I vented the vacuum chamber and forgot to turn of the ion pump. It was on for ~ 5-10 minutes. I'm not sure if it is broken or not. I talked to Alastair and he said the metal plate might be contaminated and needed to be repair. I'll keep this in mind and see what happen when I pump down the chamber.

Thermal shields and caps are ready. I cleaned them in ultra sonic bath with Isopropanol. They fit nicely to the mount.

The caps are teflon.

==Wire Heater==

I'm think about how to wire the heater around the cavity. I'm reading Frank's entries in PSL:765,768 ,776,786, . Seems like I might need to drill a few holes on the shields for the wires.  There are still more similar wire left. I'll calculate how long the wire has to be for heating the cavity up by 20 K.

Now that the layout is ok and the table is cleared, the next thing to do is open the chamber. The plan for this week will be:

==Cavities & Vac chamber==

1. clear the clean bench
2. Prepare all parts  for the new cavities that will go to the chamber. The assembly for the new cavities is almost done, I'm wating for the caps of the thermal shield.
3. Open the chamber, remove the 8" cavities.
4. Change the heaters/ thermometers. Currently, the feedthrough for the chamber is 9-pin. It is for 3 thermometer and 1 heater. The new setup will need 2 thermometers, 2 heaters. I don't know what kind of wire and where it is in the lab yet. This need to be checked.
5. Once the sensors/heaters are installed, we can close the chamber and start the mode matching.

==1st laser==

1.  The setup for the first laser should be easy. The setup from the laser to the PMC is not changed much except the BB eom for locking. I should be able to lock the first cavity soon

==2nd laser==

1. Need to think about the PMC
2. The EOM

The new optic layout is done. There are some changes from the previous version.

Some notes and concerns about the new layout:

• I made sure that the beam size in all EOMs, EAOMs are in the right size (diameter ~ 250 - 500 um) to avoid any clipping/ diffraction.
• Due to the small waist size of the new cavities and the long path between the cavity and the vacuum window. The beamsize on the input optic is quite large (almost 3mm). I'll have to check if the beam spiltter is large enough.
• I assume that the beam size from the new PMC (the setup on the left) is 370um. It might change because the design for the PMC is not settled yet, but the spacer is enough for mode matching.
• I add a beam splitter in the setup just before the vacuum window. This can be used for RFAM pickup or fiber distribution. It can be done in the future.
• a set of flip mirrors are added, for scanning two cavities with one laser. The mode match should be good enough to get TEM00 in the 2nd cavity.

Some notes about external cavity diode laser. I investigated in this about a year ago.  I think it might be a good time to work on it, since I'm modifying the  ctn layout and we can use a frequency stabilized laser (although locked to a short cavity) via fiber optic to test with a home made ecdl. 

 The tentative plan is shown below. I also move the BB eom for locking frequency(phase) next to the laser.

• The pick up for fiber distribution can be at the PBS just after the PMC where we dump the power. However the laser is not intensity stabilized yet, but I'll worry about it later.
• I add pick up for RFAM monitor. It is the unused beam after the EAOM. The power will fluctuate when ISS is active, but should be fine for RFAM monitoring purpose.

I'm doing mode matching calculation to see if the lenses can be placed in the available area. Otherwise I need to fold the beam a few more times.

I also started removing the acoustic box, some optics on the table so that I can try to position the real optics to see if they can fit on the table.

Longitudinal Mode frequency @ 420 Hz

Monday, January 28, 2013

Tests of resonant frequency specifically for longitudinal mode done on PMC because the piezo will only affect this length.  Originally the PMC spacer was constrained in motion by clamps on the PMC base, as shown below.

 Data was taken with an oscilloscope and laser vibrometer - the B&K system was not functioning correctly - and the PMC spacer was excited by hitting it with a marker.  The PMC was hit near the endcap, along the long axis of the PMC, as shown in the below image.

The results in the time domain are shown below and indicate a resonant frequency of 450 Hz.  A next step is to fit this data to a decaying sine wave.

When the above clamps were loosened to allow for more motion, the frequency dropped to closer to 350 Hz.

I'm making a new layout for the 2 laser setup. It is in progress. I just want to make a note about some features I want to have in the setup.

• Move EAOM (for intensity stabilization,ISS) some where down stream, close to the chamber. Since the monitor is behind the cavity.
• Pick up for optical fiber: This should be somewhere behind 1)EAOM, so that power can be stabilized, 2) BB EOM, so that the laser frequency is stabilized at higher frequency as well. 
• Some beam splitter/ flip mirrors to bring laser to both cavities. so that I can scan two cavities with 1 laser at the same time. This should be handy when we need to find the beat, since the beat frequency is not well determined (by AOM) anymore.
• Some space for an independent frequency stabilized laser. This is for the future, when we want to lock a laser to the 8" cavity and distribute it to other labs.  From the current setup, I think we might have to borrow the laser from the 2-laser setup, after the PMC, then lock it to the 8" cavity. Installing 3 sets of laser, PMC, refcav on the table is not easy. With this idea, we can lock the laser to a low noise cavity(8"), and just change the cable, when we want to switch to do the coating measurement.

