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  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.
  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.
  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
  1255   Thu Jul 25 18:13:11 2013 ChloeNotesECDLCurrent Driver/TEC

Current driver: the plan for the summer is to use the current driver that Tara found, the LDX-3412. Dmass has a low noise current driver that he has developed that eventually (after the summer, since it is unfeasible to finish over the summer) will be implemented in the ECDL. I believe he will give me and Tara the schematic for it at some point and we may build it later. 

I configured the TEC. We have 2 Peltier elements, the Thorlabs TEC3-2.5 and the TEC1.4-6. I used the TEC3-2.5 in the TEC, since its operating current is lower and works better with the controller we bought. I was stupid and burned myself pretty badly on the Peltier element because I had the wrong settings, and will remember that it heats up easily (be CAREFUL before touching). The TEC is working! It can adjust temperature, although the readings it gives is in resistance (which can be converted to temperature using the attached Excel file). I'm going to play with it more tomorrow to see if I can tweak the settings and understand what every button does. 

Today I also figured out how to make the laser diode wire to the 9 pin D-sub connector from the LDX-3412 current source that we found. I built the entire thing in the electrical shop, but haven't put in the reverse bias power supply. I will try to do this tomorrow to see if I can get the laser working. Since the TEC is working, I may try and tune the wavelength of the laser output and see what the noise looks like. 

Attachment 1: thermistor_temperature-resistance.xlsx
  1254   Wed Jul 24 18:13:05 2013 ChloeNotesECDLCurrent Driver

Rana wants for me to build my own low noise driver, since anything on the market isn't sufficient or is terribly expensive. Dmass does not have an extra driver in his lab, and Eric Gustafson doesn't have a spare since his SURF student is using it. Tara found a spare driver in the 40m. It is the LDX-3412 from Newport and operates up to 200 mA. Tomorrow I am going to start trying to make it work with our diode. The two diodes that we ordered operate at 200 mA (QPhotonics) and 280 mA (Thorlabs). However, both vendors provide a plot of power output vs. injected current, and it seems like at 100 mA, they will both still provide 50-100 mW of power. 

In the meantime, I will work on putting together the current driver from the Erickson paper (attached). This is an improvement on the Libbrecht and Hall design by over an order of magnitude in noise spectral density. I spent the afternoon trying to compile a list of the parts we will need. The paper is kind of complicated so I'm still trying to understand some of the parts, but I have a pretty comprehensive list of the parts we will want to get. We will likely be able to find at least some parts in the 40m lab. I may go scrounging around. 

I also attended the talk that Rana gave today about basic electronics and noise calculations. I will try and get liso on my computer before next week's talk, since it would be useful to have. 


  1253   Tue Jul 23 17:59:47 2013 ChloeDailyProgressECDLSolidworks Design


Tara heard back from the machine shop, and they can do 1/4-80 threading. I finalized the design this morning. I was sure to check whether the frequency could be sufficiently tuned, and whether the screw on the grating mount would fit into the box. After making some changes, I printed out the designs and went to the machine shop with Tara to talk about our design. It should be ready sometime next week between Wednesday and Friday. Finalized designs are on the SVN. 

Frank (from the Birmingham group) emailed us back about the ECDL. He said they used the $1000 current driver from Thorlabs (http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=10), although he recommended the $4800 Vescent current driver (http://www.vescent.com/products/electronics/d2-105-laser-controller/). He also said that there was not a good way of predicting the noise budget beyond knowing what contributes to noise at different frequency ranges: 

  • temperature/environmental noise at low frequencies
  • acoustic vibrations at a few hundred Hz to kHz
  • current noise at kHz to MHz
  • relaxation oscillations of laser diode at a few MHz

Frank also said that he would be leaving the Birmingham in September and has discontinued the ECDL project, so they haven't gotten past making a working prototype. He was otherwise very willing to help. 

I'm currently talking to Thorlabs to see if they can give us the current noise density instead of an RMS noise on their current driver. It seems that if we use the Thorlabs 100 mA driver (instead of the Thorlabs 200 mA driver we had been planning on), the noise is reduced a lot. At 100 mA, we should get an output power of ~75 mW from the Thorlabs diode and ~50 mW from the QPhotonics diode. This actually is probably sufficient for what we need, so the lower current input should not be a huge problem. From a range of 10 Hz to 10 MHz we have the following values:

  • Vescent current driver (200 mA): 0.3 uA
  • Thorlabs current driver (200 mA): 1.5 uA
  • Thorlabs current driver (100 mA): 0.2 uA

Vescent current driver does much better at lower frequency ranges, and has RMS noise of 0.05 uA between 10 Hz and 100 kHz, but is comparable over a larger range with higher frequencies. While the RMS values are promising, we aren't sure how the noise density compares over the entire frequency range... I'm hoping to hear back from Thorlabs soon about this. It seems like the Thorlabs driver is an actual possibility though. 

Tomorrow Tara and I are going to get started in the lab. Tara will show me around, and I'll try to get the TEC working. 

  1252   Tue Jul 23 11:43:00 2013 EvanDailyProgressElectronics EquipmentZach's op-amp recommendations
Zach wrote up his thoughts on how to choose the right op-amp in ATF:1752.

His recommendation for an AD743 replacement is the ADA4627. It has lower current noise and only slightly higher voltage noise compared to the AD743.

Apparently the AD743 was only discontinued in its 8-DIP form; it lives on as a 16-pin SOIC. According to the datasheet, the 8 extra pins do nothing, so I have no idea why they've chosen to manufacture it in this way (maybe they can't fit everything onto an 8-SOIC die?).
  1251   Tue Jul 23 10:29:12 2013 EricaDailyProgressfiber opticreducing drift in the recombined beam
July 22, 2013

We placed a plastic container from the GYRO lab over the spool of fiber. We wiped everything down w/ isopropanol. The cap is placed top side up and then the bottom is placed upside down on to the top of the cap. This is because the inside of the cap has ridges. There are two holes that the fiber is threaded thru. We used bubble wrap to cover it. It's not the most airtight but it should be okay. We left the aluminum foil surrounding the spool, to restrict air flow into the fiber. Then we left it there for awhile but coming back to it, there wasn't much improvement.

Evan suggested using a AD 590 to measure the temperature fluctuations of the table. Rana suggested we use the substitute for AD 743 that Zach found, which I need to find. Went to 40m to get a nicer circuit board and find a FET OpAmp with low current noise. We got a Vector Circboard 8015 and two OPA604's. We'll be building two setups so we can cross-correlate them and make sure the measurements are accurate.

tomorrow we will be soldering stuff.

  1250   Tue Jul 23 10:14:30 2013 EricaDailyProgressRefCavmeasurements of beam size, for calculations about setting up fiber

took some of the measurements for the refcav's beam path. Put in a polarizing BS and half wave plate to reduce the power going into the WinCam. Measured the output at various distances; the beam attenuated with an absorptive ND filters (OD 3 and 1.3).

I obtained a waist of 1170 um, which is rather large, about 2.26 m from the beam splitter.
Then calculating from this waist back to the laser, I get a waist of 220um about 0.5m away from the first lens (f = 171.9mm) which is rather long. I checked this with JamMT and my calculations were right... So maybe I should take data over a wider range.

I'll attach the diagram later with the measurements I took.
  1246   Mon Jul 22 18:30:20 2013 ChloeDailyProgressECDLSolidworks Design

Tara and I received the parts we ordered from Thorlabs. I will be working in the ATF lab on the corner of one of the optical tables. Tara showed me around a little; we will likely work there more tomorrow. 

I met with Tara and discussed the final mechanical design. In particular, 

  • Tara explained a way to design a mount to attach the window onto the wall of the box, and I built the mount. Although my design has the mount on the inside of the box, it is symmetric so it can go on the outside just as easily if we find that easier. 

