Broadband, millimeter-wave anti-reflective structures on sapphire ablated with femto-second laser
R. Takaku, S. Hanany, H. Imada, H. Ishino, N. Katayama, K. Komatsu, K. Konishi, M. Kuwata-Gonokami, T. Matsumura, K. Mitsuda, H. Sakurai, Y. Sakurai, Q. Wen, N. Y. Yamasaki, K. Young, J. Yumoto
BBroadband, millimeter-wave anti-reflective structures on sapphire ablatedwith femto-second laser
R. Takaku, a) S. Hanany, H. Imada, H. Ishino, N. Katayama, K. Komatsu, K. Konishi, M.Kuwata-Gonokami, T. Matsumura, K. Mitsuda, H. Sakurai, Y. Sakurai, Q. Wen, N. Y. Yamasaki, K.Young, and J. Yumoto
1, 5 Department of Physics, University of Tokyo, Tokyo, Japan School of Physics and Astronomy, University of Minnesota, Twin Cities, Minneapolis,USA Kavli Institute for Physics, Mathematics for Universe, University of Tokyo, Japan Okayama University, Okayama, Japan Institute for Photon Science and Technology, the University of Tokyo, Tokyo, Japan Institute of Space and Astronautical Science, Japanese Aerospace Exploration Agency, Kanagawa,Japan (Dated: 31 July 2020)
We designed, fabricated, and measured anti-reflection coating (ARC) on sapphire that has 116% fractional bandwidthand transmission of at least 97% in the millimeter wave band. The ARC was based on patterning pyramid-like sub-wavelength structures (SWS) using ablation with a 15 W femto-second laser operating at 1030 nm. One side of each oftwo discs was fabricated with SWS that had a pitch of 0.54 mm and height of 2 mm. The average ablation volume re-moval rate was 1.6 mm /min. Measurements of the two-disc sandwich show transmission higher than 97% between 43and 161 GHz. We characterize instrumental polarization (IP) arising from differential transmission due to asymmetricSWS. We find that with proper alignment of the two disc sandwich RMS IP across the band is predicted to be 0.07% atnormal incidence, and less than 0.6% at incidence angles up to 20 degrees. These results indicate that laser ablation ofSWS on sapphire and on other hard materials such as alumina is an effective way to fabricate broad-band ARC. I. INTRODUCTION
Sapphire, alumina, and silicon have material properties thatmake them appealing for use as optical elements in the mil-limeter and sub-millimeter (MSM) waveband, loosely definedas 30 - 3000 GHz. Compared to plastic-based materials, theyhave indices of refraction near 3, giving more aberration cor-rection power per unit lens thickness . They have amongstthe lowest absorption loss at room temperature and whencooled to cryogenic temperatures , and they have thermal con-ductance higher by factors of hundreds, making them usefulfor cryogenic applications . Sapphire has 10% birefringencemaking it an ideal half-wave plate (HWP) material for polari-metric applications. A number of astrophysical instrumentsoperating in the MSM waveband are using these materials .The high index of refraction leads to high reflection loss;the average reflectance across 30% fractional bandwidth of a1 cm thick slab of non-birefringent sapphire at 150 GHz is40%. Reduction of reflection loss is achieved by applyingan anti-reflection coating (ARC). There are two generic ap-proaches for implementing ARC: (i) applying layers of mate-rials with appropriately chosen intermediate indices; and (ii)machining sub-wavelength structures (SWS) on the native op-tical element material . An advantage of the SWS approach isthat it does not require new materials and glues. This advan-tage matches well the needs of cryogenic instruments in whichdifferences in coefficients of thermal expansion make the ap-plication of multi-layers challenging. Another advantage is a) Electronic mail: [email protected] that SWS give flexibility in synthesizing any index profile be-tween free space and the substrate material. Prescriptions ex-ist for index profiles that give fractional bandwidths exceeding100% with maximal, in some sense optimal, in-band transmis-sion .Two classes of MSM instruments that require broad-bandwidths and cryogenic optical elements are those mappingthe spatial polarization of the cosmic microwave backgroundradiation (CMB) , and others measuring the propertiesof Galactic dust . A number of these instruments haveused, or plan to use, sapphire as HWP polarization modulator.To reduce detector noise the HWP is maintained at cryogenictemperatures, typically near 4 K, and to increase instrumentthroughput a single HWP operates over a broad range of fre-quencies, making a single quarter-wave layer of ARC inade-quate. Examples of relevant past instruments include Blastpoland EBEX, which had sapphire HWPs with operating band-width of 69% and 109%, respectively . The bandwidth ofthe EBEX HWP is the largest reported to date. Ongoing andfuture experiments include POLARBEAR2, Simons Observa-tory and LiteBIRD .LiteBIRD is a Japanese-led space mission scheduled to belaunched late in the next decade . LiteBIRD’s low fre-quency telescope (LFT), designed to operate between 34 and161 GHz (a fractional bandwidth of 130%), will have an aper-ture diameter of 40 cm with a HWP operating at 20 K. Cur-rently no ARC technology on sapphire is available over thisbroad bandwidth. Implementing SWS ARC for the LiteBIRDHWP has motivated the developments we report in this paper.Although SWS have advantages as ARC, their implemen-tation on hard materials such as sapphire and alumina presentfabrication challenges . Broad bandwidths require SWS a r X i v : . [ a s t r o - ph . I M ] J u l with aspect ratios – defined as height/pitch – reaching four.Diameters of anticipated sapphire and alumina optical ele-ments, which are reaching 80 cm , require commerciallyviable machining speed. To overcome these challenges wedemonstrated a technique to fabricate mm-wave SWS on sap-phire, alumina, and silicon using laser micro-fabrication .With laser ablation, which has already been used in the pastto ablate these and other materials , there is no wear andtear of the machining tool. Even for materials that can bemachined using conventional tools, laser ablation gives finercontrol of structure shapes, because laser spot diameters canbe focused to smaller sizes than other tools. Finer controlof SWS shapes would give higher transmission over broaderbandwidth.Schütz et al. and Matsumura et al. (Refs. 24 and 26) demon-strated laser-ablated aspect ratios a = . µ m, with sapphire and alumina, respec-tively. Young et al. (Ref. 25) extended the technique to silicon,showing a = µ m. To demonstrate ap-plicability to lower frequencies and broader bandwidths, Mat-sumura et al. (Ref. 27) fabricated structures with a = . . In this paper we present progress in thedesign, fabrication, and characterization of laser-ablated SWSARC, aiming for 130% fractional bandwidth ARC centeredon 97 GHz with improved fabrication speed. In Section II, wepresent the design of the SWS. Sections III and IV give detailsof the fabrication of two sapphire samples and their transmis-sion properties. We discuss the results and give conclusionsin Sections V and VI. II. DESIGN
LiteBIRD’s LFT, one of three telescopes aboard the space-craft , will operate over a frequency range between 34 and161 GHz. The focal plane will have about 1200 bolometricdetectors tuned to nine broad-band, ∼
25% fractional band-width frequency bands. A single HWP placed at the entranceaperture of the LFT will modulate the polarization of sky sig-nals across the entire bandwidth. Thus, the goal is to demon-strate SWS ARC with 130% fractional bandwidth centered on97 GHz.Klopfenstein (Ref. 9) derived a prescription for impedancematching between free space and a sample of index n . Theprescription gives an optimal index of refraction profile anddepends on a parameter Γ m that controls the trade-off betweenthe lowest frequency of the passband and transmission ripplein-band . All values of Γ m between 0.01 and 0.1 give aver-age band transmission between 98% and 99%, and we chose FIG. 1. Geometrical parameters of pyramidal-shaped SWS. Theshape of the pyramids (right panel) is controlled by a parameter α defined by Equation 1. Other parameters are the tip width w , theperiod p , the width at the bottom of the pyramid p (cid:48) , the groove width b , and the height h . Γ m = .
