I checked the calculation for TO noise in Cole etal people and found a few problems that I didn't understand.

• In the paper, they have two solutions for TO-noise, at low and high frequency. The solution for high frequency is similar to that in Evan etal paper, but I'm not sure where the solution for low frequency are from.  I don't see this kind of calculation in Evans etal paper.
•  I repeated and plotted the TO noise calculation as used in Cole etal's paper. The TO noise plotted in their paper mostly came from the low frequency part.
• Some parameters reported in the paper might not be accurate, for example their beam radius is 250 um. However, with their 35mm spacer, 1.0 m RoC mirrors, the spotradius on the mirror should be 212 um. I haven't checked how much their materials parameters and what I used in my codes differ.
• For low frequency solution (solid blue line), with the materials parameter given in the paper, it is a factor of 1.5 higher than their result (I got 3e-3, they report ~2 e-3 around 1-10 Hz).
• For high frequency solution (solid yellow line), with the materials parameters given in the paper, the result is about a factor of 10 higher than that from Gwinc code (dashed blue line). The formulas are the same, but I used different material parameters. The two lines should be close, but they are a factor of 10 apart, just because of the material parameters. We should really make sure that the numbers are correct. Before trying to do the optimization.

My GWINC code for TO calculation can be found here. (other modified functions are in /GwincDev/ ).The main code is plotTO_algaas.m. This code uses getCoatThermoOpticsAGS.m which calls out other other functions in /gwincdev/

1. getcoatTOposAGS.m (calculated effective alpha and beta in coatings.) This function uses getcoatLayers.m to generate the layer structure. The original one started with nL, I modified it to start with nH, and end with nH.
2. getcoatThickCorrAGS.m, which computes the correction factor (gamma TO).
3. getcoatavgAGS.m, this code compute the average material parameters in coatings.
4. in /coating/AlGaAs_Refcav, I created a database file for material parameters called algaasmodels.m.

I sent this to Tara in an email, but I thought I'd include it here for posterity:

So if you compare the low frequency and high frequency equations in the Cole paper, they're different by a factor of:

sqrt(pi)*r_G/r_T,

where r_G is the radius of the beam spot (r_G = w/sqrt(2)), and r_T is the thermal diffusion length (r_T = sqrt(kappa/(2*pi*C*f)). 

Plus, if you look at the definition of low and high frequency:

w^{^2}*C*pi*f/kappa,

that is equal to (r_G/r_T)^{^2}. After giving the low and high frequency thermo-optic equations, the cole paper cites Matt Evan's paper and a Braginski paper from 2000. In the conclusion to the Braginski paper, they mention that when the frequency is high, or the spot size is low, defined as r_G<r_T or r_G/r_T < 1, the adiabatic assumption that they use breaks down. Then, in Equation 9 of the Braginski paper, they indicate that the breakdown results in an error on the order of r_T/r_G. 

Going back to the Cole paper, it appears as though for the high frequencies, they've just adjusted the low frequency equation by the adiabatic breakdown error. What I still don't understand is where the extra factor of sqrt(pi) came from, and why it's the inverse of the adiabatic breakdown error. Some of it might be typo. I'll check with Garrett to see what he has to say about it. 

[matt,tara]  We compared the TO result using GWINC, our results are similar (see PSL:1170). However, it still not agrees with result in Cole etal paper.

The result from GWINC and Cole etal's result are different in the following ways:

• TO noise from GWINC is higher their result. This might be due to different values of the effective alpha, and effective beta in the calculation. We will check this next.
• The calculated transmission for 81 layers is ~ 1.8 ppm, while they reported 10ppm. We are not sure what happen here.
•  Half wave cap solution for TO noise cancellation is not shown in GWINC.
• Thermal fluctuation as observed by a Guassian beam, S^dT_TO = const x kBT^2/ r0^2 sqrt(kappa x heat cap x 2*pi*f) depends on substrate parameters in GWINC, but their result use coatings' parameters. With coatings parameters, the thermal fluctuation will be lower, thus lower TO noise. It means that our TO result should be larger by an order of magnitude. However the results are about the same.   We think that the subsrate parameters should be used in the calculation, because thermal length in the coatings from dc up to 170kHz is smaller than the coatings thickness (~6 um).
• The calculation in GWINC assumes adiabatic assumption. However, the assumption breaks down at 270 Hz for AlGaAs coatings, and 6 Hz in substrate. That explains why the TO noise in Cole paper is almost flat from DC to 100 Hz. Mike Martin's thesis explains the TO noise at all frequency, but I haven't yet quite understood all the equations.

