[Koji, Ayaka]

Last night, I injected acoustic noise at POX table and AS table with oplev controls on (LPF is on).

1. acoustic noise at the POX table

I set the microphones and speakers at the POX table and see the acoustic coupling.

I could see slight change around 40 Hz. This can be caused by the oplev feedback loop because the speaker was on the same table as the ITMX oplev.

2. acoustic noise at the AS table

I controlled XARM with AS error signal and set the microphones and speaker on the AS table.

The resonance a 200 Hz seemed to be enhanced. But still we are not sure that it is caused by acoustic noise. Because this resonance is enhanced when the OL gain is high, and the gain adjustment was so critical that this resonance was easily enhanced even when the acoustic noise is not injected. And sometimes it has gone away.

 I calibrated MC_F signal into Hz/rtHz unit using the transfer function from MC_F to PMC feedback signal.

Here is the diagram:
  

n_mcf is MC_F signal we can get at dtt. I measured n_pmc/n'_mcf using SR.

Other information I used:

G_out = 2.49/123.49 (see the document D980352-E01-C)

Fout has 1 pole at 10 Hz (see the document D980352-E01-C)

A_pzt = 371e+6/63 [Hz/V] (see elog)

F_wt has 1 pole at 100 Hz and 1 zero at 10 Hz.

Then, calibration transfer function of H is fitted as 1e+9/f [Hz/V]:

Then, the calibrated spectrum of MC_F is below:

This calibration have about 20 % error.
Compared to the spectrum in Jenne's paper (elog), above 20 Hz it seems to be laser frequency noise. But now we have extra unknown noise below 10 Hz.

Note: calibration value of laser's PZT is ~ 1MHz/V. This is reasonable compared to the data sheet of the laser. (This is calculated by combining result of H and transfer function of the circuit box1 and FSS.)

 Yesterday, I made new mounts for microphones.

I glued a microphone on a pedestal. The cables are attached loosely so that its tension does not make any noise.
At the bottom of the mount, I attached the surgical tube forming a ring by double-side tape so that it damps the seismic vibration.

I made 6 mounts and these are all on the AS table now.
I took some data of XARM signal controlled by AS.

My plan is to find/set an upper limit on acoustic coupling noise in AS signal.
The acoustic noise can be estimated by the Wiener filter, but it is not accurate because it may see residual correlation between AS and microphone signals that should be 0 when the data is long enough.
I will find/set an upper limit by the analysis based on Neuman-Pearson criterion, that is analog of a stochastic GW background search.
If I can find the acoustic coupling noise should be below the shot noise, I am happy. If not, some improvements may be needed someday.

I calibrated the AS error signal into the displacement of the YARM cavity in the same way as I did before (elog).

The open loop transfer function is:

The transfer function from ITMX excitation to AS error signal is:

Then I have got the calibration value : 5.08e+11 [counts/m]

The calibrated spectrum in unit of m/rtHz is

REF0: arm displacement
REF1: dark noise + demodulation circuit noise + WT filter noise + ADC noise (PSL shutter on)
REF2: demodulation circuit noise + WT filter noise + ADC noise (PD input of the circuit (at 1Y2) is connected to the 50 Ohm terminator)
(The circuit and WT filter seem to be connected at back side of the rack. Actually there is a connector labelled 'I MON' but it is not related to C1:LSC-ASS55_I_ERR)

Also we changed the AS gain so that ADC noise does not affect:

However, this did not make big change in sensitivity. I guess this means that circuit noise limits the sensitivity at higher frequencies than 400 Hz.
I tried to adjust the AS gain carefully but I could not do that because of the earthquake. Further investigation is needed.

There was an earthquake around 2:30 am. Now all the mirrors except SRM are damped.

No, I did not apply open loop TF to it (actually I could not measure the open loop TF because of the earthquake last night). So I should not have said it was the displacement.

Also I changed the AS gain with whitening filter on and xarm locked. Still it does not make any change.

Since I found that the the AS sensitivity seems to be limited by circuit noise, I inserted a RF amplifier just after the AS RF output.
Now, the sensitivity is improved and limited by the dark noise of the PD.

(Note: I did not apply the open loop TF on this xml file.)
REF3: dark noise + circuit noise + WT filter noise + ADC noise
REF4: circuit noise + WT filter noise + ADC

With this situation, I injected the acoustic noise:

REF5, 6, 7: with acoustic excitation
no reference: without acoustic excitation

We could see the coherence only at the same frequencies, around 200 Hz as we saw before (elog).

We aligned and locked xarm for green.

We aligned and locked x and y arms.

MCL loop makes arms lock unstable, adds a lot of noise at frequencies 60-100 Hz. We'll fix it.

At some point we were not able to lock because of ADC overflows of PO signals. They happened if whitening filters were enabled. So we reduced the gain of POX whitening filters down to 36 dB and POY - to 39 dB. Now cavities can be locked with whitening filters.