055 as a fiducial value. With this value average trans-mission is near 99%. There are several approaches to trans-forming the index profile to a physical shape but there is nosingle closed-form solution . We employ an empirical de-sign approach: we construct physical shapes and use effectivemedium theory (EMT) and rigorous coupled-wave analy-sis (RCWA) to calculate the resulting index profile. Wechoose the physical shape that most closely reproduces thedesired Klopfenstein index profile. RCWA calculations werecarried out using DiffractMOD .We model the SWS as a grid of identical pyramids, see Fig-ure 1. We search for a pyramid shape that closely matches theKlopfenstein index profile by constructing a shape functionthat gives the width of the pyramid as a function of distance z from the substrate material w ( z ) = w + { ( p − b ) − w } { − ( z / h ) α } , (1)where the parameters are defined in Figure 1. A value of α = α ,but in all cases used p = .
54 mm and h = . a = .
7. The pitch p is set by requiring that at normal inci-dence the smallest value of the highest pass-band frequencybe ν high = c / p n s =
180 GHz. Thus p = λ high / n s = .
54 mm,where n s = .
06 is the index of c-cut sapphire. Smaller valueof p implies shorter λ high , higher ν high , and thus larger band-width. In Section V B we discuss non-normal incidence.Guidance for the minimum required h is obtained by consid-ering the lowest pass-band frequency and applying the stan-dard criterion for maximum transmission with a single ARClayer that has a uniform index n l . In that case n l = √ n s , andthe thickness of the layer should be t = λ / n l , where λ is the vacuum wavelength. For the pyramids we found em-pirically that h should satisfy h (cid:38) λ / n l = . λ = . h (cid:61) . w was determined iteratively by trying several values. We deter-mined that w = . n = b = p = p (cid:48) (see Figure 1).We used second-order EMT to calculate the effective in- FIG. 2. Top: EMT-calculated index profiles for four values of α (colored lines, Equation 1), and the Klopfenstein index profile with Γ m = .
055 (black). The other physical parameters used to calculatethe index profiles are h = . p = .
54 mm, w = . b =
0. Bottom: calculated transmittance as a function of frequencyfor SWS designs with the parameters given in the upper panel. Sharpreflection features above 180 GHz are due to the onset of diffraction. dex of refraction as a function of α , and RCWA to calculatethe expected transmission as a function of frequency; see Fig-ure 2. A convex pyramid shape with α = . Γ m . The average band transmissions for α = . , . III. SAMPLE PREPARATION AND CHARACTERIZATIONA. Sapphire
We procured three samples of c-cut sapphire that werecut from the same ingot, each 3 . ± .
002 mm thick and100 mm diameter. We used one sample and the apparatus dis-cussed in Section IV to measure the index of refraction andloss and obtained n = . ± .
002 and tan δ < × − ,which is consistent with other data . In subsequent analysisand simulations we assume that these values are common toall three samples.We fabricated the SWS on a circular area of 34.5 mm diam-eter on one side of each of two samples, to which we refer asSample 1 and Sample 2. We patterned only one side becauseLiteBIRD’s LFT HWP will be a Pancharatnam multi-stackachromatic HWP with SWS only on the outermost surfaces.In Section IV we present transmission measurements of eachsample and when they are stacked flat side on flat side.Using c-cut, non-birefringent sapphire, simplifies interpre-tation of the results. At normal incidence, which is the only experimental data we present here, any apparent birefringenceis the result of asymmetry in fabrication, not of inherent asym-metry in the material, as would be the case with birefringenta-cut sapphire. B. Laser machining
The SWS are patterned using a 15 W average power femto-second laser operating at 1030 nm; the laser parameters aregiven in Table I. The laser beam scans lines in two orthogonaldirections to make grooves, and thus produce the pyramids;see Figure 3. This scan strategy largely follows an approachwe used in the past, see for example Young et al. (Ref 25). Thefocus position is set at a fixed z = − .
75 mm throughout theablation. The surface of the disk at the beginning of ablationis at z = TABLE I. Laser SpecificationsModel: Pharos, PH1-15WWavelength 1030 nmRepetition rate 75 kHzPulse duration 290 fsPulse energy 200 µ JSpot diameter (1 / e ) 15.5 µ mFIG. 3. Sketch of the laser beam scan pattern to fabricate the SWS.Repeated ablation of groups of 53 lines produces grooves. The linesare internally spaced by less than 10 µ m and the groups are separatedby at least 72 µ m. Grooves fabricated in two orthogonal directionsleave pyramids, which are the SWS. Layers similar to the one shownin the sketch are repeated 60 times until the desired SWS height isachieved. FIG. 4. Left: Confocal microscopy image of a section of the fab-ricated SWS. The structures are physically intact across the entiresample and the average height is 2 mm. Right: Definition of mea-surement parameters. Averages of 800 measurements of these pa-rameters are given in Table II.
