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

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

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

After some discussion with Tara and David, it became apparent that it would be wise to take RIN noise and EOAM-to-PD transfer function measurements over a wider range of frequencies than was done previously.

For these measurements I'm using the same PDA10CS as before, although here I've got 0.48 mW going onto the PD (i.e., no ND filter), and the PD's internal preamp is set to 10 dB. The dc output voltage is 1.7 V. I did the RIN measurement on the SR785.

For the transfer function I used both the SR785 and the HP4395A. Because the HP4395A has 50 Ω inputs, it shows an extra 6 dB attenuation which I've undone here (since the ISS is all high impedance). The transfer function is well described by a single-pole rolloff whose DC amplitude is −0.0148 V/V and whose frequency is 330 kHz (shown in green below).

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

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

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

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

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

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

==Note==

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

 Newest version on the SVN with the latest data and Tara's commentary from my practice presentation. I'll probably end up working on this while in Louisiana if I hear back from Tara about whether I did something wrong with the noise measurements. 

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

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

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

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

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

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

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

 Today Tara and I worked on getting a noise measurement for the bare laser diode using a Michelson interferometer with different arm lengths. The setup is attached. However, at a differential arm length of 20 cm we were unable to see interference because it was too difficult to focus the beams. Tara suggested I use a symmetric Michelson interferometer to see if I can get interference, since the noise levels might be too high for such a large arm length. I then tried much smaller differential arm lengths and I was able to get interference at 1 cm and 5 cm.

I took background measurements of the noise from the SR785 (about 20 nV/rtHz) and from the blocked photodiode (electrical noise, about 50 nV/rtHz). Since these were both small, we can be confident that the measurements we took are mostly the noise from the frequency of the laser diode. 

The results from the 1 cm and 5 cm measurements are attached. We seem to have noise levels close to what we predicted (1 MHz/rtHz), which seems odd since there will be extra noise from mechanical components, temperature fluctuations, and a worse current driver than we planned to use. In addition, this doesn't explain why we weren't able to get interference at a differential arm length of 20 cm. The 5 cm measurements have even lower noise levels for some reason. I'm not sure if I'm doing something wrong with factoring in the gain, so I'm going to check my math. Gain still confuses me a little since there's a different gain on each machine I used. Overall, the measurements seem suspiciously low noise. 

I'm going to check these calculations again this weekend to make sure I didn't mess up. I will also revise my presentation so that I will be ready to present on the LLO SURF field trip. 

 Tara improved the alignment so we got a little over 1V coming from the fiber alone. We took another run of data of the recombined beam:

laser not locked to cavity:

deltaV = 3.64V

Vmin = 880mV

Vmax = 4.52V

laser locked to cavity:

deltaV = 0.17V

Vmax=.236V

Vmin=0.56V

This matches up with the original data taken.

We also took data for the noise of the spectrum analyzer.

This can be approximated at a straight line.  I took an average of the points so the noise level is at 1.9*10^-6 Hz/rtHz.

Then we took data with the laser locked to the cavity.  The power is much lower because we accidentally misaligned the beam.

As seen in the graph below, the fiber seems to be okay; the plots of the laser unlocked to the cavity match up.

deltaV = 0.17V

Vmax=.236V

Vmin=0.56V

We took data for the error signal from the servo. The slope of the error signal for ACAV path is 200kHz/V (see elog entry  1920) .  We are using this to convert from voltage noise to frequency noise.  The shape of the spectrum from the recombined beam follows the shape of the error signal.

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

See some calculation about RIN requirement PSL:1270.

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

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

 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. 

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.

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. 

 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

I wrote a code to calculate thermo-refractive noise in a finite-sized cylindrical substrate as given in Heinert etal 2011. The noise is very small ~10^-7 [^Hz/_rtHz] compared to other noise in the cavity ( no surprise here). The code can be used to estimate the TR noise in fiber optic. The calculation should be correct as I double checked with the calculation by Koji and Deep.

I followed the calculation for TR noise in cylindrical substrate [Heinert etal 2011] for our setup (1" diameter , 0.25" thick, fused silica). The result is in [m/rtHz].

To convert it to frequency noise of the laser:

1. Convert the displacement noise to phase noise in the beam first,  S_phi = S_x * 2*pi*n/lambda_0  (n is index of refraction).
2. S_f = S_phi * f   (f is fourier frequency), multiply by 4 to get the contribution from 4 mirrors.

above: TR noise in substrate. It just so small compared to other noise sources in the noise budget(~ 10^-3 - 10^-1 Hz/rtHz level that I don't see the need to add it in the complete noise budget.

Since we will use the same substrate, the noise level will be the same for short and long cavities. The different in beamsize will vary the noise level a bit.

Note: this calculation is for a Gaussian beam profile in a cylindrical substrate, to use this calculation for  fiber optic TR noise, some assumption about the mode of the beam is required.

 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. 

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

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

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

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

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

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

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

==Phase calculation==

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

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

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

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

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

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

I measured the slope of the error signal for ACAV path to be 200 kHz/V. This will be used for calibration the error point noise to frequency noise.

 See some details about the error signal's slope and calibration in psl:562.

THe setup for ACAV path is

• Input power to the cavity 1 mW.
• RF power on marconi for the driver = 13dB, to 4-way splitter then 14.75 MHz resonant EOM.
• The error point noise was measured at COMMON channel out1 on RCAV TTFSS.

Next: Measure the slope at RCAV path, measure error noise from both loops, compare to beat signal.

Plan for opening the chamber:

I'm certain that the beam reflected from the window that overlaps with the reflected beam from the cavity going to the RFPD causes a lot of noise. This should show up in the error noise. So to avoid the reflection from the window, I have open the chamber to turn the cavity axis a bit. I need to:

• calculate how much the cavity has to be turned if we will dump the beam at the lens for the RFPD.
• see if the beam path is still ok for the rotated cavities.
• Replace the cavity mount wall. The current one is too short due to the mistake in the design. I needed to use  nuts to raise the height, see pic.  Without the gap on the side, temperature control between the two cavities will be better due to smaller coupling. The walls will be ready on Monday, I might need a day or two to clean and bake them before the installation.
• use screws to hold the cavities down firmly, instead of resting on four point supports.
• I don't plan to replace the AD590s on the thermal shield. This will take too much work to remove the feed through, fix the cable. Otherwise, we can just slide the stack half way out of the chamber for replacing the wall and rotating the cavities. Plus, we can use beat signal as an error signal for Temp control.

 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. 

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.

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. 

 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. 

 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. 

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

 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. 

Fiber:

60m long

1064 nm PM FC/APC Patch Cable: Panda Style

P3-1064PM-FC

http://www.thorlabs.us/newgrouppage9.cfm?objectgroup_id=3345

PM980-XP

http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=1596

Collimator:

https://www.thorlabs.com/thorProduct.cfm?partNumber=CFC-2X-C

The ISS transfer function requirement is not complete without giving the plant transfer function, i.e., the conversion factors that take volts to watts at the EAOM, watts to volts at the PD, and everything in between.

The attachment shows the physical topology of the CTN ISS. The EAOM is a New Focus 4104, and the PD is a ThorLabs PDA10CS.

Looking at the EAOM manual, small-signal power modulation δW in response to a voltage δV is

with V_π no more than 300 V. From talking to Tara, it sounds like the input power W can be somewhere between 2 mW and 10 mW, but the power after the EAOM is going to be attenuated to 1 mW. So W is effectively 1 mW.

Also from talking to Tara, with 1 mW at the input he expects to get something like 0.6 mW out of the transmission. Half of this will go to the beat breadboard, and half to the ISS breadboard, so that's 0.3 mW incident on the ISS PD (so we have an optical throughput a = 0.3). The quantum efficiency η of the diode is something like 0.6 A/W. The PDA10CS has an internal preamp with different gain settings; the one to use here is probably g = 1.5 × 10⁴ V/A, since then we get something like 3 V dc coming out of the PD.

With these quantities, the plant transfer function (from volts at the EAOM to volts at the PD) is

which, with the above numerical values, is P =0.014 V/V, independent of frequency. So there's an attenuation of 70 or so that needs to be compensated for in the electronic part of the loop. But before anyone solders in the relevant resistors and capacitors, the plant transfer function should actually be measured.

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 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.

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 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

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. 

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.

This is an estimate of the required RIN for the CTN experiment, so that Chas can set the appropriate loop gain and shape for the ISS boxes. This estimate relies on computing the equivalent RIN level set by the expected coating Brownian noise of the cavities.

Amplitude spectral density of CTN coating Brownian noise

From figure 6 of the CTN upgrade document (T1200057-v11), the anticipated ASD of frequency noise due to coating Brownian noise is (0.25 Hz/rtHz) / f^1/2.

Calculation of transfer function from intensity to frequency

The spectral density of displacement noise induced by beam intensity flucations was computed by Cerdonio et al. (2001), PRD 63: 082003 (see eq. 24). Based on this, Tara has written Matlab code (PSL:1014) which numerically computes the transfer function of relative intensity noise to frequency noise for a fused silica cavity. Tara and Sarah (2012 SURF student) measured this transfer function using an AOM and one of Tara's 8″ cavities and found OK agreement (PSL:1029); the discrepancy is greatest near 1 Hz, where the calculated transfer function is 6 times higher than the measurement.

Computation of equivalent RIN

To compute the equivalent intensity fluctuations, I've taken the coating Brownian noise spectrum given above and divided it by the RIN-to-frequency transfer function as computed with Tara's Matlab code. [In this code I've replaced 8″ with 1.45″ and upped the finesse from 7500 (measured value) to 10000 (value assuming a transmissivity of 300 ppm and no losses).] I've then divided this by 2 mW (the assumed power incident on the CTN cavity) to get an equivalent RIN corresponding to the coating Brownian noise. This is shown in the second attached figure, along with yesterday's unsuppressed RIN measurement. The first figure shows the intensity-to-frequency transfer function. I've also included the data and code used to generate the plots (some of it is duplicated from yesterday's post).

Based on discussions with Chas, it sounds like we want to stabilize the RIN to be at least a factor of 10 below the equivalent RIN level shown in the second attachment.

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

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

      1) DoAlGaAs.m

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

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

This code calls on  optAlGaAs.m when running fmincon.

    2) optAlGaAs.m

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

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

     2.1) multidiel1.m

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

    To run the codes

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

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

  Plotting noise budget

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

I fixed the solder joints on the TEC by using heat shrink to make sure nothing short circuits. I figured it would be cautious to go ahead and do to avoid future problems. 

Tara worked with me for a bit trying to improve our temporary setup. We trimmed the legs on the laser diode so it will fit snugly into the socket. Then, we used a mirror mount adapter to fix the laser diode securely so there is less movement from this part. 

We found a collimator and used it in combination with another lens (planar/convex). We were able to line this up so that the beam spot is comparable to a handheld laser output, but this has a large cavity. Instead, we need to find (or order?) a very short focal length lens (something on the order of several mm). This is because the beam diverges way too fast to use any of the lenses we have been trying in the lab. From Thorlabs and Newport, it seems like it's difficult to find lenses with focal length <10mm. 

I also used a visible handheld laser pointer to determine the orientation of the blazing on the grating. There is an arrow marked, which is standard and points in the direction from the normal of the grating surface to the next trough in the blazing. This means that there are 2 possible orientations the grating will operate at - it is better to have the blazing point away from the laser diode. See: http://gratings.newport.com/library/technotes/technote7.asp This is good to know so that we won't have to reattach the grating to the diode mount if we do it wrong the first time. 

The machined parts should be done tomorrow so we can begin some construction. Today's setup is pictured, with the output beam on the IR card. 

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.]

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

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

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

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

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

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

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

To sum up for the SiO2/Ta2O5 coatings:

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

==AlGaAs coatings==

 For GaAs/Al_0.92Ga_0.08As (AlGaAs) coatings, the situation is a bit different from SiO2/Ta2O5. The cap has to be GaAs (nH) because Al_0.92Ga_0.08As will oxidize and change its material properties. Now that the cap will be nH, the thickness has to be 1/4 wavelength.  The last layer next to the substrate has to be GaAs (nH) too (I think because of both the better reflectivity and the fabrication process).

==optimization code==

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

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

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

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

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

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

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

I worked on my SURF progress report and abstract (due Friday, August 2). The most revised version is on the SVN. 

Tara and I went down to the lab to set up and test the current driver. In order to do this, we are using a function generator as our power supply for the reverse bias on the laser diode at a frequency of 10e-6 sec (for now, sufficient for temporary testing). We were able to see an output beam, so the current driver works! We noticed that the beam diverges VERY quickly. We will need a collimating lens with a very small focal length as a result. We played around with some lenses sitting around the lab, but they had relatively large focal lengths (we are looking at ~2-4mm this is commonly used in the literature...).

Tara found some problems with my soldering so I fixed it. I learned how to use heat shrink to make sure the solder joints don't touch, and I will be careful to do this in the future. I may go and put heat shrink on the TEC solders in order to eliminate the possibility of a short circuit. 

Tomorrow I will look at different lenses in the setup and see if I can find a small focal length lens to use. 

I figured out how to calibrate the potentiometers for the TEC. The three potentiometers (labeled P, I, and D) control how quickly the TEC can reach the desired temperature, and how much the temperature oscillates. I have all on their minimum setting, because increasing any of the potentiometers causes the actual temperature to overshoot the desired temperature many times before reaching an equilibrium. It is a very finicky system, and they don't have that much adjustability so it took me a long time to get right. I can adjust the temperature (resistance) to be within a few ohms of the desired temperature right now, which translates to within 0.01 degrees Celsius. This settles in 3-4 minutes. The reason my accuracy isn't as good as it could be is I have a makeshift mount I'm using to simulate the ECDL. When it is attached to the aluminum box, the temperature variations should be even smaller. Everything is in place for TEC to be implemented quickly into the actual ECDL. I will likely need to calibrate the potentiometers again with the ECDL. 

I need a banana cable connector to add to the circuit so I can see if I can get the current driver up and running with the laser diode. I will do this Monday.

This afternoon I worked on writing up a draft of my second progress report and abstract so that I have time to edit it before it's due next Friday. The draft right now is on the SVN in the ECDL folder. I still need a few pictures, and I left some space for stuff I plan to do next week.