Also we changed the pedestal of the lens in the beam path to the POX because the beam was too high.

The new laptop for the Beam Profiler is ready for usage.

From the last meeting, we came to the idea of having 2 laptops that are designated for the beam profiler specifically. We now one laptop over at WestBridge, and one here at 40m. This makes it easier to travel with just the Beam Profiler heads, rather than carrying the Profiler heads + laptop. This machine has been named Stella by ChatGPT. Feel free to use it! (Only runs Windows 10)

Global damping screens are in progress for the new global damping infrastructure Jamie discussed in log #8159. The main overview screen is /opt/rtcds/caltech/c1/medm/c1sus/master/C1SUS_GLOBAL.adl. The overview screen links to a few sub-screens in the same directory called C1SUS_GLOBAL_DAMPFILTERS.adl, C1SUS_GLOBAL_GLOBALTOLOCAL.adl, and C1SUS_GLOBAL_LOCALTOGLOBAL.adl.

This global damping is in intended to damp the 4 test masses along global interferometer degrees of freedom that are orthogonal to the cavity signals. Ideally the result will be that OSEM sensor noise from the damping loops is invisible to the cavity signals. Mismatches in the suspensions' dynamics and gains will cause some noise to leak through anyway, but we should be able to tune some of this out by carefully scaling the drives to each suspension.

 I made a minor modification to install some output filters in the new global damping GLOBAL box in c1sus.mdl. These will be needed for tuning the suspension drives to compensate for mismatches in the pendulums.

I recompiled and installed the model, but did not start it. Basically same as Jamie left it in 8159. Interestingly, I did not see the new POSOUT that was put in before the SUSPOS DOF filter. I made sure to reopen the .mdl file fresh before making more mods, but for some reason I do not see that update...

While doing initial measurements for the new global damping infrastructure I discovered that the ETMY loop between the OSEM actuation and the OSEM sensors has a gain that is 2.5 times greater than the ITMY.  The result is that to get the same damping on both, the damping gain on the ETMY must be 2.5 times less than the ITMY. I do not know where this is coming from, but I could not find any obvious differences between the MEDM matrices and gains.

I uploaded a screenshot of measured transfer functions of the damped ITMY and ETMY sus's. Notice that the ETMY measurement is 2.5 times higher than the ITMY. The peak also has a lower Q, despite having the same damping filters running because of this mysterious gain difference. Lowering the damping gain of the ETMY loop by this 2.5 factor results in similar Q's.

The global damping input and output matrices were installed to run for the Y-arm. Since we are using just one arm for now, only the DARM and CARM DOFs were entered into the matrices.

The input matrix was set to have elements with magnitudes of 0.5 while the output matrix was set to have elements with magnitudes of 1. The input matrix gets the 0.5 because the sensor signals must be avergaed for each global DOF, to make an 'equivalent sensor' with the same gain. The output matrix gets magnitudes of 1 so that the overall gain of the global loops is the same as the local loops. A transfer function was measured on the CARM loop to check that the overall gain is in fact the same as the measured ITMY and ETMY loops.

Simple damping filters were installed for the ITMY and ETMY as well as the global y arm CARM and DARM loops.

The ETMY output tuning filter ETMY_GLOBPOS was set to have a gain of 0.4 because there is an extra gain of 2.5 relative to ITMY in some mysterious place as discussed in log 8172.

 New excitation points were added after the global damping loops for more testing options. The updated c1sus.mdl model was re-committed to the svn. Two interesting simulink 'requirements' were found during this minor modification. First, excitation points must be placed on the top level of the diagram. If they are in a subsystem you will get compiling errors. Second, the excitation name must end in _EXC. It will compile OK if you don't do this, but the excitation points will not put out any excitations.

To do further investigation on the mysterious gain factor of 2.5 between the ETMY and ITMY POS damping loops, I measured TFs in the POS direction to the locked YARM signal for each. This provides an additional sensor, common to both, so we can see if the gain is coming from the actuation side or sensing side of the damping loops. The difference in these TFs is about 

2.895

So it seems the majority of the damping gain difference is on the actuation side with some small difference on the sensing side. In order to allow for the later splitting of YARM LSC control between ITMY and ETMY (global damping and the cavity control must be along the same coordinate system), I placed this gain of 2.95 in ITMY_LSC.

To get a first measure of the relative performance of global damping to local damping I measured some TFs between the sensor signal inputs and YARM. So first, while the cavity was still locked with just ETMY, I measured a TF between C1:SUS-ITMY_SUSPOS_EXC and C1:LSC-YARM_IN1. Second, I split the cavity control evenly between the ETMY and ITMY by adjusting C1:LSC-OUTPUT_MTRX. I turned off the local damping and turned on the common DOF global damping (called CARM at this point despite being on just one arm). I then repeated the same TF but driving from C1:SUS-GLOBAL_CARMDAMP_EXC.

