40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  PSL, Page 50 of 52  Not logged in ELOG logo
New entries since:Wed Dec 31 16:00:00 1969
ID Date Authorup Type Category Subject
  1298   Tue Aug 13 21:45:51 2013 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

I rechecked the TF between power fluctuation and frequency noise in beat measurement that I did last year. The estimated result agrees more with the measured result. This can be used to estimate the requirement for ISS for SiO2/Ta2O5 and AlGaAs coatings.

The calculation is taken from Farsi etal 2012 (J. Appl. Phys. 111, 043101), and compared with the measurement from 8" cavities, SiO2/Ta2O5 QWL with SiO2 1/2 wave cap. The code I wrote before has several mistakes, so I fixed them.

Mistakes in the original code:

  1.  Beta effective was for 1/4 cap of nL: I changed it to the right one (1/2 cap of nL). This can be done by GWINC or an analytical result.
  2.  Cut off frequency ws, wc in the paper, I divided by a factor of 2*pi make them in Hz.
  3. Missing a factor of imaginary in thermoelastic in coatings calculation.
  4. r0 in the paper is where the power is dropped by 1/e, so r0 = w0/sqrt(2) where w0 is the radius of the beam when the power is dropped by 1/e^2.

farsi_2013_08_13.png

Above: Measurement(purple) from SiO2/Ta2O5 coatings and analytical result (cyan) in comparison. Finesse = 7500 (old ACAV), absorbtion = 5ppm.  The slope at high frequency seems to be real TO noise. Notice that phases from TE and TR have different sign and cancel one another.

 

==for TO optimized AlGaAs coatings==

RIN_TO_algaas.png

Above: Calculation for RIN induced thermo noise for optimized AlGaAs coatings in Hz/Watt unit. The calculation is for 200 ppm transmission,-> Finesse ~14 000. 1.45" cavity. The cancellation in coatings will reduce the noise. The estimated effect is plot against the measurement from 8" cavity, T=300ppm, SiO2,Ta2O5 cavity.

We might have to make sure that RIN is small enough, since this time we will have no common mode rejection like what we had with just a single laser. I'll add the estimated requirement later.

Attachment 2: farsi_2013_08_13.fig
Attachment 4: RIN_TO_algaas.fig
  1300   Fri Aug 16 04:35:58 2013 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

I estimated the requirement for laser RIN for AlGaAs coatings. The result is a factor of 5 more stringent from what we need for SiO2/Ta2O5 cavity.

See some calculation about RIN requirement PSL:1270.

I estimated the RIN induced TO noise in AlGaAs cavities. Due to the TO optimization, the effect will be small and we will see only the effect from the substrate, see RIN induced noise estimate.

RIN_req_algaas.png

 This will be quite serious, if we do not have a good ISS, since we will not have common mode rejection like what we had with the single laser setup anymore. I'll look up what was the RIN performance we had before.

Attachment 2: RIN_req_algaas.fig
  1305   Fri Aug 16 22:05:27 2013 taraDailyProgressBEATnoise hunting

 Noise hunting is in progress, I checked the error noise from ACAV and RCAV loops and compared them to the beat. The beat is about an order of magnitude higher than the sum of error noise.

 NOte: slope of error signal RCAV = 1.57 MHz/V (13 dBm from Marconi, throug 4-way splitter, to BB EOM, 1mW input power).

 nb_short_cav.png

ABOVE: beat signal in comparison with noise at error points from ACAV and RCAV loops. The beat signal is about an order of magnitude higher than the error noise.

 

I'm working on optimization and noise characterization of the setup. Before measuring the beat I have to make sure that:

  • The beams to the cavities are aligned
  • The power input is 1mW for both cavities
  • I aligned the polarization of the beams into EOM for side band ( minimizing RFAM)
  • The gains for TTFSS are adjusted and recorded
  • Beams in the beat setup are aligned, and dumped properly.
  • The PD is not saturated.
  • PLL is setup properly.

I think the gain in the TTFSS is the problem. For ACAV, the scattered light from the window interferes with the main beam and causes the loop to oscillate when the gain is up. For RCAV, the EOM is a broadband one and does not have enough gain. The bump in the frquency lower than 100Hz is probably the contribution from scattered light. I have not properly dumped all beams yet.

 

Also I noticed that the beat signal has weird sidebands at +/- 100kHz, 200kHz, and 300kHz, see the figure below. I'm not sure why, I have not seen it before. I might saturate the PD making it distorted from a perfect sine wave. I'll investigate this.

beat_psd.jpg

Attachment 2: nb_short_cav.fig
  1307   Tue Aug 20 20:10:01 2013 taraDailyProgressBEATnoise hunting

Noise hunting is in progress. Today I identified that scattered light from the window is one of the problem.

I spent sometime making sure that all the beams in the input optic and the beat areas were dumped properly. I also tightened all the screws on the optics and the mounts on the table.

I mentioned in the previous entry that for RCAV, the reflected beams from the cavity and the vacuum window overlapped a little bit. The window beam was much smaller and actually closer to the edge of the main beam, so I used an iris to remove the outer path, and let only the beam in the center area go through to the RFPD. With that I could increase the gain in RCAV loop to Common/Fast = 624/750, where they used to be ~ 600/600 before. The iris might introduce some extra scattered lights, since it clips a part of the beam.

The scattered noise around DC to 100 Hz is reduced a bit, see the below figure. However, not much improvement in the flat region (100Hz and above). Plus, some mechanical peaks around 1kHz appear with higher level than before.

 beat_2013_08_20.png

I expected the scattered noise will be even lower if the cavities are tilted a bit to avoid the beams overlapping. At higher frequency, it might be the gain limit from RCAV loop where the modulation depth is very small.

Next thing to do is to increase more power in the modulation depth for RCAV.

==Note==

I found out that the sidebands in the beat signal mentioned in the previous entry changed with the gain of the TTFSS (both ACAV and RCAV). With higher gain, the sidebands are suppressed more. It might have to do with the PZT resonant of the NPRO. 

  1309   Thu Aug 22 00:29:32 2013 taraDailyProgressNoiseBudgetinstalled EOAM

I installed an electro-optic amplitude modulator (EOAM) in RCAV path. Better optimization will be needed to reduce extra noise.

 EOAM.jpg

above, the setup for ISS actuator, the first 1/2 wave plate rotates p-beam to s-beam, EOAM, 1/4 Wave plate that tuned so that the output beam is 45 degree so the power transmitted through the final PBS is reduced in half.

 

After the EOAM was added, I checked the beat noise and saw a bump at ~ 2 kHz, see the figure below(blue plot). This was from the EOAM even though there was no input drive. It disappeared after I changed the EOAM position by rotating it a bit( yellow plot). I have not finished with optimizing it yet. I'm thinking about what kind of mechanism that causes the noise here.

 

nb_short_cav.png

  1310   Thu Aug 22 13:36:19 2013 taraDailyProgressNoiseBudgetTransfer Functions (RIN to Frequency noise via photothermal)

 I went through all the code with Evan and found another mistake. This time the code should be correct, and the result is close to what we measured a year ago.

 The calculation in PSL:1014 is wrong. There should be no square root for the absorption power (Finesse/pi * absorption).  With that correction, and an assumption of absorption of 18ppm in the mirrors (9ppm on each) with Finesse of 7000, see PSL:425. The result matches with the calculation quite well.

fasi_2013_08_22.png

The validity of this result depends on the absorption factor and cavity finesse. The finesse was measured, but the absorption measurement has never been done. So it might be good to think about how to measure that.

