How about a diagram so that we can understand what this model includes?

cool

For our optical contacting, Jennifer and I are starting out with glass (microscope slides), with the setup in the EE shop next to the drill press (photos from Jennifer to follow).

Some interesting links:

• https://www.laserfocusworld.com/optics/article/16546805/optical-fabrication-optical-contacting-grows-more-robust is a write up on contacting, and the link to Dan Shaddock's paper is also useful (need to sign up to get the acutal TSP writeup)
• Thesis on Silicon Bonding (https://escholarship.org/uc/item/5bm8g42k)
• https://youtu.be/qvBoGoh_-AE

The Arduino / AC PWM interface looks good. I recommend that you maintain the code in GitHub and post a link to the repo whenever you update the code. Use detailed commit messages so that it makes sense.

For the plotting, it would be good if you can use grid lines and markers for the data points. Then we can see the difference between the data and the fits, etc.

And to avoid the hysteresis, etc. you can record the temperature in your Arduino and use feedback to make the heater just go to whatever temperature you specify. So you would have a prescribed T(t) and the PID feedback loop would just make the heater take you there. Can your Arduino read the thermocouple?

I guess you have tried it already - but does enforcing the stacks to be repeating bilayer pairs of the same thickness fail miserably? When doing this for the PR3 optic @1064nm, I found that the performance of a coating in which the layers are repeating bilayers (so only 2 thicknesses + the cap and end are allowed to vary) was not that much worse than the one in which all 38 thicknesses were allowed to vary arbitrarily. Although you are aiming for T=50ppm at the second wavelength (which isn't the harmonic) which is different from the PR3 reqs. This kind of repetitive structure with fewer arbitrary thicknesses may be easier to manufacture (and the optimizer may also converge faster since the dimensionality of the space to be searched is smaller). 

Cool starfish 🌟 . What is the interpretation of the area enclosed by the vertices? Is that the (reciprocal) cost? So the better solution maximizes the area enclosed?

Following our discussion at the Friday JC meeting, I gathered several resources and made a small simulation to show how frequency combs might be generated on platforms other than microcombs or mode-locked lasers.

Indeed, frequency combs generated directly from a mode-locked laser are expensive as they require ultra-broadband operation (emitting few fs pulses) to allow for f-2f interferometry.

Microcombs are a fancy way of generating combs. They are low-power-consuming, chip-scale, have a high repetition rate, and are highly compatible with Silicon technology. While these are huge advantages for industry, they might be disadvantageous for our purpose. Low-power means that the output comb will be weak (on the order of uW of average power). Microscopic/chip-scale means that they suffer from thermal fluctuations. High rep-rate means we will have to worry about tuning our lasers/comb to get beat notes with frequencies smaller than 1GHz.

Alternatively, and this is what companies like Menlo are selling as full-solution frequency combs, we could use much less fancy mode-locked lasers emitting 50fs - 1ps pulses and broaden their spectrum in a highly nonlinear waveguide, either on a chip or a fiber, either in a cavity or linear topologies. This has all the advantages:

1. High-power (typically 100mW)

2. Low rep-rate (typically 100MHz)

3. Relatively cheap

4. "Narrowband" mode-locked lasers are diverse and can come as a fiber laser which offers high stability.

As a proof of concept, I used this generalized Schrodinger equation solver python package to simulate 1d light propagation in a nonlinear waveguide. I simulated pulses coming out of this "pocket" laser (specs in attachment 1) using 50mW average power out of the available 180mW propagating in a 20cm long piece of this highly nonlinear fiber (specs in attachment 2).

The results are shown in attachments 3-4:

Attachment 3 shows the spectrum of the pulse as a function of propagation distance.

Attachment 4 shows the spectrum and the temporal shape of the pulse at the input and output of the fiber.

It can be seen that the spectrum is octave-spanning and reaches 2um at moderate powers.

One important thing to consider in choosing the parameters of the laser and fiber is the coherence of the generated supercontinuum. According to this paper and others, >100fs pulses and/or too much power (100mW average is roughly the limit for 50fs pulses) result in incoherent spectra which is useless in laser locking or 1f-2f interferometry. These limitations apply only when pumping in the anomalous dispersion regime as traditionally have been done. Pumping in an all-normal (but low) dispersion (like in this fiber) can generate coherent spectra even for 1ps pulses according to this paper and others. So even cheaper lasers can be used. ps pulses will require few meter-long fibers though.

Ongoing points of updates/content (list to be maintained and added)
Mariner Chat Channel
Mariner Git Repository
Mariner 40m Timeline [2020-2021] Google Spreadsheet
 

6" vs 4" optic size comparison using CAD - worth hopping into the 3D geometry using the link below, but also posting a couple of images below.

1) We can adjust all parameters relating to the suspension frame except the beam height. Is there enough clearance under the optic for the internal shield?

--> Using the representation of the MOS structure as-is, there is about 1" of clearance between the bottom panel of the first/internal shield under the 6" case, compared with 2" of clearance in the 4" case. This is not very scary, and suggests that we could use a 6" optic size.

2) Any other concerns at this point?

