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!)
Since we measured thermal noise from the coating(QWL, SiO2/Ta2O5), we want to extract loss angles of each materials. The losses are about a factor of 2 higher than the numbers reported in the literature.
So far, there are 3 calculations we have been using for coating noise estimation.
In essence, both Harry's and Hong's result can be written as a linear combination of phiL and phiH. I used Harry result to compare with Hong to see if there is any differences in the result or not, but both gave me the same answer.
The calculation is attached below. I made sure that the calculation from Hong and Harry are correct by choosing the elastic properties of the coatings to be the same as that of substrate and checking the the results agree with Nakagawa's. So the code should be correct.
Then, I varied phiL and phiH to match the measurement. The measurement is represented by the prediction by Nakagawa with the fitted loss (phiC = 4.15e-4).
Both calculations gave the similar relation between phiH (phi tantala) and phiL (phi silica) to match the measurement:
phiH = -1.4 phiL + 9.7 (Hong)
phiH = -1.44 phi L + 9.77 (Harry) (assume sigma1 = sigma 2 = 0)
The problem is if we use the nominal numbers from various reports, phiL ~ 1e-4, phiH ~ 4e-4. The result will be off by almost a factor of 2. For example, for phiL = 1e-4, this means phi H has to be 8.4e-4. Or if phi H is chosen to be 4e-4, phi L will be ~4e-4 as well. It seems that our result is higher than the predictions (under some assumptions).
Table1 below shows some possible values of phiL and phiH extracted from our result and the calculation.
But we have good evidences from Numata and short/long cavities (spot size dependent) to believe that the measurement is real coating thermal noise . The reason why the prediction is smaller than the measurement could be that the losses is actually higher in our coating. Most ring down measurements were done after 2002 while our coatings were fabricated around 1997. Coating vendors might become more careful about loss and improved their process. But the result from Numata was out in 2003, and it is about the same as ours, so I'm really not sure what can we say about this.
==numbers from literature==
Penn2003: (disc ring down) phiL = (0.5 +/- 0.3) x10^-4 , phiH = (4.4 +/- 0.2) x10^-4
Numata2003 (direct measurement) phiC = 4.4e-4;
Crooks2004(disc ring down) phiL = 0.4+/-0.3 x10^-4, phiH = (4.2+/-0.4)x10^-4 (the frequency dependent part is ignored)
Crooks2006: (disc ring down) phiL = (1.0 +/- 0.2) x10^-4 phiH = (3.8 +/- 0.2) x10^-4 (small change in TE calculation from previous paper)
Martin2009 : (blade) phiH = 3+/- 0.5 x10^-4 (at 300K)
Martin2010: (blade) phiH = (2.5-5) x10^-4 ( heat treated at 600C, several frequencies)
LMA2014: (blade) phiL = (0.43+/-0.02) x10^-4 phiH = (2.28 +/- 0.2) x10^-4
I tried to estimate the coupling from seismic to displacement noise. With the common mode rejection taken into account, the coupling from vertical acceleration to differential length between the two cavities is about 6x10^-12.
In order to get the systematic uncertainty on ϕc, we need uncertainties in other parameters that enter the noise budget. Specifically:
The above uncertainties are enough to estimate the statistical and systematic uncertainties on a fit to ϕc 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 ϕc = (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.
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'm trying to estimate the coupling between seismic to displacement noise of the cavity using COMSOL.
From the design, the strain due to the seismic noise is about 2e-11. But we want to see what happen if the support positions are moved away from the specified points a bit. This time the model is a whole cavity, not just 1/8 as I did before. This is to see results of the mis-positioned support points. However, COMSOL has some problems
Right now I have ~30 data points after 4 hrs of running the simulation. I'll get a bit more data and will see how it goes when I histogram it.
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.
I"m packing the mirrors so that they are ready to be shipped to G. Cole. The mirrors are packed properly, see picasa.
Spacer in BR noise
== COMSOL vs result from Kessler etal 2012==
The analytical result from kessler2012, assume the force acts on whole surface of the spacer (with bore hole), I check this with COMSOL by comparing the result, similar to what I did in PSL:1075. The result agrees well within 2%. This verifies that COMSOL model is correct
==thermal noise level vs annulus thickness==
Typically, the contact surface between the spacer and the mirror is only a thin annulus, see psl:1199 . And the noise level is dependent on the actual area of contact. So I run the simulation to see the dependent of the stored energy (U) vs the annulus thickness. The annulus thickness is about 2 mm +/- 0.2 mm. The displacement noise is proportional to sqrt(U).
fig1: The stored energy as calculated by COMSOL, fitted with cubic polynomial.