We did the same measurement with the current ACAV 1.45" cavity. Evan will post the result later.

Attachment 2: Farsi_compare.fig
  1311   Thu Aug 22 20:31:28 2013 taraDailyProgressNoiseBudgetinstalled EOAM

The bump at 2kHz in the beat signal that I saw before was also from RFAM. By adjusting the 1/2 waveplate in front of the sideband EOM, the bump disappears. I still don't understand why adjusting the EOAM can reduce the bump from RFAM.

 As I planned to add the eom driver to the BB EOM for sideband in RCAV path, I wanted to see the improvement without worrying about the EOAM optimzation. So I removed the EOAM, but I still saw the bump I observed before. This time it came from the RFAM. By adjusting the wave plate to match the polarization of the input beam to the EOM axis, the bump is gone.

RFAM.jpg

above: From right to left, 1) laser for RCAV, 2)&3) 1/2 and 1/4 wave plates, 4) lense, 5) Faraday isolator, 6) 1/2 wave plate, 7)BB EOM for frequency locking, 8) BB EOM for side band, the EOM driver is attached to the side (in aluminum foil wrapped box). RFAM is minimized by adjusting (6) 1/2 wave plate.

I added the EOM driver, however it was not yet modified for 14.75 MHz, so the amplification is small, see PSL:1234 . After adjusting the phase of the demodulated sigmal, the error signal slope is increased by a factor of 2. Then I remeasured the beat signal, and the beat was better by ~ a factor of 2 at high frequency. So I think now the signal is gain limited (in RCAV loop) at high frequency. This makes me confused why the error noise from RCAV loop does not match the beat signal in PSL:1307. I have to re check my work.

 nb_short_cav.png

The next few things to do are:

  • minimize RFAM (by temp control on both EOMs )
  • re-install EOAM in RCAV path, think about alignment
  • now scattered light at low frequency might come from seismic noise as well. I'll order the new floating table legs soon.
  • check other noise limit to make sure that it will not be dominating (shot noise, electronic noise)
  • modify the EOM driver, so that we have more gain in RCAV path.

 

 

Attachment 2: nb_short_cav.fig
  1313   Sat Aug 24 15:42:54 2013 taraDailyProgressVacuumpumping down the chamber

I closed the chamber. The turbo pump is on and pumping down.

 I realigned the beams so the visibilities for both cavities were 80% or more. This made sure that the beams' path would be close to the optimized path.

Now, the window reflection won't overlap with the cavity reflection, and can be dumped properly.

Note about a few things to do:

  • The beam holes on the foam might have to be fixed, the beams slightly clip at the openings. I have to check if the beams are clipped at the periscope or not.
  • modification of the seismic stack as suggested by Koji. The teflon pieces at the bottom plate are not screwed down to the stack making it hard to put the stack in the chamber. I think this should be fixed after the SiO2/Ta2O5 measurement is done and we have to reopen/ installed AlGaAs cavities.
  • There is some strayed beam from the PBS in RCAV path. This is from left over beam in S-light that reflected off, and bounced back at the PBS surface before going to the PD. This might have to be fixed too.

FYI for torque wrench setting for CTN cavity:

Quote:

cf_torque2.pdf

 The CTN cavity is 10" OD,  the Torque required is 190 InchPound.

  1315   Tue Aug 27 16:11:26 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

Since the optimized layer structure is designed, I'm checking how the coatings properties change with error in layer thickness.

G.Cole said that they can control each layer thickness within 0.3%. So I tested the optimized coatings properties by adding some random number within +/- 0.5% on each layer thickness. The results are shown below for 10 000 test.

The error check does the following:

  • start from the optimized coating structure reported in PSL:1291.
  • add random thickness to each layer, within 0.5% of each layer
  • calculate the values of interest, then histogram them.

The figure below is an example of the varying layer thickness added by rand command. They are confined within 0.5%.

layer_error.png

 1) result from the error in thickness control

error_analysis_0.5percent.png

Above: histograms of the important values. top left, reflected phase. top right, ratio between PSD of Brownian noise and Thermo optic noise at 100 Hz. Bottom left, transmission. Bottom right, total coating thickness error.

 

 comments: this test is chosen for 0.5% error which is almost a factor of 2 worse than what they claimed (0.3%), so the actual result should be better. I assumed 0.5% errof because of the irregular layer structure of the optimized coatings, there might be some more error in the manufacturing process.

  • Reflected phase: we want the reflected phase to be close to 180, so that the E-field at the coating surface is close to 0. more than 50% of the results are within 179.5degree, this means that the power build up will be ~ Finesse/pi * Power input * sin^2 (0.5degree)  ~ less than 0.4 mW, so there should be no problem about burning at the surface.
  • ratio between PSD of Brownian/Thermo optic noise. This plot imply how well the cancellation works. Since Brownian noise will almost not change (both materials have the same loss, total thickness varies less than 1%), the ratio of Br/TO noise (at 100Hz) tells how much TO cancellation is. From the histogram we are quite sure that cancellation will work most of the time.
  • Transmission is good around 200+/- 10ppm this is ok with the requirement.
  • total physical error is ~5nm while the coatings thickness is ~ 4um. so the total error is <0.1% Brownian noise calculation will not change much.

2) result from different calculated Beta values:

Here I checked what happen if the beta calculation was wrong, and the error is still within 0.5% in each layer.

In Evans paper, the effect from "Thermo-refractive" comes from the phase changes of the wave travels in each layer. So it includes the effect from dn/dT and dz. The effective beta for each layer is given as

evanB8.png[evan B8],

where alpha bar is

evanA1.png[evans A1]

Where s denotes substrate, k denotes the material in each layer (high or low indices).

So my, calculation & optimization have been using these equations.

However, in the original GWINC code for TO calculation, the calculation [B8], alphabark( used in dTR) is not the same as A1, but rather.

alphaH * (1 + sigH) / (1 - sigH)

see getCoatLayerAGS.m.  Line 16-17.

This is used in the calculation for beta effective in getCoatTOphase. Line73-74. Notice that for dTE, the alpha_bar_k is the same as used in Evans. (line 77).

the comment says "Yamamoto thermo-refractive correction". I emailed kazuhiro yamamoto, but never got a response back. So I keep using the same formula as in Evans because I don't see the reason why the expansion contribution should be different between TE and TR.

So this is the nb plot for TO noise from the optimized coating, if using yamamoto TR correction.

yamamoto_TR_correction.png

Above: nb from the optimized coatings, using Yamamoto TR correction. The cancellation becomes worse, but TO is still lower than other noise.

 

Finally, I repeat the same error analysis for random noise in the thickness (+/- 0.5%).

 yamamoto_error.png

Most of the parameters behave similarly, except the cancellation (upper right plot). Now BR is only ~ x12 larger than TO noise because of the worse cancellation. Good news is, it still below Brownian noise, the cancellation still somehow works.

 

=summary=

  • From the optimized coating structure (T=200ppm), thickness control within 0.5% in each layer will make the coating work as expected.
  • The yamamoto TR correction is still an unresolved issue, but the optimized coating will still work.
  • we should be ready to order soon.
Attachment 2: error_analysis_0.5percent.fig
Attachment 6: yamamoto_TR_correction.png
yamamoto_TR_correction.png
  1317   Wed Aug 28 20:19:44 2013 taraNotesEOMEOM driver: modification

We modified the EOM driver, so that the resonant frequency is now~ 14.75MHz. The full test will be done later.

