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 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. 

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... 

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. 

 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 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 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. 

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.

 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. 

 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... 

• 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.
  

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. 

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. 

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. 

Chas has been building an ISS and needs a spec for suppression of relative intensity noise for Tara's 1.45″ silica/tantala cavities.

I measured the RIN of the south cavity with the cavity locked. The common and fast gains were both set to 400 on the TTFSS frequency servo box. I placed a PDA100A at the transmission of the south cavity. The DC power incident on the PD was 0.370 mW and the DC voltage was 0.439 V. I plugged the PD output into the SR785 and recorded the PSD of the voltage, both for light incident on the PD and for no light incident on the PD (i.e., the noise floor). To get the amplitude spectral density (ASD) of relative intensity noise, I've taken the square root of the voltage PSD and divided by 0.439 V.

I've attached a figure showing the RIN (and the noise floor of the measurement), as well as the data and code used to generate the plot.

Both the shape and overall amplitude of the RIN are roughly consistent with what has been measured earlier (e.g., PSL:986 and PSL:736). I'm unsure whether this is the same laser that was used for the previous iteration of the CTN experiment, but it is the same model (Lightwave NPRO 126). [Edit: I've talked to Tara, and this is the same laser as was used in the previous measurements.]

Today I worked on updating my progress report and abstract. Posted to the SVN. 

Our machined parts were finished by the machine shop. I picked them up, and Tara and I washed them in a sonicator for an hour to get the oil and metal shavings off. I tried assembling things to see how things look. It seems like the laser diode mount will have enough adjustability with the diode that we will not need to have vertical adjustment ability on the grating mount. We will need to make modifications on the plate with the D-sub and BNC holes because we will need 2 D-sub connectors, and there needs to be a better way to mount the male-to-solder connectors on the plate so they don't move. 

I went to Rana's electronics talk. I'm trying to get LISO on my own computer but encountering some problems with Linux. 

Tara found a 1/4-80 screw from a mirror mount to put into the grating mount. It was long enough that we'll have adjustability. We may need to get springs to put in the grating mount slit to offset the force from the screw. 

Tara and I took apart a 5 mm focal length lens from a fiber optic and added it to our temporary setup from yesterday to test if a shorter focal length lens helps with collimating the beam. It works very well - we can get the beam to be essentially parallel at up to at least 50 cm with the right adjustments. 

I put together a shopping list tonight of things we need to get checking Thorlabs and Newport: 

PZT: 

• http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=100800 - price requires quote, but Tara referred me to this website.
• http://www.thorlabs.us/thorproduct.cfm?partnumber=AE0203D04F - Thorlabs has a product, $72.80, seems like it would also serve our purposes but I don't know which manufacturer is preferred for PZTs. 
• Newport doesn't have anything that would fit in our setup

• http://www.thorlabs.us/thorproduct.cfm?partnumber=WG11050-C - Thorlabs, $103.60
• Newport was more expensive for a similar product, $225.00 (http://search.newport.com/?q=*&x2=sku&q2=10QW40-30AR.18). Only difference is thickness. Either way, we have to shave down the mirror mount I designed since I planned for a 1/4" thickness on the window and it's actually 5-6mm everywhere online so we want a tighter seal on the window than that.

Today I tried to set up the TEC on the actual assembly. When doing so, Tara pointed out that I needed to have a separate temperature sensor to monitor the TEC, and to use to calibrate the PID gain on the TEC controller. 

I built a simple temperature sensor with a 10k thermistor. The temperature can be determined by measuring Vout and determining RT. Once RT is determined, this can be converted into a temperature using the information on the data sheet for the 10k thermistor. The schematic is attached. I chose the value for R0 based on what would maximize the difference in Vout for a 1 degree C fluctuation about room temperature (25 C) which is what will be used to tune the PID gain. I chose Vin based on what would make the signal have fluctuations of about 500 mV, which is what is needed to be readable on an oscilloscope. Once I built this circuit, I tested it. It is sensitive to temperature changes, since the output voltage changed when I covered the thermistor with my hand.

Tonight I am going to incorporate changes Tara suggested for my progress report. The updated version will be put on the SVN. Tomorrow I will try to the temperature sensor I built today to calibrate the PID gain on the TEC controller. 

I locked both cavities and trying to search for the beat signal, I have not succeeded yet.

I used lenses that could get the two transmitted beam to be close and small enough for the beat PD (new focus 1811) (we ordered  what we need but they are not here  yet).

