Broadband Millimeter-Wave Anti-Reflection Coatings on Silicon Using Pyramidal Sub-Wavelength Structures
Karl Young, Qi Wen, Shaul Hanany, Hiroaki Imada, Jürgen Koch, Tomotake Matsumura, Oliver Suttmann, Viktor Schütz
BBroadband Millimeter-Wave Anti-Reflection Coatings on Silicon UsingPyramidal Sub-Wavelength Structures
Karl Young, a) Qi Wen, Shaul Hanany, Hiroaki Imada, J¨urgen Koch, Tomotake Matsumura, OliverSuttmann, and Viktor Sch¨utz School of Physics and Astronomy, and Minnesota Institute for Astrophysics,University of Minnesota/Twin Cities, 116 Church St. SE Minneapolis, MN 55455,USA Japan Aerospace Exploration Agency (JAXA) - Institute of Space and Astronautical Science (ISAS),3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan. Laser Zentrum Hannover e.V., Hollerithallee 8, 30419 Hannover, Germany Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI),Todai Institutes for Advanced Study, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583,Japan (Dated: 12 November 2018)
We used two novel approaches to produce sub-wavelength structure (SWS) anti-reflection coatings (ARC) onsilicon for the millimeter and sub-millimeter (MSM) wave band: picosecond laser ablation and dicing withbeveled saws. We produced pyramidal structures with both techniques. The diced sample, machined ononly one side, had pitch and height of 350 µ m and 972 µ m. The two laser ablated samples had pitch of180 µ m and heights of 720 µ m and 580 µ m; only one of these samples was ablated on both sides. We presentmeasurements of shape and optical performance as well as comparisons to the optical performance predictedusing finite element analysis and rigorous coupled wave analysis. By extending the measured performanceof the one-sided diced sample to the two-sided case, we demonstrate 25 % band averaged reflectance of lessthan 5 % over a bandwidth of 97 % centered on 170 GHz. Using the two-sided laser ablation sample, wedemonstrate reflectance less than 5 % over 83 % bandwidth centered on 346 GHz. I. INTRODUCTION
Silicon is an appealing optical material for the mil-limeter and sub-millimeter (MSM) region of the elec-tromagnetic spectrum, approximately between 30 and3000 GHz. It has a high index of refraction n = 3 . tan δ < − . It thus gives higher aberra-tion correction power and higher transmission efficiencycompared to plastic lenses, as well as easier machinabil-ity and lower loss compared to alumina, which has asimilar index of refraction. The high index of refrac-tion also causes substantial reflections. Without anti-reflection coatings (ARC) the two surfaces of a 10 mmthick disc give band-averaged (∆ ν/ν = 30 %) reflectanceof 46 %.Silicon is used as a lens material for astrophysical in-struments in the MSM and as a lens and grism ma-terial in the infrared. Various ARC approaches havebeen implemented including gluing Cirlex, vapor de-position of Parylene, lithography and ion etching ofsub-wavelength structures (SWS), and SWS cut us-ing standard dicing saws. Fabricating SWS is a partic-ularly appealing ARC technique because it can providea broadband coating without the need to match indicesof several materials and because it is robust to cryogeniccycles.In this paper we present two novel approaches to fab-ricating SWS-ARC on silicon: laser ablation and dicing a) Electronic mail: [email protected] with beveled saws. Our ultimate motivation is the de-velopment of scalable techniques to produce lenses forbroadband cosmic microwave background (CMB) po-larization instruments which are observing with frac-tional bandwidths of 60–110% and are plannedwith 150% fractional bandwidth. With these instru-ments the lenses are typically maintained at cryogenictemperatures, and it is important they exhibit low in-strumental polarization.We have recently demonstrated the first laser ablatedSWS-ARC on sapphire and alumina.
Ablation of sil-icon has been investigated under different conditions, including varying power levels, wavelengths, andpulse durations. Several authors investigated theuse of gas-assisted laser ablation to produce SWS onsilicon.