As mentioned in PSL:1311, the resonant frequency on the EOM driver was not at 14.75MHz. Evan and I discussed about how to modify it and decided tof change L4 from 1.4uH to 3 uH, see the schematic here.

 

driver1.jpg

driver2.jpg

above, the driver after the inductor was replaced. The new one has a shield to reduce any magnetic field leakage. The legs are not fit with the footprint on the PCB, so I had to solder it to another wire to reach the footprint.

 

driver_TF.jpg

above: the TF of the driver measured between the drive and the mon output. Red trace shows the TF before the modification. Yellow  trace shows the TF after the modification, notice the peak is at 14.75MHz, the Q is about the same.

  1318   Wed Aug 28 21:21:38 2013 taraNotesopticGWINC for TO calculation: recap

Here is a summary for how I verify the codes for TO calculation.

So far, we have been using a set of modified GWINC codes to calculate TO noise, but I have not mentioned how did I make sure that the codes were reliable. So I'll try to explain how I check the codes here.

==What do we compute?==

  For the TO nosie calculation and the optimization, we are interested in:

  • effective dn/dT (TR coefficient) of the coatings
  • effective alpha (TE coefficient) of the coatings
  • total reflectivity of the coatings (including the phase), and transmissivity

==Beta calculation check==

For TR coefficient we can compare GWINC with an analytical result (see Gorodetsky,2008, and Evans 2008) (when # of layers ~ 50 or more), see psl:1181. I tried the solution with nH, 1/4 cap and nL, 1/4 and 1/2 cap. All results agree.

==Alpha calculation check==

 There is no complication in this calculation. The effective alpha is just the sum of all layers. This calculation is quite straight forward.

==reflectivity check==

   This was done by reducing the coating layers to one or two layers and comparing with an analytical solution by hand. I checked this and the results agreed.

 

So I think the calculations for TO noise is valid, the noise estimated from the optimized coatings is done with some error check (previous entry). I think we should be ready to order.

  1319   Thu Aug 29 13:25:49 2013 taraDailyProgressVacuumpumping down the chamber

The turbo pump is removed, and the ion pump is on. The initial value is ~7mA.

I removed the turbo pump and turn on the ion pump, see the procedure on wiki page. The initial value on the ion pump is ~ 7mA, similar to the last time we opened the chamber although this time I left the turbo pump on 4 days instead of 2 days. So I think this is the limit of this turbo pump.

 

  1320   Sun Sep 1 18:38:37 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

I updated the optimization and error analysis. The error in optimized structure is comparable to that of a standard quarter wave length structure.

      After a discussion with Rana, Garrett, and Matt, I fixed the thermo-optic calculation, and the error analysis done in PSL:PSL:1315.  The modifications are

       1)  fix the TO calculation (Yamamoto TR correction): There is a modification for TR correction that is not in Evans etal 2008, paper. I contacted M. Evans to ask about the details of this correction which is done in GWINC.  

       2)  Try another optimized coatings with the correct TO calculation:  After the correction, I ran doAlGaAs.m code, cf PSL:1269  using fmincon function , to find another optimized structure. The result is shown below.

2013_09_01_opt_nbv2.png

above) layer structure in optical thickness, the .fig and .mat file are attached below. Note .mat file contains 54 layers, you need to add 1/4 cap to the first entry to calculate the noise budget.

  2013_09_01_opt_nb.png

above) noise budget of the optimized coating.

       3)  Repeat the error analysis : This time I used the following assumptions (from G Cole)

  • the error is not random among each layer
  • the error is constant in each layer type, ie all the layers from the same material (nH or nL) have the same percentage of error,
  • error from nH and nL have the same sign. If one is thicker, another one is thicker, but the magnitude are uncorrelated.
  • nH (GaAs) has better thickness control with 2sigma = 1percent, while nL(AlGaAs), has 2sigma = 2 percent.

error_dist.png

Fig1: Above, percentage of error distribution between the two materials used in the calculation. nH(red) has 2 sigma = 1% and nL(blue) has 2sigma=1%.The same error distributions are used for both optimized layers and QWL layers in comparion, see fig2.

The section below is the algorithm used to distribute the error, this one makes the error between the two materials to be the same sign. The whole code can be found on svn.

mu1 = 0;
sigma1 = 0.5;  % 2sigma is 1percent;
mu2 = 0;
sigma2 = 1;

run_num = 5e4; % how many test we want

errH = normrnd(mu1,sigma1,[run_num,1]);  %errH in percent unit
 
errL = normrnd(mu2,sigma2,[run_num,1]);  %errL in percent unit   
errL = abs(errL).*sign(errH);                        %make sure that errH and errL have the same sign

dOpt = xout;             % xout from doAlGaAs (optimized layer)
dOpt = [ 1/4 ; dOpt];    % got 54 layer no cap from doALGaAs, need to add the cap back

dOpt_e = zeros(length(dOpt),1);


  for ii = 1:run_num;

dOpt_e(1:2:end)= dOpt(1:2:end)*(1+ errH(ii)/100 );
dOpt_e(2:2:end)= dOpt(2:2:end)*(1+ errL(ii)/100 );

 

 

===Result==

This time I calculated the change in reflection phase (TOP left), the ratio between TO noise from the coatings with error and the coatings with no error(top right), transmission (bottom left), and ratio of BR noise ( bottom right). The result from the optimized coating(blue) is compared with the QWL coating (black).

 error_compare_opt0901v2.png

Fig2: Error analysis, in 5e4 run. Blue: from optimized coatings Black:from 55 QWL coatings, from 5x10^4 runs.

Reflection phase: The reflection phase can be away up to ~6 degree. The power at the surface will be ~Finesse/pi * Power input * sin^2 (6degree) ~ 50mW. Seems high, but this is about a regular power used in the lab.

Ratio of PSD TO/TO_0 : At worse, it seems the PSD TO noise will be ~ a factor of 10 higher than the design. However, this will be still lower than BR noise. I plotted only the error distribution for optimized coatings because for QWL coatings, the ratio will be about the same, since TO is dominated by TE.

Transmission: Most of the results are within 197-200 ppm. The optimized coating has transmission ~ 197ppm. The QWL with 55 layers has transmission ~100ppm.

Ratio of BR: not much change here.

 

Attachment 2: error_compare_opt0901v2.fig
Attachment 6: 2013_09_01_opt_nbv2.fig
Attachment 7: 2013_09_01_200ppm_54v2.mat
  1321   Mon Sep 2 03:38:27 2013 taraDailyProgressNoiseBudgetbeat

It's a quiet night, so I went down the lab to measure the beat signal. We are getting close. I think I have to review my noise budget calculation and estimate the error in the measurement carefully.

So after a few things Evan and I did a few days ago:

  1. rotate the stack to get rid off the reflected beam from the window
  2. fix the insulation so the beam is not clipped on the opening.
  3. add more modulation depth to RCAV path with the EOM driver (tuned to 14.75MHz)
  4. Minimize some RFAM, by rotating the half wave plate in front of the sideband EOM

Then I measured the beat signal.

We reduce some noise from scattered light at frequency below 100 Hz, we are limited by some white noise at high frequency ~ above 1 kHz.

beat_2013_09_02.png

fig1: measurement vs noise budget

zoom_beat_2013_09_02.png

fig2: zoom in. The slope of the measured signal agrees well with the slope of thermal noise.

