam.

I used a function generator to drive the south NPRO PZT with a triangle wave. Then with the 14.75 MHz sidebands on, I used a PDA100A to watch the south cavity transmission.

Looking by eye at the carrier and sideband transmission peaks, I find an actuation coefficient of 4.4(2) MHz/V, which is higher than what Tara measured in 2010 (maybe the coefficient depends on which axial mode the NPRO is operating on?)

From the attached plot, we can also see that the mode splitting for the south cavity is 2.0(4) MHz.

We redid the mode-matching into south, and judging from CCD images it appears to be free of gross scattering effects.

In the process of moving the seismic stack around, we found that the two rubber noodles on the transmission side had fallen over (so they were being compressed transversely instead of longitudinally). We stood them upright again, but one of them broke, so we had to swap it with a spare. (We tried for a while to make a new one by coring out a cylinder, but they seem to be very brittle. Tara suspects that they're old and broken down.)

Next step is to adjust the stack as necessary to avoid reflections from the windows.

At some point I would like to do the following:

• Birefringence measurement: temporarily swap QWP before periscope with HWP, record swept transmission as a function of HWP angle
• Redo NPRO PZT calibration: record swept transmission with 14.75 MHz sidebands on, and thereby infer voltage-to-frequency coefficient

Redid optical contacting on south (for a second time) to try to get rid of scattering defects.

Spacer 95: left of ATF logo is 143, right is 137. 143 is on transmission side of chamber.

Just so we have a concise table that we can refer to:

Executive summary

1. We replaced the northeast air spring on the vacuum chamber, because it was leaky.
2. We opened the transmission side of the vacuum chamber, removed the silica/tantala cavities, and inserted the AlGaAs cavities. The configuration is as follows:
   • SN 00095: south. Logo readable when standing on north side of table.
   • SN 00096: north. Logo readable when standing on north side of table.
3. We scanned the modes of the north cavity and did some rough mode-matching to TEM₀₀. All modes (including TEM₀₀) appear to be doubled. Is this birefringence?
4. We scanned the modes of the south cavity. We we able to match into TEM₍₁₀₎₀, then TEM₉₀, TEM₈₀, etc., with relative ease (albeit with the same doubling as observed in the north cavity). However, as we got closer to TEM₀₀, we noticed the presence of two bright scattering centers near the mode axis. These scattering centers appear to be hosing the buildup of the TEM₀₀ mode in the south cavity.
5. Tara thinks we cannot proceed with the south cavity as is. We'll have to take off and reclean at least one of the mirrors.

Details

At various times, we put the transmission of the north cavity on a PDA100A and monitored the voltage on a scope while sweeping the laser PZT. For the two TEM₀₀ modes of the north cavity, the observed splitting was 11.5 ms when the PZT was driven with a 4 Vpp, 5 Hz triangle wave. Tara has previously measured the south laser PZT actuation coefficient as 3.1 MHz/V (ctn:182). This gives the frequency of the splitting as 1.4 MHz. Since the expected FSR of these cavities is 4070 MHz, this corresponds to a cavity length difference of 180 pm.

The FWHMs of the two peaks (again as seen on the scope) were 1.16 ms and 1.30 ms. With the FSR given above, this gives the finesses as 29 000 and 25 000. That's higher than what should be possible given the measured transmissivities of the mirrors [we expect a finesse 2π/(300 ppm) = 21 000], but this was a quick and dirty measurement that relies on a PZT calibration that's a few years old.

OD: 1.63"

Depth: ca. 0.9"

Minimum clearance between cap and mount: ca. 0.5"

 New setup for fiber phase noise cancellation with one AOM

 

 

I'm building this instead:

Tara has successfully formed the AlGaAs cavities. The configurations are as follows:

• Spacer 95: to the left of the ATF logo is mirror 114, and to the right of the ATF logo is mirror 143.
• Spacer 96: to the left of the ATF logo is mirror 141, and to the right of the ATF logo is mirror 132.

Mirror 137 has not been contacted.

I used the ThorLabs power meter to get the transmission coefficients for the five AlGaAs mirrors.

For each measurement, I wrote down the incident power (20 mW nominal), the transmitted power (≈3.5 µW, depending on the mirror and background light level), and the transmitted power with the beam blocked (to get the dark power).

In other news, Tara bonded mirror #114 to spacer #95. The contacting seems to be tough going because of some recalcitrant smudges on the substrate surfaces.

 Basically the same story with 132.

Incident power: 20.0(1) mW

Exposure times used: 25 ms, 50 ms, 200 ms, 500 ms, 1000 ms

Transmitted power: 3.34(2) µW. This gives a transmission of 167(1) ppm for this mirror.

TIS from 16° to 73° is 18(1) ppm.

Data and code are on the SVN at CTNLab/measurements/2014_08_05.

[Tara, Evan]

Tara also took a BRDF measurement of #114 after cleaning it.

After cleaning, TIS from 14° to 71° is 2.7(5) ppm. Much improved.

Data and code are on the SVN at CTNlab/measurements/2014_07_31.

I have started a python implementation of the AlGaAs noise budget. All parameters, functions, etc. are defined in a single notebook, and this same notebook generates the plot. The python uncertainties package facilitates estimation of uncertainties in material parameters, optical parameters, etc.

Currently, the coating thermo-optic trace is not an actual calculation; it is just a flat line culled from figure 5.9 of Tara's thesis.

The PDH shot noise trace is shown assuming an incident power of 1 mW on each cavity, a PDH modulation index of 0.2 rad, and a cavity visibility of 0.92.

[Tara, Evan]

Tara took a BRDF measurement yesterday of AlGaAs mirror #114.

In this measurement, the return beam is dumped using black anodized foil instead of a razor blade dump. This seems to make the peak at 20° disappear, and now we get a more or less monotonic falloff in scattered power.

TIS from 14° to 71° is 39(6) ppm.

Data and code are on the SVN at CTNlab/measurements/2014_07_30.

[Tara, Evan]

Yesterday we took a scatter measurement of AlGaAs mirror #143. Instead of one bright scattering center, we saw 3.

The procedure is identical to the procedure used for mirror #137, although the exposure settings and choice of angles are a bit different (see the attached plot). Also, we used 20 mW of incident power instead of 10 mW.

Total integrated scatter from 14° to 82° is 80(8) ppm.

Data, images, and plot-generating code are on the SVN at CTNlab/measurements/2014_07_28.

[Tara, Evan]

We replaced the Lambertian diffuser with AlGaAs mirror 137B1. We intentionally induced a nonzero AOI of the incident beam, so that the reflected beam could be dumped cleanly. At a distance of 25.7(3) cm back from the mirror, the reflected and incident beams were separated by 1.3(1) cm, giving an AOI of 1.45(11)°.

1. We measured the incident laser power as 9.94(2) mW.
2. We set the exposure time of the camera to 250 ms.
3. We swung the boom to 13°, 16°, 19°, 22°, 25°, 28°, 31°, and 34°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
4. We measured the incident laser power as 9.95(2) mW.
5. Because the scattered power had fallen off sharply by 30°, we turned up the exposure time to 1.00 s.
6. We swung the boom to 31°, 34°, 37°, 40°, and 43°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
7. We measured the incident laser power as 10.08(2) mW.
8. We swung the boom to 46°, 49°, 52°, 55°, 58°, 61°, 64°, 67°, and 70°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
9. We measured the incident laser power as 10.06(2) mW.

For all of these measurements, the two ND filters (OD1.5+OD3.0) were not attached; just the RG1000. With the ThorLabs power meter, we measured the combined transmissivity of these two ND filters to be 1865(14) ppm.

The first attachment shows an example CCD image. The second attachment shows the raw counts, the inferred scattered power, and the BRDF.

Yes.

We added an OD1.5, an OD3.0, and an RG1000 in front of the camera lens (note that these ODs are probably specked for something other than 1064 nm). Then we increased the exposure time to 20 ms. For the AlGaAs measurement, we may need to increase it even further in order to get good statistics.

Then we fixed the boom at 25° and varied the power using the upstream HWP + PBS combo.

For each power level, we took a measurement with the power meter, then 10 CCD images, then another measurement with the power meter. From this we are able to extract nominal values and uncertanties for the power level and the counts. The result is attached. The calibration has about a 4% uncertainty.

Note (Tara): The power measurement includes the solid angle of 3.375 x10^-3 str ( detector diameter = 0.4 inch, distance from the sample = 15.5 cm)

 I put the boom at 15° and took four sets of five exposures. Then I ran my image processing code again to get an uncertainty in the count values. I get the following:

• Beam incident, room lights on: 546(31) × 10³ cts
• Beam blocked, room lights on: 417(9) × 10³ cts
• Beam incident, room lights off: 547(34) × 10³ cts
• Beam blocked, room lights off: 410(2) × 10³ cts

For each set of five, the nominal value is the mean and the uncertainty is the standard deviation of the total counts within the 200×200 pixel region around the beam. Again the exposure time is 100 µs and there was an RG1000 filter in front of the camera lens.

Using a fractional uncertainty of 31/546 = 0.057 for yesterday's background-subtracted total counts, I reran the calibration code. The new plot is attached. The calibration slope (and its uncertainty) doesn't change much, but we can see that the uncertainties in the total counts are quite large. Do we need to improve this before moving on to the AlGaAs BRDF measurement?

[Tara, Evan, Josh, et al.]

Today we did some characterization and calibration of the scattered light apparatus.

To start with, we examined an AlGaAs mirror (s/n 173). We found that there was a great deal of diffuse light transmitted through the mirror (as seen in fig. 3 of ctn:1456). On Josh's suggestion, we put down an iris about 5" in front of the mirror. We stopped it down just enough so that both the incident and reflected beams could clear the aperture. This made the diffuse stuff disappear.

Next, we swapped out the AlGaAs mirror for a Lambertian diffuser (the same one used in Magaña-Sandoval et al.). Tara affixed the power meter to the camera boom in such a way that it could be raised or lowered in front of the camera.

We adjusted the incident power on the diffuser to be 3.00(1) mW. We then swung the boom in 5° increments from 10° to 70° from normal incidence. At each angle, we took the following:

1. Power incident on power meter with beam blocked
2. Power incident on power meter with beam unblocked
3. CCD image with beam blocked
4. CCD image with beam unblocked.

The beam was blocked using a dump located immediately upstream of the steering mirror.

The first attachment is the BRDF of the diffuser based on the power data. The second is the inferred calibration between total CCD counts (with background counts subtracted) and scattered power. The correlation is not great. We may want to retake this data with the room lights off, and also we may want to take multiple exposures per angle setting (that way we can make some estimate of the uncertainty in the CCD counts). The third attachment shows the analyzed CCD region for the 10° images; I've restricted the analysis to a 200×200 pixel region around the diffuser.

The exposure time was 100 µs, and there was a 1 µm long-pass filter (RG1000) affixed to the camera lens.

Data, CCD images, and plot-generating code are on the SVN at CTNLab/measurements/2014_07_24.

VCO driver noise measurement

To measure the noise of the PSL VCO driver, we used the same PLL set-up from previous noise measurements.  The PLL consisted of the following: IFR/Marconi 2023A, the SR560, Mini-Circuits Frequency Mixer ZX05-1MHW-S+-0.5-600MHz, Mini-Circuits 15542 BLP-5+ Low Pass Filter 50 Ohm DC-5MHz, and the Stanford Research Systems Model SR560- Low Noise Pre-amplifier with a gain of 200 V/V.  We connected another VCO to the RF port of the mixer.   The Marconi had a carrier frequency of 80 MHz, an RF level of 13 dBm and FM dev set to 1 KHz Ext. DC.  

We connected the VCO to a power supply by hooking up a 9-pin dsub breakout box into the VME interface.  The VCO driver needs 24V from the power supply.  From opening up the box, we found that there are three test points in the VME interface: TP1, TP2 and TP3.  TP1 corresponds to -24V, TP2 corresponds to +24V and TP3 is ground.  Additionally, we needed to figure out what pins to hook up the positive, negative and ground cables onto the breakout box.  +24 V corresponds to pins 9 and 4, -24 V corresponds to pin 5 and ground corresponds to pins 8 and 3.  There are also two switches that need to be connected to the ground in order for the driver to function properly.  The test switch, which corresponds to pin 1 and the wide switch, which corresponds to pin 6 are both connected to pin 3(ground).  We used the TENMA Laboratory DC Power Supply 72-2080 and it was set to 24 V and .5 A.  