The grid spacing of the resulting structuresmakes them most suitable for visible and near infraredwavelengths. To our knowledge, this paper is the first toreport on the ablation of SWS-ARC for the MSM wave-band.In Section II we describe our samples and the SWS fab-rication. In Section III we describe and discuss measure-ments of the shapes of the SWS. We discuss transmissionand reflection measurements between 70 and 700 GHz inSection IV, and summarize our results in Section V. a r X i v : . [ a s t r o - ph . I M ] J un TABLE I. Physical properties of each sample.Sample Method Sides Coated Refractive Index Thickness Diameter Resistivity[mm] [mm] [Ω · cm]Flat1 ( F1 ) No ARC No ARC 3.405 ± ± > F2 ) No ARC No ARC 3.417 ± ± > L1 ) Laser one side 3.405 ± ± > L2 ) Laser both sides 3.417 ± ± > D ) Dicing saw one side 3.405 ± ± > II. SAMPLES AND FABRICATIONA. Samples
We fabricated two samples using laser machining,called L1 and L2 , and one using a dicing saw, called D . L1 and D were processed on one side only; L2 wasprocessed on both sides. We also measured two unpro-cessed flat discs, called F1 and F2 . These samples wereused to cross-check the measurements against analyticpredictions and to determine the index of refraction andloss tangents of the other samples.The high-resistivity silicon discs for F1 , D , and L1 werepart of the same order and arrived in the same ship-ment. We therefore assumed the same material proper-ties for all three. Using reflectance measurements we fitfor the index and loss tangent of F1 and found n = 3 . < − ; see Figure 1. Samples F2 and L2 were from a second order and shipment, so we as-sumed the same material properties for both. We mea-sured transmittance of F2 , fit for index and loss, andfound n = 3 .
417 and loss tangent < − . Table I sum-marizes the information about the samples.
200 400 600Frequency / GHz0.00.20.40.60.81.0 R e f l e c t a n c e FIG. 1. Reflectance of a flat 2 mm thick silicon disc, sample F1 (blue points), and theoretical prediction (red, solid) withthe best fit index n = 3 .
405 and no loss. Measurement errors(blue) are discussed in Section IV A.
B. Laser ablation
We machined L1 and L2 with parameters that weresimilar to our earlier laser ablation of SWS on aluminaand sapphire; the parameters of the geometry and thecoordinate system are shown in Figure 2. The laser op-erated at a wavelength of 515 nm with a repetition rateof 400 kHz, 7 ps pulse width, and an average power of28.5 W for L1 and 27 W for L2 . The beam was focusedat the surface of the silicon disc and had a 1 /e widthof 8 µ m. The laser was scanned across the entire sampleat 2.5 m/sec in a raster pattern as shown in Figure 3.This pattern created a series of orthogonal grooves andpyramids with a designed pitch of 180 µ m. The scanwas repeated 80 times. The total machining time for L1 was 3.4 hours for a 5 cm diameter disc. For L2 the gridpatterns on the two sides were oriented at 45 ◦ with re-spect to each other. The total machining time for bothsides was 6.8 hours. We did not attempt to optimize theablation rate. FIG. 2. Side view sketch defining key shape parametersof the SWS. The hatched region is silicon. The changingamount of silicon relative to vacuum creates a gradual changein index of refraction along the z -axis. C. Dicing saw
Sample D was machined using a custom made beveleddicing saw. The blade had a maximum thickness of300 µ m. Imaging the profile of the first cut, we measured FIG. 3. The laser scanned L1 and L2 in a raster pattern.A single ‘scan’ consists of sequentially passing through allhorizontal (blue) lines, then all vertical (red) lines. The scanswere repeated 80 times for both L1 and L2 . Each group ofblue lines spaced by 6 µ m eventually makes a single groove.The 90 µ m gaps are the areas where material is not ablated,leaving the tips of the pyramids. that the blade tip was ≤ µ m wide and the bevel anglewas 81.6 ◦ providing a usable cutting depth of 1.04 mm.We produced pyramids by cutting 108 parallel groovessymmetrically placed about a diameter with a feed rateof 1 mm/sec, rotating the sample by 90 ◦ ± .