The error from the contact area, the simulation result are small ~3% and 2%. These are smaller than the uncertainty of loss in bulk fused silica (can be from 10^-6 to 10^-7). The effect is still small in the total noise.
I looked into the uncertainty in coating thickness of the QWL SiO2/Ta2O5 coating The thickness of 4.53 +/- 0.07 um (~1.5%)seems to be appropriate.
The thermal noise level is directly proportional to the coating thickness, so we want to estimate its uncertainty. The error in the thickness is from
The errors in nL and nH are quite small, nL ~ 1.45 +/ 0.01, nH ~ 2.06+/- 0.01. (From the literature). I also looked around the error in IBS thickness control, they are usually better than 0.1 nm, IBS, but that is the current technology. In literature around 2000s, 2% error seems to be the number estimated for the thickness control (Sullivan 2000, Badoil 2007). As a quick check, I used the same assumption for error propagation similar to that of AlGaAs coating. The result gives ~ 4.53 +/- 0.07 um for coating thickness.
Note that the error here is smaller than the difference in coating thickness for the coatings with or without half wave cap.
For 28 Layer (with cap), the coating thickness is 4.53 um, for 28 layer QWL, the coating thickness is 4.35 um. But after digging up all the information from REO, and peter king they agree that it is 28 QWL with half wave cap. I tried to compare the calculation and the photothermal TF measurement, but the effect is too small to be conclusive about the structure. So the biggest error might come from the fact that the coating has cap or not. The error is about 4%.
I'm trying to record beat measurement for a few days. The data will be taken from ATF using mDV. There are a few issues about mDV right now, I'm looking into it and asking around.
There is a problem with gps.m that converts the string to gps second. It is used in get_data where we specify the start time. I tried enter the gps second manually but it returns an empty time struct, and the get_data cannot be used.
A reminder entry: psl:978
I've added a χ2 minimization routine to nb_short_fit.m which looks for the value of ϕc (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 ϕc. 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 ϕc as 4.18(3) × 10−4, with a reduced of χ2 of 1.23.
From here, the next steps are
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 / ffsr = 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.
I got a chance to measure beat measurement. The noise budget is updated and contains all dominant noise traces.
== Beat measurement ==
1) at DC to 10Hz, the contribution is mostly from RIN driven Photothermal noise and a bit of seismic noise, a small peaks around 10Hz is probably from the stack, not the cavity sagging. The hump from DC to ~ 50Hz disappear when it is quiet. I think it is mostly scattered light associated with the seismic noise, not displacement noise due to the vibration.
2) 10Hz to 1kHz is pretty much Coating Brownian noise.
3) At 1kHz and above, it is PLL readout noise and residual frequency noise from the laser, where the gain cannot suppress enough noise. This is mostly from ACAV. The residual frequency noise = free running noise / (1+ OLGTF). The measurement of the open loop gain is explained below.
==TTFSS Loop characterization==
The OLG TF of TTFSS is measured up to 10MHz and compared with the calculation. The schematic explaning how TTFSS actuates on the laser is shown below.
The freqeuncy discriminator can be measured from the slope of the error signal (from Common out1) while scanning the laser. For RCAV Dv = 1/ (194 kHz/V) and 1/(164kHz/V) for ACAV. with 1mW input power.
The adjustable gain stage can be tuned by turning the dial knob. At 400, gain=1, and the gain changes by 10dB with every 250click.
The PZT actuator has a gain of 4.5MHz/V (measured), and the EOM actuator is 15mRad/V (or 15mHz/f Hz/V) (taken from the spec sheet).
OLG measurement is taken: RCAV OLG is measured and plotted against the theoretical approximation, see the below figure.
above: RCAV OLG TF. Note: The calculation and the measurement do not include the integrator with corner frequency at 4.6kHz.
There are some problems with ACAV loop and I could not increase the gain up as much as it used to be and the UGF is around only 200kHz , but the measurement matches the calculation. Right now RCAV servo has a better loop performance.