C. Characterization of fabricated structures
The SWS were imaged using confocal imaging. A three-dimensional image of a section of the fabricated region isshown in Figure 4. Visual inspection indicates that all SWSare physically intact with no breakage nor damaged tips. Wemeasured 160 structures at each of five locations in each sam-ple, in the center and in four edge regions, and quantified sev-eral geometrical parameters as detailed in Figure 4 and Ta-ble II. Values given in the Table are averages and standarddeviations of the 800 measurements. We established a globalcartesian coordinate system that was aligned with the grooves,and for each measured pyramid we defined xz and yz planesthat intersected the center of its peak. For both planes (andfor each pyramid) we quantified the widths w x and w y andtwo ‘saddle’ heights d x and d y , which quantified the depthsbetween pyramids in the x and y directions. The total height h t is given by the depth into trenches in the diagonal directionwhere the laser beam ablates in both the x and y passes. Webest-fit the slopes of the pyramids as imprinted in the xz and yz planes to produce measured α x and α y .There is good agreement between the design and fabricatedvalues for the pitch and total height, and there is x - y sym-metry in the measured pitch. There is good repeatability be-tween the two samples, which were fabricated several daysapart. Asymmetry of 5%-20% is apparent at the tip of thestructures, the saddle heights, and the slope values α . Thisstructural asymmetry could have been caused by laser beampolarization, which was not monitored; by the ablation scanstrategy, for example the order in which x and y directionswere scanned; or by laser beam projection, if the sample wasnot precisely normal to the beam.It took 10.5 hours to fabricate each sample giving an aver-age volume removal rate (AVRR) of 1.6 mm /min. This rateis 18 times faster than achieved in one of our earlier publica-tions . The higher rate is due to using five times higher av-eraged power and a more efficient sample scan pattern. Mat-sumura et al. (Ref. 24) report a higher AVRR of 2.2 mm /min,but with higher power (25 W) and for SWS with smaller total TABLE II. Averages of measured geometrical parameters of 800pyramids measured in five regions of each sample. The parametersare defined in Figure 4.Parameter Design value Sample 1 Sample 2(mm) (mm) (mm)Top width x ( w x ) 0.1 0 . ± .
01 0 . ± . y ( w y ) 0.1 0 . ± .
01 0 . ± . x ( d x ) 1 . ± .
04 1 . ± . y ( d y ) 1 . ± .
04 1 . ± . h t ) 2.0 2 . ± .
04 2 . ± . x ( p (cid:48) x ) 0.54 0 . ± .
01 0 . ± . y ( p (cid:48) y ) 0.54 0 . ± .
01 0 . ± . α x † . ± .
06 1 . ± . α y † . ± .
02 1 . ± . † dimensionless quantity height of 715 µ m; Schuetz et al. (Ref. 26) show that AVRRincreases with power and lower structure height.Using EMT and the average values given in Table II we cal-culated effective index profiles in x and y for each sample; seeFigure 5. To indicate the variance we included the index pro-files for all 800 measured structures as shaded regions. As thevalues in Table II indicate, the measured profiles in x matchthe design profile with α = . y . FIG. 5. The effective index of refraction calculated with EMT usingthe average values of the measured SWS (solid red and green), andwith the design values and α = . IV. TRANSMISSION
We measured the transmittance of the samples at nor-mal incidence between 33 and 190 GHz. The apparatus, aschematic of which is shown in Figure 6, consisted of a sourceof microwaves, an optical chopper operating at 30 Hz, twoparabolic mirrors, a diode detector, and a lock-in amplifier.Between the two mirrors there was an aperture of 30 mm di-ameter, a sample holder, attenuators to reduce standing waves,and two always identically aligned wire grid polarizers withcalculated efficiency exceeding 99% across the bandwidth.The transmission axis of the polarizers was aligned to within3 degrees with the x axis of the samples, and the stacked sam-ples were aligned relative to each other to within 0.5 degrees.To further reduce the effects of standing waves our reportedtransmittance at each frequency is the average of two trans-mission measurements taken with the detector positioned attwo locations spaced by λ / FIG. 6. Schematic of the transmittance measurement setup. Addi-tional details are given by Komatsu et al. (Ref. 39).
We measured the transmittance of each sample and of bothmechanically attached flat-side to flat-side. The two sampleswere held together; no glue was used. The samples werestacked with x orientations aligned parallel to each other. Eachof the measurements was conducted with the transmissionaxis of the wire grid polarizers parallel and perpendicular tothe x axis of the samples. We refer to these measurements as T x and T y , respectively, indicating that the incident and mea-sured polarization states align with the x and y orientations FIG. 7. Top Panel: Transmittance measurement of the flat sample(blue data) and two-parameter fit (solid orange) including the indexof refraction and loss tangent. The measurement was done in fivesub-bands indicated by horizontal bars. Bottom panel: residual, dataminus fit, from which we infer error bars. We conservatively take theerror bar per datum in each sub-band to be the RMS of the residualin the sub-band. of the samples. The measurements are shown in Figure 8 to-gether with the predicted transmission, which was calculatedusing RCWA and was based on the average values given in Ta-ble II and no loss. The transmittances T x and T y of individualsamples agree with predictions and are only ∼ T x and T y data for the lowest LiteBIRD fre-quency band between 34 and 46 GHz. For the second lowestband between 43 and 58 GHz the average is 97%. Other fre-quency bands have above 98% averaged transmittance. At fre-quencies above 150 GHz the transmittance of the stack is de-creasing and is lower than predicted. A χ analysis using dataover the entire bandwidth (33-190 GHz) and varying the losstangent in the fit model gives a minimum for tan δ < · − ,which is consistent with measurements with the native sam-ple.While determining the precise source for lower transmit-tance at higher frequencies is beyond the scope of this paper,we discuss several candidates. Calculations indicate that auniform 30 µ m air gap between the stacked samples couldexplain the observed