The resulting TFs are displayed in the attached figure. The blue curve is then the TF from local damping sensor noise to YARM. The green is global damping sensor noise to YARM. The suppression between local to global is in red. The global damping curve is about 50 to 100 times lower (better) than local damping. This can probably be improved with further tuning to account for remaining differences between the ITMY and ETMY.

Note, the damping loop used in the filter modules for all of these is zpk(0,[15 15],1), with a gain of 30. This purposely has little high frequency filtering so it is easier to see the influence on YARM.

Brett and Kamal

The global damping testing for the week is now complete. The c1sus.mdl simulink diagram settled on the attached screenshot. The top level of c1sus.mdl is shown on the left zoomed in over the new global damping block. The right shows the inside of that block. Also attached in the second screenshot are two of the modal damping MEDM screens. The left shows the main overview screen, the right shows the global damping filters. The overview screen is called C1SUS_GLOBAL.adl and is found in ...medm/c1sus/master/.

We have measured transfer functions and power spectra that show that global damping, with just a moderate amount of tuning (30 minutes of work) reduces the OSEM damping noise seen by YARM_IN1 by a factor between 50 and 80. Log 8193 highlights the transfer function measurements. The power spectra directly measure the noise in the cavity. I am not putting that data here because I have to catch. I will process the data and post it here later.

Overall the global damping tests appear to have been successful, isolating (not removing) the test mass damping noise from the cavity by almost 2 orders of magnitude. Presumably even more isolation is possible with more tuning.

Here is an amplitude spectrum plot of y-arm cavity noise with a 50 Hz cutoff damping filter of the form zpk(0,[50;50],1). The low passing of this filter was intentionally extremely poor in order to see the damping noise in the cavity. The blue trace is the noise with no damping, which may be considered the 'best case' scenario from a noise point of view. The green has regular local damping on the ITMY. The ETMY has no damping for this measurement because the cavity control feedback to the ETMY takes care of its control when the cavity is locked. Notice the the large increase in noise from 40 Hz to 250 Hz, up to 1 order of magnitude. This noise is from the OSEM sensors passing through the damping loops. The red curve shows the y-arm noise with the exact same damping, except it is now applied in the global scheme. In this case, the damping noise falls completely below the baseline level of the cavity and becomes indistinguishable from the 'no damping' case.

If the damping injected enough noise I'd expect we would see a drop of 50 to 80 times switching from local to global. That is, the same factor measured in the transfer functions listed in log entry 8193.  However, the damping noise is only at most 1 order of magnitude above the baseline in this measurement. We would have to increase the damping noise by about another order of magnitude before we could expect to see the global damping noise in the cavity measurement.

The units of the cavity displacement in the plot were calculated using the 1.4e12 counts per meter calibration in log 6834. The measured UGF of the LSC loop at the time was 205 Hz. The peak in the plot above 200 Hz appears to be from this unity crossing. Moving the UGF also moves this peak.

Moral of the story: global damping can isolate the damping noise pretty well from the cavity signal.

 OK. Today we did the same type of measurement for the Y arm laser as was done for the X arm laser here: http://nodus.ligo.caltech.edu:8080/40m/3759 

And attached here is a preliminary plot of the outcome - oddities with adding on the fitted equations, but they go as follows

(Red)    T_yarm = 1.4435*T_PSL - 14.6222

(Blue)    T_yarm = 1.4223*T_PSL - 10.9818

(Green) T_yarm = 1.3719*T_PSL - 6.3917

It's a bit of a messy plot - should tidy it up later...

And I'm going to answer the easy question - they're additional beat frequency temperature pair positions which seem to correspond to additional lines of beat frequencies other than the three highlighted, but that we didn't feel we had enough data points to make it worthwhile fitting a curve.

It's still not entirely clear where the multiple lines come from though - we think they're due to the lasers starting to run multi-mode, but still need a bit of thought on that one to be sure...

 Just a quick update... the Lightwave laser has now been moved up to the end of the Y arm. It's also been mounted on the new mounting block and heatsinks attached with indium as the heat transfer medium.

A couple of nice piccies...

The good news is that we seem to be running in a linear region of the PSL laser with a degree or so of range before the PSL Innolight laser starts to run multi-mode. On the attached graph we are currently running the PSL at 32.26degrees (measured) which puts us in the lower left corner of the plot. The blue data is the Lightwave set temperature (taken from the display on the laser controller) and the red data is the Lightwave laser crystal measured temperature (taken from the 10V/degC calibrated diagnostic output on the back of the laser controller - between pins 2 and 4).