--> Not really, there are degrees of freedom to absorb other issues that arise from the simple 4" --> 6" parameter shift

EASM posted at https://caltech.app.box.com/folder/132918404089

Koji, Stephen

Putting together Koji's design work with Stephen's CAD, we consider the size of a test chamber for the Mariner suspension.

Koji's design uses a 6" x 6" Si optic, with an overall height of about 21.5".

Stephen's offsets suggest a true shield footprint of 14" x 14" with an overall height of 24".

With generous clearances on all sides, a test chamber with a rectangular footprint internally of about 38" x 32" with an internal height of 34" would be suitable. This scale seems similar to the Thomas Vacuum Chamber in Downs, and suggests feasibility. It will be interesting to kick off conversations with a fabricator to get a sense for this.

This exercise generated a few questions worth considering; feel welcome to add to this list!

• do we need to have the suspended snout(s)?
• are we studying an ITM or ETM (or both)?
• relays or other optical components on the baseplate?
• angles of optical levers?
• off center mounting?
• two doors for front/back access?

[Stephen, Koji]

WIP - check layout of 60 cm suspension in chamber at 40m, will report here

WIP - also communicate the

WIP - Stephen to check on new suspension dimensions and fit into 40m chamber

[Koji, Stephen]

Kind of a silly post, and not very scientific, but we are sticking to it. During our check in today we discussed Mariner suspension frame design concept, and we chose to proceed with MOS-style (4 posts, rectangular footprint).

 - We looked at a scaled-up SOS (WIP, lots of things broke, just notice the larger side plates and base - see Attachment 1) and we were not super excited by the aspect ratio of the larger side plates - didn't look super stiff - or the mass of the base.

 - We noted that the intermediate mass will need OSEMs, and accommodating those will be easier if there is a larger footprint (as afforded by MOS).

MOS-style it is, moving forward!

Also, Checked In to PDM (see Attachment 2 - filename 40mETMsuspension_small-shields.SLDASM and filepath \llpdmpro\Voyager\mariner 40m cryo upgrade ) the current state of the Mariner suspension concept assembly (using MOS). Other than updating the test mass to the 6" configuration, I didn't do any tidying up, so I'm not perfectly satisfied with the state of the model. This at least puts the assembly in a place where anyone can access and work on it. Progress!

I am getting started on building the arduino circuit as well as setting up my computer so I can communicate between jupyter notebook and the arduino. I will need a USB adapter for my computer before I can make much more progress.

I was able to get a USB adapter for my computer so I could test my code. The Arduino can read the temperature of the room and output the values with a tenth of a second time delay. Jupyter Notebook recognizes the Arduino and can receive temperature data from it.

The arduino was able to read temperature data and send it to a python program that graphed the data.

I am trying to design a cantilever setup to find the quality factor of optically bonded silicon. The cantilever will be given an impulse, and the ring down will be measured. In order to determine the Q of the bond, the relative energy contributions from each part of the cantilever must be analyzed. The primary energy contribution should come from the bond.

The below equations come from https://roymech.org/Useful_Tables/Beams/Strain_Energy.html. I believe the relevant ones are the bending and traverse shear energies.

c = distance from neutral axis to outer fibre(m)

E = Young's Modulus (N/m2)

F = Axial Force (N)

G = Modulus of Rigidity (N/m2)(m)

I = Moment of Inertia (m4)(m)

l = length (m)

M = moment (Nm)

V = Traverse Shear force Force (N)

x = distance from along beam (m)

z = distance from neutral (m)

γ = Angular strain = δ/l

δ = deflection (m)

τ = shear stress (N/m2)

τ max = Max shear stress (N/m2)

θ = Deflection (radians)

The young’s modulus (E) of silicon is 130 to 188 GPa from a quick google search. The shear modulus (G) is 50 – 80 GPa. The calculation is easier when using a rectangular beam. In that case, (U traverse) / (U bending) ~ 1.2 * V^2/(50 * bh * M^2) * (bh^3/12 * 188) = (.376 to .16) * (V^2)(h^2)/(M^2) where M depends on the distance from the applied force.

For a circular beam, height is swapped out for diameter, K is 1.11, and I = pi/64 d^4. (U traverse) / (U bending) ~ (.26 to .11) * (V^2)(d^2)/(M^2), which means (U bending) / (U traverse) ~ (3.8 to 9) * (M^2)/((V^2)(d^2)).

However, for a cantilever beam with the bond on the neutral axis, the maximum shear energy would be at the bond. For gentle nodal suspension, the maximum bending energy would be at the top and bottom.

I am trying to use fminsearch to find the best cantilever dimensions to maximize the bond/cantilever energy ratio. Fminsearch takes in a function and a set of intial parameters. The function that is passed in should be a function of the parameters, but my getEnergy function does not work unless the COMSOL model is passed in as an argument. I tried to make a helper function, but I run into the same problem.

After running getRatio (attempted helper function):

>> getRatio
The COMSOL model is now accessible using the variable 'model'
Unrecognized function or variable 'model'.

Error in getRatio (line 3)
ratio = getEnergy(model, L, h, d)
 
>> 

The code works now. If the function is specified by a file, there should be an @ symbol front of it when it is passed into fminsearch.

