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1197   Wed Jun 12 14:49:47 2013 KojiNotesNoiseBudgetnoisebudget for 8" SiO2/Ta2O5 cavity

Careful check is necessary as usual, but for now let me say congraturation! It's beautiful!

1196   Wed Jun 12 14:32:22 2013 not KojiNotesNoiseBudgetnoisebudget for 8" SiO2/Ta2O5 cavity

 Quote: Wait. Do you mean that you found the last push to match the experiment and the calcualtion? Do you also mean there is no fitting to make it happen. Correct?

That is correct, all the numbers used in the calculations are nominal values (under some assumptions though, about how I average the coatings material properties), and the result just matches the measurement. It's magic! 1195   Wed Jun 12 01:34:27 2013 KojiNotesNoiseBudgetnoisebudget for 8" SiO2/Ta2O5 cavity

Wait. Do you mean that you found the last push to match the experiment and the calcualtion?
Do you also mean there is no fitting to make it happen. Correct?

1194   Tue Jun 11 16:46:52 2013 taraNotesNoiseBudgetnoisebudget for 8" SiO2/Ta2O5 cavity

note about the calculation for coating Brownian noise in a finite size mirror .

==Coatings Parameters==

Young's modulus, Poisson's ratio, and loss angle are taken from the volume averaged value of the coatings (Yavg = d/ ( d1/Y1 + d2/Y2) , sigma avg = 1/2 (sigma1+sigma2 ). These are used for "perpendicular" direction in Harry2002 formula.

Loss angles

• SiO2 loss angle  = 1e-4
• Ta2O5 loss angle = 2.3e-4
• coatings loss = 1.32e-4

Young's moduli

• SiO2 Young's modulus = 72e9  Pa
• Ta2O5                         =140e9  Pa
• Coatings Young's modulus = 93e9 Pa

Coatings structure

• 1/2 lambda cap of SiO2
• 26 layers
• 300 ppm transmission

==calculation codes==

• I got the file for finding zeroes of the bessel function from Matlab exchange.
• The code for calculating Br noise is attached below.
• For the finite size bdy condition, the solutions include all the besselj function of all orders (m=1 to inf). I used m from 1 to 55 in the calculation since it converged quite fast after that.
• For the integration to calculate all the elastic energy, I used Riemann sum, with stepsize of ~0.15 um. The result does not change much (less than 3%) if I go from 0.8*a to a where a is the radius of the mirror. This is important to note because our coatings do not cover the whole surface of the mirror. There is an annulus edge with ~3mm width for optical contact area. The result means that the elastic energy is still localized in the spot area.

As noted in SK2009, the estimated values for half infinite and finite size analyses are about the same (~2.5% difference) (I have not verified this). Then, the result from GWINC using Harry2002 formula is still accurate.

• The calculation in SK2009 uses an overall loss angle of the coatings, while calculation in Harry2002 separates the elastic energy in two directions,parallel and perpendicular to the surface, and also loss angles in the associated directions.  I use the perpendicular average under the assumption that most energy/deformation occurs in that direction.
• The result matches the measurement quite well. This reassures us that other noises introduced by the setup (i.e. noise in optical bonding/ noise from supporting structure/ thermoelastic/ brownian noise in the spacer) are not higher than coating thermal noise.

Attachment 1: getCoatBrownian2.m.zip
1193   Tue Jun 11 00:45:48 2013 taraNotesNoiseBudgetnoisebudget for 8" SiO2/Ta2O5 cavity

 Quote: Note: 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.

Here I applied Somiya&Kazuhiro (SK)2009 coating brownian noise calculation to the previous 8" cavity setup. The estimated noise matches up with the measured result well. The result for coating Brownian noise presented in SK is for finite size mirror. They emphasize that the estimated noise diverges from Harry2002 result (half infinite mirror) in the case of a thin mirror (thickness is less than mirror radius) which is our case (radius = 0.5inch, thickness = 0.25 inch).

I'll attached the calculation and explain some differences between the two calculations later. Here are some notes about the parameters:

• Loss angle of the coatings used in the calculation is phi perpendicular (1.326 e-4), from GWINC, (phi parallel - 1.4e-4);
• Young's modulus of the coatings is 93 GPa
• Poisson's ratio  = 0.2
• m = 45; (# of zeroes for besselj(1,x))
• stepsize for radial integral = wspot/1000

Attachment 2: sk2009nb.fig
1192   Thu Jun 6 22:28:46 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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, ST, we convert it to displacement noise with TE and TR coefficients. Sx = ST *(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.
1191   Wed Jun 5 22:25:28 2013 taraNotesNoiseBudgetTO calculation review

Since we have to review the calculation for Thermo-Optic noise (TO), I'll sketch an outline and some remarks here.

==TO noise overview==

To calculate TO noise, we have to calculate temperature fluctuations, then multiply by Thermoelastic (TE) and Thermorefractive (TR) coefficients to convert temperature fluctuation to displacement noise. Usually, in the frequency of interest, thermal length is much larger than coating thickness. Thermal fluctuations in coatings are uniform making the whole coatings expand/ contract uniformly. This assumption is important for cancellation between TE and TR. As TE effect comes from the whole coating thickness, while TR comes from only the first few layers (most of the power is reflected from these top layers). Modifying the first few layers can change TR effect significantly.

==Temperature fluctuations==

can be obtained from direct method (Levin 2008), by injecting heat with Gaussian beam profile. Example are done in Levin 2008, Evans etal 2008.