The other good news is that we can see the transition between the PSL laser running in one mode and running in the next mode along. The transition region has no data points because the PMC has trouble locking on the multi-mode laser output - you can tell when this is happening because, as we approach the transition the PMC transmitted power starts to drop off and comes back up again once we're into the next mode region (top left portion of the plot).

The fitted lines for the region we're operating in are:

Y_arm_Temp_meas = 0.95152*T_PSL + 3.8672

Y_arm_Temp_set = 0.87326*T_PSL + 6.9825

X_arm and Y_arm vs PSL comparison.

Just a quick check of the performance of the X arm and Y arm lasers in comparison to the PSL. Plotting the data from the X arm vs PSL and Y arm vs PSL on the same plot shows that the X arm vs the PSL has no observable trending of mode-hopping in the laser, while the Y arm vs the PSL does. Suspect this is due to the fact that the X arm and PSL are both Innolight lasers with essentially identical geometry and crystals and they'll tend to mode-hop at roughly the same temperatures - note that the Xarm data is rough grained resolution so it's likely that any mode-hop transitions have been skipped over. The Lightwave on the other hand is a very different beast and has a different response, so won't hop modes at the same temperatures.

Given how close the PSL is to one of the mode-transition regions where it's currently operating (32.26 degC) it might be worth considering shifting the operating temperature down one degree or so to around 31 degC? Just to give a bit more headroom. Certainly worth bearing in mind if problems are noticed in the future.

Right. I've got a whole load of info and data and assorted musings I've been saving up and cogitating upon before dumping it into these hallowed e-pages. there's so much I'll probably turn it into a threaded entry rather than put everything in one massive page.

An overview of what's coming:

I started out using http://lhocds.ligo-wa.caltech.edu:8000/40m/Advanced_Techniques/Green_Locking?action=AttachFile&do=get&target=modematch_END.png as a reference for roughly what we want to achieve... and from http://nodus.ligo.caltech.edu:8080/40m/100730_093643/efficiency_waist_edit.png we need a waist of about 50um at the green oven. Everything else up to this point is pretty much negotiable and the only defining things that matter are getting the right waist at the doubling oven with enough available power and (after that point) having enough space on the bench to separate off the green beam and match it into the Y arm.

So…

Step 1: Measure the properties of the beam out of the laser. Really just need this for reference later because we'll be using more easily measurable points on the bench.

Step 2: Insert a lens a few cm from the laser to produce a waist of about of a few 100um around the Faraday. Note that there's really quite a lot of freedom here as to where the FI has to be - on the X arm it's around columns 29/30 on the bench, but as long as we get something that works we can get it closer to the laser if we need to.

Step 3: After inserting the FI need to measure the beam after it (there *will* be some distortion and the beam is non-circular to begin with)

Step 3b: If beam is non-circular, make it circular.

Step 4: Insert a lens to produce a 50um waist at the doubling oven position. This is around holes 7/8 on the X arm but again, we're free to change the position of the oven if we find a better solution. The optical set-up is a little bit tight near that side of the bench on the X end so we might want to try aiming for something a bit closer to the middle of the bench? Depends how the lenses work out, but if it fits on the X end it will fit on the Y end.

RIght! Overview out of the way - now comes the trivial first bit

Step 1: Beam out of the laser - this will be tricky, but we'll see what we can actually measure in this set-up. Can't get the Beamscan head any closer to the laser and using a lambda/2 plate + polariser to control power until the Faraday isolator is in place. Using 1 inch separation holes as reference points for now - need better resolution later, but this is fine for now and gives an idea of where things need to go on the bench. The beam is aligned to the 3rd row up (T) for all measurements, the Beamscan spits out diameters (measuring only the 13.5% values) so convert as required to beam radius and the beam is checked to ensure a reasonable Gaussian profile throughout.

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

32 2166.1 1612.5

31 2283.4 1708.3

30 2416.1 1803.2

29 2547.5 1891.4

27 2860.1 2070.3

26 2930.2 2154.4

25 3074.4 2254.0

24 3207.0 2339.4

OK. As expected, this measurement is in the linear region of the beampath - i.e. not close to the  waist position and beyond the Rayleigh length) so it pretty much looks like two straight lines. There's no easy way to get into the path closer to the laser, so reckon we'll just need to infer back from the waist after we get a lens in there. Attached the plot, but about all you really need to get from this is that the beam out of the laser is very astigmatic and that the vertical axis expands faster than the horizontal.

Not terribly exciting, but have to start somewhere.

Step 2: Getting the beam through the Faraday isolator (FI).

Started out with an f=100mm lens at position 32,T on the bench which gave a decent looking waist of order 100 um in the right sort of position for the FI, but after checking the FI specs, it's limited to 500W/cm^2. In other words, if we have full power from the laser passing into it we'd need a beam width of more than 211 um. Solution? Use an f=150mm lens instead and don't put the FI at the waist. I normally don't put a FI at a waist anyway, for assorted reasons - scattering, thermal lensing, non-linear magnetic fields, the sharp changing of the field components in an area where you want as constant a beam as possible.  Checked with others to make sure they don't do things differently around these parts… Koji says it doesn't matter as long as it passes cleanly through the aperture. So… next step is inserting the Faraday.