05, and cut-ting 107 more grooves with a feed rate of 0.8 mm/sec.The grooves had a designed pitch p = 350 µ m and de-signed depth h = 1000 µ m to produce square pyramidswith w = 52 µ m. During machining, less than 1 % of thepyramids broke. The total machining time was 3 hours. III. SHAPE MEASUREMENTS AND RESULTSA. Measurements
We used a Nikon A1RMP confocal microscope to im-age L1 and L2 . The surfaces of D were too smooth toproduce sufficient diffuse reflection, so we used a KeyenceVHX-5000 optical microscope. Both microscopes had x, y plane resolution of 2 µ m. We imaged 9 locationson L1 and 5 locations on each side of L2 . At each lo-cation we took a series of images spaced in z by 5 µ mand constructed a 3-dimensional image and a height map.Examples are shown in Figures 4 and 5, respectively.Using the images, we measured the geometrical prop-erties of the samples, including the height h , pitch p ,and, where relevant, the width of the peak w . The abla-tion caused deeper troughs at the intersection of grooves.We determined the height of the L1 and L2 pyramids byfinding the median z coordinate of the peaks and troughs, the red and blue regions seen in Figure 5. The measuredheight is quoted as the difference between these medians.Table II gives the mean height, pitch, and width, and thestandard deviations of the values across all imaged areas. TABLE II. Geometric parameters of SWS.Sample Height a Pitch a Peak width a [ µ m] [ µ m] [ µ m] D ± ± ± L1 ±
20 182 ± b L2 (side A) 600 ±
15 179 ± b L2 (side B) 560 ±
20 179 ± ba The uncertainty quoted is the standard deviationfrom multiple imaged areas. b L1 and L2 did not have well-defined flat peaks. For D we found it more instructive to image a sideview along the y -axis and view the SWS in profile inthe x − z plane. This view is shown in Figure 6. Forthis sample, since the grooves were of uniform depth, thepyramid height was the same as the depth of the groove.We measured the depth of 17 grooves in the center ofthe sample by imaging the cut profiles. The mean andstandard deviation are given in Table II. To characterizeblade wear we also imaged two grooves, one made 100cuts after the other, a total of cut length 465 cm. Thedepth difference was 33 µ m. B. Comments Regarding the Laser Ablated Shapes
The measured pitch of L1 and L2 matches the de-sign value. It is a factor of 2.2 smaller than the pitchreported by Datta et al. who used sequential dicingwith commercially available dicing saws. It is a factor of1.8 smaller than the pitch of the SWS we recently laser-ablated on alumina and sapphire. The height of the L2 pyramids was 17 % smaller thanthe height of pyramids on L1 , while the laser power wasonly 5 % lower. We suggest the following explanation. L2 was three times thicker than L1 , implying that dur-ing ablation at similar incident power L1 was likely tobe hotter than L2 . Thorstensen and Foss reported adecrease in the ablation threshold of silicon with increas-ing temperature. Therefore the ablation threshold of L1 was lower than that of L2 . In an earlier publication wenoted that ablation along a sloped face stops when theenergy density of the beam dilutes below the ablationthreshold. The effect is purely geometrical—a normallyincident beam becomes elliptical when projected onto theablated, sloped surface—and thus the maximum slope iscalculable from a known ablation threshold. The higherthe ablation threshold, the shallower the maximum slope.We hypothesize the combination of lower laser power andhigher ablation threshold, due to the cooler substrate, FIG. 4. Perspective view of laser ablated silicon, sample L1 .The brightest parts are the peaks of the SWS. Y p o s i t i o n , µ m H e i g h t , µ m FIG. 5. Height map of laser ablated silicon, sample L1 .Double blue and green lines mark the position along which weextracted the 1-dimensional height profiles shown in Figure 7.The width between the lines corresponds to the portion of theheight map averaged to produce the profile. produced a shallower slope angle on L2 of 84 ◦ vs 85 ◦ on L1 . This is sufficient to explain the difference in heights.The ablation images show most of the pyramid tips FIG. 6. Side-view image of D . The dark areas are silicon andthe light are air. are cracked. This may be a consequence of excessivelyhigh energy density. With this silicon ablation we areusing 1 . · J/m /pulse. With sapphire, also a singlecrystal, we used an energy density per pulse that was15 times lower and observed no cracking. The majorityof the factor of 15 is due to the 3.75 times smaller spotdiameter we used with silicon, a consequence of strivingto reach smaller pitch and pyramid tips. The ablatedshape repeatability is good as shown in Figure 7. H e i g h t , µ m FIG. 7. Height profiles of L1 . The profiles were producedfrom cuts through peak centers, as shown in Figure 5. Cutsat constant y are in green; constant x are in blue. C. Comments Regarding the Diced Pyramid Shapes