Restricting the search to nothing less than the initial parameters (L = 2 cm, h = 0.3 mm, d = 0.55 mm), fminsearch outputs L = 2.0088 cm, h = 0.3000 mm, d = 0.5776 mm.

With the search restricted to L >= 1 cm, h >= 0.1 mm, and d >= 0.5 mm, fminsearch outpus L = 1.0313 cm, h = 0.1000 mm, and d = 0.5033 mm.

I am trying to get a plot of the fminsearch data, but I was not sure how to extract the data. But fminsearch has built in plots that I think capture the data pretty well.

Here is the code to generate a random list of parameters and evaluate the energy ratio of each. 

Attached is a cartoon partial view into the heat load experienced by the Mariner assembly.

The omnigraffle file with more explicit arrow labelling in the 'layers' tab is available here. The dashed red lines along to top represent vacuum chamber radiation incident on all sides of the OS/IS, not just from the top. Off picture to the right is the BS, left is the beam tube/ETM chamber -- hence the lower absored laser power (solid line) absorbtion (PR power + no HR coating absorption). 

Parameters: 

• Emissivities are listed outside the cartoon.
• Shields consist of polished aluminum outer surfaces and high emissivity inner surfaces. 
• 1 W input power, 50 W power recycling, 30 kW cavity power
• All shields held at 77K 
• IS snout radius is equal to TM radius
• 20 ppm/cm bulk silicon absoprtion, 5 ppm coating absorption

Assumptions

• Steady state condition, where the shields are able to be cooled/held to 77K
• Holes punched into the inner shield for stops, magnets, etc are assumed to shine RT light onto 123K TM
  • This is very conservative, MOS will stablize at some temp and the OS should block ~all vacuum chamber radiation not funneled through inner shield snout

Missing or wrong

• [M] Contribution of MOS conduction and emission on the outer shield heat budget
• [M] Inner shield 
• [W] OS inner surface currently modelled as one surface seeing incident RT light, need to accomodate the view factor of each of the 5 high e sides to the open maw of the OS
• [M] Conduction through shield masses, how efficient is it to link them with straps
• [M] no AR coating absorption 
• [M/W] Cold finger cooling power from room temp shield to 77K cryocooler ('wrong' label because 61W is only the heat load once shields are cooled):
  • Worst case to reach: 1.5m connection between tank flange and shield (from flange at bottom of the tank)
    • Phosphorous deoxidized copper:  5 cm diameter
    • ETP copper:  3.5 cm diameter
  • Best case: 0.5m connection, from flange at level of OS
    • Phos deox Cu: 3 cm diameter
    • ETP Cu: 2 cm diameter
  • ​​​

*Note: the current modeling script can be found at: CryoEngineering/MarinerCooldownEstimation.ipynb

Nina pointed me to the current mariner cooldown estimation script (path above) and we have since met a few times to discuss upgrades/changes. Nina's hand calculations were mostly consistent with the existing model, so minimal changes were necessary. The material properties and geometric parameters of the TM and snout were updated to the values recently verified by Nina. To summarize, the model considers the following heat sources onto the testmass (P_in):

- laser absorption by ITM bulk (function of incident laser power, PR gain, and bulk absorption)

- laser absorption by ITM HR coating (function of incident laser power and HR coating absorption)

- radiative heating from room-temp tube snout (function of snout radius and length, and TM radius)

The heat transfer out of the testmass (P_out) is simply the sum of the radiative heat emitted by the HR and AR faces and the barrel. Note that the script currently assumes an inner shield T of 77K, and the inner/outer shield geometric parameters need to be obtained/verified.

Nina and Paco have been working towards obtaining tabulated emissivity data as a function of temperature and wavelength. In the meantime, I created the framework to import this tabulated data, use cubic spline interpolation, and return temperature-dependent emissivities. It should be straightforward to incorporate the emissivity data once it is available. Currently, the script uses room-temperature values for the emissivities of various materials. 

Future steps:

- Incorporate tabulated emissivity data

- Verify and update inner/outer shield dimensions

Attachment 1 is a geometric diagram that reflects the current state of the ITM cooldown model, introduced in [30]. The inner shield is assumed to be held at 77K for simplicity, and 2 heat sources are considered: laser heating, and radiative heating from the room-temperature snout opening. The view factor F_ij between the snout opening and test mass (modeled as 2 coaxial parallel discs separated by length L - equation found in Cengel Heat Transfer) is calculated to be 0.022. The parameters used in the model are noted in the figure.

Attachment 2 is a simplified diagram that includes the heating/cooling links to the test mass. At 123K, the radiative cooling power from the inner shield (at 77K) is 161 mW. The radiative heating from the snout opening is 35 mW, and the laser heating (constant) is 101.5 mW. Due to the tiny view factor betwen the snout opening and the test mass, most of the heat emitted by the opening does not get absorbed. 

The magnitudes of heating and cooling power can be seen in Attachment 3. Lastly, Attachment 4 plots the final cooldown curve given this model. 

My next step is to add the outer shield and fix its temperature, and then determine the optimal size/location of the inner shield to maximize cooling of the test mass. This is question was posed by Koji in order to inform inner shield/outer shield geometric specs. Then, I will add a cold finger and cryo cooler (conductive cooling). Diagrams will be updated/posted accordingly.