The beam profiles in vertical and horizontal around the FI position with the f=150mm lens in place are attached. Note that the FI will be going in at around 0.56m.

Additional:

I fired up some old waistplotter routines, and set the input conditions as the measured waist after the lens and used that to work out what the input waist is at the laser. It may not be entirely accurate, but it /will/ be self consistent later on.

Vertical waist      = 105.00 um at 6.282 cm after laser output (approx)

Horizontal waist = 144.63 um at 5.842 cm after laser output (approx)

Definitely astigmatic.

Step 3: Inserting FI and un-eliptical-ification of the beam

The FI set up on it's mount and the beam passes through it - centrally through the apertures on each side. Need to make sure it doesn't clip and also make sure we get 93% through (datasheet specs say this is what we should achieve). We will not achieve this, but anything close should be acceptable.

Setting up for minimum power through the FI is HWP @125deg.

Max is therefore @ 80deg

Power before FI = 544 mW

Power after FI =     496 mW (after optimising input polarisation)

Power dumped at input crystal = 8.6mW

Power dumped at input crystal from internal reflections etc = 3.5mW

Power dumped at output crystal on 1st pass = approx 8mW

OK. that gives us a 90.625% transmission and a 20.1mW absorption/unexplained loss.

Well - OK. The important part about isolators isn't their transmission, it's about how well they isolate. Let's see how much power gets ejected on returning through the isolator…

Using a beam splitter to pick off light going into and returning from the FI. A 50/50 BS1-1064-50-1025-45P. And using a mirror near the waist after the FI to send the beam back through. There are better ways to test the isolation performance of FI's but this will suffice for now - really only want to know if there's any reasonable isolation at all or if all of the beam is passing backwards through the device.

Power before BS = 536 mW (hmmn - it's gone down a bit)

Power through BS = (can't access ejected on first pass)

Power through FI = 164 mW (BS at odd angle to minimise refractive effect so less power gets through)

Power lost through mirror = 8.3mW (mirror is at normal incidence so a bit transmissive)

Using earlier 90.6% measurement as reference, power into FI = 170.83 mW

So BS transmission = 170.83/536 = 0.3187

BS reflectivity therefore = 1 - 0.3187 = 0.6813

Power back into FI = Thru FI - Thru mirror = 155.7 mW

Power reflected at BS after returning through FI = 2.2mW

Baseline power at BS reflection from assorted internal reflections in FI (blocked return beam) = 1.9mW

Note - these reflections don't appear to be back along the input beam, but they *are* detectable on the power meter.

Actual power returning into FI that gets reflected by BS = 0.3 mW

(note that this is in the fluctuating noise level of measurement so treat as an upper limit)

Accounting for BS reflectivity at this angle, this gives a return power = 0.3/0.6813 = 0.4403 mW

Reduction ratio (extinction ratio) of FI =  0.4403/155.7 = 0.00282

Again - note that this upper limit measurement is as rough and ready as it gets. It's easy to optimise this sort of thing later, preferable on a nice open bench with plenty of space and a well-calibrated photodiode. It's just to give an idea that the isolator is actually isolating at all and not spewing light back into the NPRO.

Next up… checking the mode-matching again now that the FI is in place. The beam profile was scanned after the FI and the vertical and horizontal waists are different...

Step 3b: Non-circular? We can fix that...

A quick Beamscan sweep of the beam after the Faraday:

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

25.8 503.9 478.8

25 477.5 489.0

24 447.1 512.4

21 441.6 604.5

20 476.3 645.4

19 545.4 704.1

18 620.3 762.8

OK. It looks not too bad - doesn't look too different from what we had. Note that the x axis is in local table units - I found this useful for working out where things were relative to other things (like lenses and the FI) - but it means the beam propagates from right to left in the plot. in other words, the horizontal waist occurs first and is larger than the vertical waist. Also - they're not fitted curves - they're by-eye, best guesses and there's no solution for the vertical that doesn't involve offsets... discussion in a later part of the thread.

Anyway! The wonderful thing about this plot is that the horizontal and vertical widths cross and the horizontal focussing at this crossing point is shallower than the vertical. This means that we can put a lens in at the crossing point and rotate it such that the lens is stronger in the horizontal plane. The lens can be rotated until the effective horizontal focal length is right to fix the astigmatism.