  • We decided to have space for a 9 pin D-sub connector and 2 BNC cables (one for the current driver, one for the PZT) on our box. 

  • We decided to not make a collimator mount yet, since the focal length of the collimating lens will depend on the beam characteristics of the laser, which we will not know until we experiment with this. There aren't currently holes on the base plate for the collimator mount to screw in; we will add this later once things are more certain. 

  • For the PZT, we need to figure out how to make the grating angle/length adjustable. This can be accomplished with a screw and PZT element (based on what I've seen online, probably about 2 mm thick). We aren't sure whether the machine shop is able to make thread fine enough to put the screw directly on the grating mount (~80/inch), so Tara is emailing them to find out if they can. We can create a separate mount for a micrometer screw otherwise. This is the PZT I would like to order: http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=100800 

  • The Mroziewicz paper discusses how to determine the ideal pivot point for a grating mount of an ECDL. I looked into this, and calculated that for a cavity of about 10 cm at 1064 nm (an angle of 39.7 degrees), we want the pivot point to be about 12 cm away from the center of the grating, so I modified the design slightly to accommodate for this. 

  • I'm adding an extra hole on the base so that if we decide to use a mirror mount with an adapter instead of the grating mount (in case the diode doesn't emit light straight in one direction). Everything is also at an appropriate height so if we decide we need to use a mirror mount, the rest of the design should still function. 

The changes have been implemented in Solidworks. The finalized pieces I want to have machined are on the 40m SVN in the ECDL folder. I've also attached a couple of pictures for a quick overview. 

Since we are trying to find a good enough current driver to use, Tara thinks I can start by configuring the TEC on a piece of copper to make sure it works. I will try to do this tomorrow now that the design is ready to be sent into the machine shop. I will also figure out a good time to go over to the machine shop and discuss the design with them. 

Attachment 1: final_3d.PNG
Attachment 2: final_top.PNG
  1245   Sat Jul 20 23:39:09 2013 EricaDailyProgressfiber opticreducing drift in the recombined beam
July 18
Redid inventory of the lenses and printed out a new sheet because there are fused silica and BK7 lenses, which have different focal lengths for a given radius of curvature. It only has the lenses in the box. Tara had like 6 to 8 other ones but I don't know where they are.

Looked for papers that give numbers for noise added... Like before, I'm having trouble.

got login for SVN to work

Evan helped come up with other solutions to try to reduce the drift on signal from the recombined beam. We put UHV aluminum foil on the coil of fiber to reduce the acoustic noise but it didn't seem to have much effect on the drift. Acoustic sound affected the fiber because the drift seemed to speed up a little bit when we closed the cabinet door and jumped around. When the lab door was closed, there was a spike in the signal but thing settled down fairly quickly. We turned off both Hepa filters but like yesterday, it also didn't seem to do much. We elevated the coil off the table by using the black rectangular clamps to dampen possible transfer of movement from the table to the coil.
We locked the laser to the cavity to reduce the laser noise. The error and control signals were very steady compared to the drift in the beam signal.

We calculated the change in frequency over 1 period of drift is about 5 MHz, and for the fiber to change by 1 wavelength, it would take a temperature change of 16 mK. Looking at Rana's graph of for noise calculations (http://nodus.ligo.caltech.edu:8080/PSL_Lab/1205), we calculated the rms temperature noise due to ambient air at 100 mHz (because the period of the drift was on the order of 10s) was 100mK rms, which is an order of 10 larger than the calculated change in temperature.

The fiber passes by the laser, which is emitting a bit of heat, which may be a part of what is causing the drift.
  1244   Thu Jul 18 16:34:22 2013 ChloeDailyProgressECDLSolidworks Design

Sorry, I've been out for awhile since I had an extremely bad reaction to some medication. Only just starting to recover but I'll work during the weekend to make up for it. 

Today, I spent awhile looking at possible current drivers online. Dmass said that the Thorlabs one is not being used for any frequency sensitive measurements. After looking online, nothing seems to beat the Thorlabs driver in terms of noise level (<1 uA RMS), so maybe we will need to look into building our own current driver or buying the one online based on Libbrecht and Hall. That one is quoted at $4000-5000. 

I also spent awhile trying to figure out a new box design. I think we will want to purchase an AR coated window for the output beam, much like Birmingham. 1" diameter should be sufficient based on the size of the diode/collimator lens. Thorlabs and Newport have comparable products with regards to this (http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=1117). It is also important that the box is airtight so no dust can accumulate on the grating or diode. I was thinking of having a 2 part box, with the metal folded, but I'm not sure how easily the machine shop can do this (fold thicker metal sheets, create rounded edges). Waiting to hear back from Tara about this. 

  1243   Wed Jul 17 18:29:37 2013 EricaDailyProgressfiber opticreducing drift in the recombined beam
Went on a tour to 40m lab led by Jenne. It's basically a prototype of the ones in Livingston and Hanford. It allows LIGO to test coatings, control systems, etc. before AdvLIGO is even built.

I tried making the drift go away, but it seems to me it got better, and then got worse.
I tried turning off just one HEPA filter, then two. I couldn't really find that much stuff to insulate the fiber, so I used the bubble wrap that the coil came with to wrap around the coiled fiber. However, that didn't seem to really help at all.

With only 1 HEPA filter off (the one closest to the input), I was able to get a rise time of about 35s, which is pretty similar to what there was yesterday. With the 2 HEPA filters off, I got a rise time of about 5s.

For some reason, at one point the signal just started oscillating like crazy. I lowered the power coming from the output fiber (from 0.5 to 0.4mW) so it would be closer to the original beam (0.3mW) and there wasn't noise any more, but I'm not sure if it was because of the power differential at all.

How much drift is allowable? Does it have to be flat or is it okay if it is simply linear?

I can increase the output from the fiber to 1.3 mW.

  • A message has popped up on the oscilloscope that I've been using saying it needs to be recalibrated.
  • The wire connecting the probe to the power meter (PM100D, the red one) is coming out of the insulator.
  • Rana had me bring the SR620 to 40m so that's where it is.
  1242   Wed Jul 17 11:58:47 2013 EricaNotesfiber opticmode matching, beam recombination
July 16,2013
I tried improving mode matching by adjusting two knobs on the mirrors at once but that wasn't leading anywhere.
Evan suggested improving the polarization going into the input beam because we wanted the most linearly polarized light. So a half wave plate was placed right in front of the input collimator and another was placed before the final pol beam splitter before the photodiode. At each polarization on the first HWP, I would rotate the second HWP back and forth over a wide range of angles to get a feel for the eccentricity of the input light. At 5 degree intervals (of polarizer, so 10 degree intervals in polarization) over a 66 degree (for HWP) range, we changed the HWP in front of the input, and then oscillated the HWP at the output back in forth to see the fringing. The recorded pk-to-pk amplitude was noted using the cursors and by holding the fiber to bring about more drift.

The peak was at around 30 degrees for the HWP. I'm not sure why the two maximum do not have the same amplitude. We placed the polarizer at 30 degrees, removed the HWP at the output end, and then translated the stage. Now all the light coming out was S-polarized. We had to readjust the knobs on the input collimator stand because the power output was a little low; the half wave plate must have redirected the light a little bit.

So it turns out what I thought were fringes yesterday was just noise from the fiber, laser, etc., which we also want to detect. Something I should have noted yesterday was the drift of the DC level. Today we figured out that the drift was actually the fringing that occurred from a change in length. I could see the oscillations on the scope from when I translated the stage slowly or quickly. Then we optimized the alignment to increase the signal.

However, the length of the beam is fluctuating too much (due to temperature) so we can't keep it in the linear part of the cos^2 model for power. One thing to note is the noise seems to decrease at the max and min - not sure why.
  1241   Tue Jul 16 11:02:47 2013 EricaNotesfiber opticmode matching, beam recombination
July 15,2013

Asked Rana how to do the calculations for the noise.