After locking the frequencies, we measured the transfer function and ASD with an FFT analyzer (Agilent 35670A Dynamic Signal Analyzer).  The following data was obtained:

Marconi Noise Measurement

 To verify whether or not the noise was from the AOM driver, we measured the noise in the Marconi.   We set up a PLL to do this measurement.  We used the IFR/Marconi 2023A, the SR560, Mini-Circuits Frequency Mixer ZX05-1MHW-S+-0.5-600MHz, Mini-Circuits 15542 BLP-5+ Low Pass Filter 50 Ohm DC-5MHz, and the Stanford Research Systems Model SR560- Low Noise Pre-amplifier with a gain of 500 V/V.  We  connected another Marconi to the RF port of the mixer.   Marconi 1 had a carrier frequency of 80 MHz, an RF level of 13 dBm and FM dev set to 1 KHz Ext. DC.  The second Marconi that we used had a carrier frequency of 80 MHz, an RF level of 2 dBm to match that of the AOM driver and FM dev disabled to prevent noise.  

 Set-up:

Measurement: After locking the frequencies, we looked at the measured the PSD on an FFT analyzer (Agilent 35670A Dynamic Signal Analyzer) and obtained a measurement of the ASD.

It appears that the noise is coming from the AOM driver.  

We looked at the beat signal of the reflected beam and the beam that is double-passed through the AOM on the oscilloscope.  The first beam has a power of 813 micro-watts and beam that is double-passed through the AOM has a power of 10 micro-watts.  The beat signal fluctuation was between -24 dBm and -13 dBm.  A PLL was used to lock the frequencies.  We used the IFR/Marconi 2023A and the SR560.  The Marconi had a carrier frequency of 160 MHz, an RF level of 13.0 dBm, and FM dev of 10KHz.  The gain on the SR 560 was 200 V/V.  Once the frequencies were locked, we measured the PSD on a spectrum analyzer.  

After obtaining this data, we measured the phase noise of the AOM driver (Crystal Technologies 1080AF-AIF0-2.0 S/N 10351) since it was suspected to be a large source of noise.  We set up a PLL to do this measurement.  We used the IFR/Marconi 2023A, the SR560, Mini-Circuits Frequency Mixer ZX05-1MHW-S+-0.5-600MHz, Mini-Circuits 15542 BLP-5+ Low Pass Filter 50 Ohm DC-5MHz, and the Stanford Research Systems Model SR560- Low Noise Pre-amplifier with a gain of 500 V/V.  The AOM driver was connected to the Stanford Research Systems-Model DS345 30 MHz Synthesized Function Generator with a frequency of 6.00 Hz and Amplitude of .7 Volts and the TENMA Laboratory DC Power Supply 72-2080 with a current of .5 Amps and voltage of 28 Volts.  The AOM driver output had a 10 dB heatsink attenuator followed by a Mini-Circuits 50 ohm-31030 15542 VAT-9+ 9dB attentuator  and another Mini-Circuits 50 ohm-30727 15542 VAT-10+ 10 dB attenuator, which was connected to the RF port of the mixer.  

The settings on the Marconi for locked frequencies: Carrier Frequency: 79.992423 Hz, RF Level: 13 dBm, FM dev: 1.00 KHz, Ext DC

After locking the frequencies, we looked at the measured the PSD on an FFT analyzer (Agilent 35670A Dynamic Signal Analyzer) and obtained a measurement of the PSD.  After plotting the results, we found that the driver noise data almost completely lines up with the measurement of the noise in the set-up.  This is most like the driver noise, but it is possible that there is noise from the Marconi or SR 560, so a similar set-up will be used to analyze noise in the Marconi to determine whether or not the noise is from the AOM driver.  

The CTE of fused quartz is something like 0.5×10⁻⁶ K⁻¹, and the CTE of steel is more like 15×10⁻⁶ K⁻¹. So I suspect there's not much point in heating the glass spacer if I'm going to leave the steel end cap open to air.

A possible solution is to put a heater on the end cap, but I worry that the differential expansion of steel vs. glass will cause the end cap to pop off the spacer (it looks like it's only held on by epoxy).

A better solution is to improve the insulation on the back end of the PMC. I'll do that next.

Installation of optics for fiber phase noise measurement

After light passes through the AOM, it is reflected back through the AOM and into the fiber.  We installed a 50/50 beamsplitter, quarter wave plate, mirror, lens and photodiode to do the beat measurement.  It is required that the beam spot size is 1/3 the diameter of the photodetector.  We installed a lens at the appropriate distance to obtain a waist that is roughly 50 microns.  We hooked up the photodiode to an oscilloscope and found that the voltage fluctuates between 100-500 mV.  We are not sure why the voltage is fluctuating, but we will continue to investigate the cause.  

I took some hard yellow foam, made it into a U-shape, and wrapped it with a combination of aluminum and duct tape.

This insulation fits snugly over the PMC and its copper shield. In retrospect, the foam is probably a little too thick. I had to temporarily move the beam dump at the input of the Faraday isolator.

Putting 20 V across the 105 Ω heater produces a change of 5 V on the PMC PZT (when locked). So we need better insulation or more heating.

I took a 105 Ω Kapton heater, stuck it to a 15 cm x 25 cm patch of copper foil (thanks Steve), and wrapped the foil around the PMC. This required undoing the top braces on the mount. Currently, the PMC is just sitting on its kinematic contacts. Virtually no tune-up of the pointing was required.

There is currently no insulation, so (perhaps unsurprisingly) the heater doesn't have much of an effect on the PMC's PZT voltage.

This is now built, with a few modifications:

• The power supply bypass capacitors are 1 µF tantalum caps.
• The RC low-pass is a  4.8 kΩ resistor and a 3.3 µF capacitor, giving a 10 Hz pole.
• The base of the heating resistor is tied to the negative rail instead of ground, in order to give a greater actuation range.

Both the in-amp stage and the mosfet stage seem to work fine using a 2 kΩ resistor in place of the heater (the actual heater is more like 120 Ω, but the axial resistors in the e-shop are only rated to 0.25 W).

Instead of using a power supply as a current buffer, we can use a mosfet like so:

This is based loosely on the aLIGO PMC heater (D1001618-v1, p. 10).

If we instead want to run off of a unipolar supply, we can replace the AD620 with a noninverting op-amp. We'll lose the common-mode rejection, though.

A list of small tasks and some data points:

As of yesterday, the tank is floated. This required minimal realignment of the input pointing into the cavities.

Adjusted powers so that there is 1.04 mW incident on north and 0.96 mW incident on south.

For the south PDH loop, the highest gain we can get seems to be 590 common and 710 fast. Not great. The south error signal has terrible 270 kHz oscillation as well (~100 mVpp).

For the north PDH loop, the highest gain we can get is 807 common and 908 fast. Not perfect, but better than south. No 270 kHz oscillation here.

South path adjustments

RAM on the south PD was terrible: 259(28) mVpp at the PDH frequency; the uncertainty is dominated by slow breathing of the RAM amplitude. I need the PD rf transimpedance to convert this voltage to an actual RAM.

I tried adjusting the alignment of the south EOM, with little effect. The big effect came from slightly rotating the λ/2 plate immediately preceding the EOM: rotating by less than half a degree takes the RAM from >200 mVpp through zero and back to 200 mVpp again. The λ/2 plate was in one of those no-frills rotational mounts where sub-degree precision can be achieved only by nudging, so I instead put the waveplate into a precision mount with a worm drive and a knob. I then tuned the rotation to null the RAM on a scope. There is still some breathing of the amplitude, so that at times the RAM is 40 mVpp. Not good, but better than before.

I measured the south modulation index both before and after this change. I swept the south laser frequency and watched the transmission on the ISS PD. Before, the carrier and single-sideband transmission peaks were 1.91(1) V and 39.6(1.2) mV, respectively, and after they were 1.72(2) V and 38.2(6) mV, respectively. This means the modulation index actually increased from 0.288(4) to 0.298(3) (using the Γ²/4 approximation).

Beat measurement

Installation of optics for fiber phase noise measurement

Following the fiber output, which has a waist of ~50 microns, we calculated the proper lens to use as well as the proper distance to place the objects so that we would have a waist of approximately 150 microns going into the AOM.  Roughly 3.5 inches from the fiber output, we placed a lens: KBX052 with a focal length of 50.2 mm, followed by an AOM: 3080-194, as well as the AOM driver(1080AF-AIF0-2.0) 3 inches away from the AOM to the right. After the light passes through the AOM, we placed another lens: PLCX-24.5-36.1-C-1064, which gives another waist at the mirror placed at the end of this setup.  After the light passes through this lens, we placed a quarter wave plate: Z-17.5-A-.25-B-1064, which is followed by a mirror: PR1-1064-98-1037.

South laser slow at 1.234 V, north laser slow at 5.558 V, beat is 120(1) MHz at +5.5(2) dBm. South and north alignment has not yet been tuned up.

SR785 appears to have broken screen.

I wanted enough power to accommodate both the fiber noise measurement and the south cavity locking. I moved the HWP after the PMC from 338 degrees to 79.5 degrees. Then I moved the HWP after the south EOAM from 249.5 degrees to 280.0 degrees. This gives 1.5 mW transmitted through the PBS toward the south refcav, and a few milliwatts reflecting off the PBS and going toward the fiber.

It looks like we still have good mode-maching into the south cavity; transmission is easily seen on the camera.

Supplies

• Foam (already have)
• Aluminum tape
• Kapton heater (already have)
• High-current buffer (maybe can use linear power supply with aux inputs on back)

Computing

• Set up or co-opt channel to output to heater
• Modify PMC MEDM screen to accommodate heater

Installation of optics for fiber phase noise measurement

To couple CTN light into the fiber, we decided to pick off using the reflected port of the PBS directly after the south EOAM. In order to mode-match into the fiber, we installed two lenses (and a steering mirror) between the PBS and the fiber.

Mode matching details are as follows: the round trip length of the PMC is 42 cm and the radius of curvature of the concave mirror is 1 m; this gives a waist of 370 microns.  From there, we calculated the proper lenses needed: PLCX-25.4-64.4-UV-1064 (lens 1, focal length 124 mm) and a PLCX-25.4-128.8-UV-1064 (lens 2, focal length 250 mm). Between the two lenses is a mirror, Y1-1037-45-S, which is tilted at a ~45 degree angle to guide the light from lens 1 to lens 2.  Lens 1 and Lens 2 are roughly 2 inches away from each other. There is a fiber coupler placed 4 inches away from the second lens.

Currently, is about 1.4 mW going into the fiber, and about 150 uW coming out.

Edit: We did some more aligning and found that there is 2.2 mW going into the fiber and .7 mW coming out.

PMC alignment tune up, FI power adjustment

Coupling through the PMC was very bad today; we saw 12 mW incident and ~1 mW transmitted. I (Evan) touched the three steering mirrors before the PMC and brought the transmission up to 5 mW.

In order to have more power incident on the fiber, we changed the angle of the HWP immediately after the PMC from 306.5 degrees to 338.0 degrees.

I spent some more time talking to Larry (who is a national treasure) about how to properly estimate the statistical uncertainty on the fit to φ_c. Among other things, he suggested dispensing with the nonlinear fit to S versus f and instead performing a linear fit to log S versus log f.

I implemented this, and I got a fit of 4.43(25)×10⁻⁴ for φ_c, and PSD slope of −1.004(11). Here I've also settled on 144(42) GPa for the Young modulus of tantala.

Then putting this value for φ_c into the Bayesian notebook, I find a MAP of 1.1×10⁻⁴ for the silica loss angle, and 7.8×10⁻⁴ for the tantala loss angle. The percentile values of the PDFs don't change much.

I've incorporated these into the paper, which is now on the DCC at P1400072v3. I've gone through the noise budget code and the Bayesian notebook in order to check that all numerical values are consistent, and that they are reported correctly in the paper.

 Using this new value of φ_||, I reran the Bayesian analysis notebook and also (on Larry's suggestion) generated a plot of the marginalized PDFs with shading to indicate the 16th, 50th, and 84th percentiles. The maximum a posteriori estimates of the silica and tantala loss angles are 0.6×10⁻⁴ and 8.0×10⁻⁴, respectively. I've incorporated these new plots into the paper.

I have finished implementing the comments from the LSC P&P review.

On Steve Penn's suggestion, I went back to Harry et al. (2002) and Penn et al. (2003) and attempted to rederive the parallel loss angle φ_||, along with the experimental uncertainties.