The SWS on D were a regular array of truncated,square-based pyramids which matched the designed pitchof 350 µ m but were 25 µ m shorter than the 1000 µ m de-signed height. The height discrepancy was likely due touncertainty in the absolute surface position of the waferwhile being machined. However, the cut-to-cut repeata-bility in height was 3 µ m or better as shown by the smallmeasured variation in height across 17 successive cuts.We measured a 33 µ m decrease in structure height af-ter 100 cuts, 465 cm of cut length. This difference wasdue to either blade wear or a slightly tilted sample mount.Assuming the entire height difference was due to bladewear, we calculated 0.07 µ m of wear per cm of cut length.If a large sample was machined, it would be importantto re-zero the blade position or continuously adjust thedepth to account for wear. Measurements on a differentblade indicated negligible wear over 160 cuts, 720 cm ofcut length. More data is needed before definitive infor-mation is available regarding beveled blade wear.Sample D showed a negligible number of broken pyra-mids. We did not attempt to optimize the trade-off be-tween structure robustness, blade feed-rate, and bladewear. Datta et al. used a factor of 50 higher feed-rate,suggesting the feed-rate with the beveled saw can be in-creased. IV. OPTICAL PERFORMANCEA. Measurement Procedure
We measured the reflectance of L1 , L2 , D , and F2 intwo polarizations and six frequency bands between 70and 720 GHz: 70–120 GHz, 110–170 GHz, 140–260 GHz,215–320 GHz, 310–480 GHz, and 460–720 GHz. We mea-sured F1 at the same frequencies, but in one polarizationonly. We measured transmittance of F2 , L1 , and L2 infour bands between 70 and 320 GHz: 70–120 GHz, 110–170 GHz, 140–260 GHz, and 215–320 GHz. The measure-ments were made at the Institute for Terahertz Scienceand Technology (ITST) at the University of California,Santa Barbara. The reflectance setup is described in Bai-ley et al. The transmittance setup was similar but thesample was placed just after the source, and a gold mir-ror replaced the reflectance sample. All measurementswith samples were normalized using data runs withoutsamples.The ITST data were taken twice for each measure-ment without changing the setup. The difference betweenthese measurements was used to remove outliers and es-timate a measurement error per point. An example ofone such difference, from the pair of measurements on F1 , is shown in Figure 8. There are two primary sourcesof higher levels of noise: (1) lower source power outputnear band edges, and (2) an atmospheric water line at557 GHz. From the pair difference data we calculatedthe mean and the median absolute deviation (MAD) perband. The means were always within one MAD of zero.We removed as outliers all data with difference greaterthan 4 .
200 400 600Frequency / GHz1.00.80.60.40.20.00.20.40.60.81.0 R - R FIG. 8. Difference of two successive reflectance measurementsof sample F1 including data that pass (blue dots) and arerejected (red crosses) by the 4.5 median absolute deviation(MAD) criterion. Estimated measurement error per point(blue) is shown with one representative error per band atan arbitrary vertical offset for clarity. The horizontal extentis the bandwidth. See the text and the Appendix for moredetails. B. Measurements
Figures 9, 10, and 11 show reflectance measurementsof L1 , L2 , and D as well as the sum of transmittanceand reflectance, where relevant. The Figures also givethe upper frequency limit ν d = c/ ( np ) where diffractionbecomes significant due to the pitch of the SWS. Wediscuss this diffraction in Section IV C.To characterize the polarization properties of the sam-ples we calculated the difference in reflectance betweenmeasurements in two orthogonal polarizations. Figure 12shows the reflectance data for L2 . It also shows the levelof instrumental polarization (IP) defined as IP = T (cid:107) − T ⊥ T (cid:107) + T ⊥ . (1)Instrumental polarization represents the level of conver-sion of unpolarized to polarized light by an instrumentor one of its components. To calculate IP we used thereflectance data for each sample and assumed low loss; T = 1 − R . For L1 , L2 , and D the maximum IP, averaged R + T