ToDo

  • Estimate/measure shot noise PD noise and electronic noise in the setup. See if they match up with the measurement.
  • Review the noise budget calculation. Looking at the slope of the signal around 1kHz, I think the calculated brownian noise is lower than what it should be.
  • noise hunting, seems like scattered light at frequency below 100Hz. There are many mechanical peaks, and harmonic lines at higher frequency.
  • add the contribution from RIN induced TO noise in the nb.
Attachment 1: zoom_beat_2013_09_02.png
zoom_beat_2013_09_02.png
Attachment 3: nb_short_cav.fig
  1322   Mon Sep 2 18:31:46 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

Coating optimization and error analysis are updated, see PSL:1320.

  1327   Sat Sep 7 04:29:32 2013 taraDailyProgressNoiseBudgetbeat

Short note from tonight measurement:

1) scattered bump from dc to 100Hz is mostly from seismic. It is worse during the day. It gets smaller at around 3-4 am. Unless we have a better seismic isolation, we might not be able to see anything below 100Hz.

2) RIN shape from RCAV changes, reasons still unknown. (DC level 0.7 V)

3) I might see the effect from RIN induced TO noise at frequency ~ 1-3 kHz. (compare RIN and beat).

I'll get into details tomorrow.

  1329   Mon Sep 9 02:27:46 2013 taraDailyProgressNoiseBudgetRIN induced TO noise in beat

The measured RIN is measured and converted to frequency noise via photo thermal effect then compared to beat. The effect seems to be significant now since we lost the common mode rejection.

I measured RIN after ACAV (there is only one PD behind ACAV right now. we will add another one for RCAV soon). The magnitude is comparable from what we measured before but the peaks seem to change, see PSLPSL:1326, :PSL:1308(8"cavity) PSL:742 .

ACAV_RIN.png

The peaks around kHz  are more clear. I'm not sure where they are from, but I think it is associated with vibration on mirror mounts that causes beam jitter. Because the peaks look like mechanical peaks, and this time the cavities are shorter, the beamsize is smaller from 8" cavities, the same beam misalignment will cause the power coupled into the cavities to change more compared to that of 8" cavity. We can check that by mis-aligning the input beam a bit, and see if RIN becomes larger or not.

The coupling from RIN to frequency noise is discussed in PSL:1328

I applied that to the measurement and here is the result. Note, only the effect from one cavity (ACAV) is taken into account.

beat_2013_09_06.png

The peaks seems to match up, especially around 20-30Hz and around 1kHz, see the zoomed in picture below. This makes me think that we might be limited by RIN noise now.

rin_noise.png

 

To Do next:

  • Install ISS system on RCAV (PD behind the cavity / EOAM)
  • Re-measure the coupling from RIN to frequency noise of the cavity
  • Measure RIN and apply it to the noise budget.
  • Find out what causes RIN to change
Attachment 2: rin_noise.fig
Attachment 4: ACAV_RIN.fig
Attachment 5: beat_2013_09_06.fig
  1331   Mon Sep 9 21:19:24 2013 taraDailyProgressNoiseBudgetRIN induced TO noise in beat

I'm trying to understand the measured RIN in the setup. The evidence suggests that the measured RIN in 100Hz- 6kHz, is real intensity noise and not associated with alignment + jitter.

==Problem==

As seen in PSL:1329 that we might be limited by RIN at high frequency, I tried to figure out what cause the shape of the RIN around kHz to be mechanical -like peaks. So the problem can be minimized, and does not have to rely on ISS that much.

==Assumption==

My assumption was that they were from mirror mounts, because

  1. the frequencies were close to mechanical resonances of the mounts, see PSL:818, PSL:824 for examples. The power coupled into the cavity would reduce, and thus causing the peaks in the RIN measured behind the cavity. And
  2. the shape changes during the time of measurement. During the day, the shape is like a big bumb, while during the night, around 2-3am, the level is smaller and the individual peaks shows up instead (may be because of the lower seismic)

==Measurement==

So to test this, I measured RIN before and after ACAV (NOTE:ACAV path has PMC in it),  when

  1. The beam was well aligned to the cavity (DC from REFL PD =94mV, total level ~ 1.6V)
  2. The beam was misaligned a bit (DC from REFL PD = 175mV)

front_ACAV.jpg

above, beam path in front of ACAV, before the beam enters ACAV. The PD for RIN measurement is circled in blue.

benid_ACAV.jpg

above, beam path behind ACAV.

If the measured RIN was from the jitter, RIN after the cavity should change with the alignment, and RIN before the cavity should not change much. I made sure that the spotsize on both PDs are significantly smaller than the PD to make sure that any jitter in front of the cavity should not change the power level that much.

RIN_ACAV.png

==comments about the result==

  • The result agrees with the assumption at low frequency (DC - 30Hz),
  • However, from 100Hz and above, the measured RIN from four cases are very similar.
  • The measured coherence between the two PDs are similar in both cases (aligned and misaligned), I plotted the one from the misaligned beam. It shows that at low frequency, RIN behind and after the cavity are not caused by the same mechanism, the one behind PD might suffer more from jitter. However, at 100Hz and above, anything observed before the cavity is seen behind the cavity as well. This rules out the assumption that the alignment change due to the motions(resonant peaks) from optics.
  • As a comparison, I plotted RIN measured around 3am in brown trace, see PSL:1329, the level is smaller than those measured in the evening. It still makes me think that it is related to seismic but not alignment. I have to think about what other seismic driven mechanism might cause this intensity noise.
  • The level of RIN seems to change as well, I looked at Evan's measurement, earlier today[/PSL:1330]. The bump around 1kHz is ~ 2e-6 1/rtHz, while for my measurement, it is close to 1e-5.  I'll try to investigate more to find out what change the level of RIN.

==To do next==

  • Pick up the beam some where before PMC to check the RIN level and see where the peaks occur
  • Install PD behind RCAV, see RIN from RCAV
  • update noise budget: add RIN induced noise from ACAV and RCAV.
Attachment 2: RIN_ACAV.fig
  1332   Tue Sep 10 04:53:34 2013 taraDailyProgressNoiseBudgetRIN induced TO noise in beat

The cause of the peaks around 1kHz in RIN is solved, PMC is the reason. After damping it, the peaks disappears.

Short notes from tonight measurement:

  • RIN in ACAV is better after PMC is damped, no peaks around 1kHz anymore.
  • The peaks in the beat measurement also disappear, so we really see photo thermal noise.
  • PD for RIN measurement behind RCAV is added, RIN is measured.
  • I Will add the effect from RIN and compare with beat measurement soon.

need to buy:

  •    new PBS for PDH locking. the one for RCAV is not good because there is an unwanted reflected beam going to the RFPD.
  •  other optics for EOAM for RCAV
  1338   Tue Sep 17 19:43:45 2013 taraSummaryNoiseBudgetCoating Thermal Noise Calculator

Quote:
...
...
The attached figures show that the two techniques agree to better than 20% of the GWINC output, with most of the mismatch at higher frequencies. I'm not yet sure why that is. It could be due to my improved integration in calculating Evans' thick coating correction, it could be due to my using a different form of the equation for Braginsky's finite substrate correction for the thermo-elastic noise, or it could just be due to some minor differences in the precision of some of the input values. ..

 

 

 I checked the calculation. I think most of the discrepancies are from the thick coating correction calculation (from Evans etal paper). The error is frequency dependent, and the calculations that involve frequency dependence are temperature fluctuation and thick coating correction. The temperature fluctuations are the same from our results. So it is most likely the thick coating correction. I checked and the corrections did differ at high frequency.

 I need to take a closer look to tell exactly where the errors are. Since the error is small and only at high frequency (around the shot noise limit, 10kHz),  I don't think it will be a problem for us.