A few issues about these calculations:

• heat flow in 1-D, under the assumption that temperature gradient is mostly in z direction coating thickness d << thermal length << beam radius. Where thermal length is ~ sqrt (  kappa/ (rho*C* 2pif) )  This is not true for AlGaAs coatings where kappa is ~ 60 W/mK which gives thermal length to be~ 2370 um  [sqrt (1Hz/f)], beam radius is ~ 200um.  Cerdonio 2001, and Mike Martin's thesis have the calculation in 3-D, however, heat diffusion in coatings is not taken into account.
• Heat diffusion in coatings, is done in Fejer 2004, Somiya2009. (It is ignored in BGV1999/Liuthorne2000/cerdonio 2001)

At this point, I think Somiya paper is very good for us to look through. The calculation includes TE and TR. However, I don't quite get it yet. The calculation solve heat equation in 1-D, but has results for finite test mass. I need to spend more time on the paper.

Heinert 2011, has calculation for TR in finite size substrate. I'm not sure how to connect the results to our setup yet. Plus, for our setup, the actual coatings will be ~ 8mm in diameter, with 1" diameter substrate, the boundary conditions will be non-trivial for us.

==TE +TR coefficients==

[ coming soon]

1190   Tue Jun 4 18:02:26 2013 taraDailyProgressRefCavbeam directed to 2nd refcav

The beam is sent to 2nd cavity (RCAV). The beam is mode match roughly, since there is no PMC, the exact beam size is hard to measure. The laser resonance when RCAV_SLOWOUT @ 0.2383V. There is enough transmitted beam for alignment the beat setup behind the cavity.

1189   Mon Jun 3 11:42:03 2013 EvanDailyProgressComputersTemporary south refcav autolocker

I should mention that I've currently got the autolockers running in a screen session. If you need to turn them off you should screen -list to get a list of the current screen sessions, then reattach the appropriate session by screen -r [pid] (e.g., right now the relevant screen session has process ID 8517, so you'd type screen -r 8517), and then kill the autolockers by whatever means necessary.

1188   Fri May 31 14:23:49 2013 EvanDailyProgressComputersTemporary south refcav autolocker

Quote:

 Quote: Special bonus settings: the common gain on the TTFSS is 404 clicks, the fast gain is 426 clicks, and the offset is 967 clicks. Tara pointed out that the frequency loop would catch lock easier if the gain settings were around these low values rather that what they were previously (~600).

The offset should be ~ 500. I turned it back down.

OK. But if you sweep the laser frequency you can see a DC offset in the error signal (OUT1 on the common path on the TTFSS), and at least a few days ago it was making the loop catch in a place where it shouldn't.

Obviously the long-term solution is to track down the source of the offset and make it go away. But in the short term is there something we can do to make sure the loop doesn't lock to this false point?

1187   Fri May 31 13:21:37 2013 taraDailyProgressComputersTemporary south refcav autolocker

 Quote: Special bonus settings: the common gain on the TTFSS is 404 clicks, the fast gain is 426 clicks, and the offset is 967 clicks. Tara pointed out that the frequency loop would catch lock easier if the gain settings were around these low values rather that what they were previously (~600).

The offset should be ~ 500. I turned it back down.

1186   Thu May 30 13:15:55 2013 EvanDailyProgressComputersTemporary south refcav autolocker

Again inspired by Zach's bash autolocker, I've written a python autolocker for the south reference cavity. If the cavity loses lock, it turns off the PID loop so that the temperature does not run away to the rails. It then checks that the PMC transmission is high and proceeds to slowly ramp the laser temperature between 7.43 V and 7.50 V.

Note: the aforementioned voltage values only work because the refcav is not heated, and hence the resonance always occurs in roughly the same place (between 7.45 V and 7.48 V, depending on the day). This simple search algorithm is therefore not, not a permanent solution for autolocking the refcav once the heaters are working. For posterity, here are the other values currently hard-coded into the autolocker:

• darkThreshold: 1 V; this is the value below which the RFPD REFL DC value is taken to indicate that no light is incident on the cavity, and hence the autolocker should turn off the PID loop and then do nothing
• cavityReflThreshold: 4 V; this is the value above which the RFPD REFL DC value is taken to indicate that light is incident on the cavity, but the cavity is unlocked, and hence the autolocker should try locking
• pmcThreshold: 150 ADC units; this is the value above which the PMC is considered locked, and hence the refcav autolocker may proceed with its lock procedure. (Note: this is different than the threshold values used in the PMC autolocker.)

The autolocker can be invoked via python srefcavauto.py on controls@fb2.

Since autolocker is coded to do nothing unless the PMC transmission is high, it is best run in conjunction with the PMC autolocker (invoked via python pmcauto.py). It doesn't matter which autolocker you start first.

Special bonus settings: the common gain on the TTFSS is 404 clicks, the fast gain is 426 clicks, and the offset is 967 clicks. Tara pointed out that the frequency loop would catch lock easier if the gain settings were around these low values rather that what they were previously (~600).

1185   Tue May 28 18:23:48 2013 EvanDailyProgressElectronics EquipmentAdjusted TTFSS offset; plugged RFPD DC into daq

The common error signal on the TTFSS has a 5 mV offset, which was causing the loop to catch on the edge of the error signal, near the sideband. I've adjusted the offset pot on the TTFSS interface board from 502 to 960 to remove this offset, and the loop now catches only on the carrier.

Also, I've taken the DC path from the south cavity RFPD and plugged it into an SR560 with gain 10 and then into C3:PSL-RCAV_FMON. This is temporary, and I've done it so that I can remotely lock the south cavity more easily for the gyro beat measurement. With the gain of the SR560, refl on resonance is about 2 V at minimum.

1184   Tue May 28 11:14:17 2013 EvanDailyProgressPMCPMC autolocker

After studying Zach's bash autolocker for the ATF PMC, I've written a python autolocker for the CTN PMC. This one is much simpler and just walks the PZT voltage downward until it sees the transmission PD go high. If the PZT hits 0 V, the autolocker puts it up at 300 V and continues walking downward.

The script is in the controls home directory on fb2 and can be invoked via python pmcauto.py

1183   Fri May 24 23:57:27 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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.