200 400 600Frequency / GHz0.00.20.40.60.81.0 R e f l e c t a n c e T r a n s m i tt a n c e FIG. 9. Reflectance (blue), transmittance (orange), and theirsum (black) of L1 as a function of frequency. The average re-flectance is near 0.3 because this sample was laser ablatedon one side only. FEA predictions (red) match the data wellup to frequencies somewhat above ν d = c/ ( np ) = 485 GHz(black arrow), beyond which diffraction is expected to be sig-nificant; see Section IV C. Measurement errors per data point(orange and blue) are adjacent to their respective data andare discussed in Section IV A and Figure 8. across 25 % fractional bandwidth, from 70–700 GHz was1.2 %, 1.4 %, and 1.6 % respectively.Measurements in two polarization states on F2 , forwhich the IP should have been zero, gave band averaged(∆ ν/ν = 25 %) IP of less than 0 . . . ∼ C. Modeling
We modeled transmittance and reflectance using anelectromagnetic finite element analysis code (HFSS) and in some cases augmented it with calculations usingrigorous coupled-wave analysis (RCWA). We used the 3-dimensional image of L1 to constructa solid model of a single pyramid. This model pyramidwas imported into the FEA and placed on a 1.287 mmthick substrate (the thickness of the native sample minus0.720 mm, the height of L1 ). An infinite planar samplewas simulated using periodic boundary conditions.We reconstructed a single pyramid for each side of L2 ,placed them on each side of a 4.871 mm substrate, andsimulated L2 in the same way as L1 . To facilitate pe-riodic boundary conditions we ignored the 45 ◦ rotationbetween the patterns on the two sides.For D , we constructed a square based, truncated pyra-mid using h , p , and w as measured and reported in Ta- ble II. The pyramid was placed on a 1.037 mm thicksubstrate and duplicated using periodic boundary condi-tions.The results of the FEA simulations are shown in Fig-ures 9, 10, and 11. There was generally good agreementbetween simulations and data at frequencies up to andsomewhat above the ‘diffraction frequency’ ν d = c/ ( np ),which is marked with a black arrow. For L2 the datahave a fringe pattern that has 4 % lower frequency thanthe simulation. We comment on this in Section IV D.The frequency ν d was the lowest frequency at which weexpected diffraction and constructive interference insidethe substrate to be significant. The constructive interfer-ence was due to the periodic structure of the pyramidsand occurred at frequencies above ν d,lm = cnp (cid:112) l + m . (2)where l and m are integers. At frequencies above ν d = c/ ( np ) the FEA showed strong reflections, but the datado not.We cross-checked the results of the FEA using RCWA.Figure 13 shows the measured reflectance of D and thesimulated reflectance using RCWA and FEA. All threewere consistent below ν d = 252 GHz. Above 252 GHz,at which the effect of diffraction was expected to ap-pear with modes ( l, m ) = (1 ,
0) = (0 , Q resonances which produce sharp spikes in reflec-tion. However, the real sample was finite and consistedof pyramids which were all different in shape. A detailedcomparison between the FEA, RCWA, and the data inthe diffraction regime is beyond the scope of this paper,but it is interesting to note that measured data did notshow the strong diffraction features suggested by sim-ple calculations, indicating that the usable bandwidth ofSWS-ARC may not be limited by ν d = c/ ( np ). D. Comments Regarding Optical Performance
Since FEA simulations agreed with measurements be-low ν d , we assessed performance of L1 and D up to ν d by simulating silicon substrates coated on both sides withSWS matching those measured for L1 and D . These sim-ulations are shown in Figure 14 along with the measuredreflectance of L2 . The Figure also shows reflectance aver-aged over 25 % fractional bandwidth, as would be appro-priate for typical CMB experiments using bolometers.Beveled dicing saws are an efficient way to removematerial and are thus suitable for fabricating relativelydeep, large pitch structures. Therefore, beveled saws areparticularly suitable for applications at lower frequen-cies. Averaged over ∆ ν/ν = 25 % fractional bandwidth, R + T
100 200 300 400 500 600 700Frequency / GHz0.00.20.40.60.81.0 R e f l e c t a n c e T r a n s m i tt a n c e FIG. 10. Reflectance (blue), transmittance (orange), and their sum (black) of L2 as a function of frequency. FEA predictions(red) match the overall reflectance envelope up to ν d = c/ ( np ) = 490 GHz (black arrow), beyond which diffraction is expectedto be significant (see Section IV C) and is observed in the FEA data.