  1340   Wed Sep 18 21:55:11 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

 

Optimized coatings structure.

 

Attachment 1: opt_coatings.mat
  1342   Thu Sep 19 14:55:11 2013 taraSummaryNoiseBudgetCoating Thermal Noise Calculator

Quote:

Quote:
...
...
The attached figures show that the two techniques agree to better than 20% of the GWINC output, with most of the mismatch at higher frequencies. I'm not yet sure why that is. It could be due to my improved integration in calculating Evans' thick coating correction, it could be due to my using a different form of the equation for Braginsky's finite substrate correction for the thermo-elastic noise, or it could just be due to some minor differences in the precision of some of the input values. ..

 

 

 I checked the calculation. I think most of the discrepancies are from the thick coating correction calculation (from Evans etal paper). The error is frequency dependent, and the calculations that involve frequency dependence are temperature fluctuation and thick coating correction. The temperature fluctuations are the same from our results. So it is most likely the thick coating correction. I checked and the corrections did differ at high frequency.

 I need to take a closer look to tell exactly where the errors are. Since the error is small and only at high frequency (around the shot noise limit, 10kHz),  I don't think it will be a problem for us.

Tara noticed an accidental re-definition in my old code. I fixed it, and updated the svn. This fixes most of the discrepancies, but shifts the difference in thermo-optic to the low-frequency region.

Attachment 1 is the comparison from case 3 between mine and Tara's calculations of his optimized coating structure.

Attachment 2 is the comparison from case 2 between mine and Tara's calculations of a 55-layer 1/4-wavelength stack.

Attachment 1: ThermalUpdateEmbed.pdf
ThermalUpdateEmbed.pdf ThermalUpdateEmbed.pdf
Attachment 2: ThermalUpdateEmbed2.pdf
ThermalUpdateEmbed2.pdf ThermalUpdateEmbed2.pdf
  1343   Thu Sep 19 18:09:18 2013 taraSummaryNoiseBudgetCoating Thermal Noise Calculator

Quote:

 

Tara noticed an accidental re-definition in my old code. I fixed it, and updated the svn. This fixes most of the discrepancies, but shifts the difference in thermo-optic to the low-frequency region.

Attachment 1 is the comparison from case 3 between mine and Tara's calculations of his optimized coating structure.

Attachment 2 is the comparison from case 2 between mine and Tara's calculations of a 55-layer 1/4-wavelength stack.

 I discussed the calculation with Matt. The error in TO noise is large because it is a fraction of something small. Mostly it comes from TE part. The error in TO noise appears large (10%-20%) because the TO level is small.  Otherwise, the rests are in good agreement, and I think we should be able to order soon. 

 Below, summary of the calculation, dTE is alpha_effective * coating thickness, dTO is beta effective * lambda. 0.2% difference in dTE and 0% difference in dTR can cause error upto 40% in dTO when dTE and dTR cancel each other really well. But this will be insignificant, since the final TO levels are still in the same magnitude.

  Matt Gwinc
dTE 8.161e-11 8.141e-11
dTR -8.11e-11 -8.11e-11
dTO (dTE+dTR) 4.87e-13 2.88e-13

 

The summary of the TO cancellation is in wiki page AlGaAs

  1344   Thu Sep 19 20:38:17 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

Details for AlGaAs coatings order

  • Coating structure can be found in http://nodus.ligo.caltech.edu:8080/PSL_Lab/1340, 55 layers, T = 197ppm.
  • Coatings for 4 mirrors plane/concave, 1” diameter, 1/4” thick, with radius of curvature = 1.0m.
  • AlGaAs coatings will be applied on the concave side of the mirror.
  • Flat side is already AR coated
  • absorption loss 6-10ppm / scattered loss 3-4ppm
  • Spot radius (1/e^2 power) will be 215 um.
  • The mirrors have an annulus on the rim for optical contact with thickness ~ 3mm. This area should be kept clean.
  • The coating wafer should be inside the mirror sagitta to make sure that it will not obstruct the optical bond area. By calculation, the wafer with 8mm diameter, 4.5um thick should be ok. The maximum diameter that makes the coating to be above the sagitta is about 16mm, for 4 um thickness.
  • Required coating diameter = 5-8mm, Power loss due to clipping is less than 0.1 ppm, see below figure.

power_vs_mirror_size.png

Above, plot of ratio of power due to finite size mirror P(r) / P0,  P(r) is the power of the beam at radius r from the center. G Cole said that the wafer can be made to 8mm diameter. diameter between 5-8 mm should be good for us.

  1345   Fri Sep 20 19:26:45 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

I'm using Matt's code to do error analysis for AlGaAs coatings. This time I vary materials' parameters and compare the thermo optic noise, reflected phase and transmission. There is no alarming parameter that will be critical in TO optimization, but the values of refractive indices will change the transmission considerably.

Eric, Matt and I discussed about this to make sure that even with the errors in some parameters, the optimization will still work.

Parameters in calculation and one sigma estimated from Matt

% Coating stuff
betaL = 1.7924e-4 +/- 0.07e-4; %dn/dT
betaH = 3.66e-4  +/-0.07e-4 ;
CL = 1.6982e6   +/- 5%  ; % Heat Capacity per volume
CH = 1.754445e6   +/- 5%;
kL = 69.8672   +/- 5%   ; % Thermal Conductivity
kH = 55           +/- 5%;
alphaL = 5.2424e-6 +/- 5%; % Thermal expansion
alphaH = (5.73e-6 ) +/- 5%;
sigmaL = 0.32      +/- 10%; % Poisson Ratio
sigmaH = 0.32     +/- 10% ;
EL = 100e9    +/-20e9; % Young's modulus
EH = 100e9    +/-20e9;
nH = 3.51  +/-0.03   ; % Index of refraction
nL = 3.0     +/-0.03 ;

 

* Note: when I change nH and nL value, I keep the physical thickness of the layers constant. This is done under the assumption that the manufacturing process controls the physical thickness. The optical thickness in the calculation will be changed, as the actual dOpt = physical thickness * actual n / lambda.  And averaged values of coatings will depend on physical thickness.

 This is fixed in Line 120-180

== Effect on TO cancellation from each parameters==

 First, I calculate the TO cancellation when one of the parameter changes. Some parameters, for examples, Poisson ratios, Young's moduli, are chosen to be the same for both AlAs and GaAs. In this test, I vary only one of them individually, to see which parameters are important. The numbers indicate the ratio between the PSD of TO noise with change in the parameter and the optimized TO noise . Not the standard deviation of the parameters.

params +sigma -sigma Note
BetaL 1.02 1.12  
BetaH 1.03 1.15  
Young L 8.0 1.77  A
Young H 8.3 1.8  A
Young HL 28.3 4.7  B
       
alpha L 1.54 1.2  
alpha H 1.19 1.53  
kappa L 0.979 1.023  
kappa H 0.975 1.028  
CL 0.99 1.0143  
CH 0.99 1.0137  
sigmaL   20.6  C
sigmaH   21.7  C
sigmaHL   84.14  B
nH 1.168 1.004  
nL 11.15 6.507

 

 

  • A) + value for Young modulus is 142 Gpa, and - value is 83 Gpa, the value in the section below is 100 +/- 20 GPa
  • B) Young's moduli and Poisson's ratios for the two materials are the same value in the calculation, Young HL row calculate the TO noise when both materials have the same value of Young's modulus, while YoungH and Young L row calculate the TO noise under the assumption that only nH material or nL material has different Young's mod.
  • C) + value for Poisson is the nominal value, and - value is 0.024  the value in the section below is 0.32 +/- 10%

 Turns out that the change in Young's moduli and Poisson's ratios are quite important.