The calculated OLG TF trace(green) should go down at 1MHz or above because of the opamps' bandwidth. I used ideal Op Amps in the simulation because I don't have some op amps in my liso library. I'll see if I can fix it.
We heard back from G. Cole about the thickness resolution in the AlGaAs coating manufacturing process will be around 0.5 A. So I'm checking how the noise budget will change by rounding up the physical thickness in opt V4 to the next 0.5A. The design will still work. The round up thickness is added in the google document (for opt v4 only).
The estimated growth rate of the crystal is 4.8A/s and shutter speed is assumed to have 0.1 sec time step. This means the smallest step of the thickness control is ~0.5A. So I round up the physical thickness to the next 0.5 A and calculate the coating properties.
1) Rounding up to the next 0.5 Angstrom. The truncating process acts like a random thickness variation in the optimized coatings with maximum error ~ 0.25 Angstrom. The averaged layer thickness is ~ 800 Angstrom.
2)Results when the layers physical thickness are round up to the closest 0.5 A. The noise budget does not change much.
The coatings properties still hold, even with random error in parameters, thickness.
Note: For the error calculation I did before I used 1 sigma to be 1% for AlGaAs, and 0.5% for GaAs. The thinnest layer is AlGaAs at 35 A, so its sigma is about 0.35 A. The average thickness is 90 Angstrom, so the average error is about 0.9 A. The estimated error in the calibration process is already larger than the error from the truncation(0.25A). That's why the error analysis results are still valid.
This is a good first step, but there are two points:
1) You can NEVER use the SR785 for the FSS loop gain measurement since it doesn't go above the UGF. Use the RF network analyzer and do multiple sweeps to get the resolution using the Mott GPIB code.
2) This seems like its not good enough in the 10-100 kHz band.
3) We need to see how much phase is being lost because of the low modulation frequency and the high Q of the RFPD. Where is the plot comparing the servo model and the measurement?
open loop gain transfer function of RCAV is measured.
1) how to measure OLG TF
The requirement assumes that the residual frequency noise is 5% or less in the total noise. The servo performance is definitely ok for 1.45 inch cavity.
I realized that we have not checked the eigenmodes of 1.45" cavity yet, so I used comsol to find out several modes. The lowest mode is ~ 46kHz, and the first longitudinal mode is about 60kHz. The frequencies are high enough so that the thermal noise calculation in dc- 10kHz frequency band can be done with quasi-static assumption.
1) I tried a simple cylindrical shape, with the dimension of the spacer. The result for the first longitudinal mode is 74KHz, the analytical result is ~ 77kHz, see PSL:1135. It seems that COMSOL's result and the analytical results are comparable.
2) Then I simulated the whole reference cavity. The lowest body mode is ~ 47kHz. The body expand-contract radially, and should not change the cavity beamline length that much. The first longitudinal mode is ~ 60kHz. The color on the surface shows the rms displacement from all direction.
I compared our beat measurement with results from Numata2003 and TNI. They agree well. I'm quite certain that we reach Brownian thermal noise from coatings.
To make sure that what we measure is real Coating Brownian noise (It could be something else, i.e thermal noise in the support, spacer , or optical bond), we should compare our result to previous measurements to make sure that the numbers agree.
Numata etal and TNI reported coating thermal noise measurement from suspended cavities (no spacer). They adjusted loss in the coatings to fit the measurement. Phi coatings as reported in Numata is 4e-4 while TNI gives phi perp = phi_para = 2.7e-4. Both agree with our result, see the plot below. This means that our result is comparable with what they measured. It should be an evidence to support that we see real coating thermal noise, not contribution from something else (spacer, optical bond between the mirrors and the spacer).
Another evidence is from our previous measurement from 8" cavity.
So It is clear that our beat measurements from both 8" and 1.45" cavities are coating Brownian noise limited (around 50Hz-1kHz).
I created an svn folder for my thesis on CTN measurement.
It can be found here
PMC path is back, I aligned the polarization of the input beam to the BB EOM for TTFSS. The visibility of PMC is now ~ 80%.
I'm re-arranging the optics in PMC path a bit. The work is in progress, so ACAV path is still down.
I'm investigating why ACAV TTFSS performance is worse than that of RCAV. One thing is that ACAV has the PMC. This area has not been optimized for awhile, so I'm checking everything.