I used a 200mm lens I had handy - a rough check sweeping the Beamscan quickly indicated should be about right though. Adjusting the angle until the beam size at a distant point is approx circular - I then move the profiler and adjust again. Repeat as required. Now… taking some data. with just that lens in:

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

24 371.7 366.1

21 360.3 342.7

20 447.8 427.8

19 552.4 519.0

18 656.4 599.2

17 780.1 709.9

16 885.9 831.1

Well now. That looks quite OK. Fit's a bit rubbish on vertical but looks like a slight offset on the measurement again.

The angle of the lens looks awful, but if it's stupid and it works then it isn't stupid. If necessary, the lens can be tweaked a bit more, but there's always more tweaking possible further down the line and most of the astigmatic behaviour has been removed. It's now just a case of finding a lens that works to give us a 50 um beam at the oven position...

Step 4: Matching into the oven

Now that the astigmatism is substantially reduced, we can work out a lens solution to obtain a 50um waist *anywhere* on the bench as long as there's enough room to work with the beam afterwards. The waist after the Faraday and lens is at position 22.5 on the bench. A 50 mm lens placed 18 cm after this position (position 14.92 on the bench) should give a waist of 50 um at  24.57 cm after the waist (position 12.83 on the bench). This doesn't give much room to measure the beam waist in though - the Beamscan head has a fairly large finite size… wonder if there's a slightly less strong lens I could use…

OK. With a 66 mm lens at 23 cm (position 13.45 on the bench) after the waist we get a 50 um waist at 31.37 cm after the waist (position 10.15 on the bench). 

Closest lens I found was 62.9mm which will put the 50um point a bit further towards the wall, but on the X-arm the oven is at position 8.75 ish. So anything around there is fine.

Using this lens and after a bit of manual fiddling and checking with the Beamscan, I figured we needed a close in, fine-grained measurement so set the Beamscan head up on a micrometer stage Took a whoie bunch of data around position 9 on the bench:

Position A1_13.5%_width A2_13.5%_width

(mm) (um mean) (um mean)

-15 226.8 221.9

-14 210.9 208.3

-13 195.5 196.7

-12 181.0 183.2

-11 166.0 168.4

-10 154.0 153.1

-9 139.5 141.0

-8 127.5 130.0

-7 118.0 121.7

-6 110.2 111.6

-5 105.0 104.8

-4 103.1 103.0

-3 105.2 104.7

-2 110.9 110.8

-1 116.8 117.0

0 125.6 125.6

0 125.6 125.1

1 134.8 135.3

2 145.1 145.6

3 155.7 157.2

4 168.0 168.1

5 180.5 180.6

6 197.7 198.6

7 211.4 209.7

8 224.0 222.7

9 238.5 233.7

10 250.9 245.8

11 261.5 256.4

12 274.0 270.4

13 291.3 283.6

14 304.2 296.5

15 317.9 309.5

And at this point the maximum power available at the oven-waist is 298mW. With 663mW available from the laser with a desired power setting of 700mW on the supply. Should make sure we understand where the power is being lost. The beam coming through the FI looks clean and unclipped, but there is some stray light around.

Position A1_13.5%_width A2_13.5%_width

(bench) (um mean) (um mean)

7 868.5   739.9

6 1324 1130

5 1765 1492

4 2214 1862

The plot looks pretty good, but again, there looks to be an offset on the 'fitted' curve. Taking a couple of additional points further on to make sure it all works out as the beam propagates. I took a few extra points at the suggestion of Kiwamu and Koji - see the zoomed out plot.  The zoomed in plot has by-eye fit lines - again, because to get the right shape to fit the points there appears to be an offset. Where is that coming from? My suspicion is that the Beamscan doesn't take account of the any background zero offsets when calculating the 13.5% and we've been using low power when doing these measurements - very small focussed beams and didn't want to risk damage to the profiler head.

Decided to take a few measurements to test this theory. Trying different power settings and seeing if it gives different offset and/or a changed width size

7 984.9 824.0 very low power

7 931.9 730.3 low power

7 821.6 730.6 higher power

7 816.4 729.5 as high as I'm comfortable going

Trying this near the waist…

8.75 130.09 132.04 low power

8.75 106.58 105.46 higher power

8.75 102.44 103.20 as high as it can go without making it's saturated

So it looks like offset *is* significant and the Beamscan measurements are more accurate with more power to make the offsets less significant. Additionally, if this is the case then we can do a fit to the previous data (which was all taken with the same power setting) and simply allow the offset to be a free parameter without affecting the accuracy of the waist calculation. This fit and data coming to an e-log near you soon.

Of course, it looks from the plots above (well... the code that produces the plots above) that the waist is actually a little bit small (around 46um) so some adjustment of the last lens back along the beam by about half a cm or so might be required.

 OK. Taking these completely out of order in the easiest first...

2. The FI is between positions 27.75 and 32 on the bench - i.e. this is where the input and output apertures are. (corresponds to between 0.58 and 0.46 on the scale of those two plotsand just before both the vertical and horizontal waists) At these points the beam radius is around 400um and below, and the aperture of the Faraday is 4.8mm (diameter).