==Effect on TO cancellation, from all paramerters==

 Then, I calculate the TO noise when all parameters vary in Gaussian distribution, similar to what I did before,all parameters are uncorrelated. The histograms from 1000 runs are shown below.

error_check_params.png

  1. Top, ratio of PSD of TO noise at 100Hz. The cancellation should still work well.
  2. Bottom left, reflected phase. It is still close to 180 degree.
  3. Bottom fight, transmission. The design is 200ppm, the result spread out in a big range from  10-500ppm.

I'll try more run overnight. Each run takes about 1 second.

== combined effect from errors in layer thickness and material parameters==

Since the comparison does not need to calculate the thermal fluctuations and finite size correction all the time, I cut that calculation out and save some computation time.  Now I compare errors from

  1. Error in both layer thickness and materials parameters (red)
  2. Error in layer thickness only (green)
  3. Error in materials parameters only (blue)
  4.  Error in refractive indices only (cyan)

Each simulation contains 5e4 runs.   The Transmission varies a lot depending on the material parameters ( mostly refractive indices,  see the cyan plot).

error_thick_params_compare.png

The cancellation seems still ok. Most of the time it will not be 10 times larger than the optimized one. Only the transmission that seems to be a problem, but this is highly depends on refractive indices. It's weird that the error makes the mean of the transmission smaller.

Attachment 2: error_check_params.fig
Attachment 4: error_thick_params_compare.fig
  1351   Mon Sep 23 18:50:05 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

Quote:

 

If that's true, then it means that a 1% deviation in the index of refraction of the low index material can by a 10x increase in the TO noise. Is this really true?

 That surprises me too, but, that's what the calculation gives me. It is also strange that deviation in nH has smaller effect on to TO noise than nL does. I'm checking it. I ran the code one more time, and still got the same result.

Note: when I calculate the error in refractive indices, I assume that the physical thickness is constant = x * lambda/ n_0. Where x is the optical thicknesss. But if the the actual refractive index is not n_0, it means the optical length is not x, but x*n/n_0. I think this is a valid assumption, if they control the physical thickness during the manufacturing process.

 

update:Tue Sep 24 02:09:28 2013

compare_indices.png

The TO noise level does really change a lot when nL is nL + sigma (nL=3.0+ 0.03), dark green trace. Most of the change comes from TR noise level (not shown in the plot). TE noise remains about the same level.  It might be worth a try to find another optimization that is less sensitive to the change in value of n. I'll spend sometime working on it.

Attachment 1: compare_indices.png
compare_indices.png
Attachment 2: compare_indices.fig
  1356   Thu Sep 26 23:25:40 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

I'm trying to find another optimization that is less sensitive to change in nH and nL. Here is a few thought and a few examples.

 ==problem==

We have seen that uncertainties (withing +/- 1%)in nH and nL result in higher TO noise (up to 10 time as much) in the coating. So we are trying to see if there is another possible optimized structure that is less sensitive to the values of n. We estimate the value of nH to be 3.51 +/- 0.03, and nL to be 3.0 +/-0.03. (The numbers we have used so far are nH/nL = 3.51/3.0,  while G.Cole etal use nH/nL = 3.48/2.977.

==Optimization method==

The algorithm is similar to what I did before[PSL]. But this time the cost function is taken from different values of refractive indices. The values of nH and nL used in this optimization are

  • nH = 3.48, 3.51, 3.54
  • nL = 2.97, 3.00, 3.03.

The cost function is the sum of the TO noise level at 100Hz, Transmission, and reflected phase, calculated from 9 possible pairs of nH and nL values. The weight number from each parameters (which parameter is more important) are chosen to be 1, as a test run. I have not had time to try other values yet, but the prelim result seems to be ok.

[Details about the codes, attached codes]

Note about the calculation,

The calculation follows these facts:

  • The nominal values of nH/nL are 3.51/3.00
  • The optical thickness is designed based on the above nH and nL
  • The optimized design is reported in optical thickness which is converted to physical thickness with the nominal values of nH/nL
  • The procurement of coatings control the physical thickness (with error in thickness discussed before PSL:)
  • If the values of nH/nL changes from the nominal values, this will affect in the coatings properties because of the change in optical thickness.

 ==results from  QWL (55layers) and 4 other optimized coatings.==

  1. Left plot shows  TO noise at 100Hz in m^2/Hz unit,
  2. Middle plot:Transmission [ppm]
  3. Right plot: reflection phase away from 180 degree.

Each plot has three traces (blue, black, red) for different values of nH (3.48, 3.51, 3.54). nL is varied on x-axis from 2.97 to 3.03. The first result is from QWL coating, with 55 layers. This serves as a reference, to see how much each property changes with the uncertainty in nH and nL.

   I tried to change the cost function in the optimization code and numbers of layer to see if better optimized structure can be done. The optimized structure (V3,4,5) seems to be less sensitive to the values of n, see below.

 n_check_QWL.png

Above: from QWL coatings, 55 layers. nominal transmission = 100ppm.  We can see that the transmission of QWL coatings is still quite sensitive to uncertainties in nH and nL.


n_check_opt0.png

Above: First optimization reported before, TO noise is larger by a factor of 10 in certain case, and transmission can be up to 500 ppm. This coating is very sensitive to the change in refractive indices.


n_check_opt3.png

Above: opt3, obtained from the code using the new cost function discussed above.  55 layers, nominal transmission = 150ppm. The TO noise is less dependent on nH and nL, but the transmission is still quite high.


n_check_opt4.png

Above: opt4, the weight parameter for transmission is changed to 3, 57 layers.


n_check_opt5.png

above opt5,the weight parameter for transmission is changed to 50, Lower/Upper thickness bound = 0.1/0.5 lambda, 59 layers


n_check_opt6.png

 Above: Opt6, the weight parameter for transmission is changed to 500, Lower/Upper thickness bound = 0.1/1.2 lambda, 59 layers


From the results, optimized structure # 3,4,5 seem to be good candidates. So I ran another monte carlo error analysis on opt1 (as a reference), opt3, opt4, and opt5, assuming errors in both material properties and coating thickness. Each one has 5e4 runs. Surprisingly, the results from all designs are very similar (see the plot below). It is possible that, by making the coatings less sensitive to changes in nH/nL, it is more sensitive to other parameters (which I have to check like I did before). Or the properties are more dependent on coating thickness, not material parameters (this is not likely, see psl:1345). Or perhaps, there might be a mistake in the monte carlo run. I'll check this too.

compare_error_ana.png

 

I'll update the coating structure and forward it in google doc soon.

Attachment 2: compare_error_ana.fig
  1359   Thu Oct 3 10:34:32 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

The new optimization is less sensitive to the values of refractive indices, but the overall error will not change much if other material parameters have the uncertainties as we estimate.

Summary: see update of error analysis in PSL:1356. The issues from the previous entry are cleared

  • I made sure that the monte carlo tests were correct
  • The new optimization (called opt4, and opt5) will make the TO noise level/Transmission less sensitive to nH and nL values. But with the current estimate of uncertainties in other parameters, the performance will be about the same to that of the original optimization (called opt1).

 

1) show error analysis

  1360   Mon Oct 7 19:53:53 2013 taraDailyProgressSeismicnew table legs installed

New legs were installed.  The table is floated. The cables for signals/ power supplies will be reconnected later

 Evan and I replaced the old legs. I made sure that the leak was not in the connections and the tube. After the legs replacement, the air pump can reach 25 psi within ~25 minutes and the table can be floated.

The regulating valves are adjusted and the table is leveled.

newleg.jpg

 

  1363   Thu Oct 10 01:59:24 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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.

opt1

  • 55 Layers
  • T = 210 ppm
  • TO noise and transmission is too sensitive to the change in nH and nL
  • 1/4 cap of nH. I did not fix the cap thickness for other coatings. Since there is no reason to keep the thickness of the cap constant.
  • TO noise and transmission of this one changes a lot with uncertainty in nH/nL

 

opt3

  • 57 Laayers
  • T = 150 ppm
  • Transmission is still too sensitive to the change in nH and nL
  • TO noise/ transmission is less susceptible to change in nH/nL.
  • First layer is 0.1 lambda thick (~285 nm) I'm not sure if this will be a problem for a cap or not.

 

opt4

  • 57 Layers
  • T = 150 ppm
  • TO noise and Transmission are less sensitive to nH and nL
  • less amount of nL material, should be less sensitive to error in thickness control

 

opt5

  • 59Layers
  • T= 144 ppm
  • TO noise and Transmission are less sensitive to nH and nL
  • reflected phase is more sensitive compared to opt4
  • use less nL material
  • 0.1 lambda thick

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.

 

  1365   Fri Oct 11 15:23:54 2013 taraNotesopticcoating optimization for AlGaAs:electric field in coating layer

Electric field in coating layer is calculated. This will be used in loss calculation in AlGaAs coatings.

 

  • In each coating layer, there are two E waves, transmitted and reflected  waves. The two interfere and become an effective field.
  • The averaged electric field will depend only on the transmitted beam inside each layer, see the calculation.
  • The effective transmissivity can be calculated, for coatings with N layers between air and substrate, there will be an N+1 vector representing the effective transmission, called tbar in the code. This tbar(n) is the transmissivity in the nth layer, similar to rbar in Evans etal calculation.
  • The ratio of E field/ E input in nth layer will be tbar(1)*tbar(2)*...tbar(n)
  •  |E field/ E input |^2 of the final transmitted beam is the transmission of the coatings.  The numbers from this calculation agrees to the calculation from before.

==supplementary information==

1) average E field in layer is the transmitted E field in the layer.

avgE.jpg

 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

transE.jpg

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.

 

==result==

Efield.png

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).

Attachment 3: test_refl.m.zip
Attachment 4: multidiel_rt.m.zip
Attachment 6: Efield.fig
  1367   Mon Oct 14 21:02:00 2013 taraNotesopticcoating optimization for AlGaAs:variation in x

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.

source nL(x=0.92) nH
G.Cole 2.977 3.48
RPI 3.00 3.48
Sadao 2.989 3.49
     

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,

  • x = 0.914, nL = 2.993,
  • x=0.92,     nL = 2.989
  • x=0.926    nL = 2.986  (From Sadao's fit)

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.

  1370   Tue Oct 22 04:34:12 2013 taraDailyProgressSeismicnew table legs installed

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.

  • Extra noise that looks like scattered light goes up to 400Hz ( was around 100 Hz before, not from floating the table)
  • One of the air spring supporting the vac tank has a leak. But it is unlikely to be the source of the extra noise mentioned above.
  • The finesse of the cavities may be less than the designed value (10 000) because of the not so clean isoprop I used on the mirrors.

Note: check if the beams in the tank is blocked by wires or not.

  1374   Sun Oct 27 20:12:25 2013 taraNotesoptic photothermal noise in AlGaAs

I revised the calculation for photo-thermal noise in AlGaAs coatings, the photo thermal noise should not be a limiting source.

==review==

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

  • Solving heat equation to get temperature profile in the mirror.
  • Use elastic equation to calculate the displacement noise due to the temperature change (thermoelastic)
  • For TR, the effect is estimated from effective beta (from QWL stack) and the temperature at the surface ,as most of the TR effect comes from only the first few layers

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.

Int_cotings.png

 

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.

 

Attachment 2: Int_cotings.fig
  1376   Wed Oct 30 01:56:38 2013 taraDailyProgressoptictable work

I'm optimizing the setup, and clearing the table a little bit.

  • Self homodyne setup in ACAV path is removed. This is from Erica's setup and it is not used. The input part is left, since I might use it for fiber distribution system
  • optics on RCAV path, all polarization are optimized. This includes, the input and output polarization for EOAM, and quarter wave plate before the periscope. The input polarization for sideband EOM is left intact after the last adjustment, and it should be good. With+/- 4V input, I can change the power by +/-10%, (1.0 +-0.1 mW is the current setup). For Evan: Do not touch anything before discussing with me!!!
  • I replaced a new PBS for PDH locking in RCAV path. The old one is bad. The surface between the prisms is milky, see the pictures below for comparison. There is also beams from multiple reflection within the cube. The new one is much better. There is no ghost beam anymore.
  • I blocked all the scattered light I could find in RCAV path with Irises and beam dumps. For ACAV, I just blocked the scattered lights from the laser to the PMC. I will finish the whole setup later.
  • I rechecked the height of the beam through EOMs/EOAMs. Since it is a little tricky to center the beam through the openings. The EOMs in RCAV path are all checked. For ACAV, only those between the laser and the PMC are checked(BB for phase locking and 21.5 for PMC sideband). The 14.75Mhz sideband and EOAM will be done later. The EOAM and wave plates are removed temporarily.
  • I modified the TTFSS for RCAV to have a gain reduction switch to help locking the laser. I tried to lock RCAV, but I cannot turn up the gain. I'm not sure what I did wrong but this has to be investigated.

To do lists

  • put optics back in ACAV path and optimize them (alignment + polarization).
  • fix RCAV TTFSS . Check by measuring the TF of the modified stage/ scanning laser + checking error signal

oldPBS.jpg

above: old PBS, bad inter surface can be seen.

newPBS.jpg

above: new PBS: all surfaces are clear

  1377   Thu Oct 31 00:02:17 2013 taraDailyProgressElectronics EquipmentTTFSS

Evan found that when common gain is changed, DC offset also changes as well. I'm still looking into the problem.

 

D040105C.png

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).

  • The modifications I did two days ago were 1) adding a push switch for gain reduction and 2) replacing one resistor. The rests were changed before we got the TTFSS.
  • I checked the TF between TP1 and TP5, it works as it should be (20log( 390/100) ~ 12 dB). So this stage does not have any problem. I checked both TF and time domain signals. So the modifications are ok.
  •  Note, when I measured the TF of TP1/TP4 or TP5/TP4, the signals oscillated and became very noisy. I don't understand why, but this problem disappeared when I used TP4 and out2. Both boxes (#5,#7) have this same problem.

Common Gain - DC offset problem

  • When Common gain is increased (CG signal to U2A chip), there is an offset observed in TP4 which is after the variable gain stage. Both boxes behave similarly. <- This surprises me, as we haven't seen this (or haven't noticed this) before.
  • I checked if the offset varied with the input drive or not. I changed the input from 20mV to 40mV, with constant gain = 1000(25dB). The behavior is nonlinear (see the plot below). I checked this only on box#5.

offset.png

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?

  • This seems to be an important clue about why the loop behaves badly when common gain is increased. From today test, both boxes behave the same, so I think it might be the chips' problem.
  • Fortunately, we can use the offset adjustment(OS)
  • to cancel the offset introduced by the common gain, but we might need to add a port some where (we might be able use fast mon channels during laser scan).  So that when we increase the gain, we can adjust the offset accordingly.
  • Box#7 that I modified should be working. I don't know why I could not lock the laser before, more checking has to be done.

