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. 

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. 

(KOJI / ATTACHMENT REMOVED: DO NOT PUT COPYRIGHTED PAPERS ON THE PUBLICLY ACCESSIBLE WEB PAGE)

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. 

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. 

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• 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. 

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• 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. 

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• 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 

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• 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. 

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• 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. 

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. 

• 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.
  

 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 f^0.8(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.

 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... 

 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. 

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.

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. 

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.

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. 

 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.

==Note==

• 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 .

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

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. 

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

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. 

There is a mistake in the calculation above; the emissivity ε₂ should not appear in power balance involving the absorption of j_n by the copper, since j_n is already a net flux describing the intensity of radiation flowing into the copper. The thermal time constant of the copper is therefore d₂ρ₂c_p2/4ε′σT_b³.

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 = T_d 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).

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. 

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 ε_2.

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.

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): 

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).

 ==background==

 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)

==calculation==

 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).

==comments==

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]

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). 

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... 

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

or a face of a confused grad student

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. 

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. 

 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.

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.

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.

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. 

 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.