There is a pool of water in the lab. It is localized only around the floor near the fume hood. I'm not sure where it comes from,but it drips down from the edge of the sink where there is a small pool of water on it. I'll keep an eye on it. If there is still more leakage, I'll contact pma to take a look.

I did not see anything yesterday, so I guess the leak just started last night.

I updated the new task sheet for thermal noise probe experiment: 

The goal is to have the first beat measurement:

The plan for the upcoming week (Jan28) will be

1. finish the table layout
2. preparation for cavity installation (clear the table, opening the chamber, wire for heater). This means all the parts for in-vac use should be ready. I need to submit the thermal shield to the machine shop, and check some wiring for thermal sensing + heater.

I don't think the second PMC will be ready yet, I'll try to lock the second laser w/o the PMC first, and add PMC later.

For Feb4 week, I will

1. modify the RFPD PMC servo of the first loop. The current resonant EOMs (14.75 and 21.5 MHz will be used for refcav locking).
2. check the noise level of the current 21.5MHz RFPD as well (currently used for locking PMC) since it has not been done yet.   I'll try to modify the TTFSS box as well.
3. clean the table and make sure it ready for the new setup.

I ordered some clean supplies which will be used when I open the vacuum chamber for installing the short cavities.

• nonwoven wiper
• Needle for syringe, guage 23, style 2. (I ordered syringes before, but they didn't come with needles)
• Head cover

 Some of the items that might be needed

• copper ring seal for vac seal
•  .... (I'll write it down when something come to mind).

The EOM driver is working. For the same modulation depth, it can drive a broadband EOM using less power.

==measurement and result==

I used PMC setup to test this EOM driver because its frequency range is only ~21 - 24 MHz, and the sideband for locking PMC is 21.5 MHz. So what I did:

• Checked the performance of resonant EOM as a reference: Scanned the laser and measured the error signal, with resonant EOM. The input power to the EOM is 9 dBm (5.7 V on the RF power scale with phase shift = 3.297 + 180 degree phase flip). The error signal was 3.13 Vpk-pk.
• Replaced the resonant EOM with a BB EOM equipped with the driver. Re-aligned the beam to the PMC. (I turned down the input power to min before I connected the RF input to the driver).
• Scanned the laser again and increased the power until I got the same error signal. With the driver on BB EOM, the input power is reduced to -9.5 dBm (on the slider: 3.9V with 0.6707 phase shift, no phase flip) for the same error signal. So the board adds ~18.5 dBm.
• PMC cavity can be locked and stable.

   From the schematic, the board is supposed to have 30V output from 0.15 V output (x200). In dBm that will be 20log(200)~ 23dBm. So It is roughly ok.

fig1: BB EOM with the driver. One of the unused output is for output mon.

fig2: Error signal from scanning the laser, with BB eom and the driver, measured at mixer out.

==conclusion==

 The board is definitely working and will benefit us, definitely for locking PMC. If we use a marconi to drive a BB EOM, the max output is 13dBm. The power is halved (one to the EOM, one to the mixer). That means ~ 10dBm to the EOM (we will probably split more some where for RFAM pickup, but we can do that on the line that goes to the mixer), so assuming we have ~ 10dBm for the EOM. With the board it will be ~ 10+18.5 dBm = 28.5dBm (~6V) . It should give modulation depth of 0.09, see psl:745, This might not be enough for locking the refcav( see,psl:929. where we have beta of 0.18), but we can add another RF amplifer, or use the board for PMC servo . I'll check what are the appropriate modulation depth for locking PMC and refcav.

I clean the vented screws and peek pieces for cavity mount with ultra sonic bath, I'll check if I need to bake them or not.

I got an EOM driver from Rich Abbott, I'm checking if this thing works well or not.

The EOM driver is just an amplified resonant circuit with +/- 18V input. With the driver connected to a broadband (BB) EOM, we can use the combination to add sideband to the laser. This is better than a resonant EOM because we can pick a range of frequencies, instead of having a fixed one from the manufacturer.

 I checked the TF between input and the RF mon, the resonant peak can be moved between 20.7 MHz and 24.5 MHz by adjusting an inductor on the board. Since the RFPD for the PMC is 21.5 MHz, I'll use it to check the modulation index of a BB EOM equipped with this board.

The plan is 

1. Check the power vs modulation index from the current resonant EOM. To do this, scan the laser, measure the error signal.
2. Remove the resonant EOM, and replace it with a BB one, adjust the power, check the modulation index vs power input again

Once I verify this I will check the frequencies for refcavs and pmcs, so that I can decide the value of L and C on the board.

  We are interested in the longitudinal mode along the Y direction. That is the only one which is problematic for the servo. Please remeasure so that you excite Y and measure Y and then model the first longitudinal mode.

The other modes are interesting, but they're not the main thing we care about.