I locked ACAV at a fixed SLOW DC level (1.207 V), and varied RCAV's SLOW DC level from 1.199V, 0.33V, -0.554V, -1.477V (1FSR ~ 4GHz is about 1 V). The slider for RCAV slow is set to +/- 2V so I have not tried other values yet. It can be changed to -2V to 9 V, but I have to restart the crate which will disturb the temperature servo, so I'll try to adjust RCAV slow value using a voltage calibrator instead.

I talked to Evan about the beat measurement in GYRO lab, the SLOW DC for both lasers can be different up to 6 V (for ~100MHz beat). see gyro1832

I varied RCAV's SLOW DC first because this path does not have a PMC, so I don't have to worry about locking the PMC.

From PSl:1124 ,the beat frequency should be ~60-100 MHz, without the heater on any cavity.  I'll try the same method to check the beat frequency between the two cavities one more time. If it is still ~ 100 MHz, I'll increase the range of SLOWDC, and see if the beat will show up of not.  The setpoint was not changed that much (31.2 to 31.25), So I expect the beat frequency should still be close.

If the beat still not show up, I'll try to realign the beam.

Current setup

Vac chamber Setpoint = 31.25

Vheat for RCAV =  0

Vheat for ACAV = 0

Found the beat @ 116 MHz. RCAV SLOW =5.762V, ACAV SLOW = 1.209 V.

beat 1kHz input range, calibration  = 718 Hz/V

above, beat signal with 1kHz input range on Marconi.

Plenty of things that I need to optimize and add:

input optics (ACAV/RCAV):

• beam alignment
• optimizing quarter wave plates in front of the cavities.
• block all the reflected beams properly
• fixing the back reflection from vac window for ACAV.
• measure error point noise from both servos and compare them with beat
• optimizing TTFSS servo gain

Beat setup:

•  mode matching lens
• power on beat PD
• optimizing PLL servo
• implementing ISS

Seismic isolation

• new table legs ( I have not ordered the new set yet). The current set is broken
•  

I turned off the hepa fans over the table over the night. I came back this morning and the temperature (measured on the vacuum tank) was very stable(within 2mK) over 2 hrs.

above:BLUE Temperature measured on the can, the Y scale is in degree C. The temperature variation is within 2mK over 150 mins.

So I looked at the PD for Erica's fringe measurement, the fringe wrapping was slow, so with better temperature insulation, we should be able to hold the fringe for at least a minute.

above: The fringe signal from PD, the cursors show the max/min signal from the fringe. The signal drifts from min to max over ~ 60 seconds compared to ~10seconds as before.

So the drift we saw before was very likely to be from the temperature drift (1mK per second for 20second fringe wrap). More thermal insulation on the optic should reduce the temperature drift.

Today I calibrated the PID gain on the TEC. In order to do this, I used a silicone heat sink compound to help the thermal conductivity between the Peltier element/thermistors and the TEC. Then, I held things together using aluminum tape.

I calibrated the TEC so it reaches the correct resistance after only overshooting the value once. It is usually able to reach the correct temperature within about 30 seconds. I had the temperature sensor I built yesterday hooked up to an oscilloscope so that I can monitor the fluctuations in voltage across the thermistor (directly related to resistance). However, my flash drive doesn't work and I didn't have a spare on me today so I will try and record the oscilloscope output either this weekend or on Monday morning. This will be used to estimate the transfer function of the TEC controller. 

Important: there is a directionality to the TEC element. There is a hot side and a cold side. The cold side is attached to the laser diode mount, and the hot side is attached to a piece of aluminum we found around the lab to act as a temporary heat sink. Because of this we need to rework some of the design to thermally isolate the diode mount from the box, and let the box act as a heat sink. My proposed design is attached (I made a quick sketch of it in Solidworks). I'm still thinking about the best way to incorporate the Peltier element. 

Tara will order the collimator lens, window, and PZT this weekend. Still trying to figure out if it's possible to build a collimator mount that will be sufficient to serve our purposes. 

 I brought in a different USB drive to get data off of the oscilloscope. It took awhile to figure out how to capture the data with the best settings. I have a sample graph of the heating and cooling of the diode mount attached (converted to temperature using datasheet for 10k thermistor). Notice that I took data over about 4 degrees, so that it was possible to see the change in voltage as the temperature changed. Even then, it would be nice to have more resolution on this data. I cannot make the voltage increments smaller than 500 mV because the offset of the oscilloscope isn't enough to still see the data (I tried). I will talk to Tara tomorrow about if I can get better data on this to analyze, since this data has poor resolution. 

 Tara asked me to try to calculate the free running noise of the laser diode to have an estimate for when we actually collect this data. We will be using a Michelson interferometer with different arm lengths. I used Erica's past elog entry as a starting point (1241) and wrote a bit more explanation into my own calculations so it will be clear to me in the future and to make sure I understood everything. However, I'm unsure of how to incorporate the noise levels after calculating the power received by the photodiode, and I need to talk to Tara about how to do this tomorrow if he's around. The calculations that I have done are attached. 

• Temperature -> length
  
• Acoustic/Seismic
  
• Laser frequency drift
  

 I calculated a way to convert our spectrum measurement of voltage from the photodiode to the frequency noise of the laser in the Michelson interferometer setup. I still need to check this calculation to make sure it works, and determine the ideal differential arm length to use tomorrow. 

Today I also took a measurement of the relationship between power and voltage of the photodiode at 20dB gain. The result for that is also included in the attached file. I will clean all of the calculations up tomorrow; I suspect I've made a mistake or 2. 

 I fixed my calculations from last time and wrote it up in LaTex. It seems that we can use a differential arm length of somewhere around 10cm and it should work well for our purposes. 

Tara: I removed the pdf file, as I have warned you about this  for several times. 

Chloe: I put the PDF on the SVN. I won't make this mistake again. 

In preparation for getting the ISS up and running, Tara and I have been fooling around with the EOAM and associated half waveplates. Additionally, Tara inserted a quarter waveplate (mounted horizontally, for space reasons) after the EOAM in order to get linear amplitude modulation. The HWP before the EOAM is at 99 degrees and the QWP after the EOAM is at 51 degrees.

There's currently 8.0 mW going into the EOAM and 4.0 mW coming out after the EOAM + QWP + PBS. When 10 V dc is applied to the EOAM, the power drops to 3.7 mW. This gives a conversion factor of 3.0×10⁻⁵ W/V. The value expected from the manual is (π/2)(8 mW / 300 V) = 4×10⁻⁵ W/V, so we're not too far off. 

Tara and I have taken a measurement of the transfer function which takes volts the EOAM and produces volts at the ISS PD.

The EOAM is driven with a 4 Vpp swept sine from the SR785. Approximately 1 mW of light is incident on the south cavity, and 0.5 mW is incident on the PDA10CS positioned at the cavity transmission. The spot size is a little bigger than the PD area, since I'm unsure of the damage threshold of the PD and don't want to fry it. The PD has its internal preamp set to 20 dB of gain (1.5×10⁴ V/A) and has a quantum efficiency of about 0.6 A/W. The DC voltage of the PD is about 5.9 V. The inputs of the SR785 are dc coupled. Each data point on the transfer function is integrated over 20 cycles.

As a control, there is a second PDA10CS set up before the cavity input to capture the transfer function without the filtering effect of the cavity and associated optics. The input power is about 0.4 W and the gain is also 20 dB. In the attached plot, I've normalized this transfer function to have the same amplitude as the transmission transfer function.

Evidently, the magnitude of the plant transfer function is (more or less) 0.057 V/V.  Based on the calculation in PSL:1278 I'd expect something more like 0.024 V/V (with a = 0.5), and I'm not sure where the extra factor of 2 is coming from. I've measured the PD gain to be 11 V/W at 20 dB (by putting an OD2.0 filter in front of the PD, and then making the spot size small enough that all the light falls on the PD), which is close to what I'd expect (9 V/W, given a quantum efficiency of 0.6). We've measured the EOAM gain to be 3×10^-5 W/V. There's definitely 0.5 mW going towards the PD. So something's not adding up.

 Today I designed a better circuit to measure the TEC's response with the oscilloscope. It is called a bridge circuit, and allows for the output voltage to be centered around 0 instead. This type of circuit is often used for different sensors, and seems to fit our purposes well here. The schematic is attached here. 

After I built this circuit (modified the circuit I was previously using), I tested it with the TEC to see how the PID gain calibration looked. This took awhile to get a signal, because it seems like the oscilloscope I was using had some problems. I took data of heating and cooling shown below (didn't bother converting to temperature since we're mostly interested in how the temperature or voltage settles right now). 

A lot of the data I tried to take today had the same sort of oscillations as for the cooling data shown above (about 0.04 Hz). However, I didn't see such oscillations when I hooked the circuit up to a multimeter and monitored the voltage changes over time. In fact, the voltmeter suggested that the voltage stabilized much more quickly. I'm going to look at this again tomorrow to see if I can figure out the cause of these oscillations, and perhaps tune the PID gain on the TEC better now that I can see how the temperature settles much more easily and quantitatively. 

Today, I also finalized the Solidworks drawings for the insulator that will be used to thermally isolate the laser diode from the rest of the setup, as well as the heat sink that will be in contact with the Peltier element. These files are on the SVN, and I will try to go to the machine shop with these soon. I should have done this earlier. 

I will be presenting my project at the end of August, so Tara wants me to put together a talk so we can rehearse next week. I am going to start doing this in my free time. 

 I spent awhile reading about PID controllers in order to understand how to tune the TEC. P represents proportional gains, and deals with the present error from the set value. I represents integral gains, and deals with past errors. D represents derivative values, and uses the current data to predict future errors. They each affect how the TEC overshoots/oscillates about the correct temperature in different ways. I figured out that the oscillations that I saw yesterday in the heating and cooling data were due to improper tuning of the PID gain. I decreased the integral gain and it seemed to fix the problem. 

I also discovered that the oscilloscope was on the wrong setting, with 10x attenuation. I noticed this when converting the data from output voltage to temperature. I changed the settings to 1x attenuation and took data for heating and cooling, shown below. There only seems to be one slight overshoot when changing the temperature by about 1 degree, which is entirely reasonable. The correct temperature settles after about 1 minute. 

While these measurements were useful in tuning the PID gain so that the temperature settles quickly, there was a discrepancy in the measured resistance across the thermistor and the resistance calculated from the measurement of Vout. Using the TEC controller, I brought the resistance of the feedback thermistor to 10k, but this resulted in a Vout that predicted a thermistor resistance of 9.91k (0.2 degrees K difference). In order to zero Vout, I had to bring the thermistor resistance down to 9.892k. I'm trying to think of a way to calibrate this difference, but I'm not sure which thermistor is reading more accurately right now. I'm going to read more about using thermistors as temperature sensors to see if there is anything I can try to do for this. 

I'm also still trying to think if there's a way to adjust the P, I, and D controls so that I can actually go back to previous values. The controls are unlabeled on the TEC controller we have, so they cannot be accurately returned to specific settings. It seems well calibrated for the moment, though. 

 Tara would like me to present at the SURF Seminar Day in August (either on the LIGO field trip to the Livingston Observatory or at Caltech), so I spent yesterday and today putting together my presentation and trying to organize the work I have done/plan out what to say. The entire presentation will have to be focused on the noise calculations and design, since we are still waiting on parts to arrive (namely, the collimating lens so we can focus the beam to make a free running noise measurement). The presentation for right now is on the SVN: https://nodus.ligo.caltech.edu:30889/svn/trunk/ecdl/documents

Made some modifications to the Solidworks design. All of these have been changed on the SVN. 

• Made heat sink for TEC adjustable so it can clamp the TEC element between the heat sink and the laser diode mount, with no risk of it touching the laser diode mount. This was achieved by making a longer hole on the base plate so the heat sink can be screwed on anywhere. The heat sink will be copper because this is very thermally conductive compared to aluminum or other metals. 
• The laser diode will be thermally isolated from the rest of the setup using a piece of plastic (most likely delrin). 
• Tara and I found a lens mount we can use which allows for small height adjustments (Newport LA1V-XY, http://search.newport.com/?x2=sku&q2=LA1V-XY). This is at an optic height of 1 inch which works well with our setup. We are going to purchase this (http://search.newport.com/?q=*&x2=sku&q2=LPLH-25T) which is an adapter so that it can hold the 0.25" optic. The collimating lens' distance from the laser diode will be adjustable by the same method as the heat sink - there is a longer hole on the base plate so that the lens mount can be screwed down anywhere. 
• Added 2 D-sub holes that are properly sized (last time was a bit too small) so that we can plug in the TEC and current driver onto the ECDL box. 

Tomorrow morning I will go to the machine shop to get the base plate and left plate modified, and get them to machine a heat sink and plastic insulator. 

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

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

Mistakes in the original code:

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

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

==for TO optimized AlGaAs coatings==

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

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

 Today I got the newly machined parts. I put together the TEC element and stuff again and will calibrate the next time I get a chance. 

Erica and I practiced our presentations in front of Tara. I got a lot of feedback and I'm going to edit my presentation in my free time outside of lab. It was also useful to see someone else's work to get an idea of how to present. 

I'm working on putting together a Michelson interferometer to measure the laser diode free running noise. I don't have the actual collimating lens, so I'm using a f=5mm lens from a fiber optic. I have mirrors and I borrowed a beam splitter from the GYRO experiment. Picture below. I'm working on getting the beams to combine by adjusting the mirrors. Will continue doing this tomorrow.