Harry's original number (using a coating thickness that is 5 times too high) was φ_||,wrong = (1.0±0.3)×10⁻⁴. I found φ_||,wrong = (0.98±0.14)×10⁻⁴.

Penn's corrected number is φ_|| = 5.2×10⁻⁴, with no error bar. I found φ_|| = (5.17±0.75)×10⁻⁴.

You can see my working in the attached pdf and ipynb.

I used the 633 nm fiber illuminator and the ThorLabs power meter (set to 633 nm) to test the 60 m polarization-maintaining fiber that we have.

Power right out of the illuminator was 1.25(2) mW, and the power out of the fiber was 0.45(1) mW. Since this fiber is only specked to work above 980 nm, I'm not sure how to interpret this number.

I'd like to compare to the 35 m PX980-XP fiber we have strung from CTN to Crackle.

I performed the same test with the 1060XP fiber (50 m, not polarization maintaining). I got 0.12(1) mW transmission.

Rather than using individual loss angles from Penn as the prior pdf, I've instead reanalyzed the data from Harry et al. (2002).

The ipynb for this is on the SVN in the noise budget folder.

I reran the notebook with the following modifications:

1. I changed the prior on φ₂ to 4.4(2) × 10⁻⁴, which is the correct value from Penn. I'm not sure why I had the uncertainty at 4.4(7) × 10⁻⁴ before.
2. I changed the uncertainty on the Young modulus of tantala to 30% (up from 10%), since it sounds like we don't really believe the literature values for the Young modulus all that much.

The posterior estimate for the loss angles is now φ₁ = 1.4(3) × 10⁻⁴ and φ₂ = 4.9(2) × 10⁻⁴, which is much more in line with previously measured values. See the first set of plots.

Comparison with Penn et al.

Since we're using a prior pdf generated from Penn et al., it seems wise to check out what happens if we use a likelihood function that's generated from the same formalism that Penn et al. use. Their eq. 6 gives the relation between φ1, φ2, and φc:

(N1 d1 E1 + N2 d2 E2) φc = N1 d1 E1 φ1 + N2 d2 E2 φ2

where N1 is the number of silica layers, d1 is the thickness of each silica layer, E1 is the Young modulus of silica, and likewise for the tantala parameters. The results are attached in the second set of plots. The posterior estimate is φ₁ = 0.7(3) × 10⁻⁴ and φ₂ = 4.9(2) × 10⁻⁴, in pretty good agreement with what we get with the likelihood from Hong.

Discussion

What I've done above (decreasing the uncertainty on the prior and increasing the uncertainty in the Young modulus) amounts to strengthening the effect prior and weakening the effect of the likelihood. So it's not surprising that the posterior is now closer to the prior.

This does not resolve the issue that both the likelihood functions have slopes that are (we think) too steep. If, for example, we assumed an informative prior for φ₁ [1.0(2) × 10⁻⁴, say] but left the prior for φ₂ flat, our posterior would give a value of φ2 that is very high (9 × 10⁻⁴ in this case).

[Edit, 2014–04–17: On Larry's suggestion, I tried marginalizing instead of just slicing through the MPE. The results are the same. —Evan]

I removed the 90% reflector from the north transmission path on the ISS breadboard and then installed the fiber launcher.

The ThorLabs power meter says 440 uW going into the fiber on the CTN side; the ThorLabs fiber power meter says 260 uW coming out on the ATF side.

Here's a naive attempt at a Bayesian estimate of the loss angles of silica (φ₁) and tantala (φ₂). The attached zip file contains the IPython notebook used to generate these plots.

To construct a joint prior pdf for φ₁ and φ₂, I used the estimates from Penn (2003), which are φ₁ = 0.5(3) × 10⁻⁴ and φ₂ = 4.4(7) × 10⁻⁴ and assumed the uncertainties were 1σ with Gaussian statistics.

For the likelihood I used the relationship between φ₁, φ₂, and Numata's φ_c. This is derived from the Hong paper, and is described in the pdf inside the zip attachment.

Next steps from here:

1. We need to check with someone in the data group or in Cahill to make sure this is the right way to do the analysis.
2. We need to think harder about constructing our prior pdf.
3. We need to think harder about our uncertainties (have I accidentally double-counted some of the uncertainties?)

This formula is only sensitive to the ratio YL/YH (which I've called E1/E2).

I took the parameters from Penn, chose two fiducial coating thicknesses (a λ/4 + λ/4 coating, and a 3λ/8 + λ/8 coating), and used this (along with Penn's reported values for E₁, E₂, φ₁, and φ₂) to compute two fiducial values for φ_c. Then I solved these two equations for φ₁ and φ₂, and allowed them to vary parametrically with the ratio E₁/E₂.

 I independently computed the Hong result using the same assumptions (bulk and shear loss angles are equal, and no light penetration). I find

where I have included uncertainties for the Penn and Crooks measurements.

Laser is locked to north cavity, with slow PID loop engaged.

Current north laser slow DC voltage: 6.55 V, with some slow upward drift

TTFSS settings: 634 fast, 888 common (very lucky!)

On Tara's suggestion, I've done a fit to a coating loss angle with a power-law frequency dependence. The results are highly dependent on the band chosen for the fit (see attached plot).

For comparison, for a fit to a frequency-independent loss angle, the dependence on the band is much less prominent. For 50 Hz to 200 Hz, I get 4.12(3) × 10⁻⁴, and for 50 Hz to 700 Hz, I get 4.21(3) × 10⁻⁴.

I've tried harmonizing the Hong result (eq 94) with the Nakagawa/Harry formula, but the phi_tantala that I extract is about 9e-4, which is twice as high as previously reported values. I've spent some time hunting for a missing factor of two, but cannot find one.

The above uncertainties are enough to estimate the statistical and systematic uncertainties on a fit to ϕ_c using the Nakagawa/Harry formula for a thin, lossy coating. By minimizing an appropriately weighted chi-squared function from 50 Hz to 500 Hz and then taking into account the above substrate and coating uncertainties, I find ϕ_c = (4.15 ± 0.03 stat ± 0.08 sys) × 10⁻⁴. More details will follow, and there may need to be some refinement (e.g., I still haven't dealt with the Welch overlap issue).

This has required adjusting the values of the Young modulus and Poisson ratio from their previous values (72.7 GPa and 0.167, respectively). I haven't checked these changes into the SVN.

In order to get the systematic uncertainty on ϕ_c, we need uncertainties in other parameters that enter the noise budget. Specifically:

• Spot size, w. Currently using (182.0 ± 0.4) µm. The nominal comes from eq. 47 in Kogelnik and Li. This uncertainty can be propagated forward uncertainties in the following:
  • Cavity length, L. The spacer drawing (CTNLab/drawings/mechanical_drawings/dual_refcav/cavity_spacer_1.45inx1.5in.PDF) gives the length as (1.45 ± 0.01) inches.
  • Mirror radius, R. Nominal is 0.5 m; no idea about the uncertainty. It is not given in the test document. Currently using (500 ± 3) mm; i.e., an 0.5% uncertainty. This is the uncertainty claimed in the CVI catalog.
• Coating thickness, d. Nominal is 4.5 µm; no idea about the uncertainty. Currently using (4.53 ± 0.07) µm from Tara's calculation (given in the reply to this elog post).
• Substrate elastic modulus, E_s. Using (73.1 ± 0.1) GPa as estimated from figure 29 in McSkimin 1953 (doi 10.1063/1.1721449), which is a (heavily cited) reference I found on the NIST ceramics database.
• Substrate Poisson ratio, σ_s. Using 0.170 ± 0.004 as estimated from figures 29 and 30 in McSkimin (for Young and shear moduli, respectively) and then propagating the error forward to the Poisson ratio.
• Cavity temperature. Should use 306(1) K.
• Measurement uncertainty. Given an estimated PSD S(f) that is obtained by averaging M FFTs, the uncertainty should be S(f)/M^1/2. Tara says to take M = 50. Need number of averages for each bin. Possibly need to adjust formula to account for Welch overlap.

I've added a χ² minimization routine to nb_short_fit.m which looks for the value of ϕ_c (as defined by the Nakagawa formula) which makes the noise budget best fit the observed beat spectrum. For the weights in the χ ² function, we need an estimate of the variance of the power in each bin. Ideally, we'd take multiple spectrum measurements and average them together. Since we only have a single measurement, for each bin I've taken the five bins on either side and computed the variance.

I performed the fit in the band from 26 Hz to 405 Hz because it looks like the total noise is dominated by coating Brownian noise in this region.

The first attachment shows χ² as a function of ϕ_c. The routine assumes χ² is parabolic in the neighborhood of the optimum value (which you can clearly see it is), and from this extracts the optimum value as well as the statistical uncertainty (which is given by the curvature of the parabola). From this the routine gives ϕ_c as 4.18(3) × 10⁻⁴, with a reduced of χ² of 1.23.

From here, the next steps are

• Settle on values for the lower and upper frequency limits for the fit. If the upper frequency is increased from 405 to 705 Hz, for example, the routine gives ϕ_c as 4.26(3) × 10⁻⁴, with a reduced of χ² of 1.21. I think this is due (in part) to the fact that the noise budget is less than the measured noise near and above 1 kHz.
• Perform the fit using the Harry formula, which includes the contributions from both loss angles rather than a single averaged value.
• Compute the uncertainty arising from uncertainties in the other parameters. Tara has collected uncertainties for the material parameters in PSL:895, but we also need uncertainties in the spot size and the temperature.

I've forked the noise budget code so that we can create a version that performs a fit to the coating loss angle. It is at CTNLab/simulations/noise_budget/iscmodeling/coating/iRefCav/nb_short_fit/nb_short_fit.m.

I've retooled the noise budget plot a bit. I've referred it to single-cavity length noise by multiplying the beat ASD by Lλ/(sqrt(2)c), where L = 3.7 cm. I've also combined some of the substrate noise, spacer noise, and technical noise traces so that there are not quite so many lines on a single plot. If we really want to display each trace individually, I think we should do so with a few separate plots (e.g., a thermal noise plot, a frequency/PLL noise plot, etc.). Fewer traces makes it easier for readers to make sense of the plot.

I'm going to start on writing the fitting code. For nonlinear least squares I'm used to using the Levenberg–Marquardt algorithm through scipy.optimize.curve_fit. I'll need to read up a bit on what's available in Matlab.

I've taken the total noise trace, interpolated it so that it uses the same frequency array as the measurement trace, and performed the quadrature subtraction of the two to get the residual. I've also converted the beat to single-cavity length noise by multiplying by Lλ/sqrt(2)c, with L = 3.7 cm.

I've done (what I think is) more or less the same HOM computation as Tara for L = 3.7 cm and R = 0.5 m. Equation 51 in Kogelnik and Li gives the frequency of a mode with axial number q and transverse numbers m and n:

f / f_fsr = q + 1 + (m + n + 1) arccos(1 − L / R) / π.

As a function of sideband frequency, I've plotted the detunings of the first 50 mode orders (and their sidebands) relative to the TEM00 carrier. Solid lines indicate carriers, and dashed lines indicate sidebands. The region from 32 to 35 MHz is right out, since the sidebands of mode orders 0 and 8 are very close.

I'm inclined to say that for R = 0.5 m alone, we should pick 26 MHz and 27 MHz, just because it's well out of the way of the forbidden 32 to 35 MHz region. As far as I know, the only other RF frequency to avoid is the PMC PDH frequency, which is 21.5 MHz.

Edit: I've done the above for L = 3.7 cm and R = 1 m, and the result is attached. If we want to accommodate R = 0.5 m and R = 1.0 m, it would be better to pick 36 and 37 MHz, or perhaps 23 and 24 MHz.

[Tara, Evan]

Yesterday, we did a few final bits of optimization and then re-measured the beat spetrum.

Specifically:

• Tara tweaked the north RFPD cable to symmetrize the north PDH error signal.
• For each path, we hooked the RF output of each RFPD directly into the HP4395A and minimized the RFAM at 14.75 MHz (the PDH frequency).
  • For south, the initial RFAM was −107 dBm, and by adjusting the HWP before the resonant EOM, Tara was able to get it down to −112 dBm. This resulted in no visible change to the error signal offset (10 mV, compared to 300 mV peak-to-peak).
  • For north, the initial RFAM was −105 dBm, and by adjusting the HWP before the broadband EOM + resonant EOM (there is no intervening waveplate), Tara was able to get it below the noise floor of the spectrum analyzer (i.e., < −125 dBm). This resulted in a change to the error signal offset from 28 mV to 19 mV (compared to 300 mV peak-to-peak).
• We measured the slopes of the error signals in order to get the calibration from voltage to frequency.
• We locked the cavities with the slow digital control engaged. The south TTFSS gain was 712 slow and 796 fast, and the north TTFSS gain was 900 common and 900 fast. The south TTFSS control signal still has strong (~ 2 V peak-to-peak) oscillations at hundreds of kilohertz.
• We measured the beat, the PDH error signals, and the RIN spectra. The modulation setting on the Marconi was 1 kHz, so the conversion factor is the usual 710 Hz/V.
• After measuring the beat, we swapped out the SHP–150 on the RF input of the mixer for an SHP–100. The beat is currently at 120 MHz, and with the SHP–150 we were throwing away something like 60% of our power. Attenuation from the SHP–100 appears negligible when viewed on a scope.

The beat spectrum is attached, along with the expected coating Brownian noise estimate. I will post the estimates of the PDH and RIN contributions later.

Tara and I spent some time looking at the TTFSS boards. The offset issues appear to be caused by bad choice of offset knob on the TTFSS interface boards. Previously, Tara and I had used the offset knob to null RFAM-induced offsets in the north PDH signal. The current thinking is that when Tara re-optimized the electro-optic elements on the north path, the RFAM-induced offset changed and was therefore no longer nulled.

We have now returned the offset knobs to their optimal values as follows: we set each TTFSS to use the TEST SMA input rather than the LO/PD + mixer input, we applied a 50 Ω terminator to this input, and we then watched TP4 (after the common VGA) on a scope while adjusting the offset knobs. The optimal knob positions are 526 for the south TTFSS and 506 for the north TTFSS. Varying the common gain causes the DC offset on TP4 to change only slightly (it stays within ±5 mV for both north and south). Varying the fast gain causes the DC offset on TP17 (after the fast VGA) to vary as well; on south, this also appears to stay within ±5 mV of zero, but on north it is as high as 20 mV when the common and fast gains are turned all the way up. However, since these VGAs are each +30 dB at maximum gain, this means that the offset referred to TTFSS OUT1 is more like 20 µV, which is negligible compared to an error signal that is something like 1 Vpp.

I've taken Tara's farsi.m and changed the values of finesse F and absorption α in order to fit the magnitude of the TF measurement in PSL:1368. I've chosen 7500 for the finesse and 5 ppm for the absorption, although for this calculation they are degenerate (entering into the TF as F/α).

Using this, I've taken the RIN measurements from Friday and used them to estimate the induced frequency fluctuation in the beat readout, assuming a transmitted power of 1 mW from each cavity.

In the case when the ISS is off, the estimated effect of RIN on the current beat is significant only below 10 Hz. When the ISS is on, the RIN is insignificant over the entire measurement range. This perhaps explains the observed reduction in the beat PSD below 10 Hz when the ISS is on.

Summary: No good so far. Engaging the ISS seems to have basically zero effect on the beat. The beat overall looks worse than it did a month ago, and the shape seems to mimic the shape of the north cavity RIN. More optimization of the north EOAM is necessary.

Details: Having set up the north EOAM on Thursday (PSL:1372), I spent most of yesterday trying to get a RIN-suppressed beat measurement.

The continual drift of the laser frequency control signals was irritating, so I spent some time getting the slow digital PID controls for the lasers back up and running. At first only K_P seemed to have no effect on the laser control signals; it turns out this is because the PID Perl scripts that run on the Sun machine rescale the K_I and K_D coefficients by a timestep variable, which had been set to zero. I've set it to 1. I've chosen K_P = K_D = 0 and K_I = 0.0002 (with appropriate choice of sign for the two loops). The system is probably overdamped, but it manages to integrate the control signals down to zero in a resonable amount of time (<30 s) and I don't think it's a high priority to optimize it right now.

The south PDH error signal has noticeable 250 kHz oscillations which get worse as the common TTFSS gain is increased. The north PDH error signal is much quieter. Are we perhaps hitting a mechanical resonance of the EOM crystal? Or (dare I say it) do we have the wrong sign for the common path of the PDH loop?

I took out the hand-soldered integrating board that I built for the ISS loops; it was railing too often. The ISS setup for each path is now as follows: each ISS PD goes into the A input of an SR560, and a programmable voltage reference (Calibrators Inc. DVC–350A) goes into the B input. The voltage is chosen to match the dc voltage from the ISS PD. The SR560 is dc coupled and set to take the difference A − B. The gain is set to 5×10³ V/V, with a single-pole low-pass at 1 kHz. The output from the SR560 is fed into the EOAM.

The suppressed and unsuppressed RIN measurements are given in the first two plots. Evidently, these simple ISS loops are able to suppress the RIN by a factor of 50 or so. Also, the north RIN is much worse than the south RIN, and the hump from 100 Hz to 10 kHz is reminiscent of a poorly aligned EOAM (as seen in PSL:1311, for example). So I'd like to spend some more time fiddling with the north EOAM to see if I can improve the RIN suppression. Alternatively, perhaps we are suffering because the north path has no PMC to stabilize the pointing into the EOM, EOAM, etc.

Anyway, I pressed ahead and looked at the beat. To convince myself of the repeatability of the setup, I took a measurement with the ISS loops on, then a measurement with the ISS loops off, and then a measurement with the ISS loops on again. The result is given in the third plot. Below a few hertz, the ISS may have a positive effect. Above this, there is either no effect or a small worsening effect.

Note that the shape of the beat follows the shape of the north cavity RIN. I think we should spend a little time noise hunting and optimizing on the north path to see if we can make this go away. Note also that the beat is worse than it was back in September (PSL:1321). Two immediate culprits that I can think of are (a) the installation of the EOAM or (b) the fact that the vacuum can is no longer floated. But it could just as well be that there's something else (e.g., PDH offsets) that I neglected to optimize.

Summary: The EOAM is back from Newport and it looks like it's working. With 3 mW incident on the EOAM, we get 1 mW after the PBS. I applied a range of DC voltages between −4 V and +4 V and measured the output power. The effect is linear, with a slope whose magnitude is 17 μW/V. From the manual, we expect a slope of (π / 2) (3 mW / 300 V) = 16 μW/V, so we're pretty much spot on (assuming a half-wave voltage of 300 V).

Details: From upstream to downstream, the EOAM setup consists of a HWP, the 4104 amplitude modulator, a QWP, and finally a PBS.

• With the EOAM and QWP removed, I adjusted the HWP in order to maximize transmission through the PBS. The original angle was 98.5°, and I turned it to 94.0°. The power onto the PBS was 1.19 mW, the PBS transmitted power was 1.11 mW, and the PBS reflected power was 47 µW.
• I added the QWP back in and rotated it to maximize transmission through the PBS. (This was my interpretation of Newport's instruction to include "a quarter waveplate oriented vertical to the modulator housing".) The power onto the PBS was 1.19 mW, the PBS transmitted power was 1.12 mW, and the PBS reflected power was 35 µW. The QWP angle was 100°.
• I added the EOAM and drove it with a 10 Hz, 6 Vpp sine wave. At this point I found that my choice of QWP angle (100°) was incorrect, so I tried two other angles: 145°, which should put the QWP axes at ±45° relative to vertical, and 132°, which I found is close to equalizing the transmitted and reflected powers from the PBS (this should in principle coincide the correct operating point for the EOAM). For each of these angles, I measured the reflected and transmitted PBS powers, and I watched the DC output of the north refl PD in order to get the depth of the intensity modulation. These numbers are given in the table below.

In the end, I decided to use 145° as the QWP angle since it provided the greatest modulation depth of the three angles that I tried. Additionally, it jives with my understanding of the EOAM setup; namely, that the 4104 by itself acts as a voltage-controlled waveplate that (a) has its axes located at ±45° and (b) has zero retardance in the absence of applied voltage. Therefore, to bias it to have λ/4 retardance, one should add a QWP with its axes at ±45°.

After I took these measurements, I then rotated the HWP after the north EOM from 192° to 193° in order to get 3.0 mW incident on the EOAM setup. I then took the calibration data plotted below using the handheld voltage reference and the ThorLabs power meter.

[Tara, Evan]

We took another RIN-to-beat transfer function, as in PSL:1316. This time we've directly measured the conversion factor between power transmitted through the south cavity and voltage put out by the transmission PD. To do this, Tara purposefully misaligned the alignment into the cavity in order to get several different transmitted powers. For each misalignment, we measured the power immediately after the vacuum can using the power meter as well as the voltage out of the south PDA10CS with its gain at 30 dB. The result is (1.78 ± 0.05) V/W, and the fit is shown in the first attachment.

The second attachment shows the transfer function. I've applied the PD conversion factor mentioned above, as well as the Marconi actuation conversion factor (710 Hz/V for the 1 kHz FM setting). The red and green traces were taken with the table not floated, and the blue traces were taken with the table floated (we originally took all the traces with the table not floated, but the SR785 decided to write an empty data file and we didn't realize it until after we floated the table).

Also, I think I must have applied the wrong calibration (7.1 kHz/V) in PSL:1316; at low frequencies, the TF there is almost exactly a factor of 10 higher than the TF here.

[Tara, Evan]

Having successfully floated the table yesterday, we attempted a new beat measurement in the hopes that the large shelf below 100 Hz had disappeared. Unfortunately, this appears to not be the case. Additionally, many of our signals are plagued by unusually large, slow drifts. We're hoping that they're just thermal transients caused by all the work on the table over the past 12 hours, and that by tomorrow things will have settled down. We'll see if that's the case.

Anyway, we did the following things today:

• We reconnected cables that come in from off the table and go onto cameras, PDs, etc., paying special attention to strain relief and vibration isolation since the table now floats.
• We redid the alignment to recover ~90% visibility; this required only touching the periscope mirrors (somewhat surprising considering what we subjected the table to in order to switch out the legs).
• We got the cavity PDH loops up and running again. The control signals show unusually large drifts. We also noticed this while sweeping the lasers to align the cavities; the resonance for north in particular would wander out of the sweep range every 30 seconds even though the laser was being driven at 10 Vpp from an SRS function generator.
• We spent some time trying to null (what we assume is) RFAM-induced offset in the PDH error signals. We did this by adjusting the HWPs before each cavity EOM and nulling the offset on TTFSS common OUT1. The south cavity already had a small offset, so no adjustment was required. On the north cavity, there was a noticeable offset (~20 mV, compared to an error signal pk-pk of 220 mV), so Tara nulled it. We then found that we could get a stable lock with the laser PZT actuator alone, and that adding the EOM actuator caused the loop to oscillate (almost as if the EOM actuator was driven with the wrong sign). So we looked at the error signal again, and unexpectedly found another ~20 mV offset. Tara nulled it again and this time the lock was stable; in fact, we were able to get the common and fast gain knobs up to 1000 and 1000 (compared to 800 and 800 earlier in the day). No idea what the problem is here; possibly it drifted between the successive adjustments.
• We looked at the beat. It appears to be not much better than with the table unfloated.
• We took a measurement of RIN-induced disturbance in the beat by driving the south EOAM with a sine from the SR785 and taking the TF that takes transmission PD intensity to beat fluctuation. Unfortunately, this measurement is not consistent (in magnitude or phase) between successive sweeps. It seems to be due (at least in part) to DC drift in the beat.
• We tried turning on the crude south ISS, but it made the beat more noisy.

OK, I borrowed a Watec from the ATF. It is more sensitive than the jWin I was using, but judging by the graininess we appear to be close to the camera's noise floor. For the attached pictures I turned up the power on the RFPD from 1.0 mW to 1.5 mW, and that seemed to help a little.

I placed a CCD camera behind the steering mirror directly before the south RFPD in the hopes of getting a handle on the shape of the refl beam while the refcav is locked or unlocked. Unfortunately I think the transmission through the mirror is too low; you can barely make out the refl spot when the cavity is unlocked, and it disappears when the cavity is locked.

Previously (PSL:798), Frank and Tara used a CCD camera to monitor the reflection off the RFPD itself. This reflection has enough power to be seen on an IR card, so perhaps this is the way to go (if we trust the face of the RFPD to not distort the beam).

Last week I talked to an engineer at Newport, and he agreed that the discrepancy (1 µW/V versus 30 µW/V) seemed unusual. Tara and I are sending this EOAM back to Newport for inspection; it should ship out today. We await Newport's diagnosis with bated breath.

I also mentioned to Newport that this EOAM has a minor annoyance with the two hex screws on the bottom of the case: the screw heads jut out slightly from the case rather than sitting inside the countersink (didn't think to take a picture, sorry). This causes the EOAM to have a slight roll when sitting on its kinematic mount. Tara was able to add a washer to the 1/4-20 screw holding the EOAM in order to mostly cancel this roll, but it would be nice to not have to deal with it in the first place.

I removed 29 cm of SMA cable between the south RFPD RF output and the south TTFSS PD input in order to make the PDH error signal more symmetric. Relevant oscilloscope traces attached.

Yesterday I measured the noise of the refcav PDH loops. Because of RFAM effects, possible nonlinearity in the RFPD response, etc., the correct way to measure the loop noise is to take the PSD of the error signal (Common OUT1 on the TTFSS) while the cavity is unlocked but light is still incident on the cavity and on the RFPD.

For these measurements, the south TTFSS gain was 642 common and 702 fast, and the north TTFSS gain was 802 common and 835 fast; these are the highest gain settings I could achieve before the loops started to oscillate when locked. There was 1 mW of light incident on each cavity.

Plots and data are attached. I've converted from voltage to frequency using the slopes I found in PSL:1339. Current thoughts:

• These plots seem to say that at high TTFSS gain, we're actuating on sensing noise rather than cavity frequency noise. I'm not sure I believe this yet.
• We're dominated by (what is probably) seismic noise below a few hundred hertz.
• There's something goofy with the north TTFSS; I would say it's a grounding issue, but the fundamental peak looks more like 75 Hz than 60 Hz.

I took measurements of the carrier and sideband power transmitted through each cavity in order to get the modulation depth Γ of the EOMs. The modulation depth is related to the transmitted powers by Γ²/4 = P_SB/P_car. [Edit: I checked last night in Mathematica, and it seems the approximation Γ ≈ J₁(Γ)/J₀(Γ) is good to about 1% for Γ < 0.3.]

First I aligned the cavities to get good refl visibility (about 90%). Then I aligned the transmitted beams onto the ISS transmission PDs. Then I unplugged the EOM HV actuation on the TTFSS.

To get the transmitted carrier power, I locked each cavity as usual and then wrote down the voltage on the ISS PD. To get the sideband power, I flipped the sign of the fast actuation on the TTFSS, thereby making the servo lock on the sideband. I then wrote down the voltage on the ISS PD. I also blocked each transmitted beam to get the dark voltage on the ISS PDs.

For posterity, I also took triangle-wave sweeps of the ISS transmission, the refl DC, and the error signal. The oscilloscope traces are attached. [Edit: from a quick look at the error signal traces, I get slopes of (164±10) kHz/V for the south cavity and (199±12) kHz/V for the north cavity.]

In other news, the south PDH error signal looks a bit asymmetric; I think it might need a phase adjustment.

Neither Tara nor I can get the north New Focus 4104 to put out a significant amount of power modulation, despite going through (what we think is) the biasing procedure several times. We're getting modulation on the order of 1 µW/V, compared to 30 µW/V when we first installed the south EOAM (PSL:1287).

To review, these New Focus EOAMs consist of two lithium niobate crystals mounted with their fast and slow axes orthogonal to each other. If the crystals are the same length, then with zero applied voltage the EOAM should have no birefringence. Any applied voltage causes the EOAM to become birefringent; the voltage required to produce a λ/4 retardation between the two optical axes is called the quarter- wave voltage, and the voltage required to produce a λ/2 retardation is called the half-wave voltage (V_π).

To use the EOAM for intensity modulation, we put down a HWP before the EOAM to make sure the input beam is either p- or s-polarized relative to the optics on the table. The EOAM crystals are mounted at 45 deg., so the input beam therefore is projected in equal parts onto the EOAM's two optical axes. After the EOAM there is a QWP with its fast and slow axes aligned to the EOAM's optical axes [Edit: actually the manual says to align the QWP axes to be horizontal and vertical wrt the table, which I don't understand. At any rate, neither configuration makes the EOAM work.], and following that there is a PBS which passes only p-polarized light. The intensity of the light transmitted through the PBS is a linear function of the EOAM birefringence only when the beam entering the PBS is nearly circularly polarized, so the purpose of the QWP is to optically bias the beam so that we can actuate around zero volts on the EOAM. (The alternative is to have no QWP and instead electrically bias the EOAM to its quarter-wave voltage.)

Anywho, the procedure that Tara and I have gone through is

1. Remove the EOAM and QWP. Adjust the HWP preceding the EOAM so that the intensity through the PBS is at a minimum.
2. Put down the QWP and adjust it so that the intensity transmitted through the PBS is equal to the intensity reflected from the PBS. This should mean that the beam into the PBS is circularly polarized.
3. Put down the EOAM and align it so that the beam passes through.

After this, the setup should now give linear intensity modulation when a few volts are applied to the EOAM. For the south EOAM this procedure worked fine—by applying a few volts to the EOAM we could see the power change on the ThorLabs power meter. But with the north EOAM the power changes are much, much smaller.

[Tara, Evan]

In preparation for tomorrow's sprinkler installation, we have removed any extraneous optics, cables, and electronic equipment on and around the table. Everything on the table is now covered by a drop cloth.

I changed the values so that the feedback is 13 kΩ in series with 1.2 nF, and the inverting input is 1.3 kΩ. This puts the zero at 10 kHz.

I duplicated this with a second OP27 on the same circuit board, so now there is an integrator for each cavity.

Last night the best results seemed to be achieved with the SR560s set to G = 100 with a pole at 10 kHz.

I made a quick inverting op-amp integrator which kicks in at 860 Hz at has gain 10 at infinity. The feedback is a 5.6 kΩ resistor in series with a 33 nF capacitor. On the inverting input there is a 560 Ω resistor.

I put this after the SR560 with gain set to 100 and bandwidth set to 30 kHz. It seems like this gives good RIN suppression.

I've taken the above RIN data and combined it with the intensity-to-frequency TF in PSL:1316 to arrive at an estimate of the RIN-induced frequency noise.

By eye, I fitted the magnitude of the transfer function from Tara's farsi.m code to the following model:

The first attachment shows this fit compared to the original TF.

I used this TF (along with the dc power 0.74 mW incident on the cavity) to convert the measured RIN (suppressed and unsuppressed) into frequency noise. I multiplied the result by a fudge factor of 3 to account for the fact that the TF we measured was a factor of 3 higher than the expectation.

The result is shown in the second attachment. Since this only with G = 500, Chas's high-gain ISS board should crush the RIN well below the expected Brownian noise.

At Tara's suggestion, I implemented a simple ISS by feeding the output of the PDA10CS into an SR560 (ac-coupled) with some gain, and then the output of the SR560 into the EOAM.

I found that by turning on a 6 dB, 30 kHz low-pass filter on the SR560, I could put the gain at 500 without saturating the SR560 output. No inversion is necessary because positive voltage on the EOAM decreases the beam power (so there is already a minus sign in the loop).

I monitored the RIN by feeding the output of the PDA10CS into the SR785. The in-loop RIN is suppressed by a factor of 6 or so. Once Chas's board is here, the suppression should be much greater (since the gain will be 10⁶ at low frequencies).

The shape of the RIN spectrum has changed compared to the previous RIN measurement. The 2 kHz peak is gone, and the shelf from 100 Hz to 1 kHz has dropped. Maybe it's because Tara has damped a lot of the mechanical resonances of the table optics with rubber stoppers. The low-frequency RIN remains at a few times 10⁻⁴/rtHz. According to Tara, this is probably induced by seismic coupling (not by fluctuations from the laser), and so the right way to make it go away is to float the table.

There is a minor mystery here. Based on the previous RIN measurement, I expect the dark noise of the PDA10CS to be at 7×10⁻⁷/rtHz or so abve 1 kHz. Why have I apparently been able to measure below this noise floor in the attached plot?

I used the black voltage calibrator to give the south EOAM a DC voltage, and then used the ThorLabs power meter to read off the DC power level before the PBS that used for picking off the RFPD path.

I find the volts-to-watts conversion is (5.93±0.12)×10⁻⁶ W/V. This will, of course, change if we change the input power level into the EOAM. I guess if there's a more lasting message here, it's that we've got the orientation of the QWP after the EOAM in a pretty good place, since there's no visible nonlinearity in the attached plot.

[Tara, Evan]

Last week we tried measuring a transfer function which takes intensity fluctuation induced at the south EOAM and returns frequency fluctuation as read out by Tara's beat setup. This is therefore meant to be the measurement corresponding to Tara's code farsi.m (on the SVN at CTNLab/simulations/misc).

We used the SR785 in swept-sine mode. As measured previously, the EOAM response is 3×10⁻⁵ W/V (although I think this number should be rechecked, since we've fooled around with the EOAM in the meantime). The beat PLL readout is 7.1 kHz/V (when the Marconi is set to its 10 kHz setting). [Edit, 2013–10–18: by comparing with the newer measurement in PSL:1368, I think the Marconi must have actually been at the 1 kHz setting, so the conversion factor is 710 Hz/V and the transfer function measurement below is a factor of 10 too high.] These two numbers give the conversion factor necessary to convert from V/V into Hz/W.

The attached plot shows the measurement and the expectation from Tara's code. Here I'm using the version of the code as checked out last night, and in my local copy of the code I changed the cavity length to 1.45″ and the input power to 1 mW. Below 200 Hz, the agreement in magnitude is good: the overall shapes agree the values are within a factor of 3 of each other. The phase also appears to be good below 40 Hz or so. Above 200 Hz the transfer function is apparently dominated by some other effect.

[Tara, Koji, Evan]

On Friday when the vacuum chamber was open, we took some impulse response measurements of the seismic isolation stack. We used a HeNe laser and a PDA100A as a shadow sensor for recording the responses.

The measurement setups were as follows:

1. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the top of the cavity mount.
2. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the top surface of the seismic stack near the end of the stack.
3. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the right side of the seismic stack near the end of the stack.
4. With the shadow sensor positioned so as to register horizontal motion of the transmission corner of the seismic stack, Tara poked the left side of the seismic stack near the end of the stack.
5. With the shadow sensor positioned so as to register horizontal motion of the transmission corner of the seismic stack, Tara poked the front of the seismic stack near the end of the stack.

For each setup, two ringdows were taken with the scope AC coupled (we'll call them measurements A and B).

I used scipy.optimize.curve_fit to fit each ringdown to the sum of two damped harmonic oscillators:

where θ is the Heaviside step function. In the table below I've collected the fitted frequencies and Q factors. In the first attachment I've plotted the ringdowns, their Fourier transforms (with no windowing—very crude, but it is only intended as a very rough guide), and the fits (in red).

I haven't assigned error bars here because I think I may be overfitting; the amplitude and phase parameters and the offset parameter have huge uncertainties (many times the nominal value). However, by eye the fits of the ringdowns appear to be pretty good, and so I am inclined to believe the fitted frequency values.

 [Tara, Evan]

Tara and I opened the CTN vacuum can this afternoon. Previously, the reflection from the vacuum window was overlapping with the reflection from the south refca, so Tara repositioned the seismic isolation stack in order to get rid of this overlap. We have now realigned into the two refcavs, and neither show any reflection overlap. The attached picture shows the two reflections at the PBS pickoff for the RFPD path for the south cavity. The large spot is the refcav reflection. Slightly to the left of it you can kind of make out a much smaller spot, which is the reflection from the vacuum window.

For the north cavity, the refcav reflection is currently clipping on the QWP nearest to the vacuum can, while the vacuum window reflection makes it through the QWP and onto the RFPD path. So evidently there's no overlap here either.

We also took some measurements of the impulse response of the seismic isolation stack, but that will be covered in a subsequent elog post.

After some discussion with Tara and David, it became apparent that it would be wise to take RIN noise and EOAM-to-PD transfer function measurements over a wider range of frequencies than was done previously.

For these measurements I'm using the same PDA10CS as before, although here I've got 0.48 mW going onto the PD (i.e., no ND filter), and the PD's internal preamp is set to 10 dB. The dc output voltage is 1.7 V. I did the RIN measurement on the SR785.

For the transfer function I used both the SR785 and the HP4395A. Because the HP4395A has 50 Ω inputs, it shows an extra 6 dB attenuation which I've undone here (since the ISS is all high impedance). The transfer function is well described by a single-pole rolloff whose DC amplitude is −0.0148 V/V and whose frequency is 330 kHz (shown in green below).

Tara and I have taken a measurement of the transfer function which takes volts the EOAM and produces volts at the ISS PD.

The EOAM is driven with a 4 Vpp swept sine from the SR785. Approximately 1 mW of light is incident on the south cavity, and 0.5 mW is incident on the PDA10CS positioned at the cavity transmission. The spot size is a little bigger than the PD area, since I'm unsure of the damage threshold of the PD and don't want to fry it. The PD has its internal preamp set to 20 dB of gain (1.5×10⁴ V/A) and has a quantum efficiency of about 0.6 A/W. The DC voltage of the PD is about 5.9 V. The inputs of the SR785 are dc coupled. Each data point on the transfer function is integrated over 20 cycles.

As a control, there is a second PDA10CS set up before the cavity input to capture the transfer function without the filtering effect of the cavity and associated optics. The input power is about 0.4 W and the gain is also 20 dB. In the attached plot, I've normalized this transfer function to have the same amplitude as the transmission transfer function.

Evidently, the magnitude of the plant transfer function is (more or less) 0.057 V/V.  Based on the calculation in PSL:1278 I'd expect something more like 0.024 V/V (with a = 0.5), and I'm not sure where the extra factor of 2 is coming from. I've measured the PD gain to be 11 V/W at 20 dB (by putting an OD2.0 filter in front of the PD, and then making the spot size small enough that all the light falls on the PD), which is close to what I'd expect (9 V/W, given a quantum efficiency of 0.6). We've measured the EOAM gain to be 3×10^-5 W/V. There's definitely 0.5 mW going towards the PD. So something's not adding up.

In preparation for getting the ISS up and running, Tara and I have been fooling around with the EOAM and associated half waveplates. Additionally, Tara inserted a quarter waveplate (mounted horizontally, for space reasons) after the EOAM in order to get linear amplitude modulation. The HWP before the EOAM is at 99 degrees and the QWP after the EOAM is at 51 degrees.

There's currently 8.0 mW going into the EOAM and 4.0 mW coming out after the EOAM + QWP + PBS. When 10 V dc is applied to the EOAM, the power drops to 3.7 mW. This gives a conversion factor of 3.0×10⁻⁵ W/V. The value expected from the manual is (π/2)(8 mW / 300 V) = 4×10⁻⁵ W/V, so we're not too far off. 

The ISS transfer function requirement is not complete without giving the plant transfer function, i.e., the conversion factors that take volts to watts at the EAOM, watts to volts at the PD, and everything in between.

The attachment shows the physical topology of the CTN ISS. The EAOM is a New Focus 4104, and the PD is a ThorLabs PDA10CS.

Looking at the EAOM manual, small-signal power modulation δW in response to a voltage δV is

with V_π no more than 300 V. From talking to Tara, it sounds like the input power W can be somewhere between 2 mW and 10 mW, but the power after the EAOM is going to be attenuated to 1 mW. So W is effectively 1 mW.

Also from talking to Tara, with 1 mW at the input he expects to get something like 0.6 mW out of the transmission. Half of this will go to the beat breadboard, and half to the ISS breadboard, so that's 0.3 mW incident on the ISS PD (so we have an optical throughput a = 0.3). The quantum efficiency η of the diode is something like 0.6 A/W. The PDA10CS has an internal preamp with different gain settings; the one to use here is probably g = 1.5 × 10⁴ V/A, since then we get something like 3 V dc coming out of the PD.

With these quantities, the plant transfer function (from volts at the EAOM to volts at the PD) is

which, with the above numerical values, is P =0.014 V/V, independent of frequency. So there's an attenuation of 70 or so that needs to be compensated for in the electronic part of the loop. But before anyone solders in the relevant resistors and capacitors, the plant transfer function should actually be measured.

This is an estimate of the required RIN for the CTN experiment, so that Chas can set the appropriate loop gain and shape for the ISS boxes. This estimate relies on computing the equivalent RIN level set by the expected coating Brownian noise of the cavities.

Amplitude spectral density of CTN coating Brownian noise

From figure 6 of the CTN upgrade document (T1200057-v11), the anticipated ASD of frequency noise due to coating Brownian noise is (0.25 Hz/rtHz) / f^1/2.

Calculation of transfer function from intensity to frequency

The spectral density of displacement noise induced by beam intensity flucations was computed by Cerdonio et al. (2001), PRD 63: 082003 (see eq. 24). Based on this, Tara has written Matlab code (PSL:1014) which numerically computes the transfer function of relative intensity noise to frequency noise for a fused silica cavity. Tara and Sarah (2012 SURF student) measured this transfer function using an AOM and one of Tara's 8″ cavities and found OK agreement (PSL:1029); the discrepancy is greatest near 1 Hz, where the calculated transfer function is 6 times higher than the measurement.

Computation of equivalent RIN

To compute the equivalent intensity fluctuations, I've taken the coating Brownian noise spectrum given above and divided it by the RIN-to-frequency transfer function as computed with Tara's Matlab code. [In this code I've replaced 8″ with 1.45″ and upped the finesse from 7500 (measured value) to 10000 (value assuming a transmissivity of 300 ppm and no losses).] I've then divided this by 2 mW (the assumed power incident on the CTN cavity) to get an equivalent RIN corresponding to the coating Brownian noise. This is shown in the second attached figure, along with yesterday's unsuppressed RIN measurement. The first figure shows the intensity-to-frequency transfer function. I've also included the data and code used to generate the plots (some of it is duplicated from yesterday's post).

Based on discussions with Chas, it sounds like we want to stabilize the RIN to be at least a factor of 10 below the equivalent RIN level shown in the second attachment.

Chas has been building an ISS and needs a spec for suppression of relative intensity noise for Tara's 1.45″ silica/tantala cavities.

I measured the RIN of the south cavity with the cavity locked. The common and fast gains were both set to 400 on the TTFSS frequency servo box. I placed a PDA100A at the transmission of the south cavity. The DC power incident on the PD was 0.370 mW and the DC voltage was 0.439 V. I plugged the PD output into the SR785 and recorded the PSD of the voltage, both for light incident on the PD and for no light incident on the PD (i.e., the noise floor). To get the amplitude spectral density (ASD) of relative intensity noise, I've taken the square root of the voltage PSD and divided by 0.439 V.

I've attached a figure showing the RIN (and the noise floor of the measurement), as well as the data and code used to generate the plot.

Both the shape and overall amplitude of the RIN are roughly consistent with what has been measured earlier (e.g., PSL:986 and PSL:736). I'm unsure whether this is the same laser that was used for the previous iteration of the CTN experiment, but it is the same model (Lightwave NPRO 126). [Edit: I've talked to Tara, and this is the same laser as was used in the previous measurements.]

There is a mistake in the calculation above; the emissivity ε₂ should not appear in power balance involving the absorption of j_n by the copper, since j_n is already a net flux describing the intensity of radiation flowing into the copper. The thermal time constant of the copper is therefore d₂ρ₂c_p2/4ε′σT_b³.

I ran a 1D Comsol model of this parallel plate calculation. The geometry and materials are as described above. For the boundary condition at the outside (left) surface of the steel, I chose a step function in time that starts at 303 K and ends at 308 K. For the inner (right) surface of the steel and the left surface of the copper, I used surface-to-surface radiation conditions, with emissivities specified as above. For the right surface of the copper I chose perfect thermal insulation. This corresponds to enforcing T _b = T_d in my calculation. For a cylindrical geometry with no reference cavity present, we know by symmetry that the next flux at the inner surface of the copper shield must be zero as long as the copper is a uniform temperature; this corresponds to a perfectly insulating boundary condition.

The time constant is the time required for the copper shield to rise to 63% of the difference between its initial and final temperatures (which here is 306.16 K). From this, I find that Comsol gives the thermal time constant as 21300 s (see first attachment); my calculation gives 21200 s. As a check, I also tried different emissivities. For both emissivities equal to 1, Comsol gives 1300 s and my calculation gives 1200 s; for ε₁ = 1 and ε ₂ = 0.15, Comsol gives 8500 s and my calculation gives 7800 s; and for ε₁  = 0.08 and ε₂ = 1, Comsol gives 13900 s and my calculation gives 14600 s.

At this point I don't have an explanation as to why Comsol doesn't show the exponential suppression of the temperature fluctuations in the steel. But even without this effect, the residual AD590 noise at the copper shield is still below the NTC thermistor noise for frequencies above 2×10⁻⁴ Hz (second attachment).

Tara, Rana and I had a discussion last week about how much temperature noise from the outside of the CTN vacuum can actually makes its way to the copper radiation shield surrounding the reference cavities. In the first attachment I've attempted a first-principles calculation of this response assuming that the steel surface of the can is subjected to a uniform, fluctuating temperature. I've also assumed a plane parallel geometry rather than a cylindrical geometry just to make the math a bit easier. (In this attachment, I've said that the steady-state temperature of the inner steel surface can be taken to be the average of the outer temperature and the copper temperature, but thinking about it now it's probably almost identical to just the outer temperature. Despite what is says in the attachment, for the subsequent plots I've taken the steel temperature to be a uniform 35 C and the copper temperature to be 40 C.)

I find that the thermal response of the copper shield with regard to temperature fluctuation on the outside of the can is (as one might expect) a product of (1) the exponential damping of the temperature fluctuation as it propagates through the steel, and (2) the thermal response of the copper itself, which has a single-pole low-pass behavior. Effect (1) is just the thermal response of a half- infinite conductor, and is treated in chapter 11 of Fetter and Walecka's theoretical mechanics book. Effect (2) is found by computing the steady-state net radiation flux between the steel and the copper, then applying a harmonic perturbation to this flux and computing how much power is absorbed by the copper according to Q = mCΔT. In other words, I've applied a harmonic perturbation to the lumped capacitance model described by eq. 5.16 in the heat transfer textbook by Bergman, Lavine, et al. (6th ed.). The only sticking point is that their power balance formula [ρcV dT/dt = −ε₂σA(T₂² − T₁²)] is formulated for a grey body in equilibrium with a blackbody, rather than for two grey bodies. So in my calculation, instead of ε₂ I have an effective emissivity involving both ε₁ and ε_2.

The second attachment shows the magnitude of the transfer function. In the third attachment I've estimated the temperature noise from the AD590 and the NTC thermistor (as given in Rana's post, PSL #1205), and then plotted the temperature noise at the copper shield assuming the outside of the can is stabilized to the noise level of the AD590. It appears that this residual noise is below the noise of the NTC thermistor for frequencies above 10⁻⁴ Hz. I'm trying to get a Comsol model up and running to confirm this.

I should mention that I've currently got the autolockers running in a screen session. If you need to turn them off you should screen -list to get a list of the current screen sessions, then reattach the appropriate session by screen -r [pid] (e.g., right now the relevant screen session has process ID 8517, so you'd type screen -r 8517), and then kill the autolockers by whatever means necessary.

 OK. But if you sweep the laser frequency you can see a DC offset in the error signal (OUT1 on the common path on the TTFSS), and at least a few days ago it was making the loop catch in a place where it shouldn't.

Obviously the long-term solution is to track down the source of the offset and make it go away. But in the short term is there something we can do to make sure the loop doesn't lock to this false point?

Again inspired by Zach's bash autolocker, I've written a python autolocker for the south reference cavity. If the cavity loses lock, it turns off the PID loop so that the temperature does not run away to the rails. It then checks that the PMC transmission is high and proceeds to slowly ramp the laser temperature between 7.43 V and 7.50 V.

Note: the aforementioned voltage values only work because the refcav is not heated, and hence the resonance always occurs in roughly the same place (between 7.45 V and 7.48 V, depending on the day). This simple search algorithm is therefore not, not a permanent solution for autolocking the refcav once the heaters are working. For posterity, here are the other values currently hard-coded into the autolocker:

• darkThreshold: 1 V; this is the value below which the RFPD REFL DC value is taken to indicate that no light is incident on the cavity, and hence the autolocker should turn off the PID loop and then do nothing
• cavityReflThreshold: 4 V; this is the value above which the RFPD REFL DC value is taken to indicate that light is incident on the cavity, but the cavity is unlocked, and hence the autolocker should try locking
• pmcThreshold: 150 ADC units; this is the value above which the PMC is considered locked, and hence the refcav autolocker may proceed with its lock procedure. (Note: this is different than the threshold values used in the PMC autolocker.)

The autolocker can be invoked via python srefcavauto.py on controls@fb2.

Since autolocker is coded to do nothing unless the PMC transmission is high, it is best run in conjunction with the PMC autolocker (invoked via python pmcauto.py). It doesn't matter which autolocker you start first.

Special bonus settings: the common gain on the TTFSS is 404 clicks, the fast gain is 426 clicks, and the offset is 967 clicks. Tara pointed out that the frequency loop would catch lock easier if the gain settings were around these low values rather that what they were previously (~600).

The common error signal on the TTFSS has a 5 mV offset, which was causing the loop to catch on the edge of the error signal, near the sideband. I've adjusted the offset pot on the TTFSS interface board from 502 to 960 to remove this offset, and the loop now catches only on the carrier.

Also, I've taken the DC path from the south cavity RFPD and plugged it into an SR560 with gain 10 and then into C3:PSL-RCAV_FMON. This is temporary, and I've done it so that I can remotely lock the south cavity more easily for the gyro beat measurement. With the gain of the SR560, refl on resonance is about 2 V at minimum.

After studying Zach's bash autolocker for the ATF PMC, I've written a python autolocker for the CTN PMC. This one is much simpler and just walks the PZT voltage downward until it sees the transmission PD go high. If the PZT hits 0 V, the autolocker puts it up at 300 V and continues walking downward.

The script is in the controls home directory on fb2 and can be invoked via python pmcauto.py

The CTN PMC has a troublingly low range on its PZT; it can't even cover a single FSR when driven from 0 to 300 V. So I wanted to see if the HV supply is really delivering what it says it is.

I unplugged the HV BNC from the PMC and plugged it into a voltmeter. I got good agreement between the nominal voltage as reported by C3:PSL-PMC_PZT and the actual voltage as read out on the voltmeter. 0 V is 0V, 50 V is 50V, 300 V is 300 V, etc.

Then I put the voltmeter in parallel with the PMC PZT. The relationship between nominal voltage and actual voltage is shown below. Evidently the PZT is not being held at nominal voltage. The presence/absence of the voltmeter does not affect the location of the PMC's modes (with respect to the nominal voltage), so this tells me that the voltmeter isn't skewing the measurement.

According to the ohmmeter, the resistance of the PZT (with the HV unplugged) is 800 kΩ, so there's no obvious short.

[Tara, Evan]

The south PMC can now be controlled on fb2 via C3PSL_PMC.adl.

The plots aren't right because I took the two-mirror mode spacing formula from Kogelnik and Li without applying the necessary modifications for a 3-ring cavity. The correct formula for mode (m,n) is $f_{mn} / f_\text{FSR} = (q+1) + (m + n + 1) \arccos(1-2L/R) / 2 \pi + \eta /2$, where $q$ is the axial mode number, $L$ is the half of the round-trip length, and $\eta$ is 1 if $m$ is odd and 0 if $m$ is even. (Note: for a 4-mirror cavity, $\eta$ is 0 always.) For reference, the K&L formula for a two-mirror cavity is $f_{mn} / f_\text{FSR} = (q+1) + (m + n + 1) \arccos(1 - L/R) / \pi$, where $L$ is half of the round trip length.

Instead of making more scatter plots, for each value of $g$ I computed the distance (in MHz) from the fundamental resonance to the nearest HOM resonance (up to order 20); the result is shown in the first attachment. I then picked the most promising $g$ factors and simulated a frequency sweep across a full FSR for a 3-mirror cavity with $L$ = 20 cm and $F \simeq 300$; the results are in the second and third attachments. Each mode is labeled with its order number, as well as 'e' or 'o' depending on whether $m$ is even or odd. I picked a arbitrary uniform amplitude for the HOMs, so these plots are only meant to indicate the locations and widths of the resonances. I've spot checked these plots against a Finesse model, so I'm reasonably confident that I've got the formula right this time.

I think the moral here is that the nearest HOM resonance is going to be about 16 MHz away from the fundamental, assuming $L$ = 20 cm. If we make $L$ = 10 cm, we can get to 32 MHz, but (depending on how bad the intensity noise at 30 to 50 MHz is) this potentially requires increasing the finesse to something like 600 to get the required intensity filtering.

If we go with a 4-mirror cavity, the modes don't have this $\eta$ degeneracy breaking, and there are $g$ factors for which the nearest HOM resonance is more like 30 MHz for $L$ = 20 cm. I have plots for this, but I want to check them against a Finesse model.

The CTN ThorLabs power meter had been set on 635 nm, possibly for quite some time (e.g. this post from April 11 uses this setting). I've now set it back to 1064 nm.

It looks like measurements taken on the 635-nm setting overestimate the power of 1064-nm light by a factor of 5 or so.

 This and some other PMC design issues are now in the SVN trunk under docs/modecleaner_design/

I computed the occurrence of higher-order modes up to order m + n = 20 as a function of g factor for a ring cavity.

In the first set of plots of plots, I've fixed the cavity half-length L and chosen several values of modulation frequency f_PDH. In the second set of plots, I've fixed f_PDH and chosen several values of L. Green is the carrier, red is the lower sideband, and blue is the upper sideband. The takeaway messages from these plots are that

1. there are two or three "best" regions to place g: near 0.06, near 0.46, or near 0.54 (although 0.06 is sort of close to instability);
2. the locations of these regions are independent of the modulation frequency, at least for the frequency range we are interested in; and
3. a lower modulation frequency widens these best regions.

So I think we should go for as low a crystal frequency as possible that is consistent with having shot-noise limited intensity and a high loop speed. I know the number 20 MHz has been thrown around as the lowest reasonable PDH frequency, but I don't understand quantitatively why this is.

I tried getting the relative gain between the AC and DC paths of the New Focus 1811, essentially repeating the measurement in elog #1152 but (a) taking measurements for both the DC and AC paths and (b) taking measurements in the region 10 kHz to 100 kHz, where the DC and AC bands overlap. According to the manual, the DC path is meant to be used up to 50 kHz, and the AC path is meant to be used down to 25 kHz.

I again had roughly 1 mW of light on the PD. I took spectra with the Agilent 4395A, which has 50 Ω input impedance. For the AC path, I took the spectra in W/Hz and multiplied by 50 Ω, giving a spectrum in V/rtHz referenced to the input of the spectrum analyzer. For the DC path, I took the spectra in W/Hz, multiplied by 50 Ω, took the square root, and then multiplied by 40/(2*0.82) = 24. The factor of 40 is the value given in the manual for the relative gain between the AC and DC paths, the factor of 2 accounts for the 50 Ω output impedance of the AC path, and the factor of 0.82 accounts for the apparent 11 Ω output impedance of the DC path. (The DC voltage out of the PD was 0.66 V when fed directly into the 1 MΩ input of the scope, but dropped to 0.54 V after I inserted a 50 Ω feedthrough; the quotient of these two numbers is 0.82 and this implies that the DC path has an 11 Ω output impedance). If the relative gain value (40) as given in the manual is correct, the DC and AC spectra should overlap so long as they are dominated by intensity noise rather than detector noise.

The first plot shows the AC and DC spectra, both light and dark. The intensity noise is not as dominant over the detector noise as I had hoped. Still, in the second plot I've quadrature subtracted the dark spectra from the light spectra to produce what are in principle the spectra of the photocurrent alone. Even with the caveat that certain bins in these spectra are dominated by detector noise, it appears that the spectra don't even have the same shape. My guess is that we may already be seeing the action of the high-pass rolloff on the AC path.

It might be worth having another go at this measurement with a higher photocurrent, but I'm guessing that this isn't a great way to get the relative gain calibration.

Yesterday I used the CTN network analyzer to look at the RF spectrum of a 1.0 mW beam from the ATF Lightwave with a New Focus 1811. This beam is picked off from the main ATF laser beam pretty much immediately after the laser head; there are some waveplates, PBSs, and lenses, but no EOMs or modecleaners. The laser was free-running, with nothing plugged into the temperature or frequency BNCs.

In addition to the spectrum of the beam intensity, I took a spectrum with the beam blocked to get a measurement of the dark current. In the plots below, I've referenced everything to the current through the diode. This means taking the W/Hz spectrum from the network analyzer, multiplying by 50 Ω and taking the square root to get the V/rtHz across the analyzer's internal 50 Ω resistor, then multiplying by 2 to get the V/rtHz put out by the 1811 (since its output impedance is 50 Ω), then dividing by the 4×10⁴ V/A figure given in the 1811 manual to get the A/rtHz across the diode. To get the 'expected photocurrent shot noise' given below, I watched the DC output of the 1811, which was at 680 mV with the 1.0 mW beam and 10 mV dark. So I divided 670 mV by the 1 V/mA figure given in the manual to get the DC photocurrent. The shot noise of this photocurrent is then sqrt(2eI). I haven't measured any of these 1811 conversion factors, so I don't have complete confidence in this shot noise value. However, the value for the DC current agrees roughly with what you get if you take the power measured with the ThorLabs meter (1.0 mW) and multiply by the quantum efficiency (0.7).

You can see in the first plot that the dark current is subdominant to the photocurrent all the way out to 100 MHz, and subdominant to the expected shot noise out to maybe 40 MHz or so. In the second plot I've taken the quadrature subtraction of the blue trace from the red trace to get an estimate of the photocurrent noise alone. The spectrum looks approximately white from 10 MHz out to 50 MHz and (if you at all believe the shot noise value) is about 1.7 times the shot noise. If this truly is the level of the excess noise, then to get excess intensity noise whose PSD is equal to 1% of the shot noise PSD at 20 MHz, we'll need a cavity pole at 5.6 MHz. If the calibration is spectacularly off and the total noise is 20 times the shot noise, we'd need at cavity pole at 1.4 MHz to get the excess intensity noise PSD to be 1% of the shot noise PSD at 20 MHz. The way I've arrived at this is as follows: if S(f) denotes the value of the linear spectral density at f relative to shot noise (f = 20 MHz and S(20 MHz) = 1.7 in this case), then

and so the suppression of the excess noise after transmission through a modecleaner is

and from this f_HWHM can be chosen to give the desired amount of suppression. Edit: actually, the right way to do this is to write the excess noise PSD as a relative intensity noise (which scales as P²), and to then compute the desired amount of suppression for the maximum amount of power we're going to send through the PMC (2 W or so). Computing the suppression relative to shot noise for a 1 mW beam is not sufficient, because the suppression requirement gets more stringent as the power increases. The RIN here at 20 MHz is 3×10^-8 /rtHz, and so for 2 W beam we require a cavity pole of 420 kHz to get a factor of 100 suppression below shot noise.

I think to do this measurement properly I'll need to get a better handle on the relative calibration of the DC and RF transimpedance gains of the 1811. It might also be nice to take a measurement both before and after an existing PMC, just to see the expected filtering effect.

For a 3-mirror cavity with a single curved mirror, the g-factor is (1-p/R)^2; there is no factor of 2 in the denominator because for a ring cavity the overall cavity length is equal to the round-trip length.

Also, I think we should shoot for a transmission of at least 90%. If this is going to be for general lab use, then there will probably be situations where people want a good power throughput. The input power might be as high as 2 W if used, e.g., at the 40m with one of those Innolight Mephistos.

I added an endcap to Tara's steel PMC Comsol model and looked at the eigenmoedes for a 3-point contact. The lowest mode is a rolling mode at 2.0 kHz, followed by other modes at 3.0 kHz and 3.5 kHz. The first longitudinal stretching mode is at 16 kHz. The rectangular part of the spacer for this steel PMC has dimensions 5" x 2.6 " x 2" and a cavity length of 32 cm (first picture).

I also looked at a beefed up version of the spacer, with dimensions 10" x 4.6" x 2" and a cavity length of 78 cm (second picture). The lowest mode is again a rolling mode at 1.4 kHz, followed by other modes at 2.0 kHz, 2.2 kHz, and so on. The first longitudinal stretching mode is at 9.0 kHz. So it looks like if we want a longer cavity, we can almost double two of the spacer dimensions without shifting the resonances down significantly.

If we use a 10" x 4.6" x 2" spacer but go with a 4-mirror bow-tie design (third picture), we can get something closer to a 1.1 m cavity length. Comsol gives a lowest mode at 1.4 kHz, followed by modes at 2.4 kHz, 2.6 kHz, etc.

[Rana, Tara, Evan, Eric, Nic] 

We are designing a PMC, to do that we should be able to answer some fundamental questions about a PMC.

Why do we want a PMC?

• Intensity stabilization(is it?)
• Filtering of beam profile
• Alignment reference
• Reference for waist size and position
• Jitter suppression
• Polarization filtering

What should we consider in the design of the cavity?

• High finesse eventually causes the transmission to drop
• Cavity g should be chosen so that higher-order PMC modes are well outside the bandwidth of the TEM00 mode
• Finesse should be chosen so that laser intensity noise is suppressed below the shot noise limit at frequencies of interest
• Number of mirrors - determines whether or not we get polarization filtering
  • In a 3-mirror cavity, when one polarization is resonant, the other will be antiresonant. In a 4-mirror cavity, both will resonate simultaneously (with small differences in transmission intensity and phase).

What should we consider in the design of the spacer?

• Acoustic pickup (probably dominates over seismic pickup at frequencies we are interested in)
• Steel or silica:
  • Longitudinal mode frequencies are comparable
  • Silica is harder to machine
• Vacuum can?
• Dimensions:
  • A shorter PMC will have higher vibrational modes
  • A longer PMC has more filtering
  • A spacer that is too thin will have easily excited bending modes

Other:

• 15 MHz is too low for PDH modulation, because the bandwidth of the resulting loop is too low
• For a resonant PD, we want a low Q (a few)
• 3 mirror or 4 mirror design?

These are plots of the sagging of the front and back mirrors as a function of the longitudinal positions of the mounting holes (these positions are measured from the back of the PMC). The first plot is a coarse search, and the second is more targeted toward a region of lower sagging.

I generated these plots by taking Tara's Comsol model of the PMC body, assigning fixed displacement to the three mounting holes, and assigning a body load to the PMC body equal to the weight of the steel. Then, I extracted the displacements of four points on the front edge and four points on the back edge of the PMC borehole (these edges are where the faces of the mirrors will make contact with the body). I then took some cross-products with these points in order to get the unit normals that would result when the mirrors are placed against the deformed body. I then compute the angle between the deformed unit normals and the undeformed unit normals to get the sag of the mirrors in radians.

I'm a bit uneasy about how precision is handled in the Comsol/Matlab combination used to generate these plots. The Comsol GUI has no problem reporting displacements all the way down to 10^-24 meters, but anything smaller than 10^-15 meters or so gets truncated to exactly 0 when the results are reported in Matlab. When propagated through to the sagging computation, this means any sagging smaller than 10^-8 radians or so also gets rounded to exactly 0. You can see in the second set of plots that there are large swaths of exactly the same light blue and periwinkle, which seems to indicate a low level of precision in the computation. There's probably some obvious Comsol/Matlab setting that I'm missing, but I haven't been able to find it so far.

Regardless, it appears there is an optimum range of hole placements for the PMC body: 10 cm for the front holes and 3 cm for the back holes, give or take a centimeter or so.

I made some modifications to TTFSS box S0900371, so that it is more like the TTFSS box we are currently using for the south cavity. The modifications are as follows:

• R1, R2, and R7 are now 47 Ω
• R3 is now 100 Ω
• R4 is now 390 Ω
• R29 is now 5.1 kΩ, with an optional 6.8 nF series capacitor controlled by a switch on the side of the box. This duplicates the optional boost available on the other TTFSS.

I checked my soldering work with an LCR meter and everything seems fine, but I have not yet powered it up.

I ran another Comsol simulation with a simplified version of the PMC spacer. This time I put fixed constraints on two circular regions on the sides of the PMC near where it was clamped for the ringdown measurement. Comsol says the spacer has a mode where it twists about these clamp points, and the frequency of the mode is 270 Hz.

I think the analytical formula in terms of rho is going to be (1.57/2*pi) * sqrt(E / rho * L^2), since the Roark formula is (1.57/2*pi) * sqrt(A* E * g / w * L^2) and the weight per unit length is w = m * g / L = rho * A * g. With your values for L, A, E, and rho, this gives f1 = 16 kHz. Since A does not appear in the analytical formula, this also explains why changing the area in the Comsol model doesn't change the frequency.

Tara and I repositioned the QWP and PBS immediately preceding the periscope so that we could move the 64.4-mm ROC lens closer to the cavity. For space reasons, this lens is now forked directly to the table rather than mounted on a translation stage. I tried for a while to adjust this and the 38.6-mm ROC lens to improve the mode matching, but I can't seem to do much better than 80% visibility. We may have to adjust the 103-mm ROC lens directly after the PMC in order to go further.

In better news, we were able to couple some power into the fiber that runs into the ATF. The beam is picked off with the PBS immediately following the EAOM and then sent through two mode-matching lenses and a HWP before hitting the fiber. We're sending 10 mW in and currently getting 0.85 mW out. More work is needed to get the polarization correct and to improve the coupling efficiency. This setup will probably have to be redone at some point, since the current pickoff beam is downstream of the cavity EOM and therefore has sidebands on it. Also, we will have to redo the coupling if we touch the 103-mm ROC lens to improve the cavity mode matching.

 I dialed the 38.6-mm ROC lens back to 1.11 m, twiddled the periscope mirrors, and got only marginal improvement in the visibility.

Today I tuned the mode matching into the south cavity by adjusting the two lens translation stages. The 64.4-mm ROC lens is at 15.63 mm, and the 38.6-mm ROC lens is at 4.01 mm. We currently have 80% visibility (see first attachment). One of the lenses is at the end of the range of its stage, so we will have to work to reposition it and continue mode matching.

Tara was able to tame the cavity servo loop. The third attachment is the result of several SR785 measurements of the error signal power spectrum. I converted this to a frequency noise power spectrum (fourth attachment) by extracting the voltage/frequency calibration factor from the error signal as follows.

I smoothed the PDH error signal by convolving with a gaussian and then numerically differentiated (second attachment). The locations of the carrier and the sidebands can then be read off, along with the magnitude of the derivative at zero cavity offset. Sidebands are at −14.5 ms and +14.7 ms, and the carrier is at 0.2 ms. Since the sidebands are 14.75 MHz from the carrier, this gives the time-voltage calibration as 1.01 GHz/s. The zero crossing of the carrier has derivative 16600 V/s, and hence the PDH slope is 61 kHz/V.

 The lowest longitudinal mode for silica is 16.4 kHz, and for steel is 14.2 kHz.

I asked Comsol for the eigenfrequencies of a simplified PMC body. The outer dimensions are as in the design document (6.89″ × 2.375″ × 2.00″), and the borehole has a uniform diameter of 1.188″ (instead of stepping down to a smaller diameter part-way through the body).

Comsol says the lowest mode for silica is at 8.3 kHz, and for stainless steel the lowest mode is at 7.2 kHz. For this simulation the body is assumed to be completely free; I didn't add 3-point contacts or anything like that.

So far, we've been locking the south cavity by feeding back only on the laser frequency, not on the broadband EOM. This is because the demodulation path produces an error signal with the wrong sign for the EOM feedback, and the only way to flip the sign is to manually adjust cable lengths.

Last night I shortened the cable length between the LO 4-way splitter and the LO input to the frequency TTFSS in order to flip the sign of the error signal. The phasing is not quite optimal but it's pretty close (the cable length probably requires ~10 cm of adjustment at most). The power into the LO input was 5.9 dBm with the old cable, and is now 6.1 dBm with the new cable.

I then toggled the polarity of the inversion on the TTFSS from (+) to (−) and turned on the servo with laser frequency feedback only. I got the cavity to lock, but the error signal had huge 8 kHz sawtooth oscillations that I hadn't seen before (1st picture, below; trace 1 is cavity refl power, trace 2 is the error signal from OUT2 on the TTFSS). Then I added EOM feedback to the servo, and got huge 5 kHz sawtooth oscillations along with some spiky crap (2nd picture, below). Then I turned down the common gain knob to about 100 and the fast gain knob up to about 600, and got the loop to "stabilize" in the sense that the error signal now oscillates in the same way as before; i.e., with 200 kHz sinusoidal oscillations (3rd picture, below — note the similarity to the error signal oscillation in post 1123).

I took a quick spectrum of the error signal corresponding to the 3rd picture (attached below) with the SR785. Since the sinusoidal oscillations are happening at 200 kHz or so, this spectrum isn't capturing these oscillations.

Today I installed the Faraday isolator after the PMC. Tara and I then spent some time trying to figure out why the PDH error signal suddenly had a huge DC offset (it was because I accidentally knocked the angle control on one of the HWP mounts while installing the FI beam dump). Before installing the FI, we had observed that the loop oscillates noticeably at about 100 kHz and had hoped it was caused by back-reflection into the laser (which the FI would fix). Installing the FI seems to have no effect on the oscillations. After installing the FI I adjusted the HWP immediately following and retuned the phasing of the PDH loop by adding some extra cable to the PD SMA input. I've attached a picture showing the sweeps of the cavity refl response and PDH error signal, and a picture showing the oscillations when the loop is engaged.

I tried minimizing the rejected light out of the FI to optimize the angle of the QWP directly in front of the cavity, but this light appears to be dominated by reflections other than those off of the cavity. The rejected light consists of two distinct spots which can be seen with an IR card. I think one of them is a reflection from the lens immediately following the FI, and the other is a reflection from the 14.75 MHz EOM.

We should be able to mode match into a cavity with 1.0 m ROC mirrors using only the optics we already have on the table. 

Current mirrors: 0.5 m ROC (has -1114 mm FL)

• 370 um PMC waist at z = 0 m = 0 in
• 229.1 mm FL lens at z = 0.203 m = 8.0 in
• 209 um intermediate waist
• 85.8 mm FL lens at z = 0.923 m = 36.3 in
• 41 um intermediate waist
• 143.2 mm FL lens at z = 1.201 m = 47.3 in
• 182 um cavity waist at z = 1.944 m = 76.5 in
• Mode overlap 1.000

Proposed mirrors: 1 m ROC (has -2227 mm FL)

• 370 um PMC waist at z = 0 m = 0 in
• 229.1 mm FL lens at z = 0.203 m = 8.0 in
• 209 um intermediate waist
• 85.8 mm FL lens at z = 0.889 m = 35.0 in
• 45 um intermediate waist
• 143.2 mm FL lens at z = 1.166 m = 45.9 in
• 210 um cavity waist at z = 1.952 m = 76.8 in
• Mode overlap 0.999

The various waists for the proposed mode matching are equal to or larger than the waists for the current mode matching, so I don't think we should be any more worried about sensitivity than we already are.

 [Tara, Evan]

Tara and I spent today and Tuesday laying down the new optical path for the south cavity according to the layout in entry 1100. After quite a bit of periscope steering (mostly on Tara's part), we got flashes of TEM00 and subsequently were able to lock the laser's fast frequency control servo to the cavity resonance. Getting near the resonance requires a bit of dialing around with the set point on laser temperature servo; the values that worked today were 512 on the coarse adjust and 894 on the fine adjust.

From here, we should

1. make a new mount for the post-PMC Faraday isolator, since the existing mount is about 32 mils too high (and hence the FI has not yet been placed in the beam path);
2. fine-tune the steering into the cavity;
3. optimize the mode-matching into the cavity;
4. measure the cavity finesse;
5. pick a different lens for matching into the RFPD, since the current RFPD path length is too long; and
6. fine-tune the demodulation phase for the loop.

I ran CVI's list of 1064-nm silica lenses through a la mode looking for a good way to get the cavity beams onto the beat PD. We're looking for a spot with radius somewhere between 80 and 150 um at the PD.

I tried a few optimizations with only one lens in each beam's path, but the results weren't very good; the beam is either too large, too small, or requires excessive path length after the BS. What I've attached is the result of an optimization for two lenses in each beam's path. It gives a 102 um waist a few inches after the last folding mirror, which is nice. The spot radius at the BS is 470 um, which is not too large.

 [Tara, Koji, Evan]

Tara and Koji spent the better part of yesterday afternoon inserting the new cavity assembly into the vacuum chamber. In the process of putting the window back on the chamber, the old copper gasket may or may not have hit the inner surface of the window, so Koji performed a drag wipe. Tara and Koji then inspected the window under a high-power bulb, and I think the consensus is that there's no visible damage.

The chamber is currently pumping down. Unfortunately, there appears to be a small speck of something trapped between the window and chamber flanges, so there's a small gap on one side of the joint. We'll see if we can achieve high vacuum.