1. Photos...

Laser set up - note the odd angles of the mirrors. This is where we're losing a goodly chunk of the light. If need be we could set it up with an extra mirror and send the light round a square to provide alignment control AND reduce optical power loss...

Faraday and angled lens - note that the lens angle is close to 45 degrees. In principle this could be replaced with an appropriate cylindrical lens, but as long as there's enough light passing through to the oven I think we're OK.

3. Fitting... coming soon once I work out what it's actually telling me. Though I hasten to point out that the latter points were taken with a different laser power setting and might well be larger than the actual beam width which would lead to astigmatic behaviour.

Right. Fitting to the data. Zoomed out plots first. I used the general equation f(x) = w_o.*sqrt(1 + (((x-z_o)*1064e-9)./(pi*w_o.^2)).^2)+c for each fit which is basically just the Gaussian beam width parameter calculation but with an extra offset parameter 'c'

Vertical fit for zoomed out data:

Coefficients (with 95% confidence bounds):

       c =   7.542e-06  (5.161e-06, 9.923e-06)

       w_o =   3.831e-05  (3.797e-05, 3.866e-05)

       z_o =       1.045  (1.045, 1.046)

Goodness of fit:

  SSE: 1.236e-09

  R-square: 0.9994

The doubling oven is now ready to go for the Y arm. The PPKTP crystal is mounted in the oven:

Note - the crystal isn't as badly misaligned as it looks in this photo. It's just an odd perspective shot. I then closed it up and checked to make sure the IR beam on the Y bench passes through the crystal. It does. Just need to tweak the waist size/position a bit and then we can actually double some frequencies!

Last bit of oven matching for now.

I moved the lens before the oven position back along the beam path by about 1cm - waist should be just above position 9 in this case. Note - due to power-findings from previous time I'm maximising the power into the head to reduce the effect of offsets.

From position 9:

Position A1_13.5%_width A2_13.5%_width

(mm) (um mean) (um mean)

-1 121.1 123.6

0 112.5 113.8

1 106.4 106.1

2 102.9 103.4

3 103.6 103.6

4 106.6 107.4

5 111.8 112.5

6 118.2 120.1

7 126.3 128.8

8 134.4 137.1

9 143.8 146.5

10 152.8 156.1

11 163.8 167.1

12 175.1 176.4

13 186.5 187.0

14 197.1 198.4

15 210.3 208.9

16 223.5 218.7

17 237.3 231.0

18 250.2 243.9

19 262.8 255.4

20 274.7 269.0

21 290.4 282.3

22 304.3 295.5

23 316.7 303.1

Note - had to reduce power due to peak saturation at 15mm - don't think scale changed, but be aware just in case. And saturated again at 11. And again at 7. A little bit of power adjustment each time to make sure the Beamscan head wasn't saturating. Running the fit gives...

OK. The fit is reasonably good. Residuals around the area of interest (with one exception) are <+/- 2um and the waists are 47.5um (vertical) and 50.0um (horizontal) at a position of 9.09 on the bench. And the details of the fitting output are given below.

-=-=-=-=-=-=-=-=-=-=-=-

Vertical Fit

cf_ =

     General model:

       cf_(x) = w_o.*sqrt(1 + (((x-z_o)*1064e-9)./(pi*w_o.^2)).^2)+c

     Coefficients (with 95% confidence bounds):

       c =   5.137e-06  (4.578e-06, 5.696e-06)

       w_o =   4.752e-05  (4.711e-05, 4.793e-05)

       z_o =        1.04  (1.039, 1.04)

cfgood_ = 

           sse: 1.0699e-11

       rsquare: 0.9996

           dfe: 22

    adjrsquare: 0.9996

          rmse: 6.9738e-07

-=-=-=-=-=-=-=-=-=-=-=-

Horizontal Fit

cf_ =

     General model:

       cf_(x) = w_o.*sqrt(1 + (((x-z_o)*1064e-9)./(pi*w_o.^2)).^2)+c

     Coefficients (with 95% confidence bounds):

       c =    3.81e-06  (2.452e-06, 5.168e-06)

       w_o =   5.006e-05  (4.909e-05, 5.102e-05)

       z_o =        1.04  (1.04, 1.04)

cfgood_ = 

           sse: 4.6073e-11

       rsquare: 0.9983

           dfe: 22

    adjrsquare: 0.9981

          rmse: 1.4471e-06

We now have green light at the Y end. 

The set-up (with careful instructions from Kiwamu) - setting up with 100mW of IR into the oven.

Input IR power = 100mW measured.