feature. Measurements set an upperlimit of 24 µ m. Ruze scattering from a flat surface with30 µ m RMS roughness could decrease transmittance to 95%at 180 GHz . This roughness value is close to the 30 µ muncertainty we quote for SWS height measurements (see Ta-ble II), which could be interpreted as an effective roughness.However, transmission measurements of the single samplesindicate lower levels of effective roughness. Laser ablationof the SWS modifies the material properties near the surfaceand the modified material may exhibit higher loss comparedto the native single crystal. Evidently, any such higher lossis not sufficiently prominent to be exhibited with significantsignal-to-noise ratio with transmission measurements of theindividual samples. A combination of these effects could bethe source for the lower transmission. FIG. 8. Transmittance measurements T x and T y (blue data) of each sample (top four panels), of the samples stacked flat side to flat side(bottom row), and transmission predictions (red lines) based on the measured mean parameters given in Table II. In the bottom row, the platesare stacked with x of one parallel to x of the other. V. SYSTEMATIC EFFECTS
The two-dimensional rectangular-like nature of the z -axisprojection of the SWS is a potential source of polarimet-ric systematic effects. Systematic asymmetry in fabricationalong the two orthogonal axes, due to laser beam polariza-tion or birefringent material properties (if such is used), leadsto different effective indices of refraction along the two axes.Differential index causes differential transmission, which is asource of instrumental polarization (IP), the conversion of un-polarized to polarized light by the optical element. Even whenthe structures are two-dimensional symmetric there is differ-ential reflection at non-normal incidence, as there would withany ARC scheme; differences in transmission between S andP polarization states of the incident light lead to IP.To quantify the IP induced by normal incidence differentialtransmission we use the figure of merit IP ( ν ) = T x ( ν ) − T y ( ν ) T x ( ν ) + T y ( ν ) (2) = T ( φ = ◦ , ν ) − T ( φ = ◦ , ν ) T ( φ = ◦ , ν ) + T ( φ = ◦ , ν ) , (3)where we have introduced in the last expression the rela-tive rotation angle φ between the x orientation of the sam-ple and the direction along which transmission is probed. IP vanishes for normal incidence light when the substrate andARC are z -projected isotropic. At normal incidence Equa-tions 2 and 3 could have been written equivalently in terms of T s ≡ T ( φ = o ) and T p ≡ T ( φ = o ) , the transmissions for Sand P polarization states.At non-normal incidence and in the presence of x - y ARCasymmetry T s and T p depend on both the angle of incidence θ i and on the azimuthal angle φ of the plane of incidence,measured relative to x . We now haveIP ( φ , θ i , ν ) = T s ( φ , θ i , ν ) − T p ( φ , θ i , ν ) T s ( φ , θ i , ν ) + T p ( φ , θ i , ν ) . (4)In the following two Sections we quantify systematic ef-fects due to asymmetry in the fabricated SWS at normal in-cidence (Section V A) and due to non-normal incidence (Sec-tion V B), and discuss the level of mitigation provided by ap-propriately stacking the two-disc sandwich. We refer to ‘par-allel’ and ‘perpendicular’ configurations, in which the twoplates are stacked with their x axes parallel, or with x of oneperpendicular to x of the other, respectively. In the perpendic-ular configuration the quantities T x and T y refer to transmissionmeasurements relative to the x axis of the source-side sampleof the stack, which was Sample1. A. Asymmetry of SWS at normal incidence
Figure 9 shows IP inferred from the measured data (Fig-ure 8) for the individual samples and when stacked in the par-allel configuration. It also shows the calculated response (us-ing RCWA) using the average parameters for the x and y ori-entations in Table II. We find values of IP reaching 10% at fre-quencies below 100 GHz for the individual samples, and be-low 50 GHz for the parallel stacking. For the entire bandwidththe RMS IP is 2.5%. At frequencies higher than 50 GHz, IP inthe parallel stacking configuration is smaller than in the indi-vidual samples because of higher transmission and because ofsome averaging of the two somewhat different asymmetries.However, the calculation shows that if the plates were stackedin the perpendicular configuration there would have been astrong reduction across the band. The RMS IP is 0.07%, 35times smaller than in the parallel case; see Figure 9. FIG. 9. Instrumental polarization due to differential transmission IPfor each of the samples and when stacked with x axes parallel (bluedata points, top three panels), and RCWA predictions for IP (solid,red) based on the average measured values (Table II). For perpendic-ular stacking (bottom two panels, each with different vertical range),calculated RMS IP for the bandwidth is 0.07%. The vertical dashedline shows the 90 GHz frequency for which we made measurementsas a function of stack rotation angle; see Figure 10. Figure 10 gives data and RCWA predictions for normal in-cidence transmittance as a function of stacked sample rotationangle φ for the two configurations at 90 GHz. Concentratingon the parallel configuration first, the effective differential in-dex in x and y is an effective stack birefringence that causes8.6% modulation as a function of φ with π / . = ¯ T ( φ = ◦ ) − ¯ T ( φ = ◦ ) ¯ T ( φ = ◦ ) + ¯ T ( φ = ◦ ) , (5)with θ i = o , ν =
90 GHz, and ¯ T indicates that we averageall T values at the φ indicated and with π / π / π / π period-icity. Given the 1 σ = .
4% measurement uncertainty the dataonly give a 2 σ upper limit of IP < . ± . π / π -periodic modulation amplitudes, calculated using Equations 5and 3, are consistent with zero within measurement errors.The transmission data as a function of φ , such as presentedin Figure 10, reveal that measurements at only two orienta-tions x ( φ = ) and y ( φ = o ) as shown in Figure 9 and IPcalculated using Equation 2 combine information from dis-tinct physical effects. The effects correspond to, and canbe quantified with higher accuracy using decomposition toFourier harmonics . We fit the data of Figure 10 to themodel T ( φ , ν =
90 GHz ) = a + a cos ( φ + C ) + a cos ( φ + C ) , (6)and constrain the amplitudes and phases. We find IP = a / a = . ± .
2% and 0 . ± . a / a = . ± .