I add the photo thermal noise effect in the noise budget. With ISS, photothermal noise should be sufficiently small.
What I did
Comment about the beat
Note about RIN measurement
Note about loss angles: For SiO2 and Ta2O5 loss angles = 1e-4 and 7.5e-4 (a factor of 3 above the regular number), the noise budget matches the measurement well. I'll see if it is the same for the data from 8" cavities or not.
We made a mistake by choosing the input power to the cavities to be 0.25 mW, so today I turned them back to 1mW and measure the beat.
Note about the measurement:
To do next:
Yesterday, we did a few final bits of optimization and then re-measured the beat spetrum.
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.
Do you guys have a plot that shows the required loop gain and the achieveable loop gain with this TTFSS on the same plot?
Not yet, we will add this later. but we measured the noise at error point before and it is well below the estimated coating noise.
Plan for this week
Mon: (See Evan's entry for more detail)
I'm putting EOAM back on ACAV path. The setup is roughly optimized.
(14.75 MHz) EOM , EOAM, quarter waveplate and PBS in ACAV path are put back together. I used a half waveplate in front of the EOM to adjust the beam to S- polarization. Right now all the polarizations optimization (to all EOMs, both ACAV/RCAV path) are adjusted to S-polarization with respect to the table. We may have to fine tune it later to match the E field in the EOMs. The EOAM setup is optimized. With +/-4 V, the output power can be adjusted to 1mW +/- 0.09 mW (+/- 9%). The performance is comparable to RCAV EOAM. (10%) . I have not add another half waveplate before the EOAM yet. We can add it back later if we need to adjust the input polariztion to the EOAM.
I checked scattered light in the area between PMC and ACAV. There is a reflection from EOAM back to EOM, but I cannot really block it with an iris. It probably bounces of the case of the EOM or going back to the crystal. Anyway I'll block the beam around this path later.
I have not aligned the beam to the cavity yet, since the temperature was changing because I removed the insulation caps to patch them with black out material.
I put black out material (R @1064 ~0.4-0.6%)on the vac tank insulation caps to minimize any possible scattered light source inside the tank that might leak out. It also keep the surface cleaner from all the foam dust.
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.
Evan found that when common gain is changed, DC offset also changes as well. I'm still looking into the problem.
a part of schematic, the driving signal was sent in through test port (the switch was flipped from off to test), so the signal came through PD line in this page.
We still cannot lock RCAV with TTFSS, so I'm checking the box 2009007 (#7).
Common Gain - DC offset problem
DC offset vs input drive. DC offset is calculated from (Vmax + Vmin) /2 from a sinusoidal signal input. The signal was taken from TP4. The behavior is very non linear and it is impossible to make a table for an appropriate offset level vs common gain setting.
What to do next?
I'm optimizing the setup, and clearing the table a little bit.
To do lists
above: old PBS, bad inter surface can be seen.
above: new PBS: all surfaces are clear
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.
I revised the calculation for photo-thermal noise in AlGaAs coatings, the photo thermal noise should not be a limiting source.
photothermal noise arises from the fluctuation in the absorbed laser power (RIN + shot noise, mostly from RIN) on the mirror. The absorbed power heats up the coatings and the mirror. The expansion coefficient and refractive coefficients convert thermal change into phase change in the reflected beam which is the same effect as the change of the position of the mirror surface.
Farsi etal 2012, calculate the displacement noise from the effect. The methods are
When they solve the heat equation, the assume that all the heat is absorbed on the surface of the mirror. This assumption is ok for their case ( SiO2/Ta2O5) with Ta2O5 at the top surface, all QWL, as 74% of the power is absorbed in the first four layers (with the assumption that the absorbed power is proportional to the intensity of the beam, and all absorption in both materials are similar).
However, for AlGaAs coatings with (nH/nL) = (3.48/2.977) The E field goes in the coatings more that it does in SiO2/Ta2O5, see the previous entry. So we might want to look deeper in the calculation and make sure that photo thermal noise will not be a dominating noise source.
==calculation and a hand waving argument==
The plot below shows the intensity of the beam in AlGaAs Coatings, opt4, and the estimated intensity that decreases with exponential square A exp(-z^2/z0^2). X axis is plotted in nm (distance from surface into coatings). The thickness of opt4 is about 4500 nm. To simplify the problem, I use the exponential decay function as the heat source in the diff equation. But I have not been able to solve this differential equation yet. Finding particular solution is impossible. So I tried to solve it numerically with newton's method, see PSL:284. But the solution does not converge. I'm trying green function approach, but i'm still in the middle of it.