Building on [32], I added a copper cold finger to conductively cool the inner shield, instead of holding the inner shield fixed at 77K. The cold finger draws cooling power from a cyro cooler or "cold bath" held at 60K, for simplicity. I added an outer shield and set its temperature to 100K. The outer shield supplies some radiative heating to the inner shield, but blocks out 295K heating, which is what we want. The expanded diagram can be seen in Attachment 1. 

I wanted to find the optimal choice of inner shield area (A_IS) to maximize the radiative cooling to the test mass. I chose 5 values for A_IS (from A_TM to A_OS) and plotted the test mass cooldown for each in Attachment 2. The radiative coupling between the inner shield and test mass is maximized when the ratio of the areas, A_TM/A_IS, is minimized. Therefore, the larger A_IS, the colder the test mass can be cooled. Even though choosing A_IS close to A_OS increases the coupling between the 2 shields, the resulting heating from the outer shield is negligible compared to the enhancement in cooling.

I chose A_IS = 0.22 m² to model the inner shield and test mass cooldown in Attachment 3. The test mass reaches 123 K at ~ 125 hours, or a little over 5 days. I have pushed the updated script which can be found under mariner40/CryoEngineering/MarinerCooldownEstimation.ipynb.

I used the same model in [37] to consider how test mass length affects the cooldown. Attachment 1 plots the curves for TM length=100mm and 150mm. The coupling between the test mass and inner shield is proportional to the area of the test mass, and therefore increases with increasing length. Choosing l=100mm (compared to 150mm) thus reduces the radiative cooling of the test mass. The cooldown time to 123K is ~125 hrs or over 5 days for TM length=150mm (unchanged from [37]), but choosing TM length=100m increases this time to ~170 hrs or ~7 days. (Note that these times/curves are derived from choosing an arbitrary inner shield area of 0.22 m², but the relative times should stay roughly consistent with different IS area choices.)

I reran the cooldown model, setting the emissivity of the inner surface of the inner shield to 0.7 (coating), and the emissivity of the outer surface to 0.03 (polished Al). Previously, the value for both surfaces was set to 0.3 (rough aluminum). 

Attachment 1: TM cooldown, varying area of the inner shield. Now, the marginal improvement in cooldown once the IS area reaches 0.22 m² is negligible. Cooldown time to 123K is ~100 hrs, just over 4 days. I've kept IS area set to 0.22 m² moving forward.

Attachment 2: TM/IS cooldown, considering 2 lengths for the test mass. Choosing l=100m instead of 150mm increases cooldown time from ~100 hrs to ~145 hrs, or 6 days.

Here I describe the current radiative cooldown model for a Mariner test mass, using parameters from the most recent CAD model. A diagram of all conductive and radiative links can be seen in Attachment 1. Below are some distilled key points:

All parameters have been taken from CAD, with the exception of:

Attachment 2 contains the cooldown curves for the system components. With the above assumptions, the test mass takes ~59hrs to reach 123K, and the final steady-state temperature is 96K. (*This was edited - found a bug in previous iteration of code that underestimated the TM cooldown time constant and incorrectly concluded ~36hrs to reach 123K. The figures have been updated accordingly.)

Attachment 3-6 are power budgets for major components: TM, IS, Cage, OS (can produce for UM if there's interest). For each, the top plot shows the total heating and cooling power delivered to the component, and the bottom plot separates the heating into individual heat loads. I'll discuss these below:

The next post will describe optimization of the snout length/radius for cooldown.

Here is a more detailed analysis of varying the length and radius of the snout.

Attachment 1 plots the heat load (W) from the snout opening as a function of temperature, for different combinations of snout length and radius. The model using the CAD snout parameters (length=0.67m end-to-end; radius=5.08cm) results in ~0.3W of heat load at steady state. The plot shows that the largest marginal reduction in heat load is achieved by doubling the length of the snout (green curve), which cuts the heat load by over a factor of 2/3. This validates the choice in snout length used in the previous ELOG entry analysis. The bottom line is that the end-to-end snout length should be on the order of 1 meter, if physically possible.

The next marginal improvement comes from reducing the radius of the snout. Attachment 1 considers reducing the radius by a half in addition to doubling the length (red curve). A snout radius of an inch is quite small and might not be feasible within system constraints, but it would reduce the snout heat load to only 25mW at steady state (along with length doubling). 

The cooldown model resulting from optimizing parameters of the snout (length=1.33m, radius=2.54cm) is shown in Attachment 2. The test mass reaches 123K in ~57hrs - only 2 hours faster than the case where only the snout length is doubled (see previous ELOG entry) - and the test mass reaches steady state at 92K - only 6K colder than in the previous case. This could discourage efforts to reduce the radius of the snout at all, since increasing the length provides the most marginal gains. 

The attached plot (upper) compares the heat load delivered to the test mass from various snout lengths (end to end), as a function of test mass temperature. (At steady state, our point of interest is 123K.) Note that these curves use the original CAD snout radius of 5.08cm (2").