2% and 0 . ± . a / a and a / a . We find that (1) the π and π / a / a and a / a aremore tightly constrained compared to using Equations 3 and 5;(2) the modulation amplitude constraints calculated using thetwo techniques are consistent; (3) there is a significant detec-tion of IP, that is, π periodic modulation, in the parallel casebut not in the perpendicular case; and (4) the relatively large7.9% π / B. Non-normal incident light
Optical systems are designed to admit rays over a range ofincidence planes and angles and thus calculations of system-atic effects arising from ARC SWS asymmetry should take
FIG. 10. Stacked sample transmittance at 90 GHz (blue points) asa function of stack rotation angle φ for the parallel (top two panels)and perpendicular (bottom two panels) configurations, and RCWApredictions based on the measured parameters in Table II (red solid).The lower panel in each pair has a limited range for the ordinatevalues. Shaded regions indicate the 2% systematic uncertainty weassign to each data point in this frequency. The statistical uncertaintyper data point is 0.2%. account of the entire range of incidence planes and angles. In-cluding the full range amounts to averaging that gives smallersystematic effects compared to using a single incidence planeand the extreme incidence angle. In the discussion belowwe analyze the effects of non-normal incidence angles with-out any such averaging, and therefore the quantitative val-ues should be understood as upper limits. The analysis reliessolely on RCWA calculations of the perpendicular configura-tion; we have already established that this configuration hassmaller level of systematic effects.The upper panel of Figure 11 shows calculated IP ( φ = ) as a function of frequency for normal incidence and for the 5,10, 15 and 20 degrees incidence angle. For normal incidencethe calculation is identical to the one shown in the lower panelin Figure 9. The lower panel shows the difference betweentransmission at normal incidence and at other angles, againfor φ =
0. For LiteBIRD’s maximum planned incidence angleof 15 degrees RMS IP across the band is 0.4%, an increase of 0.3% relative to normal incidence. At 20 degrees incidence,RMS IP increases to 0.6%. For φ =
90 degrees, RMS IP val-ues at 15 and 20 degrees incidence are smaller by 0.1%.Onset of diffraction is apparent at lower frequencies withlarger incidence angles. For off-normal incidence, the fre-quency of diffraction onset – that is, at the lowest order –is ν d = cp ( n + sin θ i ) , (7)providing qualitative agreement with the RCWA calculation.We do not expect exact quantitative agreement because theRCWA calculation assumes the full average shape informa-tion for the two samples, as given in Table II, whereas Equa-tion 7 only assumes a periodic array of scattering centers. FIG. 11. RCWA prediction of IP ( φ = ) for various incidence an-gles (upper panel), and the difference of off-normal incidence spec-tra with normal incidence spectra (lower panel), all in the case ofperpendicular stacking configuration. VI. CONCLUSIONS
SWS have advantages as ARC because they obviate theneed for multiple materials and glues with precisely tuned in-dices of refraction, and because the index gradient producedcan be smoother and tailored to specific applications. SWSare superior for cryogenic applications, because there is noneed to match materials with different coefficients of thermalexpansion. Fabricating SWS on alumina and sapphire – ma-terials that have favorable optical properties in the millime-ter and sub-millimeter wave band – using standard machiningapproaches has been challenging because both materials areamong the hardest available. They rank 9/10 on the relativehardness Mohs scale, and sapphire (alumina) has a value of2500 (2000) HV on the Vickers hardness scale. In this pa-per we have extended our development of laser ablation as atool to fabricate SWS for the millimeter and sub-millimeterband. We demonstrated structures on sapphire with aspectratio a = .
7. The newly fabricated SWS give a workingbandwidth of 130% with transmission above 90% centered on97 GHz, and of 116% with transmission of at least 97% cen-tered on 102 GHz, arguably the largest bandwidths yet demon-strated in this wavelength range.Using shorter pulse duration higher power laser and a moreefficient fabrication process we have accelerated the AVRRfor sapphire by a factor of 18 to 1.6 mm /min. Further ac-celeration is achievable with increase in laser power andimprovements in fabrication efficiency.Although the native material was non-birefringent, wefound shape asymmetries in the fabricated SWS. Future dis-covery of the asymmetries’ origin will indicate the path fortheir elimination. However, we showed that proper relativealignment of samples reduces the magnitude of induced in-strumental polarization due to differential reflection by a fac-tor of 35 to 0.07% at normal incidence, and to less than 0.6%for incidence angles up to 20 degrees.These results and newer ones showing even higher ablationrates indicate that laser ablation of SWS on sapphire andon other hard materials such as alumina is an effective wayto fabricate broad-band ARC; the technique has particularlystrong advantages in the case of cryogenic applications. ACKNOWLEDGMENTS
We acknowledge the World Premier International ResearchCenter Initiative (WPI), MEXT, Japan for support throughKavli IPMU. This work was supported by JSPS KAK-ENHI Grant Numbers JP17H01125, 19K14732, 18J20148,18KK0083, and JSPS Core-to-Core Program, A. AdvancedResearch Networks. This work was also supported by theNew Energy and Industrial Technology Development Organi-zation (NEDO) project “Development of advanced laser pro-cessing with intelligence based on high-brightness and highefficiency laser technologies” and Council for Science, Tech-nology and Innovation (CSTI), Cross-ministerial Strategic In-novation Promotion Program (SIP).
DATA AVAILABILITY
The data that support the findings of this study are availablefrom the corresponding author upon reasonable request. James W. lamb. Miscellaneous data on materials for millimetre and sub-millimetre optics.
International Journal of Infrared and Millimeter Waves ,12 1996. V. V. Parshin, R. Heidinger, B. A. Andreev, A. V. Gusev, and V. B. Shmagin.Silicon as an advanced window material for high power gyrotrons.
Inter-national Journal of Infrared and Millimeter Waves , 16(5):863–877, May1995. Gregg E. Childs, Lewis J. Ericks, and Robert L. Powell.
Thermal Con-ductivity of Solids At Toom Temperature and Below . Monogram. 131. U.S.Department of commerce, 1973. National Bureau of Standards BoulderColorado 80302 september. R. J. Thornton, P. A. R. Ade, S. Aiola, F. E. Angilè, 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. Dünner, J. W. Fowler, A. E. Fox, P. A. Gal-lardo, 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. Koop-man, Dale Li, T. Louis, M. Lungu, L. Maurin, J. McMahon, C. D. Mun-son, S. Naess, F. Nati, L. Newburgh, J. Nibarger, M. D. Niemack, P. Ni-raula, 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. Ue-hara, J. van Lanen, J. T. Ward, and E. J. Wollack. THE ATACAMA COS-MOLOGY TELESCOPE: THE POLARIZATION-SENSITIVE ACTPolINSTRUMENT.
The Astrophysical Journal Supplement Series , 227(2):21,dec 2016. Asad M. Aboobaker, Peter Ade, Derek Araujo, François Aubin, CarloBaccigalupi, Chaoyun Bao, Daniel Chapman, Joy Didier, Matt Dobbs,Christopher Geach, Will Grainger, Shaul Hanany, Kyle Helson, Seth Hill-brand, Johannes Hubmayr, Andrew Jaffe, Bradley Johnson, Terry Jones,Jeff Klein, Andrei Korotkov, Adrian Lee, Lorne Levinson, Michele Limon,Kevin MacDermid, Tomotake Matsumura, Amber D. Miller, Michael Mil-ligan, Kate Raach, Britt Reichborn-Kjennerud, Ilan Sagiv, Giorgio Savini,Locke Spencer, Carole Tucker, Gregory S. Tucker, Benjamin Westbrook,Karl Young, and Kyle Zilic. The EBEX balloon-borne experiment—optics,receiver, and polarimetry.