Here is the picture of the explanation.

Rana suggested we place a lens (f=30mm to 200mm) to after the final polarizing BS so it would be easier to match the beams and so it is focusing into the photodiode. If the beam was 1-1.5mm at the mirror, then a lens shouldn't be needed before the BS. We placed a f = 30.6mm after the pol. BS but the beam profiles were not particularly alike, since the beam from the lens was diverging fairly quickly, but that definitely made it easier to see the beams because they weren't diverging. I replaced the other lens after the fiber, before the 45s BS, which made the beam profiles match a lot more.

I tried aligned the beams, but in a way that the beams really overlapped only where the photodiode was supposed to be, which was dumb. Could not read anything from it. So I redid the alignment for both beams, so they were about 3" from the table at all points and that definitely improved the matching, notably, giving a larger range over which the beams were overlapping very well.

We were able to detect some fringing just on the oscilloscope and were able to improve on by adjusting the knobs. The signal is at a certain DC level, with wiggles which are noise. However, whenever the stage, or table, or other components are touched, we can see it on the oscilloscope. Evan was concerned that the stage wasn't perfectly aligned with the beam, so translating the stage would ruin alignment ,but it didn't seem to much of a problem.

Note: Noise from laser is 10^4 (Hz/rt(Hz)).

task: need need need to find paper on fiber noise!!

Also, talked to Evan about Gouy phase and how the PMC works, different kinds of polarization modes (including some weird cashew shaped ones), and PDH setup.
Sidebands = phase references.
  1240   Tue Jul 16 10:27:47 2013 EricaNotesfiber opticmode matching, beam recombination
July 14, 2013

We just went with the setup from yesterday.

We adjusted the input fiber so that one axis is vertical. If the lens of the collimator is as close to the fiber as possible, then the two screws on the side of the collimator are perpendicular to the little notch on the collimator, which is supposed to line up with one of the axes. Then we moved around the other knobs so we ended up getting the same maximum power output

At the output, we aligned everything up. After pol. beam splitter, there was a lot of power coming out of both s and p faces. This was confusing because we used a polarizing beam splitter to pick it off from the main beam.

We checked the beam going into the fiber was linearly polarized with a polarizing beam splitter - which it was, s-polarized.

We checked the output beam - took out the 45s beam splitter and then put pol beam splitter in there, rotated fiber until s- polarization was at a max (reflected beam)

We replaced the 45s beam splitter, still a lot of power not coming out in the direction we wanted - got transmitted rather than reflected. However, the power output from each beam after the 45s BS was about equal so didn't do anything about it.

After we checked the polarizations, we placed the polarizing BS to look at the beam recombination, and there was still light transmitted and reflected. This could be that the beam was really messy, and since the polarizing beam splitter is not 100%, there was still some p-polarization. This seems to be the reason why Tara had me place this second polarizing BS.

We placed a lens (f=70mm) placed in front of output to focus the beam, profile more like that from the laser

Using a OD2 filter, we used a photodiode (PDA100A) and an oscilloscope but could not see anything. Can't see fringes, just a DC line. Translating stage doesn't do much, we fiddled around with the knobs on mirrors and stage but not much change

Then we switched to looking at the Gaussian with DataRay, but - Gaussian from beam, not Gaussian from laser - clipping edge of mirrors so had to realign.

Here we can see fringes but the beams aren't very aligned. If they were exactly aligned, then you would see total destructive and total constructive interference. Even with moving knobs, it didn't really improve. Will work it more tomorrow.

Note: The power output from both beams should be about equal intensity.
  1239   Mon Jul 15 10:55:40 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

 After a discussion with Eric and Matt, here I'll summarize about thermo optic(TO) noise calculation plus some other important noise sources.

1) goal

     We aim to measure the limiting noise in AlGaAs coatings. If we order just 1/4 quarter wave stack, no optimization, the limiting noise source will be from TO noise due to high values of thermo elastic(TE) and thermo refractive(TR) coefficients of the materials. However, by optimizing the coatings structure to cancel TO noise we can:

  • Probe thermo-elastic (TE) noise in SiO2 substrate at low frequency and coating Brownian noise(BR) at higher frequency
  • Prove that TO cancellation can be done (according to Evans etal).

We can tell what kind of noise from the slope.  BR, TO noise or TE noise in substrate have different slopes at the interested band, see fig 1.


2) Is the calculation correct?


fig1: noise budget with some fundamental noise sources. The noise budget is for AlGaAs coatings on a mirror with ROC=1m. The cap is GaAs (high index material) with 1/8 lambda thickness. See explanation below for more details.

    The fundamental noise sources in our setup (1.45" cavity, 1m roc mirror, optimized AlGaAs coatings) will be:

==BR in coatings==:   

  • The calculation is taken from Harry2002, for half infinite mirror.
  • The result is compared with Somiya&Kazuhiro2009 for finite size mirror calculation (see solid blue line and dashed cyan line). The difference is small due to our small spotsize, so using either calculation is ok for us, but Harry's calculation is less time consuming.
  • The analytical result should be valid as it was verified by Numata and TNI measurements.

==BR in substrate==:

  • The calculation is taken from Levin1998, with finite size correction by Liu&Thorne(LT2001). 
  • The loss angle for bulk fused silica is frequency dependent ~ 10-11 x f0.8(Penn2006). This loss is much lower than conservative constant loss (10^-8) (number from DCC LIGO-T0900161) from dc upto 10kHz.
  • In this calculation, for constant loss of 10^-8, BR noise in substrate is still ~ a factor of 3 lower than BR in coatings.

==TE noise in substrate==:

  • BGV1999 gave a result for adiabatic limit (most of the heat flow is in 1-D heat diffusion length is much smaller than beamsize, sqrt(kappa/C * 2pi*f)<<r0 )for half infinite space mirror, Liu Thorne2001 verify the result. I used comsol to simulate the noise (with adiabatic assumption) and it agreed with the analytical solution.
  • However for our setup with a small spot size the assumption beaks down. Cerdonio2001, computed the noise that valid for low frequency and small beamsize which is a  case for our setup (cut off frquency ~ 10 Hz). All the factors and corrections are summarized in TNI2004 measurement and Nawrodt2012.  The calculation will be valid for our setup.

==TE and TR noise calculation:

  •   The temperature fluctuation sensed by the beam is taken from BGV1999 using Langevin approach, and Mike Martin Thesis (this takes care of the fluctuation at low frequency where adiabatic assumption breaks down. The calculation assume that coating thickness << thermal diffusion length. For AlGaAs, because of its high thermal conductivity, this assumption is still hold at the bandwidth of interest.
  • The thick coating calculation is given in Evans 2008.  It is important at high frequency and coatings with low thermal conductivity. This means that TE and TR effects won't be coherent in the coatings. This is not a problem for AlGaAs due to its high thermal conductivity.
  • TE and TR coefficients calculations are treated coherently in Evans2008.  The cancellation only depends on coating structure. With a cap of GaAs (nH) 1/8 lambda thickness, the cancellation is very good reducing the TO noise below other noise upto a few kHz.
  • The cap thickness has to be withing +/- 20Angstrom so that the TO is about a factor of2 below coating BR. G. Cole mentioned that each layer thickness varies about 0.3% or less which is about lambda/(4*n) * 0.3% = 2Angstrom. So the cancellation should be ok.

TR coefficients are calculated numerically (GWINC) and analytically (Gorodetsky2008). The results match up well (less than 1% difference), if all the parameters/ averaged values are from Evans.

In GWINC there is one correction noted as "Yamamoto thermo-refractive correction", this changes the Beta eff ~ 10% causing the cancellation to be not as good (still ok up to 1kHz). I emailed Kazuhiro Yamamoto asking him if he has anything to do with this. Otherwise all the calculations and optimization are in good shape.