The PMC was tested & lowest resonant frequency was 330 Hz;  FEA model was adjusted to new frequency of 441 Hz

Results from December 18, 2012

The PMC in 058B W. Bridge was secured with several dog clamps to the laser table.  This table is not as stiff as the table in the Modal Lab in Downs, but was thought to be sufficient for this test.  Testing was done with the B&K system, using a laser vibrometer for the accelerometer and the small 8206 B&K hammer for excitation.  Below is a representation of the axis for this test, to understand where the PMC was excited and measured.

Measurements and excitations were approximately at the center of the corresponding face, as indicated in the image.

Below is a graph of the results of these measurements.  You can see that the lowest resonant frequency is at 330 Hz.

Next Steps:

Next I will update the ANSYS model to be more accurate, hopefully showing about 330 Hz as the lowest mode.

FEA Model in ANSYS:

Briefly: the previous model reported in the elog was changed by refining the mesh on the slots/cones and the bearings.  This would allow for that portion to behave more accurately.  The contacts were left as Program-controlled (any other control seemed to overestimate the contact, raising the predicted resonant frequencies). 

Below is an image of the lowest mode, at 441 Hz.  The arrow indicates the motion - the mode is roughly a transverse flagpole mode.

Now that the model has been made more accurate, steps can be taken to raise the resonant frequency. While the initial goal that was mentioned to me of 1kHz is improbable, there are certainly ways to raise the frequency and damp the modes that are problematic.

Kristen and Norna came to ATF for impact-hammering of the metal PMC in the gyro setup

LINK

 This does not look like a longitudinal mode. Do you have the frequency for the first longitudinal mode(along cavity length)? the first longitudinal mode should look like this ( this model has no fixed boundary condition, just a block in space).

[Peter, Tara], we assembled 2 short reference cavities today. The bonding between the spacers and mirrors are strong and holding the mirrors nicely.

 I got the cavity fixtures (made from delrin) from the machine shop today, so I asked Peter to help me assembling the cavities. All picture can be found here

• The mirrors are 1/4 stack SiO2, Ta2O5 T=300ppm, ROC =0.5m.
• Two spacers' serial numbers are 98 and 99.

I tested the bond by lifting the whole cavity by handling at the mirror on top only, and wiggling it a little bit. The bonds weren't broken. The hardest part was cleaning all surfaces to make sure that there was no dust.

From hindsight, I don't really need to see the fringes to do the bond. If the surface is clean, the pieces will be bonded instantly after a light pressure. If there are particles on the surface that cause fringes, the bond will not form anyway. So for Si cavity, Dmass can try to do optical contact without a setup to see the fringes.

fig1: the mirror is placed in position by the fixture. The mirror is not pressed on the spacer yet. Fringes can be seen on the polished ring on the mirror. See the video to see how the fringes vanish after applied pressure.

I made a simulation for PMC body mode, and found out that for Al PMC, the first body mode is 1kHz. And 780 Hz for stainless steel pmc.

November 27, 2012

 It is desirable for the first body mode of the PMC to be at or above 1000 Hz in order to provide consistent length for the cavity.

 ANSYS Summary

1. Geometry
   • For any given test, all parts of the assembly were changed to be the same material.  Materials tested include fused silica, aluminum, and stainless steel, and material will be specified per test.
2. Connections > Contacts
   • Most contacts determined by ANSYS were sufficient.  However, the contacts between the press-fit slots or cones and the ball bearings were adjusted for accuracy.  The "Pinball Region" was changed from "Program Controlled" to "Radius", and the radius set to between 0.1 and 0.3 meter.  This is to ensure that ANSYS recognizes these two objects are resting on each other.
3. Analysis Settings - Supports
   • The PMC assembly was modified so that the constraints could be more accurately modeled.  Split lines were added to the bottom of the PMC base to model the force applied by the dog clamps, and these small 0.5"x0.5" squares were defined as "Fixed Supports" in the ANSYS model.
   • The entire base was labeled as a frictionless support, because it is sitting on a table. 
4. Results
   • The first body mode when the PMC is made entirely out of stainless steel is 865Hz
   • The first body mode when the PMC is made entirely out of aluminum is 881Hz

Above you can see the first mode shape of the PMC.  The colors represent the displacement - deep blue indicates no motion, while red indicates the greatest amount of motion.  The animation of this mode shape shows the PMC spacer rocking transversely on the PMC base.  The PMC base does not move at all.

5. Changes to geometry (December 3rd, 2012)
   
   • Holes were cut through the PMC spacer to try to increase the first body mode frequency.  New geometry is shown in the figure below
   • 
   • There was no increase in the first body mode frequency - when made out of stainless steel, ANSYS reported the first body mode of this to be at 855 Hz

 One question that came up is whether ANSYS is importing the geometry file at the correct size.  According to the scale on the screen, it is the right size.  However, when the material is changed to resemble fused silica, the lowest body mode is 998 Hz, which is about an order of magnitude lower than expected.  This indicates some other error, possibly in importing the structure into ANSYS.

 /more to come

 I calculated brownian noise in AlAs/GaAs coatings, brownian noise and thermoelastic noise in fused silica substrate for different beam sizes. From the plot, we can see that a smaller spotsize might be better for us.

     This is a quick study to see the how spotsize on a mirror affects Brownian noise and thermoelastic noise in coatings and substrate. The radii of the beam (where the beam intensity drops by 1/e^2) used in the calculation are 91, 182, 364 um. Loss in coatings is 10^-5, loss in substrate is 10^-7. Note for 1.45" cavity with 0.5m RoC mirrors, the beam radius is 182 um.

Reminders:

• The plot is shown in displacement noise, not frequency noise from cavity.
• The psd (m^2/Hz) of coating Brownian noise is proportional to 1/w^2 (w is the beam radius)
• The psd of substrate Brownian is proportional to 1/w
• The psd of substrate thermoelastic is proportional to 1/w^3 ,at high frequency where adiabatic assumption valids. But at low frequency, when heat diffusive flow rate is comparable to the beam radii, TE noise is reduced from that of adiabatic assumption.

The Brownian noise in the coatings is more comparable to TE noise in substrate with smaller beam size although the crossing between the two noises are at higher frequency. So it should be able to see the total noise from both effects. However, to get smaller beamsize, we probably have to use even shorter cavities, or smaller RoC mirrros. So it might not be practical for us.. Nevertheless, going to smaller beam size should  be a good idea.

Note:

• for 1.45" long cavity, no choices of RoC give w = 92 um,
• for mirror with RoC = 0.5m, cavity length of 0.1 inch(2.5 mm) gives w = 92 um
• I think I made a mistake in the proposal since Brownian noise in substrate was higher than coatings' noise. I double checked it for this calculation and Brownian noise in substrate is always lower than coating brownian.

 I usually use Cerdonio's in the noise budget. But I used Thorne's to compare with COMSOL result because of the same adiabatic assumption.

 If the Cerdonio paper is correct, then just use those equations instead of the Thorne ones.

 At low frequency, the adiabatic approximation (used by BGV, Liu & Thorne) breaks down. Basically, it assumes that heat inside the material is not diffusive. The only place that heat flow must be considered is in the volume integral where gradient of expansion is non zero for the dissipation. (see Liu & Torne explanation just above eq 8). This is easier for COMSOL simulation. Since I just press the substrate with static force, and calculate the deformation of the body which, under adiabatic approximation, gives me the temperature change of the body.

 If I want to take into account the heat flow, I have to (see Cerdonio)

• solve The stress balance with temperature dependent and
• solve heat equation with expansion dependent (these two equations are coupled).

Then for COMSOL simulation I have to use different setting and I'm not exactly sure how to do this yet.

 What is the reason for the COMSOL TE noise to diverge from the analytic one at low frequencies?

Don't you have to consider the coherent TO noise between the coatings and the substrate?

The PMC round trip is ~ 0.32m. The end mirror has ROC = 1.0m. The spotsize is 384 micron.  The end mirror has radius ~2.5 mm. The clipping loss will be ~ 1*10^-43 on the curve mirror, and much smaller at the flat mirrors. The number seems very small but I think it is correct.

 This is just a simple integration for power of the beam P(a) where a = radius of the mirror (2.5mm). The total loss on all three mirrors per one trip is definitely way below 1ppm.

[add calculation]

Kriten sent me solidwork part files for the steel pmc.  I'm checking all the parts and will decide what material we want to use.

She reported that a ss pmc will have the first body mode at 780 Hz, while an aluminum one will have the first body mode at 1kHz. But we have to take thermal expansion, stiffness into account. here are some material properties

I think the thermal expansion will be a problem, but their thermal expansion coefficients are not that different. I don't know about stiffness of the body. I'll ask someone about this. Otherwise Al might be a better material if we look for higher resonant frequency.

Found the problem. My noise budget code was wrong. So after I fixed it, the TE noise in substrate result from COMSOL agrees pretty well with the analytical result (within 20%).

The result from COMSOL is plotted in dashed-black line. The result from Cerdonio is plotted in dashed pink.  Since my simulation uses the adiabatic assumption (used in BGV and Liu&Thorne paper), the results agree at high frequency. So I think the calculation is correct. I'll check some options (changing spot size, changing material) to see if TE noise can be made lower for AlAs/GaAs samples.

I attached my COMSOL file below. This is done in 3D model. It could have been done in 2-D axis symmetric setting, but I used 3-D for spacer sagging before, so I just used the same geometry I had.

 I used COMSOL model to calculated Brownian noise in substrate. This was done for cross checking my model simulation. The result from model is within 2% compared to half infinite model calculation.

I followed Levin's Direct approach to calculate Brownian noise in substrate, basically, to calculate the elastic energy inside the substrate under the applied test force. This can be done using COMSOL and analytical calculation. The comparison between the two is shown below.

U is the stored energy in substrate.

Note: I used the same COMSOL model for TE noise calculation. I just asked it to produce the strain energy in the substrate (no spacer).

The simulation is very close to the analytical result. So I think my spacer-cavity model and all the factors in the calculation are correct. The TE calculation is a little more complicated, since I have to calculate the gradient of expansion in COMSOL and it might be wrong somewhere. I'll check that. 

I realized that the mesh size was too large, even with the finest mesh for default setting. So I reduced the mesh size around the beam area and the results got closer to the analytical prediction. It is still a factor of 2 below the prediction. I'll see if I can hunt down this problem . I think it will be a good idea to verify my model by using my model to calculate Brownian noise and comparing with the result reported by Braunschwig group. 

When I defined mesh size in COMSOL, I used the predefined value provided by COMSOL. The finest mesh has maximum element size ~500 um, and minimum ~5um. Since the beam size is ~ 180 um, the maximum element size should be ~10 um. So I changed the values around, defined new area for smaller mesh until the results did not change much. I ran the simulation a few time to make sure that the solution converges. Right now my substrate has 3 regions

1. a cylinder at the center where the beam hits the mirror, Radius = 2x180um, depth=2x180um ,   Min/Max mesh size = 12.6/27 um
2. an outer region, radius = 5x180um, depth = 5x180 um, min/max mesh size = 10/50 um
3. The rest of the substrate, fine mesh

I tried to change the mesh size/boundary size a bit to get the result accurate enough without taking too much time. The TE estimation still a factor of 2 below the analytical estimate.

I'm checking the calculation for TE noise in substrate and spacer. I'm comparing the results from analytic calculation and simulation. The results still do not agree. Comsol gives a result ~ a factor of 4 lower than its analytical counterpart.

   Since the TE noise in substrate will be significant in AlAs/GaAs mirrors, the TE noise estimation should be correct. The TE calculation in substrate was done by (BGV, Liu and Thorne, and Cerdonio). The correction was noted in Numata 03 and Black 04 papers.  I think the calculation is well established because the calculations from all of the papers agree (with all corrections taken into account). So It will be nice if an FEA simulation predicts the similar result as well. 

   I followed the calculation done by Kessler etal paper where they calculated the Brownian noise in spacer. The mirror-spacer assembly is pushed by a static force with Gaussian profile, P = 2 F0 / (pi*w0^2) * exp(-2r^2/w0^2), where w0 is the spot radius = 182 um for 1.45" cavity with 0.5 mRoC mirrors, at r = w0, intensity drops by 1/e^2, F0 is the magnitude of the force (1N for my simulation) .

1.    I simulated 1/8 of the cavity which is cut by xy,yz, and zx planes.
2. Then I used COMSOL to calculated (gradient of expansion)^2,  (expansion = divergence of displacement in the body),
3. integrated over the calculated body. (get 4.18x10^-12)
4. Then multiplied by  8 to include all the sections of the cut cavity,
5. multiplied by 2 for double cavities,
6. divided by 2 for averaging the dissipated power over 1 period.
7. then followed the calculation given by Liu and Thorne. The result is still lower than the analytical model.

Note about COMSOL: I used extra fine mesh in a small volume where the beam hits the mirror, fine mesh in the rest of the substrate, and normal mesh in the spacer. This reduced the memory used in the calculation a lot and should not introduce a lot of error, since all the deformation will concentrate near the beam spot.

I have been practicing to optically contact two flat mirrors together. I think now I get it.

   Since I need to build my refcav by optically contacting mirrors to a spacer. I tried the procedure by contacting two flat blank mirrors together. I bought blank fused silica mirrors from Thorlabs, pf10-03. Here are the instructions:

1. Clean your space.
2. Wear lab gown, mask, gloves to prevent dust from your clothes
3. Use a can duster to blow away any obvious dust/dirt from the mirrors. Clean the whole mirror if possible. Any dust on the mirror back or side might fall on the surface anytime.
4. Wipe the mirror with acetone (I wiped the back and the edge first, before wiping the front face). Then switch to isopropanol. I tried drag wipe first, but it did not remove one of a particle right in front of the surface, so I had to wipe it with more pressure.
5. Contact to surfaces together. I put one on top of another. You will see a fringe pattern changes as the surfaces become close together under gravity. Press it to make it contact properly. ( I pressed with my finger for ~ a minute with ~10-20 Newton). If the surfaces are clean, there should be no fringe pattern (see fig2).  There should be no change when you remove the applied pressure.

fig1: On the right, fringe patter can be seen when two surfaces are put close together. On the left, after applying pressure the fringe should go away. The fringe pattern(purple-yellowing) on the left side indicates that these surface are not properly contacted.

 fig2:  These mirrors are optically contacted somehow, except the center. I don't know what happen here that cause white area in the center. I might be that the mirrors are not flat enough. But the rim seems to have a nice optical contact. I tried to remove the mirrors by hands but they are well stuck. I'll ask peter for more about what causes the white area here.

As I tried to do this, I got an idea of a fixture for optical contacting the spacer to mirrors. It will be a cap with a center hole for the mirror position. Here is a solidwork drawing. The part can be aluminum. I have to think about the tolerance of the piece, but from the calculation it can be an order of a  cm (to keep the beam to go through the window). So the hole can be ~ .01 inch larger than the spacer and the mirror.

I finished the drawing for refcav mount and the top plate. Everything fits together, so I'll submit the drawing tomorrow.

New things I added:

• Top plate for holding the thermal shields, and the cavities with screws.
• wall between the cavities for radiation shield.
• new top plate for the seismic stack, the dimension is similar to the one we have now, but the hole pattern is modified to fit the refcav mount
• cap for thermal shield (not shown).

The refcav mount is a bit wider than the top seismic stack plate, but it fits inside the chamber, see the assembly. So I don't think it will be a problem.

To measure the laser output profile is not actually that easy, although measured values are not so terrible.

Make sure the PBS you used is not BK7, but Fused Silica.

It would be nicer if you don't need to use transmissive optics for the measurement.
i.e. Put a fused silica AR-coated window and use the reflection.

BK7 windows may not work. BK7 has more than x10 CTE compared with Fused Silica. (7.5 ppm/K vs 0.55 ppm/K).
The absorption may also be higher.

I scanned the profile of the laser borrowed from 40m. The avg beam radius is 220um ~ 1 cm in front of the laser opening. This number will be used for a new table layout.

The laser was operated at full power (~700mW as expected). I used a mirror to attenuated the beam and use WINCAM to measure the beam profile (power incident on WINCAM was ~0.7mW). To measure the full power and avoid burning the power meter, I used a polarizing beam splitter with 1/2 wave plate to reduce the beam power by half then measured and summed the power from two sides of the PBS.

The beam shape is looking more like a blob than an oval. This might explain why the fitting does not match the measurement well.

[add fig]

I finished the design for dual cavity mount. The assembly looks fine, all parts fit together. I'll make sure that the mount can be screwed down to the current seismic stack before I submit the drawing.

After finding the optimum support points using COMSOL, I redid my cavity support design. The picture below shows the assembly of a metal base, peek pieces for support points, and copper shield. The picture shows only half of the mount.

Personal note: 

The current design, the beam height is 1.32 inch above the top seismic stack, ~5.5 inch measured from the table.

With the new cavity mount design, the beam height will be 1.5 inch above the top seismic stack.

I looked into the model a bit more to make sure that I included all the effects and get the coupling right [more to come]

fig1: displacement(beam line direction) per unit acceleration on the mirror surface. X-axis represents the position on the mirror along vertical line. Each plot represents result from different support positions. For optimum point (1.17"), the sensitivity to vertical seismic is around 2.1x10^-12 m/(m/s^2).

fig2: This plot shows the result as in fig1, with the means removed. Typically we want the tangent line at the center to be zero for minimum tilt.

1. Now I use SI units in the simulation.
2. The surface displacement along vertical direction is ~ 5 x10^-10 m. The spot radius is 100 um, so the effect from translation along vertical direction is negligible. We can assume that the beam still hits and senses the center of the mirror.
3. Check the result between support length between 1.18" +/- 0.02" (+/- 0.5 mm). This tolerence is what I estimate to be our assembly tolerence.
4. I calculated the tilt by using the tangent line at the displacement on the vertical line in the mirror center. Note that my mirror surface in the simulation is flat instead of curve. At 100 um away from the center, the surface height will change by ~ 10^-8 m due to the mirror's RoC. Meanwhile, the result from simulation (flat surface) shows that the displacement around 100 um away will change ~ 10^-12 m. However, I don't think it will effect our model much, since most of the deformation occurs around the support point, not the mirror. It means all the tilting comes from deformation on the spacer, not the mirror. So the simulation for flat mirror should be a good approximation.

I used COMSOL to estimated thermoelastic noise in 1.45" spacer.  The noise is not significant for our coating Brownian measurement. I still need to verify the model with some analytical estimation.

• The model is 1/8 of the spacer with symmetry boundary condition on each cut surface.
• The applied force is a quarter of an annulus, 2 mm width. This annulus represents the contact area between the substrate and the spacer.
• The deformation is simulated, and its gradient is calculated by COMSOL and integrated over the volume (1/8 of the cavity).
• I followed the calculation on Liu and Thorne, 2000, and get thermoelastic noise from spacer. It is lower than coating's Brownian noise at least 1 order of magnitude and will not be a limiting source for us. The plot below show spacer' TE in black dashed line.

Note:

• I should compare the simulation result with an analytical result, but I'll do that later in parallel with other work. This is not an urgent one. I'll also try to reproduce the result reported by Kessler et al. about Brownian noise in spacer as well. Then calculate the Brownian noise in our cavity.
• I'll check the spacer's TE noise for our previous 8" cavity to make sure that there is consistent with the result.

As Rana and Jan suggested, I thought about the effect of mirror's radius of curvature and DC tilt effect to cavity length noise. I ran a few simulation tests and the results were not changing much.

==cavity length noise==

The cavity length mainly changes from two effect

1) Actual position change:

2) Tilting of the mirror: If both mirrors tilt up or down together by theta, the cavity length will be longer by R*theta^2, see the attached picture. The calculation takes mirror's ROC and optical axis shifting into account.

   So, to find the best place to support the cavity, the contribution from both effects should be minimize.

==COMSOL Simulation: effects from different boundary conditions==

We have been discussing about different boundary conditions for support points whether to use fixed in all direction, fixed in only vertical direction, point support, or finite area. So I decided to check the effect from the following condition

•  Point like support, fixed in all direction
•  Point like support, fixed only in vertical direction
• Area support, fixed in all direction  (The size of the area does not change the result that much, see PSL:1061. This time I chose 1mm^2 which is 1.5x10^-3 [in^2].)

 ==result==

    There are no significant differences among the chosen boundary conditions. I varied the angle from 30, 45 and 60 degree, all the boundary conditions resulted in the same sagging behavior, so the best choice will be 30 degree as discussed in PSL:xx .The plot below shows the displacement per [m/s^2] of the mirror center along the beam line and tilt angle per [m/s^2] of the mirror, (the support angle is 30degree). With any boundary conditions, the optimum position will be quite the same (30 degree,  1.2" apart).

==where is the optimum spot? what is the coupling from seismic to cavity length?==

 From the simulation, with our restriction on support position (angle between 30 to 60 degree, 0.5 - 1.2" apart), the mirror positions always extend the cavity length. Since tilt will always increase the cavity length, we cannot cancel the effect between translation and tilt. The best way is to minimize translation and choose zero tilt as before.

About the coupling, at the optimum spot where tilting is zero, there will be no tilting motion. Displacement noise will only come from translation of the mirrors.

I talked to Jan about how to calculate thermoelastic (TE) noise in a spacer. I will use comsol to estimate the thermoelastic noise in our cavity.

  Thermoelastic noise has not been estimated for our setup. I think it will not be that high. As the previous result with 8" cavity, the measured signal was very close to the estimated coating Brownian noise. However, our noise budget will be more comprehensive if we include TE noise in the spacer.

 Basically to do that, we have to apply force on the spacer , then calculate the gradient of the strain inside the spacer [Liu and Thorne, 2000]. I think this can be done by COMSOL. I am working on it. I'll add more details on CTN wiki page later.

I checked the cavity length sensitivity to horizontal acceleration ( normal to the beam line axis). Unlike the result from vertical acceleration, the cavity length did not change smoothly with the position.  For the optimum point(30 degree, 1.18 inch apart), the displacement sensitivity due to horizontal acceleration is about a factor of 2 larger than that of vertical acceleration.

 Since both horizontal(H) and vertical(V) seismic noise on the table are comparable [psl:xxx], I want to make sure that there will be no serious displacement noise due to acceleration on vertical direciton.

On the COMSOL model, I fixed only one side of the support to push against horizontal acceleration (see pic). As the support can only push against the cavity, not pull. It should make more sense to use this boundary condition.

For the effect from H acceleration, I varied the angle from 12 to 42 degree, and distance from 0.8 to 1.2 inch. The displacement did not change smoothly with the support positions. So I could not tell which way I should choose for the optimum support. However, the displacement seems to be around 2x10^-10 inch for most of the positions. [the unit on the y axis of the plot should be inch per acceleration].

For the optimum support (1.18 Inch, 30 degree) the senstivity is about 1x10^-10 inch/ (m/s^2).

 After checking displacement and tilt of the mirrors from various support points, the tentative support positions will be 1.2"  and 30 degree, (see entry 1060 for their definitions). I'll check the sensitivity along other directions (horizontal), and see if the noise budget will be acceptable or not.

After running more simulations, I got the cavity's length sensitivity due to vertical acceleration. The angle varied between 12 to 45 degree. And the nice point seems to be 30 degree at 1.2".  I will check the length and tilt sensitivity on horizontal acceleration, and compute the noise budget to make sure that seismic noise will be acceptable. After that I'll finish the drawing for the cavity mount.

Note: I just realized that I should have used strain/acceleration unit in the displacement plot. I'll fix that later.

I ran a few more simulations to see how support area would affect the displacement. It turned out that it was not significant, for area = 0.056 x 10^-3, 0.9 x 10^-3 and 5.6 x 10^-3 [inch²]. This is good because we don't have to worry too much about the effective area of the contact points in the simulation. The errors will probably be dominated by other parameters (mostly, support positions). Judging from all the requirements, I think I'm close to making the decision for the support position.

     The plot below shows results from different support angles, (theta = [30,45,60]).

==a few comments about the plot==

• The area of the support points are not significant in the simulation, see green, red, cyan plots.
• For the support angle, it seems that the smaller theta, the less sensitivity to vertical acceleration (blue ,pink, green). However, smaller angle means the support area becomes more vertical. This will cause two issues that I can think of, (1) more force on the spacer which will increase the surface loss, (2) a bit harder to machine the mount. About the loss, I think it is still ok if the normal force from the support to the spacer is less than a factor of 5. This gives us the smallest angle of ~ 12degree, but at this angle, the optimum support point for zero tilt will be very close to the ends of the 1.45" spacer (based on the blue ,pink, green curve) and it will be unsafe to mount the cavities in case they slide out of the supports.

            I think possible choices (considering loss, machining, safety) for the support positions will be some where around 0.7-1.2 inch along the beam line, and the angle will be ~ 12 - 30 degree. I'll run more simulation to see if I can find it.

==Note==

1. I reproduced the result for 8" cavity with wire support and got the same result as before (dL/L)/(acceleration) ~ 2 x 10^-10 (1.7x10^-10, to be more exact), but the tilt is 9x10^-9 rad which is a lot larger than the results from the short cavity. So I think my simulation for short cavity is fine as I can reproduce the same result.
2. I tried to constrained the support area in vertical direction only, but the simulation failed. I think this is because of the bending of the spacer surface. If you let it slide horizontally, the surface will tilt a bit as well and cannot be kept fix in vertical direction. Then for the constrain in all directions, I don't think there will be a solution for zero coupling for the short cavity.

I used COMSOL with MATLAB to run the simulation. I tried to vary support position and checked the mirror displacement along the beam line axis and tilt angle.

With Aidan help, I am finally able to run matlab with comsol to get the results (displacement of the mirror surface and tilt).

 We are not planning to cut the cavities for support points, so we will choose the support positions on the spacer's surface, with parameter X and theta, see the figure below for their definitions.

As a start, I chose theta = 30 and 60 degree. The displacement and tilt (due to cavity sagging under its weight at 1g)as a function of support position are plotted below.

It is possible to minimize the tllt, but the displacement is still a bit bad. The result from 8" spacer, the sensitivity to acceleration is ^(dL/L) / _(m/s^2) = 2x10^-10, while the current result will be about  1x10^-10. Since the cavity is shorten by ~ a factor 4, I expect a better sensitivity to vibration.

==next==

I'll try to change the area of the support points to check its effect on the displacment.

I have to check if I can constrain the support points in one direction or not.

Faraday Isolator, for 700mW 1064 laser. This will be installed after the laser (and waveplates for polarization adjustment).

I looked at Thorlabs website and found one that meets our requirement.

IO-3-1064-HP, the max power is 15W, and the max intensity is 500 W/cm^2. If the 700mW beam has 300 um radius, the avg intensity is~ 250 W/m^2.

I'll ask around to check if this is a suitable one.

I'm still working on COMSOL, now my model has the following features:

• support points are simulated by four rectangles on the spacer surface. The support areas can be changed, and their positions can be moved along the beamline and around the cross section directions. I'm still not sure what should be the effective area for the simulation. However, the paper from Milo's group [2009] showed that the areas of the supports points do not affect the optimum position that much (but the support must be constrained in the same direction as gravity only). I have not tried to constrained the points in only one direction yet.
• I used a symmetry plane to model only half of the spacer. This will reduce some simulation time and avoid any asymmetry due to the mesh size.
• I'm trying to use matlab with comsol and print out the result. The work is stil in progress.

Note:

Milo etal. 2009 Phys Rev A 79.053829.

The table is not floated. Either the legs are broken, or there is a leak in the tube system. I think it is likely that one (or more) of the legs is broken. Since it happened before with the older legs. Their rubber part in the leg gradually failed over time. We might need to reconsider buying brand new legs again.  The pump connected to the table could not keep up with the leaking rate, so I turned it off.

I'm using COMSOL to simulate the effect of cavity sagging to find the optimum suspension points. The answer is not yet ready, I'm still working around COMSOL.

• Problem with point like contact: First I tried to simulated 4-fixed-point support, however the result was asymmetric along beam line. It might be the result from the point-like contacting areas between the support and the cavity. You can see the tilting along the beam line in the figure below. Note the constrained area  of the support effect the sagging slightly as well [add ref].

.

fig1: cavity sagging, on 4 point suspension. The cavity is not symmetric on left and right.

     So, as a start, I switched to half line support. As my cavity support will be rods placed perpendicular to the refcav, the simulation might not be off by much. Then I checked the displacement at the center of the mirrors. The result was, the further to the ends of the spacer, the less displacement of the mirrors. I think this is strange. I also remember a paper about this and their cavity dimension is similar to what we have, and their result is slightly away from the ends [ref]. I'll have to double check the result again.

Note: I think what is wrong is how I use the displacement of the mirrors along the beamline as differential length of the cavity, I have not taken into account tilting of the mirrors yet. Also, I'll try to position the venting hole downward to see if there is any differences in the result or not.

I checked the temperature control servo for the vacuum chamber and found out that it was off. I could not turn it back on yet since there was some problems with the channel. I'll ask Peter to help me on this.

About a week ago, I tried to add another channel for controlling the second PMC servo card. I did not write an elog since it was not done yet.

I created PMC2.db in /usr1/epics/psl/db. It had only one channel for C3:PSL-PMC2_GAIN. I used #C6 S2. This channel might already be used for temp control. I'll try to remove the channel and see if the problem can be solved.

modification of the previous mount, work in progress.