The Astrophysical Journal Supplement Series ,239(1):7, nov 2018. J. Sobrin, P. Ade, Z. Ahmed, A. J. Anderson, J. Avva, R. Basu Thakur,A. Bender, B. Benson, J. Carlstrom, F. Carter, T. Cecil, C. Chang, J. Ding,A. Harke-Hosemann, J. Henning, T. Khaire, S. Kuhlmann, V. Novosad,J. Pearson, C. Posada, G. Wang, and V. Yefremenko. Design and charac-terization of the SPT-3G receiver. In , volume10708, pages – ,. Millimeter, Submillimeter, and Far-Infrared Detectorsand Instrumentation for Astronomy IX, 2018, 10.1117/12.2314366. Daisuke Kaneko, S. Adachi, P. A. R. Ade, M. Aguilar Faúndez, Y. Ak-iba, K. Arnold, C. Baccigalupi, D. Barron, D. Beck, S. Beckman, F. Bian-chini, D. Boettger, J. Borrill, J. Carron, S. Chapman, K. Cheung, Y. Chi-none, K. Crowley, A. Cukierman, M. Dobbs, R. D˝unner, H. El-Bouhargani,T. Elleflot, J. Errard, G. Fabbian, S. M. Feeney, C. Feng, T. Fujino,N. Galitzki, A. Gilbert, N. Goeckner-Wald, J. Groh, G. Hall, N. W.Halverson, T. Hamada, M. Hasegawa, M. Hazumi, C. A. Hill, L. Howe,Y. Inoue, G. Jaehnig, O. Jeong, N. Katayama, B. Keating, R. Keskitalo,S. Kikuchi, T. Kisner, N. Krachmalnicoff, A. Kusaka, A. T. Lee, D. Leon,E. Linder, L. N. Lowry, A. Mangu, F. Matsuda, Y. Minami, M. Navaroli,H. Nishino, J. Peloton, A. T. P. Pham, D. Poletti, G. Puglisi, C. L. Reichardt,C. Ross, Y. Segawa, M. Silva-Feaver, P. Siritanasak, N. Stebor, R. Stompor,A. Suzuki, O. Tajima, S. Takakura, S. Takatori, D. Tanabe, G. P. Teply,T. Tomaru, C. Tsai, C. Verges, B. Westbrook, and Y. Zhou. Deploymentof polarbear-2a.
Journal of Low Temperature Physics , 199(3):1137–1147,May 2020. Hemant K. Raut, V. Anand Ganesh, Appukuttan Sreekumaran Nair, andSeeram Ramakrishna. Anti-reflective coatings: A critical, in-depth review.Number 4, pages 3779–3804. Energy Environ. Sci. R. W. Klopfenstein. A transmission line taper of improved design.
Pro-ceedings of the IRE , 44(1):31–35, Jan 1956. B. R. Johnson, J. Collins, M. E. Abroe, P. A. R. Ade, J. Bock, J. Borrill,A. Boscaleri, P. de Bernardis, S. Hanany, A. H. Jaffe, T. Jones, A. T. Lee,L. Levinson, T. Matsumura, B. Rabii, T. Renbarger, P. L. Richards, G. F.Smoot, R. Stompor, H. T. Tran, C. D. Winant, J. H. P. Wu, and J. Zuntz.MAXIPOL: Cosmic microwave background polarimetry using a rotatinghalf-wave plate.
The Astrophysical Journal , 665(1):42–54, aug 2007. S. M. Simon, J. A. Beall, N. F. Cothard, S. M. Duff, P. A. Gallardo, S. P.Ho, J. Hubmayr, B. J. Koopman, J. J. McMahon, F. Nati, M. D. Niemack,S. T. Staggs, E. M. Vavagiakis, and E. J. Wollack. The advanced actpol27/39 ghz array.
Journal of Low Temperature Physics , 193(5):1041–1047,Dec 2018. Nicholas Galitzki, Aamir Ali, Kam S. Arnold, Peter C. Ashton, Jason E.Austermann, Carlo Baccigalupi, Taylor Baildon, Darcy Barron, James A.Beall, Shawn Beckman, Sarah Marie M. Bruno, Sean Bryan, Paolo G.Calisse, Grace E. Chesmore, Yuji Chinone, Steve K. Choi, Gabriele Coppi,Kevin D. Crowley, Kevin T. Crowley, Ari Cukierman, Mark J. Devlin, Si-mon Dicker, Bradley Dober, Shannon M. Duff, Jo Dunkley, Giulio Fabbian,Patricio A. Gallardo, Martina Gerbino, Neil Goeckner-Wald, Joseph E.Golec, Jon E. Gudmundsson, Erin E. Healy, Shawn Henderson, Charles A.Hill, Gene C. Hilton, Shuay-Pwu Patty Ho, Logan A. Howe, Johannes Hub-mayr, Oliver Jeong, Brian Keating, Brian J. Koopman, Kenji Kiuchi, Akito Kusaka, Jacob Lashner, Adrian T. Lee, Yaqiong Li, Michele Limon, Mar-ius Lungu, Frederick Matsuda, Philip D. Mauskopf, Andrew J. May, NialhMcCallum, Jeff McMahon, Federico Nati, Michael D. Niemack, John L.Orlowski-Scherer, Stephen C. Parshley, Lucio Piccirillo, Mayuri Sathya-narayana Rao, Christopher Raum, Maria Salatino, Joseph S. Seibert, Car-los Sierra, Max Silva-Feaver, Sara M. Simon, Suzanne T. Staggs, Jason R.Stevens, Aritoki Suzuki, Grant Teply, Robert Thornton, Calvin Tsai, Joel N.Ullom, Eve M. Vavagiakis, Michael R. Vissers, Benjamin Westbrook, Ed-ward J. Wollack, Zhilei Xu, and Ningfeng Zhu. The Simons Observatory:instrument overview. In Jonas Zmuidzinas and Jian-Rong Gao, editors,
Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentationfor Astronomy IX , volume 10708, pages 1 – 13. International Society forOptics and Photonics, SPIE, 2018. Maximilian H. Abitbol et al. CMB-S4 Collaboration. Cmb-s4 technologybook, first edition, 2017. Bradley J. Dober, Peter A. R. Ade, Peter Ashton, Francesco E. Angilè,James A. Beall, Dan Becker, Kristi J. Bradford, George Che, Hsiao-MeiCho, Mark J. Devlin, Laura M. Fissel, Yasuo Fukui, Nicholas Galitzki, Jian-song Gao, Christopher E. Groppi, Seth Hillbrand, Gene C. Hilton, JohannesHubmayr, Kent D. Irwin, Jeffrey Klein, Jeff Van Lanen, Dale Li, Zhi-YunLi, Nathan P. Lourie, Hamdi Mani, Peter G. Martin, Philip Mauskopf, Fu-mitaka Nakamura, Giles Novak, David P. Pappas, Enzo Pascale, Fabio P.Santos, Giorgio Savini, Douglas Scott, Sara Stanchfield, Joel N. Ullom,Matthew Underhill, Michael R. Vissers, and Derek Ward-Thompson. Thenext-generation BLASTPol experiment. In Wayne S. Holland and JonasZmuidzinas, editors,
Millimeter, Submillimeter, and Far-Infrared Detectorsand Instrumentation for Astronomy VII , volume 9153, pages 137 – 148.International Society for Optics and Photonics, SPIE, 2014. Nathan P. Lourie, Peter A. R. Ade, Francisco E. Angile, Peter C. Ash-ton, Jason E. Austermann, Mark J. Devlin, Bradley Dober, Nicholas Gal-itzki, Jiansong Gao, Sam Gordon, Christopher E. Groppi, Jeffrey Klein,Gene C. Hilton, Johannes Hubmayr, Dale Li, Ian Lowe, Hamdi Mani,Philip Mauskopf, Christopher M. McKenney, Federico Nati, Giles No-vak, Enzo Pascale, Giampaolo Pisano, Adrian Sinclair, Juan D. Soler, Ca-role Tucker, Joel N. Ullom, Michael Vissers, and Paul A. Williams. Pre-flight characterization of the BLAST-TNG receiver and detector arrays. InJonas Zmuidzinas and Jian-Rong Gao, editors,
Millimeter, Submillimeter,and Far-Infrared Detectors and Instrumentation for Astronomy IX , volume10708, pages 52 – 66. International Society for Optics and Photonics, SPIE,2018. A. Monfardini C. Tucker P.A.R. Ade A. Shitvov A. Benoit M. Calvo A.Catalano J. Goupy S. Leclercq J. Macias-Perez A. Andrianasolo N. Pon-thieu G. Pisano, A. Ritacco. Development and application of metamaterial-based half-wave plates for the nika and nika2 polarimeters, 2020. H. Sugai, P. A. R. Ade, Y. Akiba, D. Alonso, K. Arnold, J. Aumont,J. Austermann, C. Baccigalupi, A. J. Banday, R. Banerji, R. B. Barreiro,S. Basak, J. Beall, S. Beckman, M. Bersanelli, J. Borrill, F. Boulanger,M. L. Brown, M. Bucher, A. Buzzelli, E. Calabrese, F. J. Casas, A. Challi-nor, V. Chan, Y. Chinone, J.-F. Cliche, F. Columbro, A. Cukierman, D. Cur-tis, P. Danto, P. de Bernardis, T. de Haan, M. De Petris, C. Dickinson,M. Dobbs, T. Dotani, L. Duband, A. Ducout, S. Duff, A. Duivenvoorden,J.-M. Duval, K. Ebisawa, T. Elleflot, H. Enokida, H. K. Eriksen, J. Er-rard, T. Essinger-Hileman, F. Finelli, R. Flauger, C. Franceschet, U. Fuske-land, K. Ganga, J.-R. Gao, R. Génova-Santos, T. Ghigna, A. Gomez,M. L. Gradziel, J. Grain, F. Grupp, A. Gruppuso, J. E. Gudmundsson,N. W. Halverson, P. Hargrave, T. Hasebe, M. Hasegawa, M. Hattori,M. Hazumi, S. Henrot-Versille, D. Herranz, C. Hill, G. Hilton, Y. Hirota,E. Hivon, R. Hlozek, D.-T. Hoang, J. Hubmayr, K. Ichiki, T. Iida, H. Imada,K. Ishimura, H. Ishino, G. C. Jaehnig, M. Jones, T. Kaga, S. Kashima,Y. Kataoka, N. Katayama, T. Kawasaki, R. Keskitalo, A. Kibayashi,T. Kikuchi, K. Kimura, T. Kisner, Y. Kobayashi, N. Kogiso, A. Kogut,K. Kohri, E. Komatsu, K. Komatsu, K. Konishi, N. Krachmalnicoff,C. L. Kuo, N. Kurinsky, A. Kushino, M. Kuwata-Gonokami, L. Lam-agna, M. Lattanzi, A. T. Lee, E. Linder, B. Maffei, D. Maino, M. Maki,A. Mangilli, E. Martínez-González, S. Masi, R. Mathon, T. Matsumura,A. Mennella, M. Migliaccio, Y. Minami, K. Mistuda, D. Molinari, L. Mon-tier, G. Morgante, B. Mot, Y. Murata, J. A. Murphy, M. Nagai, R. Nagata,S. Nakamura, T. Namikawa, P. Natoli, S. Nerval, T. Nishibori, H. Nishino,Y. Nomura, F. Noviello, C. O’Sullivan, H. Ochi, H. Ogawa, H. Ohsaki,I. Ohta, N. Okada, L. Pagano, A. Paiella, D. Paoletti, G. Patanchon, F. Pi- acentini, G. Pisano, G. Polenta, D. Poletti, T. Prouvé, G. Puglisi, D. Ram-baud, C. Raum, S. Realini, M. Remazeilles, G. Roudil, J. A. Rubiño-Martín, M. Russell, H. Sakurai, Y. Sakurai, M. Sandri, G. Savini, D. Scott,Y. Sekimoto, B. D. Sherwin, K. Shinozaki, M. Shiraishi, P. Shirron, G. Sig-norelli, G. Smecher, P. Spizzi, S. L. Stever, R. Stompor, S. Sugiyama,A. Suzuki, J. Suzuki, E. Switzer, R. Takaku, H. Takakura, S. Takakura,Y. Takeda, A. Taylor, E. Taylor, Y. Terao, K. L. Thompson, B. Thorne,M. Tomasi, H. Tomida, N. Trappe, M. Tristram, M. Tsuji, M. Tsujimoto,C. Tucker, J. Ullom, S. Uozumi, S. Utsunomiya, J. Van Lanen, G. Ver-meulen, P. Vielva, F. Villa, M. Vissers, N. Vittorio, F. Voisin, I. Walker,N. Watanabe, I. Wehus, J. Weller, B. Westbrook, B. Winter, E. Wollack,R. Yamamoto, N. Y. Yamasaki, M. Yanagisawa, T. Yoshida, J. Yumoto,M. Zannoni, and A. Zonca. Updated design of the cmb polarization exper-iment satellite LiteBIRD.
Journal of Low Temperature Physics , 2020. Y. Sakurai et al. Design and development of a polarization modulatorunit based on a continuous rotating half-wave plate for LiteBIRD. InJonas Zmuidzinas and Jian-Rong Gao, editors,
Millimeter, Submillimeter,and Far-Infrared Detectors and Instrumentation for Astronomy IX , volume10708, pages 28 – 39. International Society for Optics and Photonics, SPIE,2018. L. A. O. Araujo, C. R. Foschini, R. G. Jasinevícius, and C. A. Fortulan. Pre-cision dicing of hard materials with abrasive blade.
The International Jour-nal of Advanced Manufacturing Technology , 86(9):2885–2894, Oct 2016. V.K Jain, S.K Choudhury, and K.M Ramesh. On the machining of alu-mina and glass.
International Journal of Machine Tools and Manufacture ,42(11):1269 – 1276, 2002. I.P. Tuersley, A. Jawaid, and I.R. Pashby. Review: Various methods ofmachining advanced ceramic materials.
Journal of Materials ProcessingTechnology , 42(4):377 – 390, 1994. H. A. Kishawy and A. Hoseini.
Machining difficult to cut materials: Basicprinciples and challenges . 2195. Springer International Publishing, 2019. Hong Li, Si-Yu Li, Yang Liu, Yong-Ping Li, Yifu Cai, Mingzhe Li, Gong-Bo Zhao, Cong-Zhan Liu, Zheng-Wei Li, He Xu, Di Wu, Yong-Jie Zhang,Zu-Hui Fan, Yong-Qiang Yao, Chao-Lin Kuo, Fang-Jun Lu, and XinminZhang. Probing primordial gravitational waves: Ali CMB PolarizationTelescope.
National Science Review , 6(1):145–154, 02 2018. Tomotake Matsumura, Karl Young, Qi Wen, Shaul Hanany, HirokazuIshino, Yuki Inoue, Masashi Hazumi, Jürgen Koch, Oliver Suttman, andViktor Schütz. Millimeter-wave broadband antireflection coatings usinglaser ablation of subwavelength structures.
Appl. Opt. , 55(13):3502–3509,May 2016. Karl Young, Qi Wen, Shaul Hanany, Hiroaki Imada, Jürgen Koch, To-motake Matsumura, Oliver Suttmann, and Viktor Schütz. Broadbandmillimeter-wave anti-reflection coatings on silicon using pyramidal sub-wavelength structures.
Journal of Applied Physics , 121(21), 6 2017. V. Schütz, K. Young, Tomotake Matsumura, Shaul Hanany, J. Koch, OliverSuttmann, Ludger Overmeyer, and Qi Wen. Laser processing of sub-wavelength structures on sapphire and alumina for millimeter wavelengthbroadband anti-reflection coatings. 11:204–209, 01 2016. T. Matsumura, R. Takaku, S. Hanany, H. Imada, Hirokazu Ishino,N. Katayama, Y. Kobayashi, K. Komatsu, K. Konishi, M. Kuwata-Gonokami, S. Nakamura, H. Sakurai, Y. Sakurai, Q. Wen, K. Young, andJ. Yumoto. Prototype demonstration of the broadband anti-reflection coat-ing on sapphire using a sub-wavelength structure. pages 54–60, January2018. 29th IEEE International Symposium on Space Terahertz Technol-ogy, ISSTT 2018 ; Conference date: 26-03-2018 Through 28-03-2018. J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner. Femtosecondlaser ablation of silicon–modification thresholds and morphology.
AppliedPhysics A , 74(1):19–25, Jan 2002. J. Ihlemann, A. Scholl, H. Schmidt, and B. Wolff-Rottke. Nanosecond andfemtosecond excimer-laser ablation of oxide ceramics.
Applied Physics A ,60(4):411–417, Apr 1995. X.C. Wang, G.C. Lim, H.Y. Zheng, F.L. Ng, W. Liu, and S.J. Chua. Fem-tosecond pulse laser ablation of sapphire in ambient air.
Applied SurfaceScience , 228(1):221 – 226, 2004. Q. Wen et al. In preparation. Eric B. Grann, M. G. Moharam, and Drew A. Pommet. Optimal design forantireflective tapered two-dimensional subwavelength grating structures.
J.Opt. Soc. Am. A , 12(2):333–339, Feb 1995. F. T. Chen and H. G. Craighead. Diffractive phase elements based on two-dimensional artificial dielectrics.
Opt. Lett. , 20(2):121–123, Jan 1995. Ralf Bräuer and Olof Bryngdahl. Design of antireflection gratings withapproximate and rigorous methods.
Appl. Opt. , 33(34):7875–7882, Dec1994. T. K. Gaylord and M. G. Moharam. Analysis and applications of opticaldiffraction by gratings.
Proceedings of the IEEE , 73(5):894–937, 1985. M. G. Moharam, Eric B. Grann, Drew A. Pommet, and T. K. Gaylord. For-mulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings.
J. Opt. Soc. Am. A , 12(5):1068–1076,May 1995. Synopsys. Diffractmod product overview. . S. Pancharatnam. Achromatic combinations of birefringent plates part i.an achromatic circular polarizer.
Indian Academy of Sciences , 41:130–136,1995. Kunimoto Komatsu, Tomotake Matsumura, Hiroaki Imada, HirokazuIshino, Nobuhiko Katayama, and Yuki Sakurai. Demonstration of thebroadband half-wave plate using the nine-layer sapphire for the cosmic microwave background polarization experiment.
Journal of AstronomicalTelescopes, Instruments, and Systems , 5(4):1 – 14, 2019. J. Ruze. Antenna tolerance theory—a review.
Proceedings of the IEEE ,54(4):633–640, 1966. John D Kraus.
Radio Astronomy . Cygnus-Quasar Books, 1986. Shaul Hanany, Johannes Hubmayr, Bradley R. Johnson, Tomotake Mat-sumura, Paul Oxley, and Matthew Thibodeau. Millimeter-wave achromatichalf-wave plate.
Appl. Opt. , 44(22):4666–4670, Aug 2005. Claudia Brückner, Boris Pradarutti, Olaf Stenzel, Ralf Steinkopf, StefanRiehemann, Gunther Notni, and Andreas Tünnermann. Broadband antire-flective surface-relief structure for THz optics.
Opt. Express , 15(3):779–789, Feb 2007. Beat Neuenschwander, Beat Jaeggi, Marc Schmid, Vincent Rouffiange, andPaul-E. Martin. Optimization of the volume ablation rate for metals at dif-ferent laser pulse-durations from ps to fs. In Guido Hennig, Xianfan Xu,Bo Gu, and Yoshiki Nakata, editors,
Laser Applications in Microelectronicand Optoelectronic Manufacturing (LAMOM) XVII , volume 8243, pages43 – 55. International Society for Optics and Photonics, SPIE, 2012. Paul Boerner, Melik Hajri, Norbert Ackerl, and Konrad Wegener. Exper-imental and theoretical investigation of ultrashort pulsed laser ablation ofdiamond.