The greatest marginal reduction in heat load comes from increasing the end-to-end snout length to 1m, as concluded in the prevous ELOG. This drops the heat load from just under 0.5W (from snout length 0.5m) to 0.15W. Further increase in snout length to 1.5m drops the heat load to well under 0.1W. After this point, we get diminishing marginal benefit for increase in snout length. 

The effect on the TM cooldown curve can be seen in the lower plot. A snout length of 1m drops the steady-state TM temperature to under 100K. Then, like above, increasing the length to 1.5m makes the next non-negligible impact. 

Here we lay out the Mariner cryocooler requirements and discuss the most recent cooldown model, which includes a cryocooler that cools down the inner shield and a separate LN2 dewar that cools the outer shield.

The chosen cryocooler must supply at least 2x the cooling power to the TM than the heat loads on the TM, at 123 K. Implicit in this requirement is that in the absense of temperature control, the cooling power must be enough to cool the TM to well below 123 K.

Attachment 1 is the latest Mariner ITM cooldown model. This updated model is pushed to mariner40/CryoEngineering/MarinerCooldownEstimation.ipynb. Before running the notebook you can toggle between IS cooling sources: LN2, DS30, CH-104, or in the future any crycoolers we are considering. All attachments are generated using the cooling curve of the DS30. 

Since the OS is no longer a heat load on the cryocooler, the IS gets cooled more efficiently and reaches within 5 K of the coldhead. The heat loads on the TM (snout, apertures, laser heating) make its temperature plateau just under 100 K. It reaches 123K in ~50 hours.

Attachment 2 is a power budget for the TM. We see that at 123K, the heat loads sum to ~0.4 W. The cooling power at this temperature is around 1 W. The DS30 satisfies our cryocooler cooling requirement; however vibration requirements / vacuum interface compatibility still need to be determined.

Lastly, Attachment 3 is an updated block diagram of the heat transfer couplings considered by the model. (The model also considers radiative links between the inner shield and cage, and inner shield and upper mass; these are omitted from the diagram for simplicity.)

Summarizing the current Mariner ITM cooldown model assumptions:

- Inner shield and outer shield have snouts of equal length (1 m end-to-end)

- Laser off during cooldown

- Inner shield cooled by DS30; outer shield cooled by LN2 tank

- ITM barrel emissivity = 0.9

Takeaways:

A simplified block diagram can be found in Attachment 4. 

I simulated the Mariner cooldown with an additional LN2 tank connected to the main cold strap shared by the cryocooler. LN2 can aid in the initial cooldown from room temperature, and once the inner shield is sufficienly cold the cryocooler can take full control. (The LN2 should not be on the whole time - once the inner shield crosses 77K the LN2 would be contributing heat.) In the model I chose the inner shield temperature of 90K to signal when to turn off the LN2 (any lower and the IS temperature starts to flatten out as it approaches 77K).

The closer the LN2 tank sits towards the chamber/IS (and away from the cold head), the better. This is because the cold head of the cryocooler drops rapidly to ~60K, and the LN2 joint would contribute to heating the cold head. Plus, the cooling of the IS is more efficient if the LN2 source is closer. The model assumes the LN2 tank sits halfway between the coldhead of the cryocooler and the inner shield.

The last assumpion made is that the LN2 tank volume is large enough such that the tip in contact with LN2 remains at 77K. 

In Attachment 1, the dashed traces show the cooldown of the cold head, inner shield, and test mass without the additional LN2 cooling. The solid traces include LN2 cooling and use the assumptions above in green. We see that the inner shield is cooled significantly faster with LN2 (on par with the cold head until 150K). As a result, the heat load the inner shield puts on the cold head is reduced, and that reduction more than compensates for the additional heating on the cold head from the LN2 at 77K. Thus the cold head cools much faster in the first 10 hours. The kinks in the cold head/inner shield traces are presumably from the system re-equilibriating after the LN2 source is shut off - it's not clear why the cryocooler doesn't immediately continue the downward trend.

The effect on the test mass is more subtle, but we see the test mass cools to 123K ~2 hours faster (in 28 h). I was then curious if we could get the same gains by simply moving the cryocooler/cold head halfway closer to the inner shield. This simulation is in Attachment 2 - it takes ~1 h longer for the test mass to reach 123K, since we don't get the added cooling power from the LN2.

While there's merit to the additon of LN2, maybe an improvement of a few hours isn't enough to justify the increase in complexity.

Here is the model including an additional LN2 tank aiding in inner shield cooldown, applied to Voyager [Attachment 1]. The same assumptions have been made as in the previous ELOG. The LN2 is switched off once the inner shield reaches 90K.

Using LN2 in such a way cools down the test mass to 123K 5 hours faster. This is a ~6% improvement from the original 85 hours of cooldown [Attachment 2]. Note that the fundamental radiative cooling limit for a Voyager-like test mass is ~68 hours.

Here is a summary of the cryocooler discussion hosted at JPL. 

Dave Glaister of Ball Aerospace presented on their low-vibration cryocooler assemblies (CCAs). A summary of their work can be found in this paper. Ball has their own cryocooler vibration testing setup that they use to assess/characterize their platforms. They did not show frequency-dependent vibration noise with/without their assemblies, but they advertized up to 50x reduction in noise at 50-60 Hz. The paper above does show a spectrum of sorts (unknown units) but it does not display data below 50 Hz. Notably, they have experience in augmenting the Sunpower DS-30 cooler which meets the Mariner cooling requirements (though their CCAs should be cooler-agnostic). 

Notes from their meeting:

- Fanciest Sunpower DS-30 CCA (with all the bells+whistles): $2 million; 12-24 month lead time. Results in few mN of vibration.

- Yukon Soft Ride CCA for Sunpower DS-30 - lowest cost; in the $100,000 range if they use cheaper electronics.

          -vibration attenuation 8x

- They suggested the option of circulating gas instead of a cryocooler for our needs: helium gas lines; keep compressor outside IFO to eliminate almost all vibration.

The Yukon CCA seems to be a reasonable baseline to discuss with them. They can customize to our needs. We should ask them to provide us with vibration measurements of the DS-30 cooler with and without their Yukon CCA down to 1 Hz.

Have been using the 40m Coatings repo code by Gautam (with some modifications to make dichroic designs under Ta2O5_Voyager), as well as the parameters compiled in the Mariner wiki for Silica-tantala thin films. Here are some of the top picks.

ETM

For ETM, the target transmissivities are 5.0 ppm @ 2128.2 nm and 50.0 ppm @ 1418.8 nm. After different combinations of differential evolution walkers, numbers of layers, thickness bounds, a couple of different optimization strategies, the optimum design has consistently converged with 19 - 26 layer pairs (total of 38 - 52 layers). The picks are based on the sensitivities, E_field at the boundary, and a qualitatively uniform stack (discarded "insane-looking" solutions). The top picks in Attachment 1 may be a good starting point for a manufacturer. In order of appearance, they are:

1. ETM_210218_1632
2. ETM_210222_1621
3. ETM_210302_1210
4. ETM_210302_1454

ITM

For ITM, the target transmissivities are 2000 ppm @ 2128.2 nm and 50.0 ppm @ 1418.8 nm (critically coupled cavity for AUX). The lower trans for 2128.2 nm made this easier faster to converge, although the number of thin film layers was equally centered about ~ 50 layers. Haven't explored as much in the parameter space, but the top picks in Attachment 2 are decent for approaching manufacturer. In order of appearance, they are:

1. ITM_210303_1806
2. ITM_210204_1547
3. ITM_210304_1714

Update on ETM

New optima are being found using the same basic code with some modifications, which I summarize below;

1. Updated wavelengths to be 2128.2 nm and 1418.8 nm (PSL and AUX resp.)
2. The thickness sensitivity cost "sensL" previously defined only for 2128 nm, is now incorporating AUX (1418 nm) in quadrature; so sensL = sqrt(sens(2128) ** 2 + sens(1418)**2)
3. There is now a "starfish" plot displaying the optimized vector cost. Basically, the scores are computed as the inverse of the weighted final scalar costs, meaning the better stats reach farther out in the chart. One of these scalar costs does not actually belong to the optimization (stdevL) and is just a coarse measure of the variance of the thicknesses in the stack relative to the average thickness.
4. Included a third wavelength as transOPLV (for the OPLEV laser) which tries to get R ~ 99 % at 632 nm
   1. Imagine,... a third wavelength! Now the plots for the transmissivity curves go way into the visible region. Just for fun, I'm also showing the value at 1550 nm in case anyone's interested in that.
5. Adapted the MCMC modules (doMC, and cornerPlot) to check the covariance between the transmissivities at 2128 and 1418 for a given design.
6. Reintroduced significant weights for TO noise and Brownian noise cost functions (from 1e-11 to 1e-1) because it apparently forces solutions with lower thickness variance over the stack (not definitive, need to sample more)

Still working to translate all these changes to ITM, but here are samples for some optimum.

• Attachment 1 shows the spectral reflectivity/transmissivity curves with a bunch of labels and the transparent inset showing the starfish plot. Kind of crazy still.
• Attachment 2 shows the stack. Surprisingly not as crazy (or maybe I have internalized the old "crazy" as "normal")
• Attachment 3 shows a very simple corner plot illustrating the covariance between the two main wavelengths transmissions.

Update on ETM/ITM coating design;

- Following what seemed like a good, intuitive suggestion from Anchal, I implemented a parameter called Ncopies, which takes a stack of m-bilayers and copies it a few times. The idea here was to have stacks where m is the least common multiple of the wavelength fractional relation e.g. m(2/3) = 6 so as to regain some of the coherent scattering in a stack. Unfortunately, this didn't work as planned for m=6, 3, and 2.

- While the target transmissivities are reached with comparably fewer layers using this method, the sensitivity and the surface E field are affected and become suboptimal. The good thing is we can do the old way just by setting Ncopies = 0 in the optimization parameters yaml file.

- An example of such a coating is in Attachment 1.

- I decided to just add the 'varL' scalar cost to the optimizer. Now we minimize for the variance in the coating stack thicknesses. As a target I started with 40% but will play with this now.

Yeah, the magnitudes are the inverse weighted scalar costs (so they lie on the appropriate relative scale) and indeed larger enclosed areas point to better optima. I would be careful though, because the lines connecting the scalar costs depend on the order of the vector elements (for the plot)... so I guess if I take the cost vector and shuffle the order I would get a different irregular polygon, but maybe the area is preserved regardless of the order in which the scalars are displayed...

Differential evolution strategies 'benchmarking' for thin film optimization

Since I have been running the ETM/ITM coatings optimization many times, I decided to "benchmark" (really just visualize) the optimizer trajectories under different strategies offered by the scipy.optimize implementation of differential evolution. This was done by adding a callback function to keep track the convergence=val at every iteration. From the scipy.optimize.differential_evolution docs, this "val represents the fractional value of the population convergence".

Attachment 1 shows a modest collection of ~16 convergence trajectories for ETM and ITM as a function of the iteration number (limited by maxiter=2000) with the same targets, weights, number of walkers (=25), and other optimization parameters. The vertical axis plots the inverse val (so tending to small numbers represent convergence).

tl;dr: Put simply, the strategies using "binary" crossover schemes work better (i.e. faster) than "exponential" ones. Will keep choosing "best1bin" for this problem.

The HR coating specifications are:

ETM Transmission specs

2128.2 nm	5.0 ppm 2 ppm
1418.8 nm	50.0 ppm 2 ppm

ITM Transmission specs

2128.2 nm	2000.0 ppm 200 ppm
1418.8 nm	50.0 ppm 2 ppm

Analysis

• Main constraint: Relative arm finesses @ 2128.2 nm should not differ by > 1%.
• Secondary constraint: Relative arm finesses @ 1418.8 nm may differ, but the ETM and ITM pair should ensure critically coupled cavity to benefit ALS calibration PD shot noise.

Just took the finesse of a single arm:

and propagated transmissivities as uncorrelated variables to estimate the maximum relative finesse. Different tolerance combinations give the same finesse tolerance, so multiple solutions are possible. I simply chose to distribute the relative tolerance in T for the test masses homogeneously to simultaneously maximize the individual tolerances and minimize the joint tolerance.

A code snippet with the numerical analysis may be found here.

Tue Jun 8 11:52:44 2021 Update

The arm cavity finesse at 2128 nm will be mostly limited by the T = 2000 ppm of the ITM, so the finesse changes mostly due to this specification. Assuming that the vendor will be able to do the two ETM optics in one run (x and y), we really don't care so much about the mean value achieved in this run as much as the relative one. Therefore, the 200 ppm tolerance (10% level) is allowed at the absolute level, but a 20 ppm tolerance (1% level) is still preferred at the relative level; is this achievable?. Furthermore, for the AUX wavelength, we mostly care about achieving critical coupling but there is no requirement between the arms. Here a 20 ppm tolerance at the absolute level should be ok, but a 2 ppm tolerance between runs is highly desirable (although it seems crazier); is this achievable?

Here is a set of curves describing the single-pass downconversion efficiency in the 20 mm long PPKTP crystals for the DOPO. I used the "non-depleted pump approximation" and assumed a plane-wave (although the intensity matches the peak intensity from a gaussian beam). Note that these assumptions will in general tend to overestimate the conversion efficiency.

The parameters use an effective nonlinear coefficient "d_eff" of 4.5 pm/V, and assume we have reached the perfect (quasi) phase matching condition where delta_k = 0 (e.g. we are at the correct crystal operating temperature). The wavelengths are 1064.1 nm for the pump, and 2128.2 nm for degenerate signal and idler. The conversion efficiency here is for the signal photon (which is indistinguishable from the idler, so am I off by a factor of 2?)...

Attachment 1 shows the single pass conversion efficiency "eta" as a function of the pump power. This is done for a set of 5 minimum waists, but the current DOPO waist is ~ 35 um, right in the middle of the explored range. What we see from this overestimates is an almost linear-in-pump power increase of order a few %. I have included vertical lines denoting the damage threshold points, assuming 500 kW / cm ^2 for 1064.1 nm (similar to our free-space EOMs). As the waist increases, the conversion efficiency tends to increase more slowly with power, but enables a higher damage threshold, as expected.

At any rate, the single-pass downconversion efficiency is (over)estimated to be < 5 % for our current DOPO waist right before the damage threshold of ~ 10 Watts, so I don't think we will be able to use the amplified pump (~ 20-40 W) unless we modify the cavity design to allow for larger waist modes.

The important figure (after today's group meeting) would be a single pass downconversion efficiency of ~ 0.5 % / Watt of pump power at our current waist of 35 um (i.e. the slope of the curves below)

[Paco]

I've re-run the HR coating designs for both ETM and ITM using interpolated dispersions (presumably at room temperature). The difference is shown in Attachment #1 and Attachment #2.

Basically, all features are still present in both spectral transmission plots, which is consistent with the relatively flat dispersions from 1 to 3 um in Silica and Tantala thin films, but the index corrections of a few percent from low-temperature estimates to room-temperature measured (?) dispersions are able to push the HR transmission up by a few (2-3) times. For instance, the ETM transmission at 2128.2 nm goes up by ~ 3. The new number is still well below what we have requested for phase I so this is in principle not an issue.

A secondary change is the sensitivity (the slope around the specified wavelength) which seems to have increased for the ETM and decreased for the ITM. This was another consideration so I'm running the optimizer to try and minimize this without sacrificing too much in transmission. For this I am using the stack as a first guess in an attempt to run fast optimization. Will post results in a reply to this post.

[Paco]

Alright, I've done a re-optimization targetting a wider T band around 2128 nm. For this I modified the scalar minimization cost to evaluate the curvature term (instead of the slope) around a wide range of 10% (instead of 1%). Furthermore, in prevision of the overall effects of using the updated dispersion, I intentionally optimized for a lower T such that we intentionally overshoot.

The results are in Attachment #1 and Attachment #2.

[Paco, Nina]

We have been working on an estimate of the wavelength dependent emissivity for the mariner test mass HR coatings. Here is a brief summary.

We first tried extending the thin film optimization code to include extinction coefficient (so using the complex index of refraction rather than the real part only). We used cubic interpolations of the silica and tantala thin film dispersions found here for wavelengths in the 1 to 100 um range. This allowed us to recompute the field amplitude reflectivity and transmissivity over a broader range. Then, we used the imaginary part of the index of refraction and the thin film thicknesses to estimate the absorbed fraction of power from the interface. The power loss for a given layer is exponential in the product of the thickness and the extinction coefficient (see eq 2.6.16 here) . Then, the total absorption is the product of all the individual layer losses times the transmitted field at the interface. This is true when energy conservation distributes power among absorption (=emission), reflection, and transmission:

The resulting emissivity estimate using this reasoning is plotted as an example in Attachment #1 for the ETM design from April. Two things to note from this; (1) the emissivity is vanishignly small around 1419 and 2128 nm, as most of the power is reflected which kind of makes sense, and (2) the emissivity doesn't quite follow the major absorption features in the thin film interpolated data at lower wavelengths (see Attachment #2), which is dominated by Tantala... which is not naively expected?

Maybe not the best proxy for emissivity? Code used to generate this estimates is hosted here.

[Paco, Nina, Aidan]

Updated the stack emissivity code to use the Kitamura paper fused silica dispersion which has a prominent 20 um absorption peak which wasn't there before... (data was up to 15 um, and extrapolated smoothly beyond). The updated HR stack emissivities are in Attachments #1 - #2. A weird feature I don't quite understand is the discontinous jump at ~ 59 um ... 

[Paco, Nina, Aidan]

We ran our stack emissivity calculation on different AR stacks to try and make a decision for the TM barrel coatings. This code has yet to be validated by cross checking against tmm as suggested by Chris. The proposed layer structures by Aidan and Nina are:

1. *| Air || SiO2 x 800 nm || Ta2O5 x 5 um || Silicon |*
2. *| Air || Ta2O5 x 10 um || Sio2 x 20 nm || Silicon |*
3. *| Air || SiO2 x 100 nm || TiO2 x 1 um || Silicon |*

Attachments # 1-3 show the emissivity curves for these simple dielectric stacks. Attachment #4 shows the extinction coefficient data used for the three different materials. The next step is to validate these results with tmm, but so far it looks like TiO2 might be a good absorbing film option.

Agree with this. Quickly running tmm on the same "stacks" gave the Attachment #1-3. (Ignore the vertical axis units... will post corrected plots) and extend the wavelength range to 100 um.

[Paco]

I used the HITRAN database to download the set of ro-vibrational absorption lines of CO2 (carbon dioxide) near 2.05 um. The lines are plotted for reference vs wavenumber in inverse cm in Attachment #1.

Then, in Attachment #2, I estimate the broadened spectrum around 2.05 um and compare it against one produced by an online tool using the 2004 HITRAN catalog.

For the broadened spectrum, I assumed 1 atm pressure, 296 K temperature (standard conditions) and a nominal CO2 density of 1.96 kg/m^3 under this conditions. Then, the line profile was Lorentzian with a HWHM width determined by self and air broadening coefficients also from HITRAN. The difference between 2050 nm and 2040 nm absorption is approximately 2 orders of magnitude; so 2040 nm would be better suited to avoid in-air absorption. Nevertheless, the estimate implies an absorption coefficient at 2050 nm of ~ 20 ppm / m, with a nearby absorption line peaking at ~ 100 ppm / m. 

For the PMC, (length = 50 cm), the roundtrip loss contribution by in-air absorption at 2050 nm would amount to ~ 40 ppm. BUT, this is nevery going to happen unless we pump out everything and pump in 1 atm of pure CO2. So ignore this part.

Tue Nov 9 08:23:56 2021 UPDATE

Taking a partial pressure of 0.05 % (~ 500 ppm concentration in air), the broadening and total absorption decrease linearly with respect to the estimate above. Attachment #3 shows the new estimate.

For the PMC, (length = 50 cm), the roundtrip loss contribution by in-air absorption at 2050 nm would amount to ~ 1 ppm.

[Paco]

There was an error in the last plot of the previous log. This was correctly pointed out by rana's pointing out that the broadening from air should be independent of the CO2 concentration, so nominally both curves should coincide with each other. Nevertheless, this doesn't affect the earlier conclusions -->

The PMC loss by background, pressure broadened absorption lines at 2049.9 nm by CO2 is < 1 ppm.

The results posted here are reflected in the latest notebook commit here.