However, the coatings optimized for TO noise should still be working. Evans etal 2008 discuss about how the cancellation works because the thermal length is longer than the coating thickness. The calculation (TE and TR) treat that the temperature is coherent in all the coatings ( they also do the thick coatings correction where the heat is not all coherent, and the cancellation starts to fail at several kHz). So the clue here is that the cancellation works if the heat (temperature) in the coatings change coherently.
For photothermal calculation, if we follow the assumption that all heat is absorbed at the surface (as in Farsi etal), we get the result as shown in psl:1298, where most of the effect comes from substrate TE . In reality, where heat is absorbed inside the coatings as shown in the above plot, heat distribution in the coatings will be even more coherent, and the effect from TE and TR should be able to cancel each other better. Plus, higher thermal conductivity of AlGaAs will help distribute the heat through the coatings better.
This means that the whole coatings should see the temperature change more coherently, thus allowing the TO cancellation in the coatings to work. The assumption that heat is absorbed on the surface should put us on an upper limit of the photothermal noise.
This means that photothermal noise in the optimized coatings should be small and will not be a dominating source for the measurement.
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 KP 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 KI and KD coefficients by a timestep variable, which had been set to zero. I've set it to 1. I've chosen KP = KD = 0 and KI = 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.
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.
Note: last week I picked up the modified diffraction grating mount. I forgot to bring it in today but I'll put it back in the ATF lab on Thursday.
I've spent the last week reading a few papers Tara sent me about mode matching/old elog entries by various people. I couldn't find Tara around the lab today, so I'll try and talk to him this week to figure out exactly what I'm doing. I'm still a bit confused about how to do the setup, although I've been starting to sketch what I'm planning on doing. I'm also messing around with a few mode matching programs to help me plan my setup.
I sent up the power supply for the PD and confirmed it works. I'm going to try to talk to Tara tomorrow or Friday so I know what I need to do in the next week. My midterms are starting so I may have a hard time being around the lab much until afterwards.
After installing the table legs, I have been trying to measure the beat. However, there is an unknown scattered light noise up to 400 Hz. I'm still trying to fix that.
Here are some bullets about what happened, I'll add the details later.
Note: check if the beams in the tank is blocked by wires or not.
Even though it shouldn't be there, there is probably a coupling directly from RIN to the reflected PDH signal on each cavity. So you should measure all 3 terms (RIN 2 PDF for each cavtiy, and RIN 2 Beat).
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.
I checked the dependent of coatings properties with the uncertainty in x (amount of Al in Al_x Ga_(1-x) As). The effect is already within the uncertainties in materials parameters we did before and will not be a problem.
G. Cole told us about the variations in Al contents in the coatings. Right now the values are 92% +/- 0.6%.
(92.10, 91.43, 91.34, 91.57, 92.73, 92.67). Although the deviation is small, the Al content does not always hit 92%, but 92+/- sigma%. So I decided to check the effect of x on the optimization.
The materials properties that change with x are heat capacity, alpha, beta, heat conductivity and n. The values of those as functions of x can be found on ioffee except n. So I looked through a couple of sources ( rpi, sadao) to get n as a function of x, (Note: E0 and D0 are in eV, they have to be converted to Joules when you calculate chi and chi_so). GaAs (nH) has a well defined value ~ 3.48+-0.001, nL has a bit more uncertainty, but it is within the approximated standard deviation of 0.03 . The table below has numbers from the sources. For RPI, I use linear approximation to get nL for x = 0.92 @ 1064nm.
The dependent of n on x is about -0.578 *dx. The numbers from RPI and Sadao are about the same. This means that for the error of 0.6% in Al. nL can change by 0.578*0.006 = 0.0035. The number is almost a factor of ten smaller than the standard deviation of nL and nH I used in previous calculation (0.03). For examples,
This means that the uncertainty in nL/nH (+/- 0.03) we used are much larger than the effect coming from uncertainty in x. This is true for other parameters as well.
I got the modified grating design into the Caltech machine shop; this part should be done by tomorrow. We decided to use 2 vertically placed 1/4-80 holes which will have adjustment screws. This will allow for tilt adjustment.