Attachment 2: alGaAsnb.fig
  1238   Fri Jul 12 15:25:56 2013 ChloeDailyProgressECDLSolidworks Design




 Grating mount: I examined different ways to attach the grating to the grating mount. Our options are epoxy or some sort of actual mount the grating fits into. I finally decided that we should use epoxy for the following reasons:

  • Epoxy is much easier to align and attach than a mount would be, since a mount would rely on being machined extremely precisely
  • Epoxy has a much lower coefficient of thermal expansion (about 60 ppm/K) by about a factor of 4 than aluminum or any metal we would use to build the mount (about 230 ppm/K). This means that epoxy will be less affected by temperature, so it will affect our cavity length a lot less. 
  • It is impossible to design a stable mount that adjusts to clamp in the grating, while still being fixed solidly to the grating mount. I spent a long time brainstorming different designs, and looking at mounts from Thorlabs and Newport for ideas. Any mount that would clamp the grating in well would require some adjustability for small variations in the grating size, and as a result, cannot be fixed onto the grating mount without an excessive number of parts. 


Change of PZT: Our PZT choice relies on how much the PZT will need to be able to move. This changes the length of the cavity as well as the angle of the diffraction grating, and the screw on the PZT will be used to tune the angle. I calculated we will have a 400 nm change in wavelength per mm of the screw length changed, meaning we will only be making changes of less than a mm in the screw length. It made the choice of PZT from before seem a bit excessive. 

Instead, I was thinking of having a very short micrometer screw (http://eksmaoptics.com/opto-mechanical-components/adjustment-screws-870/micrometer-screws-870-0040/) with a chip piezoactuator (http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=100800). I'm not sure how to build the threading into Solidworks or if this will be possible to mount, though. Need to keep looking into this... 

Shortening collimator tube: I have been corresponding with Thorlabs today about their collimator tube. It is made out of aluminum, and therefore we can probably saw off half of it and leave part of it threaded to mount in the collimator mount. Thorlabs also offers custom modifications, but this will likely take awhile and cost a lot more money. 


All of the changes I discuss above were implemented into the Solidworks figures. I just need to figure out the PZT and the parts should all be ready to be machined. I will also try to update the Wiki page this weekend since I haven't for a long time... 


  1237   Fri Jul 12 00:51:39 2013 EricaNotesfiber opticmode matching
I finally got MatLab installed on my computer from Caltech.
You can get programs installed by being a Caltech student/faculty, through IMSS. Here is the website:

One of the things, I was unsure about and talked to Evan about mode matching where should the output waist be and how does one calculate it. Previously, I took the mode field diameter from the fiber, the focal length of the lens in the collimator, and then calculated the waist q parameters (from Kogelnik 1966), like I did calculating from the PMC. However, that leaves some questions - once the waist from the fiber is determined, when mode matching, should the incoming waist from the PMC be placed at the lens, or at the distance we calculated the waist to be from the lens in the collimator?

Other potential problems is possible change in the distance from the lens to the fiber in the collimator if one accidentally rotates it while attaching the collimator to the stand.

This can be resolved by looking the Gaussian profile and measuring the radii at various distances, to calculate the waist (see http://nodus.ligo.caltech.edu:8080/PSL_Lab/1222). Then when mode matching, one would try to place the waist at the lens in the collimator. I measured the Gaussian profile from the input side by switching the output and input sides of the beam so the laser was directed into the output end of the fiber, without altering the input end (distance from fiber to collimator, without removing fiber from stand and collimator, etc).

Then I measured the waist after the two fixed lenses from the PMC, to ensure the theoretical calculations for the waist were correct.

When checking the waist coming after the PMC, our calculations from the Gaussian profile did not agree with the location of the waist we observed with our eyes. Evan discovered that the lens we were using was not fused silica (UV) as most lenses are but BK7 (C), which for a given radius of curvature, has a different focal length than fused silica. So the lens we thought was f = 143.2mm had a focal length of f = 127.1 mm. Once this change had been made in the calculations, it agreed with our observations.
This means I'll have to redo the inventory because some of the lenses are fused silica, others are BK7.

Here is the final determination of the location of the waist coming from the PMC and the setup I used to determine it.

This is the new mode matching setup.

After setting it up, I obtained an output of 15%. 1.24mW out of 8.4mW.
  1236   Thu Jul 11 17:51:12 2013 ChloeDailyProgressECDLSolidworks Design

 Tara got me the information about the adjustable collimator tube he ordered (http://www.thorlabs.us/thorproduct.cfm?partnumber=SM1L30C). I built a mount in Solidworks and added it to the assembly. I also contacted Thorlabs and am discussing how easy it will be to shorten the tube, since we don't need it nearly as long and the length gets in the way a bit. This should be doable. 

I decided that we would go for a box where everything is screwed onto a baseplate, and a lid is screwed to the sides of the baseplate. The reason for this is that the base plate will be much easier to build on than building on the bottom of a box. The screws are on the side instead of the top because this will be easier to have machined, and the design is more compact leaving less room for noise when the lid is disturbed. 

I'm currently looking at a few tasks that I will try and complete soon: 

  • How do we plan to mount the grating? Most literature uses Epoxy, but it may be less noisy to design something on the grating mount to hold the grating and clamp it in. I'm examining which will create less noise. 
  • Is the choice of PZT ok? This involves several things. We need to consider the distance the PZT needs to be able to move and whether it will fit inside the grating mount we have designed. 
  • Will we be using D-Sub or BNC connections? BNC is better for rf, but it only has one channel on each coaxial cable so it is bulker. D-Sub is much more compact, and we can wire several channels at once. Right now I am planning on using D-Sub for the TEC wiring, probably a 9 pin connector using 4 for the +/- thermistor and the +/- Peltier element connections. The current driver may be in the rf range if we want to create sidebands, in which case we will want to use BNC cables. I'm looking into this. 

Attached is a picture of the current setup, built in Solidworks and the lid built separately. I'm not going to bother attaching the Solidworks files until things are more finalized. 

Attachment 1: lid.PNG
Attachment 2: sketch_without_lid.PNG
  1235   Thu Jul 11 01:40:19 2013 EricaDailyProgressfiber opticmode matching
Tara changed the lenses in the beam path so I redid calculations for mode matching. Here is the setup.

I placed the lenses and obtained about 1% (1.54 uW out of 5.2 mW).
  1234   Thu Jul 11 01:36:13 2013 EricaNotesRefCavgraph from measurements on EOM driver
  1233   Thu Jul 11 00:19:52 2013 taraDailyProgressopticboth cavities are locked

Both cavities are locked (not optimized yet). Since it has been awhile that both are locked, here is a picture.


 Rcav is locked by Fast feedback only. I still have to check the polarity for PC feedback.  I adjusted the phase between the LO and PD for RCAV loop to get a nice error signal. I noticed that there is an offset in the error signal, I will try to adjust the polarization of the beam in front of the EOM to see if I can reduce this offset from RFAM.

To do:

  • lock rcav with both fast and PC feedbacks
  • optimize the setup ( reducing RFAM, minimize back reflection)
  • setup the beat path (mode match + alignment)
  • setup the ISS path
  • check the beat frequency
  • re organizing the wiring on the table.
  • replace the current SMA cables with the semi-rigid ones, once all the equipments are in place.




  1232   Wed Jul 10 17:54:58 2013 ChloeDailyProgressECDLSolidworks Design

I attached the Solidworks parts that I built. I put these together with the parts we are ordering from Thorlabs (they have the Solidworks parts on their website) and have an image of the assembly attached as well. 

 I spent today building the elements we want machined in Solidworks. We have a few pieces we need to get machined: 

  • Laser diode mount: This will hold the socket that Tara ordered (Thorlabs S8060), and we can easily replace the laser diodes in this socket since they are both the same package. 
  • Grating mount: The grating will be glued to the front of this, and a PZT will be used to adjust the distance. The PZT I am looking at is here (http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=703300). Still need to check that this is our best choice, I'm shopping around more. 
  • Base/enclosure: We could either design our own base where the elements screw in solidly and put a lid on the structure, or we could use a commercial box (this one could work http://www.alliedelec.com/search/productdetail.aspx?SKU=70166638). Using a commercial box will only require minor modifications to the design. I want to talk to Tara about how easy it would be to modify a commercial box. The TEC will be attached to the base or box like the Birmingham group. 
  • I'm waiting on dimensions of the collimator so I can also build a collimator mount that the adjustable tube will sit in. 

We're seeing if the current driver Dmass uses is from Thorlabs. If it is, it means the commercial driver is good enough and we can purchase this. 

I haven't looked at tolerance values for shop processes yet because I'm not sure how important this is, or exactly how to do it. I know the general idea, but not sure how to deal with the actual calculations yet. I'll work on this more tomorrow once I talk to Tara again. 

Attachment 1: base.SLDPRT
Attachment 2: diode_mount.SLDPRT
Attachment 3: grating_mount.SLDPRT
Attachment 4: lid.SLDPRT
Attachment 5: sketch_with_lid.PNG
  1231   Tue Jul 9 19:35:20 2013 taraDailyProgressopticbeat board is back

I installed the beat board back behind the cavities. I still have not finished aligning both beams to the 1811.

  • Note about ACAV ( this path has PMC on it): After new mode matching with more visibility (from 80% to 95%), I can increase more gain and the error noise is getting lower. However, there is a problem with the beam reflected from the window of the tank. It overlaps with the main beam and cannot be blocked. I think this is the reason why we cannot suppress the error noise down to what we had before. I still need to convert the error noise back to frequency noise to see if it is below the estimated coating noise or not. If not, we have to reopen the chamber and tilt the cavity a bit. Rcav does not have this problem, the back reflection is away from the main beam and can be dump properly.
  • Note about RCAV: Erica and I plan to finish the EOM driver test tomorrow. After that I'll use it to drive the broadband EOM for locking RCAV to the cavity. The plan is to use one marconi to drive two EOM at the same frequency (14.75 MHz). We use a 4-way splitter for 2 EOM and 2 demodulations. I don't know how using same frequency for EOM will turn out (cross talk problem), but I want to see the first beat measurement within this week.
  • Note about beat setup: Evan calculated the mode matcing for beat setup, but I had to modify it. The first lenses were moved out of the board and mounted between the vacuum tank and the board due to space limitation. This might add some extra resonant peaks in the beat setup due to the long posts for lenses. The spot diameter on the PD is about 130um, which should be fine because 1811's diameter is ~300 um.
  1230   Tue Jul 9 17:57:49 2013 ChloeNotesECDLPreparing for parts to arrive

I spent the morning figuring out how to wire the TEC/thermistor/TEC controller together. After reading through the manual from last time (http://www.thorlabs.com/Thorcat/15900/TED200C-Manual.pdf), I also have a pretty good idea of how to change the settings of the controller so that it will work. I have some notes of my own but it's mostly self contained to the manual. When the parts arrive, I should be prepared to make the TEC work. 

(Note from last time: we will be using a 10 kilo ohm thermistor as a temperature sensor, which Tara ordered as well)

I downloaded Solidworks on my computer, which turned out to be more complicated than it would seem. Haven't used the program in a long time, so it took awhile to get reacquainted. I have a prototype of the final design we will send to the machine shop (attached), but some measurements still need to be figured out. In particular, I need to figure out the dimensions of the PZT we will be using so I can design the hole in the apparatus properly to mount the PZT. I also need to figure out how this will be screwed down onto a table or into a box. Possibly have more holes to contain screws?

In my free time, I'm still reading about how to measure the frequency noise. 

Attachment 1: approximate.SLDPRT
Attachment 2: sketch_of_part.PNG
  1229   Tue Jul 9 14:47:44 2013 EricaNotesBEATWriting progress report
July 7, 2013
Took pictures of the setups for mode matching and recombining the beams. I added beam lines. I will be putting these in my report.

I need to basically overhaul my report. Here is an outline. My first draft was essentially just the introduction. I need to add more of what I did, basically making it like a lab report.

Here are also notes on reading the beat frequency.

  1228   Mon Jul 8 21:52:04 2013 taraDailyProgressopticmode matching to refcavs

 I redid the mode matching for both refcav, the visibilities are up to ~ 93% and 95% for RCAV and ACAV.

  • For RCAV (refcav with PMC), the visibility was ~ 80% before, now it is ~95%. (The numbers are measured from the reflected beam on the RFPD)
  • For ACAV (refcav without PMC), the visibility is now ~ 93%. This is pretty good, compared to ~ less than 85% from previous setup when we used an AOM.

I'll add the new layout for the current situation soon.



  • We care about mode matching because we already saw that any light that was not coupled into the cavity was reflected back to the laser and caused extra noise.
  • By changing the lens, the beams for fiber optic (both for Gyro and Erica's experiment) have to be re calculated. I'm sorry about that .
  1227   Mon Jul 8 18:00:12 2013 ChloeNotesECDLParts to Order

I made more edits to my SURF progress report. I need to remember to make good looking graphs in Matlab without being reminded by Tara. I just submitted the pdf of the final version. It is also on the SVN in the ECDL documents folder. 

I spent more time trying to understand the difference between heterodyne and homodyne detection, and trying to figure out which method I would want to use for my ECDL measurements. My understanding is that homodyne detection involves superimposing the output beam with a modified version of itself, and measuring the beat frequency spectrum. Heterodyne detection involves superimposing the ECDL signal with a reference signal and measuring the beat frequency spectrum. I believe we will be using heterodyne detection because we have a very good reference laser at 1064 nm and this saves the trouble of having to modify the output beam. However, the literature has not been super descriptive for a beginner, and the exact mechanism of making this happen still confuses me. I will continue looking into this. 

I also spent some time figuring out how we will wire the TEC and TEC controller. It seems fairly straightforward. See http://www.thorlabs.com/Thorcat/15900/TED200C-Manual.pdf, page 13. This explains how we will wire things. We will use an LED that can signal to us when the TEC element is on. I still need to figure out the thermistor we will use as a temperature sensor... 

For future reference, the 2 parts that Tara ordered are:

  • laser controller: Thorlabs TEC200C
  • Peltier element: Thorlabs TEC3-2.5
  1226   Fri Jul 5 17:35:19 2013 EricaNotesRefCavPurpose of CTN, crackle lab; also measurments for EOM and driver

Finished writing the progress report. However, I need to write it in LaTex.

Learned more about the Coating Thermal Noise lab (CTN) and how to read off the noise from a noise budget. The CTN labís goal is to be able to determine the thermal noise of the coatings on the mirror on the end of the cavity. (see entry 1100 for diagram) . This noise is due to molecules that make up the coating jostling around at room temperature. Previously they used 8 in. cavities but shortened it to 1.45in to increase the noise level so it could be more easily detected. With the 1.45 in cavities, the noise should be around 0.15 Hz/sqrt(Hz).

I figured out my misunderstanding with the crackle lab. The frequency I used was the audio band of the crackling. The laserís wavelength is 633nm so the frequency is 4.7*10^14 Hz. Using the equation df/f = dL/L, the frequency noise is (df) is about 470 Hz/sqrt(Hz). This is well under the theoretical noise from the CTN, which means the beam from CTN can be used if its theoretical noise can be attained.

Helped Tara take some measurements of the EOM and its driver. An EOM Ė electro-optic modulator has an oscillator attached to a material, such as glass. The oscillator sends a current which pulls and pushes on the material, which changes its index of refraction. This can change the beamís phase, frequency, polarization, and amplitude. The goal was to test the efficiency of the driver. The resonant frequency was 20.695 MHz. The first set of measurements had a constant input power of -39.7 dBm while the frequency was varied from 13.9 MHz to 31.6 Mhz. Any frequency out of this range resulted a signal that was too small to have a good value. Then we varied the power from -50 dBm to -38 dBm, with the frequency held at 20.655 MHz.

I will include graphs and data tables at a later time. Diagrams to come soon.
  1225   Wed Jul 3 17:05:55 2013 ChloeNotesECDLParts to Order


Today I made some edits to my progress report for SURF, mainly with the graphs in Matlab. I tried to make them look better. The updated version is on the SVN. 

I spent the rest of the day reading papers about how to measure frequency noise and some basics on the Peltier effect so I could understand how the TEC will work. I'm going to start figuring out the wiring and stuff so that we will be prepared when the parts arrive. 

  1224   Wed Jul 3 09:46:48 2013 EricaDailyProgressfiber opticmode matching
July 2, 2013

Started writing up the progress report due July 9. Need to find more papers about the different types of noise from a fiber.

I talked to Eric Q about the crackle lab. In the interferometer at LIGO, there are blade springs with mirrors that hang from them. The laser reflects off of these mirrors; a horizontal displacement of the mirror leads to a vertical displacement of the blade spring. Noise in the laser can lead to perturbations of the mirror, and therefore, perturbations of the blade springs, which can mask real signals. His setup is a Michelson interferometer with the mirrors placed at the end of masses hanging from blade springs. See attachment 1 for a diagram of the setup. His requirement for noise is 10^-15 m/sqrt(Hz) for the spring, with a displacement of about 1 cm, operating at a frequency of about 100 Hz. Using the equation in attachment, it says we need a frequency noise of 10^(-11) Hz/sqrt(Hz) which is much lower than what I expected so I will have to ask again to clarify.

Recombined the beams from the fiber and the laser and set up a photodiode. Placed the collimator from the fiber optic on a translational stage because it allows us to minutely change the length in order to more easily change the relative phase difference between the two beams. Talked to Evan about finding the beat frequency. We want to adjust the lengths of the two beams such that the phase between them is pi/2, so there is completely destructive interference => wL/c = (2n+1)pi/2.
Attachment 1: 130703-095332.jpg
  1223   Tue Jul 2 17:40:22 2013 ChloeNotesECDLParts to Order


Today, the last of the parts we've decided on were ordered. 

Dmass said they do not have any extra current drivers, nor does Eric Gustafson. Eric said that if we can find a commercial board, I can ask Alex Cole (one of his SURF students) to show me how to put the commercial board into a standard LIGO module. Not sure if we'll do this or not. 

I spent the day finishing up my first progress report for SURF and uploaded it to the ECDL folder on the 40m SVN. Tara wants to look at this before I submit it next week. 

I've also started reading about how to measure the frequency noise, so I can start planning for making measurements when the laser diode arrives. 

To Do:

  • Figure out what to do for a current driver
  • Decide how to measure the frequency noise (read up on this)
  • Figure out how to wire the TEC to the laser diode so everything is ready when parts arrive. Read up a lot online about the theory behind this. 
  • Look for metal boxes to house the ECDL
  1222   Tue Jul 2 11:21:24 2013 EricaDailyProgressfiber opticmode matching
Sorry I type up my progress, but keep on forgetting to submit.

June 27, 2013

Talked to Evan to better understand GYRO. The goal of GYRO is to be able to differentiate between tilt and actual noise. There is a laser that is split and goes in opposite directions around a cavity which has mirrors on opposite corners and beam splitters on the other 2 corners; the laser is locked to the cavity. This setup uses the Sagnac effect. We are sending the CTN laser over because it has a lower noise, due to the shorter cavity, and will serve as reference for the noise level for the GYRO setup. I emailed Zach to ask about more specifics on the GYRO noise because he has a better idea but he has not yet replied.

I used a WinCam and a program called DataRay to look at the Gaussian profile of the beam at various differences from the output of the fiber(see setup here: http://nodus.ligo.caltech.edu:8080/PSL_Lab/1213). I took the radii from the two profiles at each distance, averaged them, and plotted that as a function of distance from the lens in the collimator and photodiode in the WinCam. This is to find the beam waist and its location because the current setup did not result in a beam waist at a location we predicted. See attachment 1.

I fit the equation 20 from Kogelnik and Li, 1966 to the graph and obtained a waist of 35um, at z = -0.0237 m. To check, I used equation 22, theta = lambda/(pi*w0) and the slope of the graph, to solve for w0. This ended up agreeing with the 35um.

June 28, 2013

Read papers Tara gave. Looked around for ones on related topics.

Took the new waist from yesterday's data and found a new setup. BPS program doesn't seem to work. After closing and reopening JamMT, 4 lenses show up on the diagram despite the fact I only chose 2 lenses, so I'm not sure what was going on. I ended up just doing trial and error in the program, until I got a setup that fit my parameters.

Setup is in attachment 2. The lens with f= 85.8mm is the lens that is already on the table. I added lenses with f=74.9mm and 143.2mm to mode match.

The beam waist and its location seems to match what was calculated.

I played around with different locations and got a maximum output of 48um. Unfortunately, I didn't look at the power further up the beam so I don't know what percentage. The power output at various locations seem rather strange because the data didn't converge to a single maximum, despite having made the most adjustments I could at each point.

July 1, 2013

Tried to find out more about self-homodyne detection and noise that the fiber optic contributes. Tried to find Eric Q but can't seem to ever find him so I emailed him to talk about crackle lab.

Went to Alan's talk today on the sources of gravitational waves. They include compact binaries, core collapses, spinning neutron stars, and cosmic gravitational wave background.

With 2 mW power, I was able to obtain 100uW from setup seen in attachment 1. I set up a half-wave plate, beam splitter, and mirrors to be able to recombine the beam tomorrow.
Attachment 1: snip_of_beam_profiling_6_27.JPG
Attachment 2: P1020518.JPG
  1221   Mon Jul 1 17:39:09 2013 ChloeNotesECDLParts to Order


Today, I spent the day working on the first progress report for SURF, which Tara would like by Wednesday. I have everything complete except a nice figure of the planned experimental setup, which I will do tomorrow. 

I also emailed Dmass about getting a current driver from the Cryo lab that we can modify and use. 

I've also been corresponding with the companies that sell the laser diodes. It seems like neither can guarantee exactly 1064 nm wavelength, nor does either offer any way to preselect a diode. However, we should be able to tune the wavelength using temperature, since both diodes change at 0.3 nm/degree C. Tara is placing an order for several of the items today. 

  1220   Mon Jul 1 15:14:35 2013 EvanNotesTempCtrlVacuum can temperature noise: theoretical and Comsol results


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

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

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

There is a mistake in the calculation above; the emissivity ε2 should not appear in power balance involving the absorption of jn by the copper, since jis already a net flux describing the intensity of radiation flowing into the copper. The thermal time constant of the copper is therefore d2ρ2cp2/4ε′σTb3.

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

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

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

Attachment 1: comsol_stepresp.pdf
Attachment 2: copper_timeconst.pdf
  1219   Sun Jun 30 22:58:45 2013 ChloeDailyProgressECDLNoise Calculations

I redid the plots from my meeting on Friday with Rana and Tara in Matlab, comparing different components. They are attached here. I'm still trying to get the minor gridlines to show up. 

Plot 1: Comparing noise levels of different experiments to determine which we will use as our standard. 

Plot 2: Comparing noise levels after the ECDL and servo of different diodes. Different diodes have different sizes, which affects the value of parameter X. They are all made of GaAs so other parameters are not affected. We have decided to order the Thorlabs and QPhotonics diodes. The Lumics diode has suspiciously low noise - perhaps the theoretical approximation breaks down in this case. 

Plot 3: Comparing noise levels after the ECDL and servo of different gratings. The gratings are only affected by the efficiency. We will go with the Thorlabs 1200/mm 1um blaze wavelength grating, since we want a blaze wavelength close to the wavelength of light we are selecting for (see Tara's ECDL note on the SVN), and we want as many grooves possible for maximum resolution. 

Plot 4: Comparing noise levels after the ECDL and servo of different cavity lengths. This plot is much better than the Mathematica one; we can see that longer cavities have lower noise, but a smaller FSR. We will likely go with 60-10 cm. 

Also attached is a sketch of our mechanical setup, agreed upon during the meeting on Friday with Rana and Tara. 

This week, I will get a draft of my first report done before the long weekend for Tara to look over. This will probably involve looking over some old concepts to write up something comprehensive. I will also be waiting for a response from QPhotonics and Thorlabs about preselecting diodes, and I need to talk to Dmass about using a current driver. Start looking at metal boxes in the 40m  and building the parts in Solidworks if I have time. 

Attachment 1: compare_experiments.png
Attachment 2: compare_diodes.png
Attachment 3: compare_gratings.png
Attachment 4: compare_length.png
Attachment 5: 100_0068.JPG
  1218   Sun Jun 30 22:22:52 2013 EvanNotesTempCtrlVacuum can temperature noise: theoretical calculation

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

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

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

Attachment 1: vacuum_can.jpg
Attachment 2: transfer_thetab.pdf
Attachment 3: temp_suppression.pdf
  1217   Fri Jun 28 17:59:15 2013 ChloeNotesECDLParts to Order

Yesterday I spent awhile reading literature, then met with Rana and Tara. Rana wanted us to produce a sketch of the physical layout of our ECDL and generate some graphs comparing different parameters (diodes, gratings, cavity lengths) so we could determine exactly what parameters we'd need to order parts. Last night I made the plots in Mathematica (BAD). This morning I did the sketch of the mechanical layout of the ECDL. Will make a nicer sketch with the changes made today and post here this weekend. 

I calculated a few values: the grating should be placed at an angle of 39.7 degrees in order for the first order diffraction go back into the cavity. I checked the tuning range, and concluded for a frequency change of 100 MHz - 4 GHz, we will see a change of output beam angle on the order of microradians. This means we will not need a mirror to make sure the output beam is directed correctly for frequency changes. 

Tara and I met with Rana again. I got mocked excessively for using Mathematica, and will remake all the plots in Matlab this weekend. We decided on some parts to order, which are listed at the end of this entry. Other things to do:

  • We want our apparatus to be in a metal box to lower noise. Will build inside the box. Check the 40m lab to see any metal boxes laying around, and check online (Newark, Allied). We want a setup with a lid that can be very rigidly screwed on. 
  • Ask Dmass about using the current driver in the Cryo lab. We don't want to have to order this online, it's expensive!
  • Talk to the companies that sell laser diodes to make sure that the laser diodes are precisely 1064 nm. If not, see if we can arrange something where they preselect a diode, since we need very high accuracy. 
  • We will design the TEC/current driver connections to the laser diode once we have parts, since it'll likely require some fiddling around and this is a prototype. We will prefer BNC cables to D-Sub. 
  • Eventually make some of the more unique parts of the apparatus in Solidworks so we can get it machined. 


Parts to order (bolded): 

1. Laser diodes: We plan to order 2, both are compatible with the diode mount. 
2. Laser diode mount: This has a built in TEC (Peltier element)

Thorlabs HLD001 ($464.10): accepts the 9 mm package, TEC max current of 3A, 10 kilo ohm thermistor (https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=4135
3. TEC controller: We need to buy both a controller (compatible with mount) and the cable connector (https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3355)
  • Thorlabs TLD001 ($750.00): controller output up to 200 mA
  • Thorlabs CAB400 ($66.00): cable connector, 9 pin D-Sub connector, 1.5 m long
4. Diffraction grating: Checked the messed up graphs from Mathematica and the efficiency being halved approximately halves the noise, and there isn't anything particularly weird going on here. 
Thorlabs GR25-1210 ($102.00): 1200 grooves/mm, 25x25x6mm, 1 um blaze (http://www.thorlabs.com/thorproduct.cfm?partnumber=GR25-1210)
The total estimated cost so far is $2394.54

This weekend I will:
  • remake all the plots in Matlab and post here
  • contact Thorlabs and QPhotonics about preselecting diodes that are almost exactly 1064 nm, figure this out so we can order ASAP (already sent them emails)
  • check with Dmass about a current driver in the Cryo lab that we can use
  • make a nice sketch of the layout and post here
  • update pdf with all progress made so far



  1216   Fri Jun 28 14:52:11 2013 taraNotesECDLlaser noise requirement for locking to a refcav

I estimated some requirement for an ecdl such that it is possible to be locked to a high finesse refcav. For 1.45" cavity, finesse = 1e5, the frequency noise of the ecdl has to be less than 400Hz/rtHz (assuming flat noise from 1kHz to 1MHz).


 We are developing an ecdl, however, we have to check if it can be locked to a high finesse refcav. If so we can use an ecdl in CTN/ cryo style experiments where an ecdl is locked to a refcav. Cryo had some problems with locking a laser to their cavities because of the noise at high frequency, see CRYO elog)


 For a good error signal in PDH locking, the laser linewidth of the laser measured in 1ms - 1us should be smaller than the cavity width (2xcavity pole).

  • Linewidth of the cavity = FSR/Finesse, for the current cavity FSR = 4GHz, Finesse = 1e5-> cavity linewidth = 400kHz.
  • linewidth^2 = integrate frequency noise from 1kHz-1MHz ~ frequency noise PSD[Hz^2/Hz] x 1e6 [Hz] , so S has to be ~ 400 Hz/sqrtHz or lower. (watch out for the unit).


The requirement of 400 Hz/rtHz or below seems to be do able, see Chloe's calculation. However, this number is from Finesse = 1e5, with 1.45" cavity length. If we use different cavity with different FInesse, the number will change as well.  The frequency noise requirement (assuming flat from 1kHz to 1MHz) is 400 x [FSR/4GHz] x [ 1e4/ Finesse] [Hz/sqrtHz]

  1215   Thu Jun 27 09:12:58 2013 EricaNotesfiber opticmode matching

June 26, 2013

Spent the day trying to mode match. 

First I used the power meter to measure the output of the fiber but its response was very slow so it was hard to align the beam and make adjustments so I hooked up a camera instead.  Then when the light could be seen on the camera, I would switch to the power meter to see if I could incrase the power and have a quantity for the power output. The whole process took a long time because there were many parameters and I trouble at times aligning the beam. 

Higher up in the beam path the power is 7mW.  The highest power output I have obtaned is about 850 uW, which is improvement from the intitial 7 nW. 


Note: Optimize one parameter before changing another (1 lens). 

  1214   Wed Jun 26 17:13:21 2013 ChloeDailyProgressECDLNoise Calculations

Today I spent the morning searching the literature on Web of Knowledge to see if anyone had ways to reduce the noise level of an ECDL further by tweaking the parameters of the Littrow configuration (our current plan, where first order beams coming off the diffraction grating go back into the laser diode). It may be worth examining configurations with more mirrors to lengthen the cavity, but otherwise my search was not particularly helpful. We may need to start looking at the Littman-Metcalf configuration??? This theoretically reduces linewidths more but has lower efficiency. The diffraction grating is immovable, and an adjustable mirror is used instead to reflect light back onto the diffraction grating. 

Tara got me the information for me to calculate how a servo would reduce the noise of the ECDL further. I worked most of the afternoon to understand the principle behind the feedback, and ran calculations after searching the literature for reasonable numbers. Using a piezoactuator, we can reduce the noise at low frequencies, but it does not solve our problem at high frequencies (above 10 MHz), where there is essentially no noise reduction. See the attached pdf with the updates included (pages 5-8). 

Tomorrow I will see if I can find a piezoactuator that has a large actuator gain, which would cause more noise reduction at higher frequencies. Otherwise, building an ECDL will not be very useful for us to use at LIGO... 

Attachment 1: Noise2.pdf
Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf
  1213   Wed Jun 26 09:44:09 2013 EricaNotesfiber opticmode matching

June 25, 2013

Read some papers on noise due to fiber optics as well as cancellation of phase noise. 

We borrowed a fiber optic cable from 40m, that maintains polarization.  Realized that I did not include the collimator in calculations for mode matching, so I redid it.  The collimator I chose has f = 2mm, with the distance between the fiber and lens 3.5 um.  The lenses used to mode match have focal lengths f = 143.2mm and f= 74.9 mm. 



I have set this up on the table, but have yet to do alignment with the cable. Tomorrow (June 26), I'll try to get the laser beam into the cable. 

 Other tasks:

  • talk to ATF and crackle lab to understand what they are doing in the lab and what their noise budget is
  • look at how much noise a fiber adds and whether that level is under our noise budget
  • find out how noise is measured at end of fiber
  • finish filling out safety sheets

To clean lenses:

  • wear gloves,
  • work at the table with clean air. 
  • turn on the bright light (need to see what it's called) to better see particles on the lens
  • If there is dust, first spray with air cannister
  • if it's still dirty, use acetone, methanol, and then isoproponol to clean using tweezers and lens tissue.  make sure not to touch lens with tweezers
    • if it's very dirty, start w/ acetone and go down the solutions as stated above
    • if not, can start w/ methanol


Attachment 1: P1020393.JPG
  1212   Tue Jun 25 18:13:36 2013 KojiPhotosDrawingsThe structre of the twin reference cavity setup

or a face of a confused grad student


  1211   Tue Jun 25 17:51:34 2013 ChloeDailyProgressECDLNoise Calculations

I spent this morning looking at the mounts and other mechanical parts necessary for the ECDL. This afternoon, I met with Tara to discuss how I should run some noise calculations for including a servo to reduce frequency noise. I will deal with the mechanical logistics later while we are waiting for the diode, etc. from Thorlabs. 


Its true that this approximation is valid for low frequencies, but we are interested in the total RMS frequency noise for cavity locking, not just the spectral density.

So you do have to take into account the frequency dependence. IF there is a lot of noise at 100's of MHz, these lasers will be totally useless to us.

I corrected this, since the paper did have an equation about how the power spectral density is reduced by frequency. This is in the updated noise pdf attached. We no longer have a low enough noise level to do the crackle experiment below 100 Hz or above 10 MHz using our original estimates. This makes running calculations including a servo important. 

I also played around in Mathematica trying to see what value of X would be sufficient to reduce the noise level. Uploading the notebook isn't working right now. It shows that in order to reduce the noise level to meet the requirements for the Crackle experiment, we need a parameter X of about 3000. This is quite large, and would require a cavity of length 30 m. Alternatively, we could reduce the noise by:

  • A different laser diode that had low enough noise to begin with, or a very small reflectivity
  • A diffraction grating that had a very high reflectivity
  • Finding a very good TEC, which would reduce thermal noise (most websites don't seem to offer this data...)
  • Note that at this time, it seems unfeasible to go with any current driver besides the one designed by Libbrecht and Hall, since the current noise limits how low the diode's noise can be at high frequencies

Tonight or tomorrow, I will try to shop around to see if other laser diodes have slightly nicer specs. I will also look to see if other papers encountered the same problem. 


Attachment 1: Noise2.pdf
Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf Noise2.pdf
  1210   Tue Jun 25 14:14:17 2013 ranaDailyProgressECDLNoise Calculations


 Its true that this approximation is valid for low frequencies, but we are interested in the total RMS frequency noise for cavity locking, not just the spectral density.

So you do have to take into account the frequency dependence. IF there is a lot of noise at 100's of MHz, these lasers will be totally useless to us.

  1209   Tue Jun 25 09:58:08 2013 EricaNotesfiber opticmode matching

for June 24, 2013

 I used MatLab and JamMT to mode match a laser beam coming from the PMC to the cavity for Tara (see diagram at post 1100).  It is for the lower or left PMC.   Used various equations from Kogelnik and Li, 1966, to determine the q value and beam waist at various points, particularly equations 16, 18,10 and 41.  The revised setup is in attachment 1.

I went to the LIGO laser safety training session led by Peter King. He discussed the importance of safety training, various biological effects lasers can have on the body, particularly the body, and how to work around lasers safely.  Safety glasses have an OD number for different wavelengths and should be checked at the door before entering a lab. We have two forms that we need to fill out. 

Then I went on to mode matching the fiber optic to the laser with the previously mentioned programs and will try coupling the fiber optic tomorrow.



Attachment 1: refcav_mm.JPG
  1208   Mon Jun 24 21:27:02 2013 taraNotesRefCavsetup for 2nd refcav

I'm in the process of locking the 2nd cavity. The work is in progress. 

  •  The 2nd TTFSS is working fine. I tested it by using the 2nd TTFSS to lock the first refcav. The error signal was similar to what I got from the first TTFSS.
  •  Mode matching was revised (See Erica's entry).
  • Heatsink for the 2nd laser was ready, I added it on the laser.

To Do:

  • prepare for the 2nd EOM, I need to think about an oscillator driving and EOM. Since there is no resonant EOM, I'll use Rich's EOM driver on a BB EOM for sideband.
  1207   Mon Jun 24 17:48:30 2013 ChloeDailyProgressECDLNoise Calculations



Today, I wrote up my noise calculations in a nicer way so that I have it on hand in the future. They are attached here. I found a mistake from the last elog entry, so it turns out that we are looking at a linewidth of about 440 kHz (or a PSD noise of 191 Hz/rtHz). This still meets the requirements of the experiment, and can be adjusted as necessary, since I can still increase the length of the cavity to decrease the noise. 

 There was another mistake in my calculations (sorry!) so we are actually looking at a possible linewidth of about 5.3 kHz (or noise level of 0.03 Hz/rtHz). This is very low, so we are looking at using a current driver from Thorlabs since we have room in our noise budget, and this would make the assembly much easier since the parts fit together. Waiting for a response from Thorlabs about their noise levels for current drivers.

Attached are the corrected calculations. 

I added some additional explanation for the fact that the noise reduction was not dependent on frequency (see attached). I also added references for the data that I used. 

I spent awhile dealing with Thorlabs customer service trying to figure out about their lowest noise current driver (250 mA), which is the LDC205C. They are still working on getting an answer as to the noise level of this current driver. 

The next step is to start considering the mechanical setup of the ECDL and see if we need to order any special mounts for this. Tomorrow I will draw up more of a sketch for the mechanical apparatus, since Tara had talked about possibly getting some parts machined. 

Attachment 1: Noise.pdf
Noise.pdf Noise.pdf Noise.pdf Noise.pdf Noise.pdf
  1206   Mon Jun 24 11:14:04 2013 ChloeDailyProgressECDLNoise Calculations


Today, I wrote up my noise calculations in a nicer way so that I have it on hand in the future. They are attached here. I found a mistake from the last elog entry, so it turns out that we are looking at a linewidth of about 440 kHz (or a PSD noise of 191 Hz/rtHz). This still meets the requirements of the experiment, and can be adjusted as necessary, since I can still increase the length of the cavity to decrease the noise. 

 There was another mistake in my calculations (sorry!) so we are actually looking at a possible linewidth of about 5.3 kHz (or noise level of 0.03 Hz/rtHz). This is very low, so we are looking at using a current driver from Thorlabs since we have room in our noise budget, and this would make the assembly much easier since the parts fit together. Waiting for a response from Thorlabs about their noise levels for current drivers.

Attached are the corrected calculations. 

Attachment 1: Noise.pdf
Noise.pdf Noise.pdf Noise.pdf
ELOG V3.1.3-