We checked the half wave cap solution for  minimizing TO noise. WIth a half wave cap of nl, the TO noise is smaller by ~ a factor of 2 in Hz^2/Hz unit.

Matt and I checked the  calculate the TO noise for a half wave cap solution. The noise goes down by a factor of 2. 

A few issues that we still have to investigate:

• A thin layer of nh: we talked to Mike, he said that to prevent the oxidation that occurs on GaAs layer (nL), a thin layer of AlGaAs(nH) has to be applied on top. We are not sure how thick the layer will be, we should ask G Cole, so that we can estimated the effect before hand.
• The TO noise with  half wave cap may already be lower than substrate thermoelastic (TE) noise. I'm checking the TE calculation and find out that the value for thermal expansion of fused silica is 3.9e-7 in Gwinc, but 5.5e-7 elsewhere (add sources). If it is really 5.5e-7, this will be higher than the current TO noise already. I'll look into it.
• A factor of 2 : This comes from double sided PSD or either 2 mirrors. I'll change that to our standard here (1-sided PSD, with single mirror).
•  The cancellation might change for different numbers of doublet. Since we plan to have ~ 100-200 ppm, the actual TO noise may be different than this calculation (2ppm). I try using 56 layers (1/2 lambda cap of nL included) which give us 100ppm, and TO noise is below coating brownian from DC to 200 Hz. This is a pretty good result which should be expected. Since we reduce the number of doublet, the effect from TE becomes smaller, (still larger than TR). Thus the different between the two (the total TO noise) is smaller.
  
• Different cap thickness may bring down TO noise more than half wave cap does. I just try the cap with 0.1 wavelength of nL (for 40 doublet stack), and TO noise goes down by another factor of 2. This might apply for 56 stack as well. I'll check.

I checked all the discrepancies in the calculations between GWINC and that of Cole. The issues are almost cleared, only the value of effective beta, (dn/dT) that still remains.

  The PSD of TO noise in [m^2/Hz] is given by S_x(f)= S_T (f) x (dTE + dTR).  See Evans etal Phys Rev D 78, 102003.  Where:

• S_T (f) = Temperature fluctuation as sensed by a Gaussian beam
• dTE = dx/dT, or rate of change of mirror position with respect to temperature change due to thermoelastic mechanism.
• dTR = rate of change of mirror position with respect to temp change due to thermo-refractive mechanism

S_T(f) can be calculated analytically, see BGV, Phys Lett A 271 , (2000) 303-307 eq9, this also assumes adiabatic approximation. In Mike Martin's thesis, the temp fluctuation is generalized  to all frequency (by contour integral, I'll show the details later). The parameters for calculating S_T(f) are taken from that of substrate (in GWINC), but Cole's paper and Mike's thesis use that of the coatings. That makes Cole's result about a factor of 7 higher than that from GWINC. Matt and I discussed this with Mike, he thought that the calculation should use the substrate's properties since the thermal length in the frequency of interest is much larger than the coating thickness.

The issue with which parameters should be used might be a less serious problem if (dTE + dTR) can partially cancel out making the whole TO noise much smaller. Basically dTE is ~ alpha* coatings thickness, where alpha is the thermal expansion coefficient of the coatings. dTR is ~ beta_eff * lambda.  The calculations for dTE from GWINC and Cole are about the same (1.1 x 10^-10) [m/K], where the effective beta are different by about and order of magnitude. Cole reports the value of beta effective to be -5.5 x10^-10 , meanwhile GWINC gives me 0.5x10^-10.

This means that the TE and TR,as calculated from GWINC are more comparable, and the TO result is reduced significantly. While the TO result from Cole is mostly TR. I calculated the TR following the 1/4 stack approximation in Evans paper and got the same result as in Cole. I'm checking what happen in GWINC code for TR calculation.

I found out why the calculated values of the coatings' effective beta from GWINC and Cole etal paper are different. The order of Low/High refractive index material have something to do with the beta effective calculation.

Here are some facts about the coatings and calculation:

• The AlGaAs coatings used in the paper have no 1/2 wave cap. The structure is consisted of only 1/4 wave layers. Start with nH on top, and end with nH at the substrate (SiO2).
•  The PSD from thermo-refractive is SdT x Beta_eff x lambda. Where SdT is temperature fluctuation, Beta_effective is the overall dn/dT of the coatings,see the entry below for more details.
• In GWINC, Beta_eff is calculated numerically, taking each layer and calculating the reflectivity, then sum all the effect together. The result for Beta_eff is different, if the first layer (the top one) is changed between nH or nL. ( 5e-5 and 5e-4, cf PSL1178).
• The approximated Beta_eff, for 1/4 high reflective coatings, which is reported in BGV 2000, and Evans 2008 is given by B_eff ~ (nH^2 *BL + nL^2*BH) / (nH^2 - nL^2) (which was used in Cole's paper to calculated their TO noise). BGV gave a sketch of this calculation in their paper (which I have not yet thoroughly understood). One problem is that, the result for B_eff obtained from this formula is the same whether the coatings start with nH or nL. This should be wrong, since most of the TR effect comes from the very first layers. The order of nH/nL should matter.
• Computed values of B_eff from Gwinc code and the simplified formula agree if both start with nL. This makes me think that there is some assumptions in the simplified B_eff formula that the first layer is nL (which is customary, in SiO2/Ta2O5 coatings ).

So, I believe that the calculation for TO noise I have right now is correct. And for 100 ppm transmission (56 layers) with 1/2 wave cap, the TO noise is significantly reduced (add plot).  We should be able to finalize what we want for the AlGaAs mirrors soon.

 Beff ~ (nH^2 *BL + nL^2*BH) / (nH^2 - nL^2) is valid only if the top layer is 1/4 layer of nL, [Gorodetsky, Phys Lett A 372 (2008)].  The complete calculation for general case is given in the reference. If the layer starts with nH, beta eff is = (BetaH + BetaL) / (4x(nH^2 - nL^2) ).  So, GWINC and analytical approximation agree, Yay! .

The effective beta reported in Cole's paper is 5e-4, but it should be ~ 5e-5 for coatings start with nH. The real thermo optic noise for their setup will be lower ( because TE is about the same level as TR). Their real TO noise should be a factor of 5.5 below the reported one (in Hz^2/Hz unit).

Note: There are still issues about the thermal fluctuation and the cut off frequency. These will greatly change the shape of the TO noise and the total noise level. I'm still investigating it.

The 1/2 wavelength cap with nL does reduce the TO noise. But we need to know exactly how thick the nH film on top will be, so the real TO effect can be estimated accurately.

 The noise budgets below show noise from coating brownian, TO noise and TE in substrate. The three plots are from 52,54 and 56 Layer coatings.

 All the designs have 1/2 cap of nL, with nH ending on the substrate surface.  There are no significant differences in the noise level at low frequency, since TE noise in substrate starts to dominate. I used the substrate

parameters in thermal fluctuations, so the cut off frequency for TO calculation is low (~ 3 Hz instead of ~ 200 Hz). The design can go for 56 layers.

I'm thinking about another solution, where the top layer is nH, followed by 1/4 layers. If the first nH is 1/8 lambda thick, TO can be cancelled nicely (for 56Layer + nH cap). The transmission is 140 ppm , which is in the chosen range (100-200ppm). But I feel that the 1/8 cap is not good for a high reflectivity mirror, since the phase of the reflected light within  that layer is not really inphase or out of face with the light reflected at the air surface. I'll think about it more to see if it would be a good solution or not.

Here is an outline for TO calculation. I tried to summarize it and make it as simple to follow as possible.

•  Use Levin's direct approach to calculate thermal fluctuations seen by the beam.
• Apply power injection at the coating surface, with proper boundary condition, take coating into account. (Evans2008 see thick coating correction, Somiya2009)
• To calculate the loss due to the dissipated heat, we need to solve heat equation. The loss associated with the injected heat is proportional to (gradient of temperature)²
• The calculation for gradient of temperature has to be calculated in both longitudinal and transverse direction, as thermal length is comparable to the beam size [Cerdonio 2001]. Other papers usually approximate grad T = dT/dZ, which is 1-D treatment [Evans2008, Somiya2009]. The effect from Heat flow in transverse direction shows up at low frequency, where the noise level becomes lower.
• When solve heat diffusion equation, apply boundary condition for finite size mirror (somiya2009).
• Once we have thermal fluctuations, S_T, we convert it to displacement noise with TE and TR coefficients. Sx = S_T *(TE + TR)
• TE and TR coefficients can be calculated from the layer structure. The cancellation will occur only at lower frequency where temp fluctuations in coatings are uniform. At higher frequency the effect from TE and TR will sum up in quadrature (if heat equation is solved in coatings), see thick coat correction section in Evans2008.

This means that for TO optimized coatings, we have to make sure that TE and TR coefficients are comparable for maximum cancellation. The calculation for TE and TR are quite well defined, [Fejer2004, Evans2008, Gorodetsky2008]. This part is independent from temperature fluctuation calculation outlined above. So we can choose the optimized design and then calculate the total TO noise level later. The proposed optimization can be found in psl:1183. (Here is the result for 1/8 cap of nH).

Note:

1. Basically most of the calculations outlined above are done in Somiya2009, except transverse heat flow. If we consider transverse heat flow in coatings and substrate, the result will be valid at low frequency as well.
2. The decision for G Cole etal to use substrate parameters in temperature fluctuations as suggested by Rana seems to be ok, since their calculation also include the thick coat correction (Evans2008), it means that temperature fluctuations in coatings are taken into account.  However, the cutoff frequency might be  off a bit, since the equation for transverse flow is only in substrate (BGV1999, cerdonio2001). I think the real cutoff frequency should be higher because kappa is larger in the coatings, and transverse heat flow becomes more significant at higher frequency. 
3. Somiya paper also include Brownian noise in Coatings with finite size substrate/coatings (see fig2) which is not done in Harry etal 2002. Finite size effect increases the noise level by a lot, I think this might explain why the beat result we measured from 8" cavities is a bit higher than the estimated noise using the result from Harry etal. I'll check that later.
4. I'm not quite sure about The TO calculation in Somiya. The injected heat from TO and TE are added independently, however, the result is similar to that of Evans (with half infinite limit). I'm checking it.

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

1) goal

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

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

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

2) Is the calculation correct?

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

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

==BR in coatings==:   

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

==BR in substrate==:

• The calculation is taken from Levin1998, with finite size correction by Liu&Thorne(LT2001). 
• The loss angle for bulk fused silica is frequency dependent ~ 10^-11 x f^0.8(Penn2006). This loss is much lower than conservative constant loss (10^-8) (number from DCC LIGO-T0900161) from dc upto 10kHz.
• In this calculation, for constant loss of 10^-8, BR noise in substrate is still ~ a factor of 3 lower than BR in coatings.

==TE noise in substrate==:

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

==TE and TR noise calculation:

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

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

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

I used the ThorLabs power meter to get the transmission coefficients for the five AlGaAs mirrors.

For each measurement, I wrote down the incident power (20 mW nominal), the transmitted power (≈3.5 µW, depending on the mirror and background light level), and the transmitted power with the beam blocked (to get the dark power).

In other news, Tara bonded mirror #114 to spacer #95. The contacting seems to be tough going because of some recalcitrant smudges on the substrate surfaces.

I have started a python implementation of the AlGaAs noise budget. All parameters, functions, etc. are defined in a single notebook, and this same notebook generates the plot. The python uncertainties package facilitates estimation of uncertainties in material parameters, optical parameters, etc.

Currently, the coating thermo-optic trace is not an actual calculation; it is just a flat line culled from figure 5.9 of Tara's thesis.

The PDH shot noise trace is shown assuming an incident power of 1 mW on each cavity, a PDH modulation index of 0.2 rad, and a cavity visibility of 0.92.

To do:

• Finish implementing true TO calculation
• Add photothermal (requires RIN data)
• Add seismic (requires seismic data, seismic stack TF data)

I've implemented the TO calculation following Evans et al. (2008), along with the so-called Yamamoto correction for the CTE.

These changes are on the SVN.

The first attachment shows the photothermal TFs which take absorbed power (in watts) to the mirror displacement (in meters) as sensed by our 215-µm beam. Since last night, I've fixed the coating TE part and committed the updated ipynb to the SVN.

The second attachment shows the noise budget, with the photothermal shot noise contribution.

Same data and same isolation model as for the silica/tantala noise budget. Since we have new table legs, we should retake this data (and make a spectral histogram).

The resonance frequencies of the stack are given as 10 Hz and 35 Hz in the noise budget. Are these for the old stack? I recall that with the new stack we measured resonances at 3, 7, and 10 Hz.

Also I want to double check the sequence of interpolation steps we've used on the silica/tantala noise budget. There are some seismic peaks and silica/tantala beat peaks that almost (but don't quite) match up in frequency, and I wonder whether this is an artifact of the interpolation.

 I'm aligning the AOM and maximizing the diffracted beam's power by positioning the AOM and adjusting the beam size by moving the lens.

For single pass, the maximum efficiency I could get is only ~60%, so for double pass, the power will be down to 36%, but for now I'll settle with this number.

I could not find the manual for Crystal technology AOM 3080-194. The closest one is model 3080-197 which is attached below.

I'm not sure what is the difference between the two model, but 3080-197 has 70% diffraction efficiency.

Because of adjusting the lens, the RefCav's beam path also changes, now I have to realign RefCav again.

  Another step for AOM alignment is adjusting the mirror that reflects the transmitted beam back to the AOM again.

The distance between the mirror and the center of the AOM should be the same as ROC of the mirror.

After this I should be able to start locking ACav.

 did you measure the power of the vco? How much is it if you tune it to maximum?

Here a copy of a general datasheet for the 3080-194. maximum efficiency is ~80% @2W RF power. You should ask peter about the detailed datasheet which comes with each AOM and contains measured values for the one you are using. Measured values depend on the beam size and RF power. Typical values are 87% in reality.

 Oh, I see, the beam diameter is 1100 um, I use 150um. I'll try changing the beam size and see what happens. Thanks Frank. I'll measure the power of the VCO too.

 have a look into the datasheet which came with the AOM. Don't make it too large. Clear aperture is about 1.7mm max. You can also have a look into the manual of the 35W laser (ATF lab). It contains a copy of one of these datasheets as well (with the graph of efficiency vs beam size). You don't need more than 60%, but you should try to get around 50% for the double-passed beam as we don't have so much laser power in total available. Assuming the original 15mW on the RF detector you need about 45mW for the acav now and 15mW for the refcav, so 60mW total after the PMC. With the current 95mW out of the laser it should be no problem( in principle). After the isolator and EOM you might have something about 85mW upstream of the PMC which means you need 70% transmission through the PMC. Anyway, a larger beam size gives you better eff.  If you make it 500um or so you should get 50% in the double-passed configuration.

 I manage to get 70% efficiency from P wave. When I try S wave, I get 78% which is close to the specified value. So for double pass, the efficiency should be upto 50%. The beam size is ~550 um.  I redo the mode matching calculation for the AOM (and also RefCav and ACav) and move the beam a bit to the side of the table so that the insulation box won't get in the way.

I'm aligning double pass AOM. After maximizing the power of the 1st order of the transmitted beam, I place the R=0.3m mirror to reflect the beam  back to the AOM.

The mirror is mounted on a translational stage for a fine adjustment.

At the right distance L away from the AOM(L = ROC), the size of the reflected beam at the AOM should be the same as the incoming beam.

Thus, there are 3 things to adjust.

First is the angle of the quarter wave plate that rotates the polarization of the beam after 2 passes by 90 degrees.

Second, the angle of the mirror, and

third, the distance of the mirror. At right position the power of the 1st order beam should be maximized.

I might have to change the position of the PBS that reflected the AOM double passed beam. Currently, the PBS is placed before 2 mirrors that move the

beam to the side of the table to avoid the insulation box. The problem is the double passed beam might clip on the mirror. So now I put the PBS after the steering mirrors, just in front of the AOM, but this limits the space for mode matching. I'll have to check which one will be better. From the attached picture,  two PBS's are placed on two possible locations. On the bottom right the, and down at the middle next to the AOM.

I switched the cable from the 10W controller to the original controller for 100 mW laser. It is working well now, the cables are tied properly.

For now, I don't need to use the FSS servo card to scan the laser frequency.

I'm using a function generator for fast channel (PZT), and a voltage calibrator for slow channel (thermal control.)

The alignment is in progress. With the aid of a CCD camera and a macroscopic lens, looking for the beam position on the mirror is getting easier.

Currently I see some light at the back of the cavity.

As suspected in CTN: 2346, the mode matching of the cavities is deteriorating and eventually alignment is getting screwed due to possible lab temperature fluctuations. I left yesterday with south cavity mode matching to about ~70% but in the morning today, I found that the resonance is completely lost and a higher order mode with vertical fringes is resonant. Same is the case with North one which had shifted to a much higher order with vertical fringes. So clearly, I need to switch back on the vacuum can temperature stabalization.

This morning Megan tried to lock RefCav, but the alignment was off. I realigned it, and now it's locked.

C3:PSL-MGAIN  4.4 dB

C3:PSL-FAST 16.6 dB

Recently we were given the idea of sending the beam to the photodiode at Brewster angle. If we do so, ideally one particular polarization (parallel to the plane of incidence) will not reflect back. So if we send the beam polarized in this direction (or set the incidence plane such that these conditions are matched), we can minimize the reflection from PD significantly.
Sounded like a good idea, so I started reading about the InGaAs detector we have. Unfortunately, the datasheet of the C30642 detector we use does not mention either the fraction of In in InGaAs or the refractive index of it. So I went into the literature found these two papers:
Kim et al. Applied Physics Let Vol 81, 13 23 (2002) DOI: 10.1063/1.1509093
Adachi et al. Journal of Applied Physics 53, 5863 (1982); doi: 10.1063/1.331425
Using the empirical coefficients and functions from these paper, I calculated the refractive index for InGaAs for various fractions of x and the corresponding Brewster angles (Find Attached).
However, just after doing the analysis, we realized that doing this is not really possible. The Brewster angle is arctan(n2/n1) where n2 is the medium light is going into. This implies the Brewster angle would always be greater than 45 degrees and detector won't really absorb much light at this angle. So currently the conclusion is that this idea won't work.
However, there might be some error in our assumption of InGaAs as a transparent medium as the calculations do not take into account absorption of the photon at all. Attaching the python notebook too in case someone figures this out.

See https://dcc.ligo.org/LIGO-T1100564/public

See also: https://arxiv.org/abs/1710.07399 or https://doi.org/10.1364/AO.57.003372

There are a large number of ants making a trail from the ATF lab to the PSL lab.  They seem to be heading into a hole next to the lab door.  I just saw a queen ant poke its head out of the hole.  

Ants in the ATF lab are taking their ussual route along the AC conduit.  There are Terro baits laid ever 3-4 meters and they have almost emptied every one. The trails continue to the mechanical plant room accross the hall (room 259ME)

Laying down Terro ant poison now. Will buy more.

Thu Jan 11 13:33:04 2018

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. 

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. 

 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. 

 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. 

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. 

 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. 

[Tara, Evan]

Having successfully floated the table yesterday, we attempted a new beat measurement in the hopes that the large shelf below 100 Hz had disappeared. Unfortunately, this appears to not be the case. Additionally, many of our signals are plagued by unusually large, slow drifts. We're hoping that they're just thermal transients caused by all the work on the table over the past 12 hours, and that by tomorrow things will have settled down. We'll see if that's the case.

Anyway, we did the following things today:

• We reconnected cables that come in from off the table and go onto cameras, PDs, etc., paying special attention to strain relief and vibration isolation since the table now floats.
• We redid the alignment to recover ~90% visibility; this required only touching the periscope mirrors (somewhat surprising considering what we subjected the table to in order to switch out the legs).
• We got the cavity PDH loops up and running again. The control signals show unusually large drifts. We also noticed this while sweeping the lasers to align the cavities; the resonance for north in particular would wander out of the sweep range every 30 seconds even though the laser was being driven at 10 Vpp from an SRS function generator.
• We spent some time trying to null (what we assume is) RFAM-induced offset in the PDH error signals. We did this by adjusting the HWPs before each cavity EOM and nulling the offset on TTFSS common OUT1. The south cavity already had a small offset, so no adjustment was required. On the north cavity, there was a noticeable offset (~20 mV, compared to an error signal pk-pk of 220 mV), so Tara nulled it. We then found that we could get a stable lock with the laser PZT actuator alone, and that adding the EOM actuator caused the loop to oscillate (almost as if the EOM actuator was driven with the wrong sign). So we looked at the error signal again, and unexpectedly found another ~20 mV offset. Tara nulled it again and this time the lock was stable; in fact, we were able to get the common and fast gain knobs up to 1000 and 1000 (compared to 800 and 800 earlier in the day). No idea what the problem is here; possibly it drifted between the successive adjustments.
• We looked at the beat. It appears to be not much better than with the table unfloated.
• We took a measurement of RIN-induced disturbance in the beat by driving the south EOAM with a sine from the SR785 and taking the TF that takes transmission PD intensity to beat fluctuation. Unfortunately, this measurement is not consistent (in magnitude or phase) between successive sweeps. It seems to be due (at least in part) to DC drift in the beat.
• We tried turning on the crude south ISS, but it made the beat more noisy.

I went through the table today looking for ghost beams. Most were already dumped. For those that weren't, I put down a dump or an iris.

I again looked at TTFSS OUT2 with the cavities unlocked (i.e., the open-loop error signals) and found that the low-frequency seismic/scatter wall appears only on south. So I hunted around south for a while. I found a series of ghost beams reflecting off the EOAM input and hitting dangerously close to the EOM output aperture. So I moved the EOAM forward a few inches, then adjusted its kinematic mount to offset these beams a bit. The EOAM should be realigned, and we should check to make sure the ghost beams are not entering the EOM again.

With the increased space between the EOM and EOAM, I installed a flipper mirror that takes the beam to the 1811. Then I minimized the RAM (from –54 dBm to –72 dBm with 85 mV dc).

FM dev: 10 kHz

Averages: 10, 50, 100, 500

I added a flipper mirror before the north EOAM, as well as a HWP before the resonant EOM (so that we can independently control the polarization entering the two EOMs). I optimized the RAM, but saw no improvement in the beat.

I found that the beatnote detector was actually saturating and the output was not a good pure sinewave. I've reduced the laser powers reaching the intensity to avoid that so that 20 dB coupled output of beatnote remains around 200 mVpkpk. Following is the summary of changed settings:

However, the beatnote did not change because of these changes showing that moku is strictly sensitive to zero crossings of the acquired signal rather than its shape near the edges.

Checking PLL OLG

Measured the OLG using out1/out2 method.  Did the G/(1+G) invertion to OLG directly on the SR785. Plotted in attachement 1.

Looks like a UGF of about 16.5 kHz

BN spectrum

Current beat note is at 8.98 MHz.  North cavity heater is set to 0.77422 W and will probably need to be raised a little to get us a little higher in BN frequency.

PLL settings are:
Marconi FM Devn: 10 kHz
SR560 Gain: 20
Beat note strength: -1.17 dBm

Calibrated BN spectrum is attached below, attachment 2

These measurments followed some dumping work around the refcav relfection photodiodes. See, PSL:2084.

PLL

OLG was measured using out1/out2 method.  The G/(1+G) invertion to OLG was done directly on the SR785. Plotted in attachement 1.

UGF is about 37 kHz

BN spectrum

Current beat note is at 17 MHz.  North cavity heater is set to 0.77320 W.

PLL settings are:
Marconi FM Devn: 10 kHz
SR560 Gain: 50
Beat note strength: -3.3 dBm

Calibrated BN spectrum is attached below, attachment 2

Data in third attachement and commited to the ctn_labdata git.

[Tara, Evan]

Tara took a BRDF measurement yesterday of AlGaAs mirror #114.

In this measurement, the return beam is dumped using black anodized foil instead of a razor blade dump. This seems to make the peak at 20° disappear, and now we get a more or less monotonic falloff in scattered power.

TIS from 14° to 71° is 39(6) ppm.

Data and code are on the SVN at CTNlab/measurements/2014_07_30.

[Tara, Evan]

Tara also took a BRDF measurement of #114 after cleaning it.

After cleaning, TIS from 14° to 71° is 2.7(5) ppm. Much improved.

Data and code are on the SVN at CTNlab/measurements/2014_07_31.

 Basically the same story with 132.

[Tara, Evan]

We replaced the Lambertian diffuser with AlGaAs mirror 137B1. We intentionally induced a nonzero AOI of the incident beam, so that the reflected beam could be dumped cleanly. At a distance of 25.7(3) cm back from the mirror, the reflected and incident beams were separated by 1.3(1) cm, giving an AOI of 1.45(11)°.

1. We measured the incident laser power as 9.94(2) mW.
2. We set the exposure time of the camera to 250 ms.
3. We swung the boom to 13°, 16°, 19°, 22°, 25°, 28°, 31°, and 34°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
4. We measured the incident laser power as 9.95(2) mW.
5. Because the scattered power had fallen off sharply by 30°, we turned up the exposure time to 1.00 s.
6. We swung the boom to 31°, 34°, 37°, 40°, and 43°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
7. We measured the incident laser power as 10.08(2) mW.
8. We swung the boom to 46°, 49°, 52°, 55°, 58°, 61°, 64°, 67°, and 70°. At each angle, we took 5 CCD images with the beam incident, and 1 CCD image with the beam blocked.
9. We measured the incident laser power as 10.06(2) mW.

For all of these measurements, the two ND filters (OD1.5+OD3.0) were not attached; just the RG1000. With the ThorLabs power meter, we measured the combined transmissivity of these two ND filters to be 1865(14) ppm.

The first attachment shows an example CCD image. The second attachment shows the raw counts, the inferred scattered power, and the BRDF.

Incident power: 20.0(1) mW

Exposure times used: 25 ms, 50 ms, 200 ms, 500 ms, 1000 ms

Transmitted power: 3.34(2) µW. This gives a transmission of 167(1) ppm for this mirror.

TIS from 16° to 73° is 18(1) ppm.

Data and code are on the SVN at CTNLab/measurements/2014_08_05.

[Tara, Evan]

Yesterday we took a scatter measurement of AlGaAs mirror #143. Instead of one bright scattering center, we saw 3.

The procedure is identical to the procedure used for mirror #137, although the exposure settings and choice of angles are a bit different (see the attached plot). Also, we used 20 mW of incident power instead of 10 mW.

Total integrated scatter from 14° to 82° is 80(8) ppm.

Data, images, and plot-generating code are on the SVN at CTNlab/measurements/2014_07_28.