Attachment 4: 52lay.fig
Attachment 5: 54Lay.fig
Attachment 6: 56lay2.fig
1182   Fri May 24 18:33:07 2013 EvanDailyProgressPMCIs something wrong with the PMC PZT?

The CTN PMC has a troublingly low range on its PZT; it can't even cover a single FSR when driven from 0 to 300 V. So I wanted to see if the HV supply is really delivering what it says it is.

I unplugged the HV BNC from the PMC and plugged it into a voltmeter. I got good agreement between the nominal voltage as reported by C3:PSL-PMC_PZT and the actual voltage as read out on the voltmeter. 0 V is 0V, 50 V is 50V, 300 V is 300 V, etc.

Then I put the voltmeter in parallel with the PMC PZT. The relationship between nominal voltage and actual voltage is shown below. Evidently the PZT is not being held at nominal voltage. The presence/absence of the voltmeter does not affect the location of the PMC's modes (with respect to the nominal voltage), so this tells me that the voltmeter isn't skewing the measurement.

According to the ohmmeter, the resistance of the PZT (with the HV unplugged) is 800 kΩ, so there's no obvious short.

Attachment 1: pmc_pzt.pdf 1181   Fri May 24 04:04:58 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

 Quote: 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.

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.

1180   Wed May 22 00:04:48 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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.

1179   Tue May 21 19:52:18 2013 EvanDailyProgressComputersPMC MEDM screen on fb2

[Tara, Evan]

The south PMC can now be controlled on fb2 via C3PSL_PMC.adl.

1178   Tue May 21 01:06:43 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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 Sx(f)= ST (f) x (dTE + dTR).  See Evans etal Phys Rev D 78, 102003.  Where:

• ST (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

ST(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 ST(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.

1177   Wed May 15 20:07:12 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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. Attachment 2: TO_compare_cap.fig
1176   Tue May 14 02:06:15 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

[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, SdTTO = 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.

1175   Mon May 13 14:09:36 2013 ZachNotesDAQC2ATF model rebuilt
1174   Mon May 13 01:34:27 2013 EvanNotesPMCChoice of modulation frequency for PMC

The plots aren't right because I took the two-mirror mode spacing formula from Kogelnik and Li without applying the necessary modifications for a 3-ring cavity. The correct formula for mode (m,n) is $f_{mn} / f_\text{FSR} = (q+1) + (m + n + 1) \arccos(1-2L/R) / 2 \pi + \eta /2$, where $q$ is the axial mode number, $L$ is the half of the round-trip length, and $\eta$ is 1 if $m$ is odd and 0 if $m$ is even. (Note: for a 4-mirror cavity, $\eta$ is 0 always.) For reference, the K&L formula for a two-mirror cavity is $f_{mn} / f_\text{FSR} = (q+1) + (m + n + 1) \arccos(1 - L/R) / \pi$, where $L$ is half of the round trip length.

Instead of making more scatter plots, for each value of $g$ I computed the distance (in MHz) from the fundamental resonance to the nearest HOM resonance (up to order 20); the result is shown in the first attachment. I then picked the most promising $g$ factors and simulated a frequency sweep across a full FSR for a 3-mirror cavity with $L$ = 20 cm and $F \simeq 300$; the results are in the second and third attachments. Each mode is labeled with its order number, as well as 'e' or 'o' depending on whether $m$ is even or odd. I picked a arbitrary uniform amplitude for the HOMs, so these plots are only meant to indicate the locations and widths of the resonances. I've spot checked these plots against a Finesse model, so I'm reasonably confident that I've got the formula right this time.

I think the moral here is that the nearest HOM resonance is going to be about 16 MHz away from the fundamental, assuming $L$ = 20 cm. If we make $L$ = 10 cm, we can get to 32 MHz, but (depending on how bad the intensity noise at 30 to 50 MHz is) this potentially requires increasing the finesse to something like 600 to get the required intensity filtering.

If we go with a 4-mirror cavity, the modes don't have this $\eta$ degeneracy breaking, and there are $g$ factors for which the nearest HOM resonance is more like 30 MHz for $L$ = 20 cm. I have plots for this, but I want to check them against a Finesse model.

Attachment 1: minDetPlot3mirror.pdf Attachment 2: fsrSweep3a.pdf Attachment 3: fsrSweep3b.pdf 1173   Fri May 10 01:24:01 2013 taraNotesTempCtrltemp sensor on heat shields

AD590s on both thermal shields are not working. I was wrong when I checked them at the first time.

The temp sensors in the vacuum tank for monitoring temperature on heat shields are wired as shown in the picture. The resistor,R, is 30k ohms. According the the datasheet, the current from AD590 should be ~ 300uA, (30kx300uA = 9V). But what I read from the voltage across the readout R was 20V which was over the input range of EPICS (+/-10V). This happened on both of them. I compared the readout with a left over AD590, and got ~ 9.3 V readout which was expected at room temp.

At first I thought it might still be working linearly and useable if I just switched to lower R. However, with R=12 k, the readout voltage was 18V (I expected 20x(12/30) =8V). So certainly, this is not working.

I think the reasons they are broken is that they were overheated when I soldered them. I tried to be careful, but, apparently, that was not enough.

I'll check if there are spare AD590s in the lab or not, otherwise I'll order some more.

1172   Wed May 8 01:11:09 2013 taraNotesDAQslow feedback to laser via EPICS is on

Slow feedback for 2nd laser is ready.

EPICs channel:

• C3:PSL-RCAV-FMON was created for fast mon to laser.
• C3:PSL-RCAV_SLOWOUT was created for SLOW feedback. The channel was originally named C3:PSL-FSS_VCOMODLEVEL J9 input 11 and 12, VMIVME-4116, C2 S4.

The output of EPICS channels have capacitors installed in parallel for low pass filter.

1171   Mon May 6 17:08:25 2013 Matt A.NotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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.

1170   Mon May 6 03:11:44 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

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.

1169   Thu May 2 23:40:46 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

I used GWINC code to calculate TO noise in AlGaAs coatings, with some modifications to the code I can get the result that is comparable to Cole etal's result. However, there seems to be some minor details that I have to check. The half wave cap solutions for TO cancellation is not verified by the current calculation yet.

What I modified and checked in the code:

• The variable called thermaldiffusivity in the code is actually treated as thermal conductivity in the calculation, so all calculations in the past are still correct.
• The layer structure in the code was originally for Ta2O5/SiO2. The first layer started with SiO2 (low index material,nL), and ended with Ta2O5(high index material,nH) at the substrate surface. However, the AlGaAs coatings start with nH and ends with nH. I changed the calculation for effective thermal expansion accordingly. With the correct layer structure and materials parameters from Matt, the TO nosie is closer to JILA's result. However, the shape is still not the same, what reported in JILA is almost flat across 1-100 Hz. The calculated transmission from the layers is 1.8 ppm, but the paper says 4ppm. I'm looking into this.  Above figures: top plot is the result from GWINC. Its title should be Al0.92Ga0.08As coatings, not SiO2/Ta2O5, bottom picture is taken from Cole, etal. TO noise crosses coating brownian noise around 3 Hz for both plots, however the slope is very different. NOTE: the y axes are in Hz^2 / Hz.

As a quick check for the proposed half wavelength cap solution to reduce TO noise, I modified the layer structure and computed TO noise. Since they did not mention what kind of material for the cap I tried:

1. 81 layers, starts with nH, ends with nH, the first layer is 0.5 lambda thick. This is not working. 2. 82 layers, starts wit half wave nL, followed by the original 81 layers. This also does not work. Both cases have comparable TO noise, but transmissions are different. I'll check their formula and GWINC to see where the differences are.

 Quote: [matt, tara] Got AlxGa1-xAs material parameters from Matt Abernathy. I plug the numbers (all in SI) in GWINC, but the result is still not quite similar to that in Cole etal paper.  ioffe has materials parameters for TO noise calculation. Specific heat: 0.33+0.12x J/gK  Mass density rho = 5.3165-1.5875x g/cm^3 Thermal conductivity,kappa: 0.55-2.12x+2.48x^2 W/cmK  (There is also thermal diffusivity = kapp/(rho*specific heat) [m^2/s]. The results are the same) Thermal Expansion: (5.73-0.53x)·10-6/K dn/dT: 3.66-2.03x *10^-4/K This is from a paper, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities", by Talghader and Smith. Keep in mind that this paper has an important Erratum if you want use values from it. Unfortunately, this paper measures dn/dT at a max wavelength of 1030nm, so it's not quite accurate, but probably good enough. Note: One of the variables in GWINC code is ThermalDiffusivity. But the numbers used in previous TO plot is thermal conductivity of materials. I'll check the TO calculation codes and see if it is just a naming error, or the calculation is actually wrong.

Attachment 3: RefCav_TOnoise.png Attachment 5: RefCav_AlGaAs_TOnoise.png 1168   Thu May 2 03:03:48 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

[matt, tara] Got AlxGa1-xAs material parameters from Matt Abernathy. I plug the numbers (all in SI) in GWINC, but the result is still not quite similar to that in Cole etal paper.

ioffe has materials parameters for TO noise calculation.

Specific heat: 0.33+0.12x J/gK
Mass density rho = 5.3165-1.5875x g/cm^3
Thermal conductivity,kappa: 0.55-2.12x+2.48x^2 W/cmK  (There is also thermal diffusivity = kapp/(rho*specific heat) [m^2/s]. The results are the same)
Thermal Expansion: (5.73-0.53x)·10-6/K

dn/dT: 3.66-2.03x *10^-4/K
This is from a paper, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities", by Talghader and Smith. Keep in mind that this paper has an important Erratum if you want use values from it.
Unfortunately, this paper measures dn/dT at a max wavelength of 1030nm, so it's not quite accurate, but probably good enough.

Note:

One of the variables in GWINC code is ThermalDiffusivity. But the numbers used in previous TO plot is thermal conductivity of materials. I'll check the TO calculation codes and see if it is just a naming error, or the calculation is actually wrong.

1167   Wed May 1 15:28:06 2013 not ZachNotesPMCDebra matrix for PMC design

Quote:

I can't take it anymore: what the $#@& is a Debra matrix??  Quote: Considerations for PMC design is corrected and updated This is what I understand from Eric's explanation. It is just a table, on the first column of each row, you put in various designs. On the first row of each column you put in design consideration. Each matrix mij element tells you if the design i satisfies issue j or not. The best design satisfy most requirements, and it will be easy to see. For PMC design, I put the value from each design in each matrix element. I'll change font color to blue to show if the number in the matrix element satisfy our condition. 1166 Wed May 1 11:57:02 2013 ZachNotesPMCDebra matrix for PMC design I can't take it anymore: what the$#@& is a Debra matrix??

 Quote: Considerations for PMC design is corrected and updated

1165   Wed May 1 01:45:55 2013 taraNotesPMCDebra matrix for PMC design

Considerations for PMC design is corrected and updated

1164   Tue Apr 30 18:01:41 2013 EvanDailyProgressPDCTN power meter now set to 1064 nm

The CTN ThorLabs power meter had been set on 635 nm, possibly for quite some time (e.g. this post from April 11 uses this setting). I've now set it back to 1064 nm.

It looks like measurements taken on the 635-nm setting overestimate the power of 1064-nm light by a factor of 5 or so.

1163   Tue Apr 30 01:15:26 2013 taraNotesNoiseBudgetAlAs/GaAs layer structure optimized for TO

I'm computing  coating Brownian and thermo optic noise (TO)  in AlGaAs coatings using GWINC code to compare it with the result reported by G Cole etal. Brownian noise from my result is similar to theirs, but TO noise is still not correct.  I'm working on it.

==Background==

We have talked about what kind optimizations should we go for AlGaAs coatings in order to minimize TO noise. There are two choices for us to consider

1. using the layer structure as proposed in T1200003, or
2.  adding a half wavelength cap on top of the quarter wave stack coatings as suggested by the authors.

Since the second option is more desirable in terms of manufacturing because of its simplicity, I decided to check if it really can  bring TO noise below coating Brownian noise. If it is true, we can use it for our mirrors.

==calculation==

• I use GWINC code for TO noise and brownian noise calculations to verify the result if they are agree or not.
• Materials parameters used in the calculation are taken from the paper. But most of the coatings material properties of an individual layer of AlxGa1-xAs are not provided. There are only the average values of thermal expansion, heat capacity, thermal conductivity, dn/dT.  There are refractive indices (nh/nl = 3.48/2.977) and layer structure (81 layers, starts with nh, ends with nh). So, as a start, the values for high index material and low index material are the same as the averaged values.

==result==

• My Coating thermal noise level is 8.4*10^-35 m^2/Hz while their result is 9.8 *10^-35 m^2/Hz, @ 1Hz. This is not very bad, since there are some differences in the formulas between GWINC and their calcualtion.
• However, my TO is off the roof, almost 2 orders of magnitude above their result. I'm checking if it is because of the code is wrong(typo in the parameters) or the fact that I used all the averaged values.

1162   Mon Apr 29 23:13:36 2013 EvanNotesPMCChoice of modulation frequency for PMC

 Quote: I computed the occurrence of higher-order modes up to order m + n = 20 as a function of g factor for a ring cavity. In the first set of plots of plots, I've fixed the cavity half-length L and chosen several values of modulation frequency fPDH. In the second set of plots, I've fixed fPDH and chosen several values of L. Green is the carrier, red is the lower sideband, and blue is the upper sideband. The takeaway messages from these plots are that there are two or three "best" regions to place g: near 0.06, near 0.46, or near 0.54 (although 0.06 is sort of close to instability); the locations of these regions are independent of the modulation frequency, at least for the frequency range we are interested in; and a lower modulation frequency widens these best regions. So I think we should go for as low a crystal frequency as possible that is consistent with having shot-noise limited intensity and a high loop speed. I know the number 20 MHz has been thrown around as the lowest reasonable PDH frequency, but I don't understand quantitatively why this is.

This and some other PMC design issues are now in the SVN trunk under docs/modecleaner_design/

1161   Mon Apr 29 09:17:20 2013 EvanNotesPMCChoice of modulation frequency for PMC

I computed the occurrence of higher-order modes up to order m + n = 20 as a function of g factor for a ring cavity.

In the first set of plots of plots, I've fixed the cavity half-length L and chosen several values of modulation frequency fPDH. In the second set of plots, I've fixed fPDH and chosen several values of L. Green is the carrier, red is the lower sideband, and blue is the upper sideband. The takeaway messages from these plots are that

1. there are two or three "best" regions to place g: near 0.06, near 0.46, or near 0.54 (although 0.06 is sort of close to instability);
2. the locations of these regions are independent of the modulation frequency, at least for the frequency range we are interested in; and
3. a lower modulation frequency widens these best regions.

So I think we should go for as low a crystal frequency as possible that is consistent with having shot-noise limited intensity and a high loop speed. I know the number 20 MHz has been thrown around as the lowest reasonable PDH frequency, but I don't understand quantitatively why this is.

Attachment 1: hom_vary_fpdh.png Attachment 2: hom_vary_L.png 1160   Thu Apr 25 20:53:13 2013 EvanDailyProgressLaserLightwave RF intensity noise for PMC design

I tried getting the relative gain between the AC and DC paths of the New Focus 1811, essentially repeating the measurement in elog #1152 but (a) taking measurements for both the DC and AC paths and (b) taking measurements in the region 10 kHz to 100 kHz, where the DC and AC bands overlap. According to the manual, the DC path is meant to be used up to 50 kHz, and the AC path is meant to be used down to 25 kHz.

I again had roughly 1 mW of light on the PD. I took spectra with the Agilent 4395A, which has 50 Ω input impedance. For the AC path, I took the spectra in W/Hz and multiplied by 50 Ω, giving a spectrum in V/rtHz referenced to the input of the spectrum analyzer. For the DC path, I took the spectra in W/Hz, multiplied by 50 Ω, took the square root, and then multiplied by 40/(2*0.82) = 24. The factor of 40 is the value given in the manual for the relative gain between the AC and DC paths, the factor of 2 accounts for the 50 Ω output impedance of the AC path, and the factor of 0.82 accounts for the apparent 11 Ω output impedance of the DC path. (The DC voltage out of the PD was 0.66 V when fed directly into the 1 MΩ input of the scope, but dropped to 0.54 V after I inserted a 50 Ω feedthrough; the quotient of these two numbers is 0.82 and this implies that the DC path has an 11 Ω output impedance). If the relative gain value (40) as given in the manual is correct, the DC and AC spectra should overlap so long as they are dominated by intensity noise rather than detector noise.

The first plot shows the AC and DC spectra, both light and dark. The intensity noise is not as dominant over the detector noise as I had hoped. Still, in the second plot I've quadrature subtracted the dark spectra from the light spectra to produce what are in principle the spectra of the photocurrent alone. Even with the caveat that certain bins in these spectra are dominated by detector noise, it appears that the spectra don't even have the same shape. My guess is that we may already be seeing the action of the high-pass rolloff on the AC path.

It might be worth having another go at this measurement with a higher photocurrent, but I'm guessing that this isn't a great way to get the relative gain calibration.

Attachment 1: intensity1.pdf Attachment 2: intensity2.pdf 1159   Thu Apr 25 10:57:52 2013 taraNotesPurchasesPomona BNC cable

I plan to order RG58 bnc cables from Pomona, here is a list of what I need

catalog

1. Cables for Fast monitor (from TTFSS to electronic shelf) (~15ft , x2)
2. For slow feedback (from the shelf to the laser controllers) (~20ft x2)
3. For EOM temp control feedback (I'm not sure where the nim crate will be, this will be decided soon).
1158   Tue Apr 23 22:28:53 2013 taraNotesTempCtrltemp sensor on heat shields

I checked both temp sensors on the heat shields. They are working. I can see the change in resistance when I the heater is on. It seems to be a wiring problem. I'm investigating it.

1157   Tue Apr 23 18:43:39 2013 taraDailyProgressRefCavHOM for new sideband frequencies

35.5 MHz and 38MHz sideband frequencies are chosen for  1.45 " refcav. These frequencies will be suitable for cavities formed by 0.5/0.5m RoC mirrors and 1.0/1.0m RoC mirrors.

a) For0.5m/0.5m RoC mirrors 1.45" cavity, f1 = 35.5MHz.           b) For0.5m/0.5m RoC mirrors 1.45" cavity, f2 = 38MHz  c) For 1m/1m RoC mirrors 1.45" cavity, f1 = 35.5MHz                d) For 1m/1m RoC mirrors 1.45" cavity, f2 = 38MHz

Since we will use a crystal oscillator to drive the EOMs, I have to check how much power we need for the sideband.

If the crystal oscillator can provide us with enough power, we can use the crystal to drive a broadband EOM directly. Otherwise we will need an EOM driver, or a resonant EOM.

==shot noise level vs mod index(Beta)== To see how much should the mod index be, I plot shot noise level vs Beta, with Power intpu = 1mW and 2 mW, and Finesse = 1e5 (for  T=300 ppm mirrors)and 2e5 (For AlAs/GaAs coatings), with mode match = 80%. It seems that for the lowest shot noise level, we need beta = 0.8.

For resonant EOM, mod depth = 0.2 rad/V, for BB EOM, mode depth = 15mrad/V , see psl:745.  These correspond to 4V (25dBm) and 53 V (47dBm) for the resonant and BB EOMs, respectively.

1156   Mon Apr 22 18:21:58 2013 ranaDailyProgressLaserLightwave RF intensity noise for PMC design

Some interesting papers on the intensity noise in NPROs (Ingo Freitag is an author on both):

From Roland Schilling: Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser

1155   Mon Apr 22 17:13:24 2013 taraNotesDAQslow feedback to laser via EPICS is on

The medm screen for the 1st laser is completed, the servo is on an stable. Refcav has been locked for a few hours as of now.

• The output for slow feedback is on J9, slot 9/10 (VMIVME 4116 C2 S3). This is an unused channel previously assigned to PSL-ISS_ISET, I checked ISS.db file to look for the VMIVME address. For the slot number, I look up the channel name in D980535-C-C document.
• I added low pass filters (~100mHz) to both input and outputs of EPICS.
• All EPICS channels for slow feedback and perl scripts are in SLOW_LASER.db file.
• The startup.cmd file is updated accordingly.
• servo gain is optimized. ??? What does that mean??? How about some performance plots? (About the bode plot, I'm trying to get a transfer function of the NPRO slow input, with that I can estimate the bode plot of the loop. As of now I just adjust the PID gain so that the loop is stable) fig1: FAST feedback to the laser is shown in blue plot, vertical axis:1V/div, horizontal axis:  4 sec/ div. I adjusted proportional gain first, to get only a few overshoots with acceptable rise time. fig2: Then I adjusted integral gain to eliminate the offset, and Derivative gain to reduce overshoot. More about PID gain can be found here. Current Value KP = -0.0002, KI =-0.00015, KD = 0.

I set the output to be between -2 V to 9 V. Since we need to lock it to GYRO later, it has to be able to be tuned to match the gyro laser. Currently, Gyro laser is operated around 35 Deg C which is similar to 8V input to slow feedback.

I'm trying to draw a cartoon for DAQ wiring in CTN lab for future reference. This is what I have so far. I'll add it in WIKI page. 1154   Mon Apr 22 02:25:58 2013 ChloeDailyProgressECDLECDL Grating/Current Controller

Grating choices:

In the literature, people seem to use 1800/mm spacing. Attached are efficiency graphs found on Thorlabs for 1200/mm and 1800/mm spacing. At 1064nm (which is where we are interested in tuning to), the efficiency drops off for the 1800/mm spacing grating. This could be fixed if we use an angle close to perpendicular, or we may be better off using the 1200/mm grating, which has an average efficiency of about 35% at 1064nm, vs an average of 20% for the 1800/mm grating. It is a question of efficiency vs. resolution.

Current Controller:

We are currently examining a current controller designed by Libbrecht and Hall (1993), since it has been shown to have lower noise than before. There is a commercially available controller based on the design from their paper (http://www.vescent.com/products/electronics/d2-105-laser-controller/). I did some literature search and it seems that there was a design by Erickson (2008) which is an improvement on the design by Libbrecht and Hall. This paper is attached... we may try to use this design instead. Tara and I will meet on Thursday to determine if the requirements we want to have on our experiment to have low noise, and then choose whether to pursue the Erickson controller further.

Attachment 1: 1200mm_grating.PNG Attachment 2: 1800mm_grating.PNG Attachment 3: Erickson08au.pdf        1152   Sat Apr 20 13:41:36 2013 EvanDailyProgressLaserLightwave RF intensity noise for PMC design

Yesterday I used the CTN network analyzer to look at the RF spectrum of a 1.0 mW beam from the ATF Lightwave with a New Focus 1811. This beam is picked off from the main ATF laser beam pretty much immediately after the laser head; there are some waveplates, PBSs, and lenses, but no EOMs or modecleaners. The laser was free-running, with nothing plugged into the temperature or frequency BNCs.

In addition to the spectrum of the beam intensity, I took a spectrum with the beam blocked to get a measurement of the dark current. In the plots below, I've referenced everything to the current through the diode. This means taking the W/Hz spectrum from the network analyzer, multiplying by 50 Ω and taking the square root to get the V/rtHz across the analyzer's internal 50 Ω resistor, then multiplying by 2 to get the V/rtHz put out by the 1811 (since its output impedance is 50 Ω), then dividing by the 4×104 V/A figure given in the 1811 manual to get the A/rtHz across the diode. To get the 'expected photocurrent shot noise' given below, I watched the DC output of the 1811, which was at 680 mV with the 1.0 mW beam and 10 mV dark. So I divided 670 mV by the 1 V/mA figure given in the manual to get the DC photocurrent. The shot noise of this photocurrent is then sqrt(2eI). I haven't measured any of these 1811 conversion factors, so I don't have complete confidence in this shot noise value. However, the value for the DC current agrees roughly with what you get if you take the power measured with the ThorLabs meter (1.0 mW) and multiply by the quantum efficiency (0.7).

You can see in the first plot that the dark current is subdominant to the photocurrent all the way out to 100 MHz, and subdominant to the expected shot noise out to maybe 40 MHz or so. In the second plot I've taken the quadrature subtraction of the blue trace from the red trace to get an estimate of the photocurrent noise alone. The spectrum looks approximately white from 10 MHz out to 50 MHz and (if you at all believe the shot noise value) is about 1.7 times the shot noise. If this truly is the level of the excess noise, then to get excess intensity noise whose PSD is equal to 1% of the shot noise PSD at 20 MHz, we'll need a cavity pole at 5.6 MHz. If the calibration is spectacularly off and the total noise is 20 times the shot noise, we'd need at cavity pole at 1.4 MHz to get the excess intensity noise PSD to be 1% of the shot noise PSD at 20 MHz. The way I've arrived at this is as follows: if S(f) denotes the value of the linear spectral density at f relative to shot noise (f = 20 MHz and S(20 MHz) = 1.7 in this case), then and so the suppression of the excess noise after transmission through a modecleaner is and from this f_HWHM can be chosen to give the desired amount of suppression. Edit: actually, the right way to do this is to write the excess noise PSD as a relative intensity noise (which scales as P2), and to then compute the desired amount of suppression for the maximum amount of power we're going to send through the PMC (2 W or so). Computing the suppression relative to shot noise for a 1 mW beam is not sufficient, because the suppression requirement gets more stringent as the power increases. The RIN here at 20 MHz is 3×10-8 /rtHz, and so for 2 W beam we require a cavity pole of 420 kHz to get a factor of 100 suppression below shot noise.

I think to do this measurement properly I'll need to get a better handle on the relative calibration of the DC and RF transimpedance gains of the 1811. It might also be nice to take a measurement both before and after an existing PMC, just to see the expected filtering effect.

Attachment 1: intensitynoise_1.pdf Attachment 2: intensitynoise_2.pdf 1151   Thu Apr 18 19:54:01 2013 taraNotesDAQEPICS channel for slow feedback to laser

I created a channel for feedback to slow DC to the laser head. The servo will be done digitally using a perl script similar to what we have for the vacuum can.

There are unused channels for temperature monitor, so I modify them for FAST MON instead.

In the database file "cavities.db" in the sun machine, I changed [C3:PSL-BOX_SENS1] to [C3:PSL-ACAV_FMON]. For input +/- 10 V.

The next thing is to create perl scripts for the servos. Then find an output channel for feeding back to the laser.

I made an medm screen for controlling the slow feedback signals to both lasers. Channels that will be created are:

input

• C3:PSL-ACAV_FMON

soft channels

• C3:PSL-ACAV_PID_KP
• C3:PSL-ACAV_PID_KI
• C3:PSL-ACAV_PID_KD

output

• C3:PSL-ACAV_SLOWOUT
1150   Tue Apr 16 13:24:46 2013 EvanNotesPMCDebra matrix for PMC design

For a 3-mirror cavity with a single curved mirror, the g-factor is (1-p/R)^2; there is no factor of 2 in the denominator because for a ring cavity the overall cavity length is equal to the round-trip length.

Also, I think we should shoot for a transmission of at least 90%. If this is going to be for general lab use, then there will probably be situations where people want a good power throughput. The input power might be as high as 2 W if used, e.g., at the 40m with one of those Innolight Mephistos.

1149   Mon Apr 15 10:59:35 2013 taraNotesPMCDebra matrix for PMC design

 Quote: Considerations for PMC design: Stiffness(Acoustic susceptibility) & heavy material: With heavier material, the pmc motion on the support becomes smaller.(RXA: please quantify with a formula) Filtering factor (Finesse/FSR/Cavity pole), g-factor: Filter out intensity noise around 10 MHz (RXA: please quantify with a formula) Design for thermal expansion cancellation between the spacer and the end cap: So that the PMC is less sensitive to ambient temperature  3 or 4 mirrors?  3 is polarization selective. For general lab use with power less than 1 W,  3 mirror design should be good. (RXA: I don't follow this logic at all) RXA: In general, all of these considerations need some sort of quantitative detail. Make a DeBra Matrix so that we can evaluate.

Some requirements for the PMC:

==Cavity pole==

For intensity filtering. The modulation frequencies for the refcavs is ~ 15-25 MHz, we want the intensity fluctuation at this frequency to be shot noise limited.  We have to determine what should be the frequency pole. Intensity noise around 1MHz - 30MHz will be ~ 1/f^2, see the paper by Harb etal, eq1 and fig9, get the paper from psl:1156. Under the assumption that RIN remains constant, at 20MHz the laser will already by shot noise limited (@ 1mW input).  laser intensity noise / shot noise ~ 0.16. (laser intensity noise here means intensity noise from spontaneous emission/ pump-source intensity noise/ dipole fluctuation noise/ noise from intra cavity losses, any thing except shot noise) Thie pole can change with the cavity length and Finesse, [ Finesse = FSR/(2*cavity Pole)] , so our choices for mirror reflectivity, cavity length will affect this number as well. So for a fixed set of mirrors (fixed finesse), longer perimeter means lower cavity pole, but the cavity will be more susceptible to acoustic coupling.

==First longitudinal body mode==

It should be at high frequency ( for high UGF servo). The shorter the length, the higher the frequency. See PSL:1134.

== g-factor==

For a stable cavity, g factor has to be between 0 and 1.  Another reason: We should choose g-factor such that HOMs do not coincide with other cavity axial modes (FSR apart). For a ring cavity with 2 curve mirror R1,and R2, g = (1- p/R1) x (1 - p/R2) where p is the round trip length. (For 3-mirror cavity, g = (1 - p/(R))^2 . See HOM calculation.

==Stiffness==

we want a solid, bulk shape PMC, not thin long one. This will make the PMC less susceptible to acoustic noise.

==Higher order mode suppression==

Other transverse modes will be suppressed by a factor of (1-r)^2 / (1 +r^2 -2rcos(2*pi* dfmn/ FSR)  where dfmn is the gouy phase shift of m+n mode, r =r1*r2*r3.. (reflectivity of each mirror in the cavity) see evan's note. Transverse modes of the output of the NPRO can be found by scanning the PMC and measure the transmitted beam. Other modes beside TEM00, will be reflected back from the refcav and incident on the RFPD. This will cause the mode mismatch and increase shot noise level. Usually, higher r (higher Finesse), will suppress more HOMs.

==Build up power==:

= Pin x Finesse/ pi. CVI mirrorsfor high damage threshold power have maximum power for cw around 10MW/cm2. So I use this number as an upper limit for the power threshold. Assuming the power input is ~ 30 mW, average spotsize is 350 um. This gives ~ 8W/cm2. So Finesse can be up to ~ 3e6.  (10 MW/cm2 > (Finesse/pi) x 8 W/cm2) .

Some assumptions:

• Losses(scatter/absorption) on each mirror is ~ 100 ppm. It seems that a super polished mirrors in vacuum has ~ 10 ppm loss. This comes from a Finesse measurement of the previous 8" refcavs, see psl:1046. The calculation shows that loss in one cavity is 25 ppm (for 2 mirrors), and 160ppm for another cavity. Since the PMC mirrors will be in air, and probably not as good as refcav mirrors, dust in air might accumulate over time and causes extra loss on the mirrors, 100 ppm loss assumption might be ok for this calculation.
• PZT range is about 15um @1000V, as shown in the catalog, see PSL 1052 for the details, (we can drive it with ~0-300 V, so ~ 4um displacement),see PSL:1052

Let's see some of the designs that are available. Then we can decide which one we should modify to suit our requirement.

1. Design1 iLIGO PMC: Isosceles triangular PMC, fused silica, perimeter = 0.42m, flat-curve (1m ROC)-flat mirrors. Round Trip = 0.42m See T-080195,here (it says the pole is 7 MHz).
2. Design2 (Dmass' PMC): stainless steel PMC, perimeter =0.4m , same mirrors as those of design1, so its finesse is the same.
3. Design3, AdvLIGO PMC style (4 mirrors, bow-tie): stainless steel (see PSL:)
 Cavity pole /FSR/ Finesse g-factor Stiffness 1st Longitudinal body mode Approximate dimension(height x width  x length) Note Design1 cav pole = 7MHz / FSR=714MHz / Finesse =50 0.34 14 kHz 2" x 2.4" x 7.1" The values are for p-pol, waist radius = 370um. Design2 cav pole =  9MHz  /FSR = 925MHz / Finesse = 50 0.46 16.6kHz [PSL:1134] 2 x 2.6 x 6 assuming similar mirrors from design 1, w0 = 353 um. Design3

Attachment 1: laser_rin.jpg 1148   Sun Apr 14 23:35:03 2013 EvanNotesPMCPMC eigenfrequencies, now with endcap

I added an endcap to Tara's steel PMC Comsol model and looked at the eigenmoedes for a 3-point contact. The lowest mode is a rolling mode at 2.0 kHz, followed by other modes at 3.0 kHz and 3.5 kHz. The first longitudinal stretching mode is at 16 kHz. The rectangular part of the spacer for this steel PMC has dimensions 5" x 2.6 " x 2" and a cavity length of 32 cm (first picture).

I also looked at a beefed up version of the spacer, with dimensions 10" x 4.6" x 2" and a cavity length of 78 cm (second picture). The lowest mode is again a rolling mode at 1.4 kHz, followed by other modes at 2.0 kHz, 2.2 kHz, and so on. The first longitudinal stretching mode is at 9.0 kHz. So it looks like if we want a longer cavity, we can almost double two of the spacer dimensions without shifting the resonances down significantly.

If we use a 10" x 4.6" x 2" spacer but go with a 4-mirror bow-tie design (third picture), we can get something closer to a 1.1 m cavity length. Comsol gives a lowest mode at 1.4 kHz, followed by modes at 2.4 kHz, 2.6 kHz, etc.

Attachment 1: pmc_3pt.jpg Attachment 2: big_pmc_3pt.jpg Attachment 3: 4mirror_pmc_3pt.jpg 1147   Sun Apr 14 16:51:21 2013 ranaHowToTempCtrlestimated beat frequency

No, both have to be stabilized to reduce the control signals sent to the lasers.

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