Output green power = 0.11mW

(after using 2 IR mirrors to dump IR light before the power meter so losing a bit of green there light too)

And it's pretty circular-looking too. Think there might be a bit more efficiency to be gained near the edges of the crystal with internal reflections and suchlike things but that gives us an UGLY looking beam.  Note - the polarisation is wrong for the crystal orientation so used a lambda/2 plate to get best green  power out.

Efficiency is therefore 0.11/100 = 0.0011 (0.11%) at 100mW input power.

Temperature of the oven seems to be around 35.5degC for optimal conversion.

Took a picture. Ta-dah! Green light, and lots more where that came from! Well... about 3x more IR available anyway.

Every so often things just work out. You do the calculations, you put the lenses on the bench, you manually adjust the pointing and fiddle with the lenses a bit, you get massive chunks of assistance from Kiwamu to get the alignment controls and monitors set up and after quite a bit of fiddling and tweaking the cavity mirror alignment you might get some nice TEM_00 -like shapes showing up on your Y-arm video monitors.

So. We have resonating green light in the Y-arm. The beam is horribly off-axis and the mode-matching, while close enough to give decent looking spots, has in no way been optimised yet. Things to do tomorrow - fix the off-cavity-axis problem and tweak up the mode-matching... then start looking at the locking...

 Locked!

The Y-arm can now be locked with green light using the universal PDH servo. Modulation frequency is now 277kHz - chosen because it seems to produce smaller offsets due to AM effects

To lock, turn on the servo, align the system to give nice circular-looking TEM_00 resonances, and wait for a good one. It'll lock on a decent mode for a few seconds and then you can turn on the local boost and watch it lock for minutes and minutes and minutes.

The suspensions are bouncing around a bit on the Y-arm and the spot is quite low on the ETMY and a little low on ITMY, but from this point it can be tweaked and optimised.

OK… the Y-arm may be locked with green light, which was the goal, and this is all good but it's not yet awesome. Awesome would be locked and aligned properly and quiet and optimised. So...  in order to assist in increasing the awesome-osity, here are a few stream-of-consciousness thoughts and stuff I've noticed and haven't had time to fix/investigate or have otherwise had pointed out to me that may help...

Firstly, the beam is not aligned down the centre of the cavity. It's pretty good horizontally, but vertically it's too low by about 3/4->1cm on ETMY. The mirrors steering the beam into the cavity have no more vertical range left, so in order to get the beam higher the final two mirrors will have to be adjusted on the bench. Adding another mirror to create a square will give more range AND there will be less light lost due to off 45degree incident angles. When I tried this before I couldn't get the beam to return through the Faraday, but now the cavity is properly aligned this should not be a problem.

A side note on alignment - while setting cameras and viewports and things up, Steve noticed that one of the cables to one of the coils (UL) passes behind the ETMY. One of the biggest problems in getting the beam into the system to begin with was missing this cable. It doesn't fall directly into the beam path if the beam is well aligned to the cavity, but for initial alignment it obscures the beam - this may be a problem later for IR alignment.

Next, the final lambda/2 waveplate is not yet in the beam. This will only become a problem when it comes to beating the beams together at the vertex, but it WILL be a problem. Remember to put it in before trying to extract signals for full LSC cavity locking.

Speaking of components and suchlike things, the equipment for the green work was originally stored in 3 plastic boxes which were stored near the end of the X-arm. These boxes, minus the components now used to set up the Y-end, are now similarly stored near the end of the Y-arm.

Mechanical shutter - one needs to be installed on the Y-end just like the X-end. Wasn't necessary for initial locking, but necessary for remote control of the green light on/off.

Other control… the Universal PDH box isn't hooked up to the computers. Connections and such should be identical to the X-arm set-up, but someone who knows what they're doing should hook things up appropriately.

More control - haven't had a chance to optimise the locking and stability so the locking loop, while it appears to be fairly robust, isn't as quiet as we would like. There appears to be more AM coupling than we initially thought based on the Lightwave AM/PM measurements from before. It took a bit of fiddling with the modulation frequency to find a quiet point where the apparent AM effects don't prevent locking. 279kHz is the best point I've found so far. There is still a DC offset component in the feedback that prevents the gain being turned up - unity gain appears limited to about 1kHz maximum. Not sure whether this is due to an offset in the demod signal or from something in the electronics and haven't had time left to check it out properly yet. Again, be aware this may come back to bite you later.

Follow the bouncing spot - the Y-arm suspensions haven't been optimised for damping. I did a little bit of fiddling, but it definitely needs more work. I've roughly aligned the ETMY oplev since that seems to be the mass that's bouncing about most but a bit of work might not go amiss before trusting it to damp anything.

Think that's about all that springs to mind for now…

Thanks to everyone at the 40m lab for helping at various times and answering daft questions, like "Where do you keep your screwdrivers?" or "If I were a spectrum analyser, where would I be?" - it's been most enjoyable!

Y-end PDH electronics.

The transfer function of the Y-end universal PDH box: