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  3   Sun Nov 8 14:38:56 2009 FrankLaserDAQchannels for the temperature scan

the channels used for the refcav temp scan are:

  • C:PSL-PMC_PMCTRANSPD  > transmitted light of refcav2
  • C:PSL-FSS_RCTRANSPD > transmitted light of refcav1
  • C:PSL-PMC_RMTEMP > analog programming voltage of the heater power supply

locked the laser to cavity2 using the PZT and scanning the temp of cavity1

  301   Fri Aug 20 00:04:14 2010 FrankSummaryDAQchannels from PSL RT system

i disconnected all signal from the PSL RT system running on fb0 this afternoon, so this model doesn't have to run anymore.
They are all hooked up to the VME system now.

I will remove the configuration file for those channels from the fb0 framebuilder the next day. Right now it's still running but not used anymore...

  836   Fri Feb 24 00:03:25 2012 Koji, FrankDailyProgressSeismiccharacterized old and new stack

after carefully thinking about options how to get better results and closer to the coating thermal noise within the next 10 days we decided to open the vacuum chamber and work on the seismic isolation. The the current sensitivity limit is kind of flat and seems to continue like that towards lower frequencies (which we can kind of see when floating the table).

As we could not clearly identify other sources which are limiting us at the moment we decided to improve the seismic isolation next, which might help us measuring CTN at lower frequencies where it is higher. In parallel we will also add the thermal shields and the heater. So we can reduce the drift between the cavities which then makes it possible to reduce the range of the Marconi and so lower the contribution of phase noise. We already locked it to the Rubidium clock which also lowers the phase noise and should make it possible to see CTN below 1kHz.

With the heater we can also tune the beat frequency towards lower frequencies which

  1. increases the SNR on the beat PD as we operate it currently beyond the specs (125MHz max)
  2. lowers the phase noise contribution from the PLL LO (gets lower with lower frequencies)

We first replace the old springs of the stack with the new ones characterized here. Measurements will be posted in a separate entry.

In parallel we will work on the air springs to isolate the whole chamber. But we won't get those parts until mid/end next week so it will be kind of a last-minute change before the LSC meeting.

Things finished so far:

  • replaced RTV springs
  • characterized old and new stack
  • mounted sensors to shields
  • added copper tubes to stack

To-do list:

  • make PTFE part to clamp cables to top stack plate
  • finish wire connections to feedthrough and check everything
  • close chamber and pump down
  • re-align cavities
  • modify base plates for beat breadboard
  • replace one mirror mount base on breadboard




  611   Wed Jun 1 23:49:57 2011 taraNotesFSScharacterizing fss loop

I'm checking the TTFSS loop to understand why the UGF is so low (~100k instead of ~ 500k). I started from comparing the EOM path between that of the old FSS and the current one. Their shapes are not similar. The current TTFSS does not roll off at high frequency as the old fss does.


   The previous fss (blue) has UGF around 500 kHz, while the current TTFSS has UGF around 100k, see this entry. So I check what's the designed TFs for EOM paths between the two servos look like. These TFs, simlated from LISO model, are taken between the end of the common path and just before the signal is amplified by a high voltage opamp. See the schematic below for the details. 

    LISO codes for simulation can be found in the attached file section. File eom_old.fil for old fss note that I used ideal opamp for ad847 in old fss (I don't have it in my lib). File 11g.fil is for current TTFSS


fig1: TF from EOM path. From current TTFSS(red) and old FSS(blue).



 fig 2, EOM path in old fss, where I used LISO to simulate the TF. Note that I used ideal opamp for ad847.



 fig3, EOM path in current TTFSS.


I'm working on measuring TF of the whole loop and compared it with the simulation. The result will be posted later.

Attachment 2: eom_old.fil
#EOM path
# Tara C, 2011_06_01

c C13 .047u  nin n1
r R17  1.1k  n1 n2
r  R14  24.9k  n2 n3
c  C18   3300p n2 n3

... 40 more lines ...
Attachment 3: 11g.fil
#EOM path 
#TTFSS D040105
# Tara C, 2011_06_01

c  C11 330p  nin n3
r  R14 3.01k  n3 n4
r  R15 100    n4  n5
l  L1  220u   n4 n6
c  C13 30p    n6 gnd
... 41 more lines ...
Attachment 5: EOM_ttfss.png
  612   Thu Jun 2 21:22:02 2011 taraNotesFSScharacterizing fss loop

I listed what I need to do to fully characterize the fss loop.


1) Measure the whole TF of the loop. This will be compared with the simulation.

2) Simulate the whole TF of the loop. This requires:

      2.1) Use LISO to simulate the TFs of FAST path and PC path

      2.2) measure the TF of the pzt (actuator for fast path)

      2.3)measure the TF of the EOM (actuator for PC path)

3) Make a SIMULINK model

  362   Wed Sep 15 22:43:41 2010 taraDailyProgressPMCchecking pmc servo

I checked PMC circuit to make sure that the schematic matches the actual board.

This is important because we want to make sure that it works exactly the way it should.

This is also useful when we want to modify it.

I check R and C on the board, everything seems fine except R2.

It says 9091 F which matches the schematic (9.09 k), but a multimeter reads 4.5 K, I might measure it wrong.

I also measured the TF between TP2 and TP4, I'll attach the result.

When I measured TF between TP3 and TP8,  I did not fully push the card into the socket, and this killed PA85 when I applied high voltage to the card.

Koji found me an unused Mach-Zender card at 40m. I replaced its PA85 for PMC card.

I tried it. This time, I made sure that the card was properly in its place, I screwed it down to the crate.

Then I connected PD cable, LO cable, HVout then HVin.

However, it sitll does not work , no high Voltage coming out. Only low voltage ~0.5 V which changes with the value on the PMC DC control slider.

I don't know if I accidentally killed it during the transplant operation.

It's a very bad day to be PA85.

Attachment 1: D980352-D.pdf
  1805   Sun Jan 8 14:43:50 2017 yinziDailyProgressTempCtrlcircuit board update and measurements

Andrew switched out the bypass capacitors to ceramic ones over break. Now all of the channels are functional, so I guess that was the problem (I don't know what the physical problem would have been before, though).

Here are some measurements of the frequency response.

Channel 1

Channel 2

Channel 3

Here's the noise. I don't know why it has the "edges", I'm pretty sure I made the measurements the same way as I was doing before and used the same stiching script... I might repeat these measurements later, but it's at least an idea.

Channel 1 has much higher noise. Possibly because there are power lines that cross over the area, whereas for 2 and 3 the power lines are routed from the side? Could be another reason though...

Data and scripts attached.

Attachment 5: plots_01082017.m
%another plotting script
%sorry the numbering is all out of order
%1-2 mag and phase channel 2
%3 - phase channel 3
%4 - phase channel 1
%5 - mag channel 1
%6 - mag channel 3
%7-10 noise channel 3
%11-14 noise channel 2
%15-18 noise channel 1
... 52 more lines ...
Attachment 6: freqStitch.m
%%  This is a module for stiching spans of overlapping PSDs of different frequency bin size from SR785
%   Assuming a logerithmic scale of frequency, it is desirable to 
%   stich the smaller frequecy ranges to the bottom of the larger ones
%   wilst truncating out bins in the larger span.
%Feed in frequency matrix f(n,m) with correesponding floating point
%%  Synopsis:
%     [freqStitch,dataStitch] = freqStitch(freqPoints,dataPoints)
... 62 more lines ...
Attachment 7: data_array.mat
  1256   Fri Jul 26 11:07:44 2013 EricaDailyProgressBEATcircuit for measuring temperature fluctations on CTN table
July 23, 2013
Went to a lecture Alan gave for the CGWAS on data analysis in the morning at Cahill (http://www.cgwas.org/index.php/Caltech_Gravitational-Wave_Astrophysics_School_2013). I had more data, signal from the recombined beam over different time periods that I took so I put those into graphs.

I practiced soldering stuff.
Wet the sponge below the iron. You can test to see if iron is hot if you hear the sizzle when you touch the iron to the sponge. A good idea is to cover the iron w/ new solder, since the old solder on the tip has oxidized.
Solder will go where it is hot, so you need to heat both the board and the wire to get a good connection. Good joints look like volcanoes.

Circuit design:
Evan figured out a circuit to for the AD590, as seen below.

The 20k resister determines the voltage that goes to the rest of the circuit. A high pass filter follows, with a capacitor on the order of 100 uF and resistor about 1 M ohm. This takes out the DC signal and AC couples the circuit. The filter will also ignore fluctuations that are slower than 100s. The two resistors connected to the op amp have a gain of 100. The op amp can only have an output up to 15V so with a gain of 100x, it can only take in 0.15 V before it saturates.

We used a breadboard where we can just plug in the components to see if the circuit works like it want it to. For the high pass filter, we used two 22 uF capacitors in parallel = 44 uF (22uF is the largest WIMA capacitor - film capacitor; anything higher will be ceramic and have a lot more noise; also they may be polarized which is a bit more hassle when wiring stuff up) and two 1 Mohm resistors to make a 2M ohm resistor.

We connected the circuit to a function generator and oscilloscope. The function generator was also connected to the oscilloscope (using T connector).
There was a 100x gain, as expected.
Note: make sure the oscilloscope is DC coupled, or else another capacitor will be put into the circuit in the oscilloscope and you won't get the correct signal.
Also, be careful about making the amplitude too large because that can saturate the op amp. If you do both of these things, then you get this weird signal that is trying to be a square wave but failing.

Note: AD590 has a polarization. The pin with the little bump sticking out should be connected to the positive side.
Attachment 1: P1030056.JPG
  1257   Fri Jul 26 11:22:45 2013 EricaDailyProgressBEATcircuit for measuring temperature fluctations on CTN table
July 24, 2013

Took the tour to JPL today. Got to see the twin of Curiosity that they assembled before the real one so they could adjust procedures for assembly and the Mars Yard where they drive the rover over various types of terrain. There is also the Scarecrow which is essentially just the frame and wheels, which is used to simulate the smaller gravity on Mars.

Soldered parts to the circuit board. I'll be putting both circuits onto the same board, using about half of the board total, so that we can attach more components later, if needed.
Only one side of the board has metal around the holes so we placed the components on the non-metalized side, and had the connects protruding to the opposite side.

Used scrap wire that was in the base of the stand to connect various joints that were close to each other. Also folded over excess wire from components to make connections. Any longer wires that weren't used were cut off.

Using red for positive, black for negative, and green wire for ground, as is standard.
  1258   Fri Jul 26 11:45:28 2013 EricaDailyProgressBEATcircuit for measuring temperature fluctations on CTN table
July 25, 2013

finished building the circuit today. Had the positive, negative, and ground wires running above the board, while the one jumper wire from the output to the negative input under.
Twisted the positive, negative, and ground wires together using a drill, as well as the positive and negative wires that will connect to the AD 590. We made these longer so we can connect to the power supply and place the AD590 at opposite ends of the table.

Tested the circuit, used an amplitude of 0.01Vpp and 0.1 Hz for frequency to drive circuit, which was what we did on Monday. The output signal is a square wave which was strange but found out the problem: the bnc cable driving the circuit was put in the sync output of the function generator, instead of the function output.
Fixed this, and the circuit behaves as we expect.

Discovered that I used a 36 kohm resistor instead of a 33 k ohm resistor, so now we have a gain of about 110, which is close to that of 100.

We used aluminum tape to connect the AD590 and insulating tape to prevent shorting. The output signal was at some DC voltage, which we expect at first due to the power supply turning on, and it should die away, but it didn't, or was very very slowly. So Evan placed a 15k Ohm resistor in parallel w/ the 2M ohm resistor in the high pass filter to lower the time constant, which brought the signal close to zero. Once he took the resistor away, then the signal would drift up to the previous DC level. The circuit was responding as expected when he placed a cooler object by it, so the signal went down, and the signal went up when we held the AD 590.

We tried this in the CTN lab but it didn't seem to work; there was a lot of noise. I'll test it again tomorrow.
A possibility is the power supply could be noisy.
  431   Wed Dec 15 11:26:39 2010 frank, taraNotesBEATcleaning optics to get rid of scattering light

We are cleaning optics to reduce possible scattering light sources. Optics behind PMC are quite dusty. Improvement in the beat measurement was observed during the process, the

actual data is yet to be measured.


 Dirty optics might cause the beam to scatter, and the scattered light could end up in the RFPD for PDH locking. Its random phase will

mess up the error signal causing extra noise in our measurement. So we try to clean the optics and see if we can improve our measurement.


The circled optics in the picture are cleaned already. Aligning and optimizing is yet to be done.

Red plot was taken today after cleaning a few lens, blue plot was taken after cleaning all the lens shown in fig1.

Although blue curve has higher noise upto 200 Hz, this might come from beam misalignment after removing lens for cleaning.

I'll try to re configure gain setup to see improvement.


Attachment 1: clean_2010_12_15.jpg
Attachment 2: beat_2010_12_15.png
  433   Fri Dec 17 02:23:38 2010 frank, taraNotesBEATcleaning optics to get rid of scattering light

I'm continuing with cleaning optics. The optics in cyan circles in the attached picture are cleaned today.

One of the RFPD (currently, for RCAV), has no protecting glass, and it is very dirty. I used an air can to blow some dust away.

 Most of the improvement in the noise spectrum comes from the cleaning of the RFPD, and it is still dirty.

I notice that there is a peak at 60 Hz coming up in the measurement, there was none before. I have to look into this

and make sure that no electronic noise is coming up.

Attachment 1: clean_2010_12_16.jpg
Attachment 2: beat_2010_12_16.png
  636   Fri Jul 22 20:51:13 2011 frank, taraDailyProgressopticcleaning opto mechanical parts

As we removed some optics on the table, we use pressurized air to blow away dust/dirt on the mechanical parts (mount/ post/ lens holder) Optics have not been cleaned yet. We will clean it before we put everything back on the table. The cleaned parts are kept in a plastic box.



  640   Tue Jul 26 18:42:16 2011 raphael, taraDailyProgressopticcleaning opto mechanical parts

Today we removed the optics behind the PMC, ACAV, and cleaned the table.

  •   Optic mounts and posts are cleaned by pressurized air, and kept in a plastic box.
  •   Lens and mirrors are kept in optic cases.
  •   ACAV is moved to the end of the table, ion pump is unplugged.
  • Table is cleaned with methanol, but some grease( under acav) is still on it.

NOTE: I just realized that the HEPA filter above the table close to the entrance ( the one that has the laser) is unplugged.

I could not find any available outlet to plug it back yet. We should turn it on soon.





  644   Thu Jul 28 01:54:21 2011 frank, taraDailyProgressopticcleaning opto mechanical parts

  Today we started working on the layout. There is one mistake in the layout, the mirror behind AOM for REFCAV is too close to the insulation box, so we have to fix the layout.


 The oil on the table actually comes from holes on the table. About 5-6 screw holes had lot of oil, so I flushed them with methanol a few times.


The HEPA filter is plugged in and turned on. I unplugged one of the monitors and used the outlet for the filter.


 The window is measured to be ~ 6 inches in diameter. Thus, the assumption in the design that the centers between two cavities are 3 inches is ok. If necessary, it can go up to 4 or 5 inches.



The layout is updated. The spot size in both AOMs are adjusted to 220 um.


  647   Fri Jul 29 00:42:19 2011 frank, taraDailyProgressopticcleaning opto mechanical parts

 We preparing optics for the new layout. To reduce scattering noise, most of the Y1-1064 mirrors we have been using will be replaced by super polished mirrors. 


We think Y1-1064 mirrors can cause scattering noise in the setup because the coating surfaces look very milky.


fig1: Y1-1064 mirror.

     We have ~ 10-20 super polished mirrors. Some of them are good, some of them are rejected from the site. The good one will be used for periscope/ beat setup.  I tested a couples of the rejected mirrors, but they can reflect both p and s beams with high efficiency. We will ask Peter to find out what is wrong with them.


fig2: Left and right, super polished mirror.


fig3: left, mirrors' case, right, certificate.


    I have cleaned about half of the required optics, I think we should be able to lock the first cavity before next Wednesday.

  1263   Mon Jul 29 22:30:34 2013 taraNotesopticcoating optimization for AlGaAs

Since we are trying to optimize a layer structure for AlGaAs coatings. It is a good idea to summarize some notes about all the coatings details. Thanks Koji for the discussion about the coaitngs.

==some background about SiO2/Ta2O5 QWL with 1/2 wave cap coatings==

 For quarter wave layer stack (QWL) SiO2/Ta2O5 coatings, SiO2 and Ta2O5 are the material with low (nl) and high refractive indices (nh), respectively. Due to the stronger structure of SiO2, we usually have a cap of SiO2  as a protective layer on top. This cap has thickness of 1/2 wave length. The reason is that the reflected beam from the interface between the cap and the next layer will be in phase with the first reflected beam at the air-coating surface, see the figure below (top).

If the SiO2 cap is 1/4 thick, the reflected beam from the interface between the cap and the next layer will destructively interfere, causing the reflectivity to go down (see the picture below, middle). 

However, if the cap is Ta2O5 (nH) material, it can be QWL thickness, and the phase from every reflected beams still interferes constructively (picture below, bottom).


Note: As we can see, the incoming beam and the reflected beam are 180 degree out of phase. It means that the E field at the coatings surface will always be zero. This will prevent the burning on the surface of the coating. With this, the standing wave in the cavity will always have zero E field at the coating surface, see below picture.

This is not AR coat, since all the reflected beams interfere constructively. The reflected beams from AR coating will destructively interfere among each layer.


To sum up for the SiO2/Ta2O5 coatings:

  • SiO2 is stronger than Ta2O5, so we use it for the end cap.
  • Because SiO2 has lower n than that of Ta2O5, the cap thickness has to be 1/2 wave thick so that all the reflected beams interfere constructively.
  • We want the reflected phase to be 180 degree away from the incident beam so that the surface won't get burnt from the building up E field. (If the E field is non zero, it will be amplified by a factor of Finesse/pi).  My previous optimization for AlGaAs that used 1/8 cap was wrong because the reflection phase was not 180. This means that by adjusting the cap thickness to optimize the TO noise is not a good method, since the reflection phase is not close to 180 anymore. The optimization has to take the phase into account.


==AlGaAs coatings==

 For GaAs/Al0.92Ga0.08As (AlGaAs) coatings, the situation is a bit different from SiO2/Ta2O5. The cap has to be GaAs (nH) because Al0.92Ga0.08As will oxidize and change its material properties. Now that the cap will be nH, the thickness has to be 1/4 wavelength.  The last layer next to the substrate has to be GaAs (nH) too (I think because of both the better reflectivity and the fabrication process).

==optimization code==

 There is an assumption about the layer structure used in the optimization code that the cap is nL(SiO2), 1/2 layer. The coatings layers are even number ( doublets of SiO2/Ta2O5). I'm making sure all the assumptions in the code are fixed. Here is a preliminary result.



above: Layer structure, the first layer (cap) is GaAs (nH). In the optimization, I keep the cap thickness to be 1/4, and vary the rest.


above: Noise budget of the optimized layer. TO noise is below BR noise from DC up to 1kHz.

The reflectivity of the coatings is -0.9997 + 0.0209i  (reflection phase = 180 - 1.2 degree). I'm not sure if this is good enough, maybe better optimization can be done.

Note: My layer structure is really different from what rana did in T1200003. For my structure, the layers near the cap vary a lot before getting close to 0.25 when the layers are close to the substrate. The result from 1200003 is the opposite. The layers near the cap are about 0.25, and start to diverge when the layers are close to the substrate.


above:  Optimized coatings result from T1200003. The optimization probably assume the cap of low index material, but the following layers evolution are opposite of what I got. That's why I'm not sure about my optimization.


I'll upload my codes soon so that people can check my optimization.

  1269   Wed Jul 31 00:31:39 2013 taraNotesopticcoating optimization for AlGaAs

The codes for optimizing Thermo-optic noise in coatings are up on svn.

I adopt some codes that have been on svn for awhile and modified them for AlGaAs coatings. There are two main codes

      1) DoAlGaAs.m

         This file is modified from DoETM.m found in .../iscmodeling/coating/AlGaAs/doETM.m . The optimization method is using Matlab's fmincon function to search for coatings structure that minmize TO noise. Some modifications include:

  • (Line16-18 )Number of layer. For AlGaAs, the number of layer will be odd number (start with GaAs, end with GaAs), I fixed the layer structure to be odd number.
  • (Line74) Cap. During the optimization, the first cap is kept constant. For a cap made with high refractive index material (nH), the layer thickness is 1/4 lambda, see previous entry.

This code calls on  optAlGaAs.m when running fmincon.

    2) optAlGaAs.m

        This file is the modification of optETM.m found in ../iscmodeling/coating/AlGaAs/optETM.m .It calculates the reflectivity and the TO coefficients from the given layer structure. The modifications are:

  • (Line41-45) Layer structure, the cap start with nH. The material for substrate is SiO2 with nsub = 1.45.
  • (Line60) Desired transmission, as a test, I chose 200 ppm.
  • (Line88) Calculation for TO coefficients (StoZ), I switched from getCoatThermoOptics.m to getCoatThermoOPticsAGS.m. Codes with AGS suffix in /GwincDev folder are fixed for AlGaAs coatings structure. This code calls many functions in /GwincDev folder.

     2.1) multidiel1.m

       This code is used in optAlGaAs.m it calculates the reflectivity and impedance of the given coatinns structure. There is no modification to it. The code can be found in .../coating/coating_optimization_new/

    To run the codes

    check out .../iscmodeling/ folder from the svn. The optimization is in .../iscmodeling/coating/AlGaAs_TO_opt_CTN/ folder, but you need other functions in other folders.

    Once you run DoAlGaAs.m, the optimized layer will be in matlab workspace called xout. This is the layer structure withtout 1/4 cap. Check if there is a layer with thickness of 0.002 or not. I ran the code several times, sometime it shows up. Just rerun the code and get the layer that is around 0.1 or thicker. The 0.002 is just the lower bound used in fmincon search in doAlGaAs.m.

  Plotting noise budget

 The noise budget of the optimized layer can be plotted with /coating/AlGaAs_Refcav/nb_algaas.m . Currently, at line 38-39, the code will take xout  and create a layer structure with 1/4 cap on top of it. The reflectivity of the coatings is in rCoat workspace item after running the noise budget code. It should be close to -1 + 0i

  1291   Fri Aug 9 17:58:01 2013 taraNotesopticcoating optimization for AlGaAs

Better TO optimized coatings calculation is done. Now the Transmission, phase reflection, and TO noise are optimized.

From previous elog, these are explanation about the optimization codes.


The codes for optimizing Thermo-optic noise in coatings are up on svn.

I adopt some codes that have been on svn for awhile and modified them for AlGaAs coatings. There are two main codes


    2) optAlGaAs.m

        This file is the modification of optETM.m found in ../iscmodeling/coating/AlGaAs/optETM.m .It calculates the reflectivity and the TO coefficients from the given layer structure. The modifications are:

  • (Line41-45) Layer structure, the cap start with nH. The material for substrate is SiO2 with nsub = 1.45.
  • (Line60) Desired transmission, as a test, I chose 200 ppm.
  • (Line88) Calculation for TO coefficients (StoZ), I switched from getCoatThermoOptics.m to getCoatThermoOPticsAGS.m. Codes with AGS suffix in /GwincDev folder are fixed for AlGaAs coatings structure. This code calls many functions in /GwincDev folder.


 So optAlGaAs.m calculates a parameter y which is the cost function that is minimized in fmincon in doAlGaAs.m code.  Originally the cost function y includes the difference between the expected transmission and the transmission from the given layer, and the level of TO noise which are:

y = [(T - <T>) / <T>]^2   + sTO (f0).   The goal is to minimize y.   Where

  • T = transmission of the mirror with the optimized layers
  • <T> is the required Transmission
  • sTO(f0) is TO noise at f0
  • Each effect is weighted differently

This cost function does not care about the total phase of the reflected beam. T is the absolute value of the transmission, so the information about the phase is removed, and the optmized coatings calculated from this cost function won't have phase close to 180 degree. The previous result showed 180-1.2 degree.

So I added the phase of the reflection in the cost function, with appropriate weight, and ran the optimization.

==Phase calculation==

rCoat is the reflectivity of the coatings, by using atan(imag(rCoat)/real(rCoat)), we obtain the phase of the reflectivity. I tried to you atan2(y,x) to get the phase of 180, but it does not work well with the optimization. I'm not sure why. So I use atan function, and check the value of rCoat after the optimization to make sure that rCoat is close to -1 + 0i. The result is shown below.


above: the layer structure, optimized for 200ppm, y axis is in unit of lambda in the layer. The first layer is the 1/4 wave cap, the last layer is the layer just before the substrate.


above: noise budget for the optmized structure, the reflection phase is 180- 1e-6 degree.

 The layer structure is attached below in .mat format. Note: the structure does not include 1/4 cap on top.

== summary of the modifications of optAlGaAs.m==

  • (line 90 - 95) add calculation of the phase of the reflectivity
  • line 97 the cost function includes phase of the reflectivity that is close to 180 degree (r is close to -1 + 0i). The weigh functions  from TO noise/transmission/phase are chosen so that each factor are about the same, and the result looks reasonable ( coating thickness ~0.1 - 0.3 lamda, correct reflectivity, correct transmission).
Attachment 2: TOoptimized_2013_08_09.fig
Attachment 4: TO_opt_200ppm_layer.fig
Attachment 5: 2013_08_09_TOopt_200ppm.mat
  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.


 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).

Attachment 3: test_refl.m.zip
Attachment 4: multidiel_rt.m.zip
Attachment 6: Efield.fig
  1550   Sat Jun 20 10:14:50 2015 EvanNotesopticcoating optimization for AlGaAs:electric field in coating layer

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

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

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

Attachment 1: Efieldtrans.pdf
  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%.


 1) result from the error in thickness control


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.


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%).


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.



  • 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
  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.


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.


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.


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 );




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).


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
  1322   Mon Sep 2 18:31:46 2013 taraNotesopticcoating optimization for AlGaAs:error analysis

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

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


Optimized coatings structure.


Attachment 1: opt_coatings.mat
  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.


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.


  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).


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
  1346   Fri Sep 20 21:19:29 2013 Matt A.Notesopticcoating optimization for AlGaAs:error analysis

In our meeting, Eric mentioned that there might be some uncertainty in how the average coating properties are calculated.

To see how much it matters, I set the average properties to either that of the high-index (H) or low-index (L) material, and calculated the ratio of the new thermo-optic noise to the original calculation (TO'/TO) and the ratio of the new thermo-optic noise to the unchanged Brownian noise (TO'/Br) for Tara's optimized coating structure. The results are in the table below:



Change: TO'/TO TO'/Br
No Change 1 0.015
C_c = CH 0.99 0.014
C_c = CL 1.01 0.015
k_c = kH 1.12 0.016
k_c = kL 0.89 0.013
alphaBar_c = aH 358 5.17
alphaBar_c = aL 384 5.55
alphaBar_k = alphas 372 5.37
alphaBar_k_TR = alphas 3.12 0.045
alphaBar_c = alphaBar_kH 2.88 0.042
alphaBar_c = alphaBar_kL 2.047 0.030
alphaBar_k_TR = alphaBar_k 5.775 0.084
alphaBar_k = alphaBar_k_TR 145 2.096

 C = Heat Capacity/Volume, k = thermal conductivity, alpha/a = thermal expansion

alphaBar_c and alphaBar_k are more complicated, since they take into account the Poisson ratio and Young's modulus of the coating materials, and may be wildly different from the thermal expansion coefficient. alphaBar_c is an average of alphaBar_k values, and when I use "alphaBar_k = alphas", I'm indicating that alphaBar_k is an array, and I have replaced that array with an array of the corresponding thermal expansion coefficients. As we can see in the final four rows of the table, alphaBar_c has a much smaller affect if we use an alphaBar_k value with all its added moduli and ratios instead of just regular thermal expansion. alphaBar_k_TR is the array of values used in the "Yamamoto Correction" to calculate the appropriate alphaBar for the thremo-refractive noise.

This all indicates to me that while most of the averages won't have much effect on our cancellation, a mistake in the calculation of alphaBar_k will.

The difference between alphaB_k and alphaBar_k_TR (in the last two rows of the table) is also interesting. Kazuhiro Yamamoto tells us this equation is correct, and explains the correction here. It's apparently because there is no added strain in the substrate due to the change in the refractive index, while there is strain for the thermal expansion.


  1347   Sat Sep 21 23:49:29 2013 ranaNotesopticcoating optimization for AlGaAs:error analysis

 I don't understand these values for n.  

How can nH be 3 or 11? Isn't just that nL is ~1.45 and nH is ~2 ?  I would guess that the sigma for these is only ~1% of the mean values.

  1348   Sun Sep 22 00:27:09 2013 some random goonNotesopticcoating optimization for AlGaAs:error analysis


 The numbers in the table are the ratio between the TO noise when the parameter is changed by 1sigma and the TO noise calculated form the nominal value.

About the Poisson's ratios, Matt asked me to check for the values between 0.024 to 0.32, and the TO cancellation becomes much worse. I looked up papers about AlGaAs' Poisson's ratios. Most of the literature report the value ~0.32. I think we don't have to worry about it that much.


Krieger etal 1995 Table2, and ref 16 17 thereof.

Wasilewski et al1997 page 6, also discuss about the calculation and the measurement of poisson value in GaAs and AlAs, the value is still in the range of 0.27-0.33, not 0.024. The value of 0.27 is already considered very low.

zhou and usher has a calculation for poisson's ratio of AlAs. they report ~0.32, see table 2. and there references.

So I don't think Poisson's ratios of the materials will be a problem for us, since the reported numbers agree quite well.


  1350   Mon Sep 23 18:07:22 2013 ranaNotesopticcoating optimization for AlGaAs:error analysis


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?

  1351   Mon Sep 23 18:50:05 2013 taraNotesopticcoating optimization for AlGaAs:error analysis



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


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
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.


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.


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.


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.


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.


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


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


 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.



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

  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.


  • 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



  • 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.



  • 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



  • 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.


  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.

  1039   Fri Aug 10 19:50:37 2012 taraDailyProgressBEATcode schmidtt trigger for beat

I used Schmidtt trigger process to track frequency of beat measurement. This is a first step for digital PLL.


      we are trying to do offline PLL digitally, so we can avoid extra frequency noise from the LO used in PLL. The first step is to track down frequency of the beat measured by the PD.

==the code==:

       I use Schmidtt trigger algorithm to covert analog signal to digital (the plot below show (-1,1) instead of (0,1) for easier comparison with the analog signal). The data below is taken from beat measurement  with +/- 5000 count. The level is set to +/- 0.2 from amplitude of +/-1. Then I record how long the digital signal stay at 1, or 0 before the signal flip, then use that time to calculate the frequency of half cycle and plot it in the below figure.



Plot: Above, measured signal from daq (blue) and digitized signal via Schmidtt trigger (Green). Below, frequency of beat as obtained by the calculation from the digitized signal. Note the different time span between the two plots.



     I have not FFT the frequency drift in time series yet because I just realize that the way I collect the frequency drift vs time might be a problem. The time step for frequency drift would be varied from point to point depending on the current drift frequency. For example,sat at 1Hz, the signal crosses zero twice per second, and twenty times per second at 10Hz. This means the data density (point per time) between the two frequencies are different, see the below zoomed picture. And it might cause a problem when I do FFT with varied dt size.   To fix this, I 'll try to assign constant frequency to fill in the space. Once the problem is fixed, I can just FFT the signal. I'll think about using PLL code as well and compare the two methods.


plot2: zoom in of the first figure.



 This is overdoing it. Please just post the existing beat data somewhere and I can show you how to do it easily with a few lines of matlab code. Then you can go back to your usual noise hunting.

 Here is the demodulated beat signal, with 32kHz sampling rate, 120 second time strecth. I used SR560 to amplify the demod signal so that pk-pk value is ~10 000 counts. The data is store in demod.data with a signal column .


Attachment 3: schmidtt.zip
  1041   Thu Aug 30 02:52:01 2012 taraDailyProgressBEATcode schmidtt trigger for beat

I'm trying to check if the schmidtt trigger algorithm will work as our beat readout or not (observe beat from dc to 1kHz), I also revisit IQ readout technique that we tried before as well. I'm analyzing the data and found that some data was not taken carefully (from chosen the wrong time). Here I'll just explain my plan and setup:

Objective: Check if readout methods (Schmidtt PSL:xxx, IQ PSL:xxx readout) are suitable for beat measurement or not. Do they provide a valid result?,

Method:  Compare the result obtained from the mentioned method with a reliable result. My plan is to use PLL to measure the frequency noise of a Marconi at various setup and use it as our reliable result. The setup is similar to what I did in PSL:Xxx, but I did not use 10MHz standard frequency input for Marconi.

   Setup 1: simple demodulated signal.  [add fig] . Both marconis' carrier frequencies were ~ 160MHz. Then the two signals were demodulated down to 1kHz and sent to DAQ (@32kHz). Three levels of frequency deviation (10kHz, 1kHz, 100Hz) were set on Marconi. The data will be used for testing Schmidtt trigger technique



fig2: setup for measurement 2 and 3.

   Setup2:  IQ technique.  With this setup, I measured I-Q signals with three different setting The signals were also demodulated to 1kHz and the frequency deviation were chosen to three levels (10kHz, 1kHz, 100Hz)as well.

  Setup3:  This setup was similar to that of setup 2, but the setting was different. I kept the frequency deviation at 100kHz, and varied the demodulated frequency instead. I chose 1 kHz, 3kHz, and 9 kHz. This data will be used for checking if our beat frequency drift around 9 kHz, will the read out still ok or not.

  1042   Fri Aug 31 00:48:00 2012 taraDailyProgressBEATcode schmidtt trigger for beat

 I compared results from three different readout techniques, it seems that my Schmidtt algorithm does not work at frequency above 10Hz for our required sensitivity, but IQ readout is very promising.

First, to check if I can produce the same results from the same data analyzed by two different technique  (Schmidtt, and IQ). I used 2 data set (chI and chQ) for IQ read out technique, then for Schmidtt technique, I used only chI data. Then I compared the results with what I got from PLL (I used the old data because I have not measured the new one yet, but it should give a rough idea).


fig1: comparison between IQ readout and Schmidtt technique. Black line is the old measurement for Marconi noise, 10khz input range.


The signal was demodulated down to ~1kHz and obtained by 32kHz DAQ. The data was taken with 150s time stretch. It turned out that the Schmidtt method is not sensitive enough.  IQ readout seems to be senstive down to 2 x10^-2 Hz/rtHz. The mismatch between the IQ and PLL was probably the setup between the two are different. (I have not measured the noise level of the current setup with PLL yet).


So I moved on to use IQ readout with other data. I chose marconi input frequency modulation range to be 1kHz and 100Hz. IQ method can measure down to 3x10^-3 Hz/rtHz. (I'll still have to verify this with PLL, but from a quick look it seems that the results are very reliable (I don't use any delay line in IQ read out at all and I can get sensitivity better than 10^-2 Hz/rtHz). It seems to be very promising for our beat readout.

I will try to compare this will results from PLL, if they agree. I'll move on to use this method to measure the noise level of marconi with frequency modulation function off (we can not do that by PLL technique). The result will give us an upper limit of the Marconi noise plus the readout technique noise which can be used in the noise budget.


fig2: Marconi noise at different settings, measured by IQ methods. The demodulated frequency is 1kHz. This plot is intended to show the sensitivity of IQ method which can be used to measure coating noise upto 1kHz (if the noise from an oscillator used for demodulation is not too noisy).  I have not plot the results from PLL on the same plot yet, but I have attached Marconi noise measured by PLL in fig3 below (data from 2010).


fig3: Marconi noise at different setting (Carrier @160MHz). The noise level for 1kHz and 100 Hz input range are almost the same and agree with what I got from IQ readout.



  •  I will check how sensitive IQ read out be (by compared it with PLL). However, I also notice one possible problem with this technique. The peaks around 1kHz, from demodulated signal, and its harmonics can be seen clearly in the plot . (there is also this mysterious peak at90 Hz as well, I'm not sure yet where it comes from). It means that if our beat frequency drifts around, the psd of the beat will have weird bumps all over those frequencies.
  • Think about digital delay line, I have not succeeded yet. I'm still confused with the calibration of this technique, but if IQ readout is working ok, I can use this method for beat measurement.


Attachment 2: compare_IQ_schmidtt.fig
Attachment 4: IQ_compare.fig
  1043   Mon Sep 3 01:02:46 2012 taraDailyProgressBEATcode schmidtt trigger for beat

I used IQ readout method to measure the frequency noise of Marconi. The sensitivity was good, it was lower than 10^-3 Hz/rtHz up to a few hundred Hz.


From previous entry, I finished up the measurement and analyzed the data. I did two things:

  • Compared IQ read out with PLL technique, (green and red against black and dark green): The measurements agree well so I think IQ method is reliable.
  •  Measured Marconi noise( carrier@160MHz, modulation off) when the marconis were locked and not locked with one Rb clock( pink and neon green). When the modulation is off, we cannot use PLL to measure marconi's frequency noise. So I used IQ to measure the noise.  



From the measurements, I can conclude that IQ method has enough sensitivity at least down to 10^-3 Hz/rtHz (might be up to 1kHz) (neon green).  One thing we should keep in mind is that the frequency noise from marconi is still quite high at 1kHz, even with modulation frequency is off. So we still have problem with measure noise up to 1kHz .

Anyway, I have not determined the noise floor of IQ method yet. I will think about it. If we can keep the beat frequency drift small enough, IQ methods should be ok for beat measurement.

Attachment 2: IQ_compare.fig
  392   Mon Nov 15 18:05:34 2010 taraDailyProgressBEATcoherence <fbeat|RCAV>, <fbeat|ACAV>

 I realigned the beam to PMC, ACAV, RCAV, optimized gain, and find a significant coherence between ACAV_RCTRASPD and RCAV_TRANSPD.


I haven't re-aligned the beam to each cavities for awhile, and the alignment was quite bad.

PMC_RCTRANSPD: 9.4 - > 10.9 V

RCAV_RCTRANSPD: 1.7 ->2.07 V

ACAV_RCTRANSPD: 0.8 -> 1.3 V

So I need to optimize the gain setup again, see detail below. 

I measured beat signal and coherence before and after realigning. 

For coherence, I see nothing significant except <beat | ACAV>, see fig1, so I did not save the rest of the measurement.

After I realigned the beam, there is a big coherence between ACAV andRCAV see fig 2.

the coherence between PMC and RCAV follow the same trait as that of PMC and ACAV, but slightly less, so I show only PMC and ACAV.

However,  the beat note before and after realigning the beam are still the same, see fig3.


I'll add RIN from  RCAV/ACAV/PMC .




gain setup


PMC: Gain 16

         RF_ADJ 5.7 V


FSS: Common gain 21.5

         FAST gain 21.2

        RF_ADJ  10

These values allow maximum Transmission power and stable lock (I checked this by unlock and lock the cavity and see if the signal is stable after loss lock)

Attachment 1: coherence_before_realign.png
Attachment 2: coherence_after_realign.png
Attachment 3: beat_2010_11_15.png
  487   Thu Feb 10 01:16:42 2011 TaraNotesBEATcollection of beat data, H1 arm noise, and SR560 noise

I plot beat noise PSD, with estimated H1 arm noise, and SR560 noise converted to frequency noise in the current beat measurement. From the approximation, SR560 noise will be smaller than H1 noise.


 The conversion for SR560 noise to frequency noise is computed by finding the slope of signal from self beat measurement.

parameters are from Frank's entry below

amplified (DC-coupled) signal from mixer using SR560, LP@30Hz, gain20 in channel C3:PSL-GEN_DAQ15

185.0MHz :  -2.405V
154.2MHz :   0.005V
123.2MHz :   2.263V


The pkpk values is then (2.263V - -2.405V)/gain20 = 0.2334 V over 185 MHz - 123.2 MHz = 61.8 MHz range.

Thus the signal is = (0.2334V)/2 sin ( pi df/ 61.8 MHz)

This gives the maximum slope = 0.2334 V* pi /2 /61.8 MHz, or  ~ 170 MHz/V.

SR560 noise is estimated to be flat, 5nV, at high f, a corner at 10Hz which gives 5 uV at 10mHz.

multiplied by 17 MHz/V to get frequency noise from SR560.



Attachment 1: beat_2011_02_09.png
Attachment 2: beat_data.mat
Attachment 3: code_2011_02_09.m
load beat_data.mat


% correction for 160mHz high pass (AC couple)

... 7 more lines ...
  488   Thu Feb 10 12:00:55 2011 ranaNotesBEATcollection of beat data, H1 arm noise, and SR560 noise

 Here's the plot from the H2YAC doc that explains the idea.

If we can get down to ~1 Hz/rHz at 1 Hz, it would be nice for measuring the suspension performance at that point.

Attachment 1: Screen_shot_2011-02-10_at_10.39.43_AM.png
  817   Thu Feb 9 22:32:51 2012 FrankNotesBEATcollection of some numbers for future calculations

mixers  (which we currently have (and use) in the lab):

  1. ZFM-3-S (datasheet)
    - 0.04 to 400 MHz
    - Level 7
    - conversion loss @160MHz: 4.79dB typ
    - VSWR RF Port : 1.15:1
    - VSWR LO Port : 2.46:1
    - 1 dB COMP.: +1 dBm typ.
  2. ZX05-1MHW (datasheet)
    - 0.5 to 600 MHz
    - Level 13
    - conversion loss @160MHz: 5.2dB typ
    - VSWR RF Port : 1.17:1
    - VSWR LO Port : 2.37:1
    - 1 dB COMP.: +9 dBm typ.

cables  calculator for cable loss, which has a huge amount of different cable types in it's database. : http://vk1od.net/calc/tl/tllc.php

velocity ~0.66 to 7*c

RG-58C/U: loss 32 dB for 500ft @160MHz
                    Delay  5ns/m

RG-142    loss 25 dB for 500ft @160MHz
                   Delay  4.7ns/m


4-way splitter ZBSC-413 (datasheet)

additional insertion loss 0.5dB
power Input: 1W max


ZHL-1A.pdf (datasheet)
 - gain 16dB
 - output power: 28dBm min. (1dB compression)
 - noise figure: 11dB
- VSWR 2:2 (in and out)
 - 2 to 500 MHz

ZFL-500LN (datasheet)
 - gain 24dB 
 - output power: 5dBm min. (1dB compression)
 - noise figure: 2.9dB
- VSWR 1.5:1 (in) and 1.8:1 (out)
 - 0.1 to 500 MHz


  486   Thu Feb 10 00:21:55 2011 FrankSummaryBEATcomparison VCO feedback signal and "cable technique"

data taken at 02/06/2011 10:10:00 UTC, duration = 24h

updated plots:



data files:






structure of data files like this:

y1 =
   name: 'C3:PSL-ACAV_VCOMON'
   min: [1440x1 double]
   mean: [1440x1 double]
   max: [1440x1 double]
   rate: 0.0167
   start: 981022215
   duration: 86400
   data: [1440x1 double]

raw data in min/mean/max
calibrated (mean) data in data

  983   Mon Jun 11 12:02:39 2012 SarahDailyProgressDocumentationcomsol

 I am trying to model the change in cavity length due to acceleration using COMSOL. After obtaining the software I am attempting to first model a simple beam bending under acceleration. Using the Structural Mechanics physics for a beam and a stationary study, I first fixed the beam at one end and added a prescribed acceleration. Currently the results are not as expected, and the beam is not bending under acceleration. Adding a force instead of acceleration gives the expected results of beam bending. Additionally working in a time dependent study as opposed to a stationary study produces expected results of beam bending under acceleration. However, it should work with a stationary study, so I am still trying to figure out how to use the software and get this model working.

I have already constructed the model for the cavity with the 1.45in x 1.5in spacer, and once I get the beam simulation working, I should be able to apply a similar study to this model. 

  984   Tue Jun 12 16:04:33 2012 SarahNotesDocumentationcomsol progress

 Attached is the file with the latest progress I have made in modeling the change in cavity length due to acceleration. I ran a time dependent simulation using the beam physics under the structural mechanics catagory. The deformation results are plotted in a 3D plot in the attached file. The results attached were obtained with the cavity supported at .25 inches from both ends of the spacer. I still have yet to determine how to get comsol to give me the actual change in length as a result. Additionally this is only a rough model, because the acceleration only applies to the points on the cavity as opposed to the entire cavity itself. I plan to introduce more physics to correct this, as well as plot change in length versus support points to find the optimal points of support for the cavity.

Attachment 1: cavity_.25in.mph
  1056   Thu Oct 4 23:28:06 2012 taraNotesRefCavcomsol simulation for cavity suspension

I'm using COMSOL to simulate the effect of cavity sagging to find the optimum suspension points. The answer is not yet ready, I'm still working around COMSOL.


  • Problem with point like contact: First I tried to simulated 4-fixed-point support, however the result was asymmetric along beam line. It might be the result from the point-like contacting areas between the support and the cavity. You can see the tilting along the beam line in the figure below. Note the constrained area  of the support effect the sagging slightly as well [add ref].


fig1: cavity sagging, on 4 point suspension. The cavity is not symmetric on left and right.

     So, as a start, I switched to half line support. As my cavity support will be rods placed perpendicular to the refcav, the simulation might not be off by much. Then I checked the displacement at the center of the mirrors. The result was, the further to the ends of the spacer, the less displacement of the mirrors. I think this is strange. I also remember a paper about this and their cavity dimension is similar to what we have, and their result is slightly away from the ends [ref]. I'll have to double check the result again.

Note: I think what is wrong is how I use the displacement of the mirrors along the beamline as differential length of the cavity, I have not taken into account tilting of the mirrors yet. Also, I'll try to position the venting hole downward to see if there is any differences in the result or not.


  1058   Wed Oct 10 01:38:49 2012 taraNotesRefCavcomsol simulation for cavity suspension

I'm still working on COMSOL, now my model has the following features:

  • support points are simulated by four rectangles on the spacer surface. The support areas can be changed, and their positions can be moved along the beamline and around the cross section directions. I'm still not sure what should be the effective area for the simulation. However, the paper from Milo's group [2009] showed that the areas of the supports points do not affect the optimum position that much (but the support must be constrained in the same direction as gravity only). I have not tried to constrained the points in only one direction yet.
  • I used a symmetry plane to model only half of the spacer. This will reduce some simulation time and avoid any asymmetry due to the mesh size.
  • I'm trying to use matlab with comsol and print out the result. The work is stil in progress.



Milo etal. 2009 Phys Rev A 79.053829.

  1060   Wed Oct 10 21:31:57 2012 taraNotesRefCavcomsol simulation for cavity suspension

I used COMSOL with MATLAB to run the simulation. I tried to vary support position and checked the mirror displacement along the beam line axis and tilt angle.


With Aidan help, I am finally able to run matlab with comsol to get the results (displacement of the mirror surface and tilt).

 We are not planning to cut the cavities for support points, so we will choose the support positions on the spacer's surface, with parameter X and theta, see the figure below for their definitions.


As a start, I chose theta = 30 and 60 degree. The displacement and tilt (due to cavity sagging under its weight at 1g)as a function of support position are plotted below.


It is possible to minimize the tllt, but the displacement is still a bit bad. The result from 8" spacer, the sensitivity to acceleration is (dL/L) / (m/s^2) = 2x10^-10, while the current result will be about  1x10^-10. Since the cavity is shorten by ~ a factor 4, I expect a better sensitivity to vibration.


I'll try to change the area of the support points to check its effect on the displacment.

I have to check if I can constrain the support points in one direction or not.


I'm still working on COMSOL, now my model has the following features:

  • support points are simulated by four rectangles on the spacer surface. The support areas can be changed, and their positions can be moved along the beamline and around the cross section directions. I'm still not sure what should be the effective area for the simulation. However, the paper from Milo's group [2009] showed that the areas of the supports points do not affect the optimum position that much (but the support must be constrained in the same direction as gravity only). I have not tried to constrained the points in only one direction yet.
  • I used a symmetry plane to model only half of the spacer. This will reduce some simulation time and avoid any asymmetry due to the mesh size.
  • I'm trying to use matlab with comsol and print out the result. The work is stil in progress.



Milo etal. 2009 Phys Rev A 79.053829.


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