 

  1379   Fri Nov 1 00:22:40 2013 taraDailyProgressopticmore optimization

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.

foam1.jpg

foam2.jpg

  1381   Tue Nov 5 01:11:15 2013 taraDailyProgressElectronics EquipmentTTFSS

Quote:

 

 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)

  • minimize RFAM,
  • bring back the beat signal, optimized gain setup. A lot of improvement around 10 - 50 Hz.
  • measured error noise from each PDH loop, with slope of the error signal to calibrate it to frequency noise
  • measure RIN

Tue:

  • measure photothermal coupling from RCAV (may remeasure ACAV)
  • measure cavity pole, to check the cavities' finesses
  • check calibration on PLL

Wed

  • replace the broken air spring with a new one.
  • fix harmonic lines in the beat
  • update the calculation for the noise budget ( electronic noise, etc)
  • Turn on ISS

Thur

  • beat measurement
  1383   Wed Nov 6 01:14:58 2013 taraDailyProgressElectronics EquipmentTTFSS

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.

beat_2013_11_05.png

Setup:

  • input power: 1mW
  • TTFSS gain (C/F): RCAV (760/980), ACAV (630/650)

Note about the measurement:

  • The noise at error point from ACAV is pretty high (~up to 100 nV/rtHz around 6 kHz). Better characterization will be done later to see if the suppression is enough or not. I made sure that this measurement is good up to ~2kHz, (this was done by changing the gain level a bit and beat level did not change).
  • Table was floated, but the air springs was not activated. I hope we will get better signal around 20-100 Hz once the air spring is re-installed.
  •  Intensity noise->photothermal around a few hundred mHz, cause the PLL to drift away from the input range. This effect becomes worse when the input power is increased.
  • RIN from ACAV is about a factor of 10 higher than that of RCAV.
  • I measured the beat with ISS on/off on ACAV, nothing were significantly different. So maybe it is not a problem for now.

To do next:

  • I'll compare this measurement with the one from 8" cavity to see if the results agree or not. They are different mirrors, but from the same coating run. I suspect that the loss in these mirrors are higher than what we estimate (Ta2O5=2.5e-4, SiO2 1e-4).
  • Think about the error in the measurement (calibration, spotsize etc).
Attachment 2: beat_2013_11_05.fig
  1384   Thu Nov 7 05:08:13 2013 taraDailyProgressNoiseBudgetphotothermal noise in SiO2/Ta2O5

I add the photo thermal noise effect in the noise budget. With ISS, photothermal noise should be sufficiently small.

 

What I did

  • Measure beat
  • Measure RIN after ACAV and RCAV
  • Measure TF between TRANSPD and beat, compare the result with Farsi's calculation to determine the absorption (8ppm, with Finesse = 1e4) [add more details]
  • Apply the measured RIN to Farsi calculation to get the conversion from RIN to frequency noise ( I did not use the measured TF because I have not measured the whole range yet, and the calculation matches the measurement quite well).

beat_2013_11_07.png

Comment about the beat

  • At DC -30 Hz, the noise seems to be a combination of photothermal noise, and seismic induced scattered light. Air spring might not help as much as I thought.
  • Above 2kHz, it's not clear if it is gain limited on ACAV loop or not, but this is likely. We can check by measure the PSD of the error signal and convert it to frequency noise.
  • Frequency stabilization of ACAV is significantly inferior than that of RCAV. I don't know if it is the result from PMC or not. More investigation is needed.

Note about RIN measurement

  • RIN (measured behind the cavities) depends considerably on the TTFSS gain, luckily, at optimum gain level, RIN is pushed down enough.
  • RIN from ACAV is almost a factor of 10 worse than that of RCAV @ the optimum gain setting
  • There might be coupling from BB EOM to RIN (due to the mismatches E field between the EOM and the beam). This may explains why RIN is getting worse if common gain is increased a bit before the loop oscillate. Will check that.

 

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.

Attachment 2: beat_2013_11_07.fig
  1385   Fri Nov 8 03:36:44 2013 taraDailyProgressopticredo- PMC path

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.

  1386   Mon Nov 11 19:37:13 2013 taraDailyProgressopticredo- PMC path

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%.

  1387   Tue Nov 12 15:27:32 2013 taraNotesDocumentationthesis on ctn

I created an svn folder for my thesis on CTN measurement.

It can be found here

 

 

  1388   Wed Nov 20 18:19:01 2013 taraDailyProgressNoiseBudgetphotothermal noise in SiO2/Ta2O5

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).

beat_compare.png

Another evidence is from our previous measurement from 8" cavity.

  • The measurement also agrees with Numata's 2003 result, with phi coatings = 4e-4, see PSL:1018.
  • And the signal scales correctly with a factor of ~ 9 (from shorter cavity, and from smaller spotsize^2), seeT1200057. Had it been noise from optical bonding/ spacer (independent from spotsize), the scale factor would have been 8/1.45 ~ 5.5. The scale from substrate Brownian will also be different because of 1/w_spot dependent. Thermoelastic/ thermoopitc will have different slope.

So It is clear that our beat measurements from both 8" and 1.45" cavities are coating Brownian noise limited (around 50Hz-1kHz).

 

Attachment 2: beat_compare.fig
  1389   Mon Nov 25 15:28:12 2013 taraNotesRefCaveigenmodes of 1.45" refcav

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.

spacer_only_z.png

 

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.

 

spacer_br_8_edge.png

 

spacer_br_8_edge_z.png

Attachment 1: spacer_eigenmode.mph
  1390   Mon Dec 16 15:14:43 2013 taraNotesElectronics EquipmentOLG of RCAV TTFSS

 open loop gain transfer function of RCAV is measured. 

 1) how to measure OLG TF

  • see, PSL:592 about how to measure the OLG from TTFSS.
  • current schematic [add fig]

2) setup

  • 1mW input to the cavity
  • gain common/fast = 730/950
  • Mod depth =
  • Boost off 
  • U3 -> 11.84 dB

Result:

openloopTF.png

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.

Attachment 2: openloopTF.fig
  1392   Wed Dec 18 21:05:28 2013 taraNotesoptic photothermal noise in AlGaAs: thickness resolution

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.

 05Atrancate_err.png

 

2)Results when the layers physical thickness are round up to the closest 0.5 A. The noise budget does not change much.

05Atruncate_nb.png

05Atruncate_T.png

05Atruncate_err_ana.png

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.

Attachment 5: 05Atrancate_err.fig
Attachment 6: 05Atruncate_err_ana.fig
Attachment 7: 05Atruncate_nb.fig
Attachment 8: 05Atruncate_T.fig
  1393   Tue Dec 31 19:33:47 2013 taraSummaryNoiseBudgetbeat measurement

I got a chance to measure beat measurement. The noise budget is updated and contains all dominant noise traces.

 

== Beat measurement ==

beat_2013_12_24.png

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.

TTFSS.png

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.

RCAV_OLG.png

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.

ACAV_OLGTF.png

 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.

  1399   Fri Jan 24 21:13:13 2014 taraDailyProgressDAQmDV in ATF

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

  1400   Wed Jan 29 05:44:51 2014 taraSummaryNoiseBudgetNoise budget fitting: need uncertainties

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 uncertainties in nL and nH: since the physical thickness is lambda/(4*n), the error in n goes to the error in d.
  • Manufacturing process.

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%.

ELOG V3.1.3-