200 400 600Frequency / GHz0.00.20.40.60.81.0 R e f l e c t a n c e FIG. 11. Reflectance of D (blue) and FEA simulations (red)using the geometry shown in Table II. The black arrow at ν d = c/ ( np ) = 252 GHz is where diffraction first becomessignificant within the sample. reflectance drops below 5 % at 87 GHz. Doubling ofthe height of the pyramid would halve this frequencyto approximately 44 GHz. Laser ablation is more effi-cient when patterning smaller structures. When aver-aged with 25 % fractional bandwidth, reflectance on thesimulated two-sided L1 drops below 5 % at 144 GHz.The bandwidth with less than 5 % reflectance extendsup to ν d = 485 GHz, and higher if ν d turns out to notlimit the performance of the SWS. That these are real-istic predictions is demonstrated by measurements of L2 (Figure 14). Defining the high frequency edge of an ‘ef-fective band’ as ν d and the low frequency edge as ν l , welist the effective bands for L1 , L2 , and D , in Table III.The frequency ν l is that frequency at which the 25 % frac- R e f l e c t a n c e
200 400 600Frequency / GHz05 I P ( % ) FIG. 12. Upper panel: Reflectance from two orthogonal po-larizations (blue, green) for L2 , and running averages over a25 % fractional bandwidth (magenta and cyan). Lower panel:Instrumental polarization calculated from the reflectance data(blue) and a running average over 25 % fractional bandwidth(red). tional bandwidth averaged reflectance drops below 5 %.The Table also gives the average reflectance within theeffective band.We attribute the difference in fringe frequency betweenthe simulation of L2 and data (Figure 10) to a crude ap-proximation of the sample. As discussed in Section IV C,the simulation is based on duplicating only one pyramidfor each side of the surface, thus ignoring variations inshape, pyramid height, and thickness of the remainingmaterial.All three data sets, the simulated two-sided D and L1 , and the measured L2 , suggest a straight pyra- (cid:1)(cid:2)(cid:1)(cid:1)(cid:2)(cid:3)(cid:1)(cid:2)(cid:4)(cid:1)(cid:2)(cid:5)(cid:1)(cid:2)(cid:6)(cid:7)(cid:2)(cid:1) (cid:1) (cid:1) (cid:1) (cid:7)(cid:1)(cid:1) (cid:1) (cid:3)(cid:1)(cid:1) (cid:1) (cid:8)(cid:1)(cid:1) (cid:1) (cid:4)(cid:1)(cid:1) (cid:1) (cid:9)(cid:1)(cid:1) (cid:1) (cid:5)(cid:1)(cid:1) (cid:1) (cid:10)(cid:1)(cid:1) (cid:1) (cid:2) (cid:3) (cid:2) (cid:4) (cid:5) (cid:6)(cid:7) (cid:4) (cid:2) (cid:11)(cid:12)(cid:13)(cid:14)(cid:15)(cid:13)(cid:16)(cid:17)(cid:18) (cid:1) (cid:19) (cid:1) (cid:20)(cid:21)(cid:22) FIG. 13. Top: The measured reflectance (blue), and the sim-ulated reflectance using RCWA (green) and HFSS(red).TABLE III. Optical performance of SWS-ARC.Sample Effective band Average reflectance a [GHz] [%] L1 b L2 D b a Averaged over the Effective band. b From two sided FEA simulation using measuredSWS shape. mid is not the optimal shape. There is a lobe of in-creased reflectance at frequencies above the onset of low-reflectance. Impedance matching theory suggests the im-plementation of a Klopfenstein profile to reduce thislobe. V. SUMMARY
We presented two novel approaches to producing ARCon silicon for the MSM: laser ablation and dicing withbeveled saws. The optical performance is summarizedin Table III. The SWS, laser ablated on both sides of asilicon disc, reduced 25 % band averaged reflectance tobelow 5 % over a fractional bandwidth of 83 % centeredon 346 GHz. The dicing saw structures were larger, inboth pitch and height, making them effective at lower fre-quencies. The dicing saw structures reduced reflectanceto below 5 % over a fractional bandwidth of 97 % centeredon 170 GHz. These effective bandwidths are sufficient formost currently deployed cosmic microwave backgroundinstruments, but would need to be increased to 150 %fractional bandwidth to meet the needs of all upcominginstruments. The effective band of both methods was R e f l e c t a n c e
100 200 300 400 500 600 700Frequency / GHz0.00.10.20.30.4
FIG. 14. Comparison of the three samples in reflectance(blue) and reflectance averaged over 25 % fractional band-width (magenta). D (top) and L1 (middle) are simulationsof two-sided samples while L2 (bottom) is measured data.The dashed black lines indicate reflectance of 5 %. limited by the structure height at low frequencies andpitch at high frequencies.Machining times for both methods were similar. Ittook 3.4 hours to ablate one side of a 20 cm disc and3 hours to machine 16 cm with dicing saws. Machiningtime for both methods can be improved by optimizingthe machining parameters. To our knowledge, this isthe first SWS-ARC for the MSM produced using thesetechniques. ACKNOWLEDGMENTS
We thank two anonymous referees for detailed andhelpful comments. The authors acknowledge use of re-sources provided by the University of Minnesota Imag-ing Center ( http://uic.umn.edu ) and Minnesota Super-computing Institute ( ). Theresearch described in this paper used facilities of the Mid-west Nano Infrastructure Corridor (MINIC), a part ofthe National Nanotechnology Coordinated Infrastructure(NNCI) program of the National Science Foundation.The transmittance and reflectance measurements wereperformed at the ITST Terahertz Facilities at UCSB,which have been upgraded under NSF Award No. DMR-1126894. This work was partially supported by JSPSKAKENHI Grant Number 15H05441; the Mitsubishifoundation (grant number 24, JFY2015, in science andtechnology); the World Premier International ResearchCenter Initiative (WPI), MEXT, Japan; and the JSPSCore-to-Core Program, Advanced Research Networks.
Appendix: Data Cuts and Error Estimation
To remove outliers and estimate uncertainty per pointwe used the difference between two subsequent data runson the same sample with the setup unchanged. The dif-ference vs frequency for F1 is shown in Figure 8 and weuse these data as an example. The same procedure wasused with pair differences for all measurements.Pair difference distributions and cumulative distribu-tions for each of the 6 measurement bands are shownin Figures 15 and 16, respectively. The data are notGaussian-distributed and therefore the standard devia-tion σ is a poor estimator for the variance for the ma-jority of the data. We used the median absolute de-viation (MAD) instead. For a Gaussian distribution σ/ MAD = 1 .
48, however this ratio ranged between 2.5and 2 × for the 6 pair difference measurements of F1 . The calculated standard deviations for each of the 6bands are shown in Figure 15.We removed all points that were more than 4.5 MADfrom the mean of the difference data. This cut removedthe majority of the long outlier tail; see Figure 16. Wechose this criterion because for a Gaussian distribution3 σ = 4 . | R − R | did not depend on which data set was la-beled 1 or 2. These measurement errors are plotted atan arbitrary vertical offset in Figures 1, 8, 9, 10, 11, and12. The horizontal extent shows the width of each of thefrequency bands.We tested the sensitivity of our calculated values tovarious data cuts. The values which could be affectedare average reflectance on L2 , and the maximum IP for D , L1 , and L2 . Using the cumulative distributions, we re-moved data in each band with the largest pair differencevalues using thresholds which kept 70 %, 80 %, 90 %,or 95 % of the data. Across these removal criteria wefound average reflectance on L2 changed by 0.1 percent-age points. Maximum IP changed by less than 0.3 per-centage points for D and L1 and by 0.8 for L2 . J. W. Lamb, Int. J. IR and Millimeter Waves , 1997 (1996). R. J. Thornton, P. A. R. Ade, S. Aiola, F. E. Angil`e, M. Amiri,J. A. Beall, D. T. Becker, H.-M. Cho, S. K. Choi, P. Corlies, K. P.Coughlin, R. Datta, M. J. Devlin, S. R. Dicker, R. D¨unner, J. W.Fowler, A. E. Fox, P. A. Gallardo, J. Gao, E. Grace, M. Halpern,M. Hasselfield, S. W. Henderson, G. C. Hilton, A. D. Hincks,S. P. Ho, J. Hubmayr, K. D. Irwin, J. Klein, B. Koopman, D. Li,T. Louis, M. Lungu, L. Maurin, J. McMahon, C. D. Munson,S. Naess, F. Nati, L. Newburgh, J. Nibarger, M. D. Niemack,P. Niraula, M. R. Nolta, L. A. Page, C. G. Pappas, A. Schillaci,B. L. Schmitt, N. Sehgal, J. L. Sievers, S. M. Simon, S. T. Staggs,C. Tucker, M. Uehara, J. van Lanen, J. T. Ward, and E. J.Wollack, Ap. J. Suppl. , 21 (2016). J. R. Eimer, P. A. R. Ade, D. J. Benford, C. L. Bennett, D. T.Chuss, D. J. Fixsen, A. J. Kogut, P. Mirel, C. E. Tucker, G. M.Voellmer, and E. J. Wollack, in
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