I found a mixer and a splitter in the CTN lab plus the appropriate adapters to use. I'm still working out how the cable length difference will affect the sensitivity of our measurement.
I have the PD removed from the Gyro table along with the lenses that were used to focus the beam to go into the PD. This was more difficult than I expected to remove these pieces since I'm short and didn't want to disturb the other setup. We are still need several things:
I'll go pick up the modified grating mount from the Caltech machine shop tomorrow so that I can wash it tomorrow afternoon (I don't have much time tomorrow) and do more on Wednesday.
Electric field in coating layer is calculated. This will be used in loss calculation in AlGaAs coatings.
1) average E field in layer is the transmitted E field in the layer.
I attached a short matlab file for a simulation of the combined field. Ein in each layer will be the transmitted beam through the layers. For a value of r close to 1, we get a standing wave. Try changing the value of r in test_refl.m to see the effect
2) Calculation for the transmitted field in each layer
I borrow the notation from Evns etal paper (rbar), the calculation code multidiel_rt.m is attached below. Note: the final transmission calculated in the code is the transmission from the coating to the substrate. To calculate the transmission to the air, multiply the last transmission by 2*n_sub/(n_sub + n_air) which is the transmission from sub to air. Since the thickness of the substrate is not known with the exact number, it will not be exact to the transmision calculated in GWINC or Matt A's code (which do not take the sub-air surface into account), but they will be close, because the reflected beam in the last interface will be small compare to those in the coatings.
The penetration of E field for QWL and different optimized coatings are shown here. The transmissions in the legend are calculated from MattA./GWINC and the values in the parenthesis are calculated from multidiel_rt.m which include the effect from the substrate-air surface. This makes the values in the parenthesis smaller (as more is reflected back and less is transmitted).
Today, I met with Tara and discussed the delay line, which will be used to tune the wavelength of the bare laser diode and measure the free running noise of the ECDL. I will write up notes of what we talked about and how the delay line will work and post these soon, along with a list of items I will need.
Collecting materials for delay line: I will be using an RF photodiode and the series of lenses from the Gyro setup, which Evan is not using right now. I'm in the process of disassembling and reassembling this setup on the table that I'm using. Evan said the mode matching was already messed up, so I will be working on focusing the beam. I will be using NPRO light from the CTN lab via a fiber cable.
Tara helped me modify the piece I found last time, which goes under the collimating lens mount to fix the optical height. I learned how to tap a hole in the metal. I moved the ECDL setup and got the current driver back up and running, and was able to focus the beam using the collimating lens we purchased. The setup so far is attached.
Tara and I decided on a modification to make to the grating mount which will allow for us to make vertical tilt adjustments (we will have 2 holes with adjustment screws, not one). I am going to draw this in Solidworks so that I can get it machined tomorrow at the Caltech machine shop.
I recalculated the coatings properties, with the values of nH and nL to be 3.48 and 2.977. Note about each optimization is included here. Transmission plots are added in google spread sheet. I'll finish the calculation for E field in each layer soon.
Note about each optimized coating version: different versions were obtained from different cost functions, and different number of layers.
Judging from TO noise level, Transmission and reflected phase, I think opt4 is the best choice for us. The structure consist of thick nH layers and thin nL layers. This is good for us in terms of thickness control.
Tara mentioned that the TEC may not work as well without some of the silicone thermal paste so I added some and returned the PID gains. Sure enough, this helped the temperature stabilize (and now I know if it stops working to clean out the Peltier element with isopropanol).
I emailed DMass about finding a PCB for building the low noise current controller. (I was supposed to do this last week but it slipped my mind)
I moved the laser diode and socket to the actual laser diode mount (from the Michelson setup used in August). Since the laser diode extrudes, we do not have the problem I mentioned last time with the base plate since the hole for mounting the collimating lens is now close enough that we should have enough adjustability to focus the beam. I searched the ATF lab and found a piece of metal about 3mm high, which will fix the difference in height of the diode mount and the collimating lens mount. However, this piece needs to be trimmed down, which I will try to discuss with Tara. Not sure if we have those capabilities here or if I need to take it to the machine shop?
I wasn't able to find Tara today but I need to talk to him about:
Finally, I'm still working on editing my SURF paper. I'm new to LaTex so it's taking me awhile to perform the edits Rana suggested.
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: