Millimeter-Wave Broadband Anti-Reflection Coatings Using Laser Ablation of Sub-Wavelength Structures

2 MB·

by  Tomotake Matsumura

ResearchArticle 1
Millimeter-Wave Broadband Anti-Reflection Coatings
Using Laser Ablation of Sub-Wavelength Structures
TOMOTAKE MATSUMURA1, KARL YOUNG2, QI WEN2, SHAUL HANANY2, HIROKAZU ISHINO3, YUKI
INOUE4, MASASHI HAZUMI5,6, JÜRGEN KOCH7, OLIVER SUTTMAN7, AND VIKTOR SCHÜTZ7
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1 1JapanAerospaceExplorationAgency(JAXA)-InstituteofSpaceandAstronauticalScience(ISAS),Rm1624,3-1-1Yoshinodai,Chuo,Sagamihara,
0 Kanagawa252-5210,Japan
2 2SchoolofPhysicsandAstronomy,andMinnesotaInstituteforAstrophysics,UniversityofMinnesota/TwinCities,116ChurchSt.SEMinneapolis,MN55455,
r USA
a 3OkayamaUniversity,3-1-1Tsushima-naka,Kita-ku,Okayama700-8530Japan
M 4TheGraduateUniversityforAdvancedStudies(SOKENDAI),1-1Oho,Tsukuba,Ibaraki305-0801,Japan
5InstituteofParticleandNuclearStudies(IPNS),HighEnergyAcceleratorResearchOrganization(KEK),1-1Oho,Tsukuba,Ibaraki305-0801,Japan
1 6KavliInstituteforthePhysicsandMathematicsoftheUniverse,TheUniversityofTokyo,5-1-5Kashiwanoha,Kashiwa,Chiba,277-8583,Japan
3 7LaserZentrumHannovere.V.,Hollerithallee8,30419Hannover,Germany
1Correspondingauthor:[email protected]

]
M
CompiledApril1,2016
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We report on the first use of laser ablation to make sub-millimeter, broad-band, anti-reflection coatings
p
- (ARC) based on sub-wavelength structures (SWS) on alumina and sapphire. We used a 515 nm laser to
o
r producepyramid-shapedstructureswithpitchofabout320µmandtotalheightofnear800µm. Transmis-
t
s sion measurements between 70 and 140 GHz are in agreement with simulations using electromagnetic
a
[ propagationsoftware. ThesimulationsindicatethatSWSARCwiththefabricatedshapeshouldhavea
fractionalbandwidthresponseof∆ν/ν = 0.55centeredon235GHzforwhichreflectionsarebelow
3 center
v 3%. Extensionofthebandwidthtobothlowerandhigherfrequencies,betweenfewtensofGHzandfew
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THz,shouldbestraightforwardwithappropriateadjustmentoflaserablationparameters.
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2 OCIScodes: (310.1210)Antireflectioncoatings; (050.2065)Effectivemediumtheory; (050.6624)Subwavelengthstructures;
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(050.6875)Three-dimensionalfabrication.
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. http://dx.doi.org/10.1364/ao.XX.XXXXXX
1
0
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v: 1. INTRODUCTION peated observations each with a different filter bank and/or
i opticalelementsoptimizedforthespecificfrequencyband.But
X Themmandsub-mmregionsoftheelectromagneticspectrum
withbroad-bandwidthobservations,allopticalelementsalong
are important for observations of a variety of astrophysical
r thelightpath,includinglenses,filters,vacuumwindows,and
a sources.Extinctionbygalacticdustislowatthesewavelengths
polarizationmodulators(ifapplicable)shouldexhibithighopti-
andthereforeotherwiseobscuredobjects,suchasgalacticem-
calefficiency,namely,hightransmission.Hightransmissionis
bedded protostar regions, the black hole at the center of the
achievedbyminimizingabsorptionthroughappropriatechoice
Milky Way, and dusty high redshift galaxies become observ-
ofmaterialsandminimizingreflectionsbyusinganappropriate
able[1–3].Also,thecosmicmicrowavebackground(CMB)radi-
anti-reflectioncoatings(ARC).
ation,whichencodesawealthofinformationabouttheorigin
andevolutionoftheUniverse[4],peaksatmmwavelengths. Sub-wavelengthstructures(SWS)havebeenwidelyexplored
Thereisahostofinstrumentsconductingobservationsatthese asARCinthevisibleandinfraredregionswheretheyareoften
wavelengths. referredtoasmoth’seyestructures(forareviewseeRautet
One of the demands for many astrophysical observations, al.[5]).SWS-basedARCshavetheadvantagesthattheycanpro-
including those targeting the polarization of the CMB, is to videarelativelylargeoperatingbandwidthwithlowreflection
achievebroadfrequencycoverage. Simultaneousbroadband- whileatthesametime(1)thereisnoneedtomatchindices,thick-
widthwithinasingleinstrumentenablesefficientuseoftele- nesses,andmaterialtypesbetweenmultiplelayersofdifferent
scope and observing time, obviating the need to conduct re- materials,and(2)thestructureisrobustincryogenicapplica-
ResearchArticle 2
tionsbecauseitismadeofthesamematerialasthesubstrate,
obviatingtheneedtomatchthermalcoefficientsofexpansion
betweendifferentmaterials.
RecentlySWSARCshavebeenimplementedinthemm-wave
bandonrexolite[6],highdensitypolyethylene[7],andsilicon
[8].Inthesecasesthefabricationapproachreliedonmechanical
machiningorinjectionmolding.Butneitherdirectmechanical
machiningnorinjectionmoldingispracticalforthesmallfea-
tures and high aspect ratios required when the materials are
hard or have high melting temperatures, as is the case with
aluminaandsapphire. Figure1: Cross-sectionalviewofthedesignedSWS.Theyare
Bothaluminaandsapphirehaveopticalpropertiesthatmake madebylaserablationofgroovesinthesubstrate. Thefilling
themappealingforuseinmmwavebandinstruments. They fraction increases toward the substrate, gradually increasing
havehighindexofrefractionn(cid:39)3givinglenseshighcorrecting the index. The specific design parameters are: p = 330 µm,
powerwithrelativelysmallcurvaturesandthicknesses;a-cut h=810µm,ands=60µm.Thewidthwisafunctionofthez
sapphire’sbirefringenceisnear10%enablingthemakingofthin coordinate.
retarders;bothmaterialsarenearlyopaqueintheIRandhave
highthermalconductancemakingthemidealabsorbingfilters
ofhighfrequencyradiationincryogenicinstruments. (Rosen EM-FEA.
etal.[9]givesimilarmotivationsfortheirdevelopmentoftwo- Atnormalincidencetheupperband-edgeoftheSWS-ARC
andthree-layerARConaluminabasedonlayeredepoxies.) issetbyνu =c/(pns)≈290GHz,abovewhichdiffractionsets
LaserablationisanalternativeapproachforfabricatingSWS in [18]. This is well reproduced by the EM-FEA calculations
structures.Severalauthorsreportedonthecombineduseofdry assharpreflectionspikes;seeFigure3. Thelowerband-edge,
chemicaletchingandlaserablationonsilicontoproduceARC definedhereasthefrequencyatwhichbandaveragedreflections
inthevisibleandnearIR[10–14]. Herewereportonthefirst dropbelow3%,isapproximatelyνl ∼c/h∼110GHz.Weuse
useoflaserablationtogeneratemillimeter-waveSWSARCon abandwidthof∆ν/ν=30%foraveragingthereflections.
aluminaandsapphire.Inourapplicationtherearenochemical
etchants, and the process takes place in regular atmospheric 3. SAMPLEPREPARATION
environment. InSection2wedescribethedesignoftheSWS.
A. Materials
ThesamplesandfabricationprocessaredetailedinSection3.
Section4givesourmeasurementsofthegeometricalshapeand Weusealuminaandc-cutsapphire;thephysicalparametersof
mm-wavetransmissionoftheSWSsamples. Wediscussand thenativesamplesaregiveninTable1.C-cutsapphireisnon-
summarizeourresultsinSections5and6. Togetherwiththis birefringentforradiationatnormalincidence.Bothsamplesare
paper,whichconcentratesontheopticalpropertiesoftheablated laserablatedonone-sideonly.Theindexofrefractionofthetwo
surfaces,wearereferringreadersinterestedinthetechnicalities materialsismeasuredusingdifferentsamplesofaluminaand
ofthelaserablationtoacompanionpaper[15]. sapphirebutofthesamepuritylevel;theyarelistedinTable1.
B. Fabrication
2. DESIGN
Ablationisdoneusinga515nmlaseroperatingwith7pspulses
OurnominaldesignfortheSWS-ARCisshowninFigure1.It andarepetitionrateof400kHz.Atfocusthebeamhasa1/e2
consistsofasquarearrayofpyramidseachwithsquarecross widthof30µm.Thebeamisscannedinarasterpatternacross
section. AsinallSWS-ARCsthegoalistoachieveagradient thesurface,firstinonedirectionthentheorthogonal,asshown
in the index of refraction through an increase in the area fill schematicallyinFigure4. Theprogressionoftheablationas
fractionofthematerialasradiationpropagatesinthe−zdirec- afunctionofthenumberofpassesisshowninFigure5. The
tion. Withanappropriatelydesignedgradient,reflectionscan aluminawasmachinedusing200identicalpasses,coveringthe
beminimizedoverabroadrangeoffrequencies.Thefillfraction center27×27mm2ofthesample.Machiningtimewas5hours.
forournominaldesign, definedas f(z) = w(z)/p, isshown Thefullsurfaceofsapphirewasmachinedinaseriesof3.3×3.3
inFigure2. Theapproximatereflectionpropertiesofamate- mm2sub-areas.Eachsub-areawasscanned50timesusingthe
rialwith f(z)canbecalculatedusingeffectivemediumtheory samescanpatternasinFigure4beforemovingtothenextsub-
(EMT)[16],whichgivesaconversionfrom f(z)toaneffective area. Total machining time was 5.6 hours. Schütz et al. [15]
indexneff(z);neff(z)isalsoshowninFigure2.Thereflection describethemachiningprocessinmoredetail.
isthencalculatedusingastandardmulti-layercoatingapproach
withalargenumberofstackedthinlayers,eachwithitsneff. 4. MEASUREMENTS
Figure3showsthereflectionpredictedforthenominaldesign
usingn (z)ascalculatedusingEMTandusingelectromag- A. Shape
eff
neticfiniteelementanalysis(EM-FEA)approach[17].Wefound WeuseaKeyenceVHX-5000opticalmicroscopeandaNikon
thatincomparisonstoEM-FEAEMTproducesreflectionval- A1RMPconfocalmicroscopetoimagethelaserablatedsurfaces.
uesthatarewithin10%ofthenumericalcalculationsaslong Themicroscopestakeaseriesof2-dimensionalimagesspaced
astheratioofpitchtowavelengthsatisfies p/λ <∼ 0.1. Devia- equallyinz. Thein-planeresolutionis1.7µmorhigherand
tionscouldincreaseforlargerratios,dependingonthespecific dependsonthespecificmicroscope.Thespacinginzis10µm
structures simulated. With p = 330 µm EMT is expected to fortheopticalmicroscopeand1.3−4µmfortheconfocalmi-
beaccurate(within10%)onlyforfrequenciesbelow∼90GHz. croscope,dependingonimagelocation. Thisseriesofimages
Thereforeinthispapercomparisonstomeasureddatauseonly isusedtoreconstructa3-dimensionalimageofthesample. A
ResearchArticle 3
Table1:Measuredsamplepropertiesand1σmeasurementerrors.
diameter(mm) thickness(mm) indexa
Alumina amorphous;99.6%pure 42 2.21±0.01 3.04±0.02
Sapphire c-cut;99.99pure 51 3.832±0.003 3.074±0.003
a
Theindicesofrefractionvaluesweremeasuredonsampleswiththesamepuritylevelthatwerenotlaser-ablated.Thereforesomedifferencebetweenthemeasuredindices
andtheactualindicesofoursamplesisexpected.
Figure3:EM-FEA(blue),EMT(green),andEM-FEAaveraged
across 30% bandwidth (red) predictions of reflection for the
designgeometryonalumina,ns =3.1.Thetotalsamplethick-
ness,includingtheSWS,is4.62mm,andtheSWScoatingwith
thedesignparametersisassumedonbothsides. ForEMTwe
calculated n (z) asshowninFigure2with150layers. The
eff
verticalreddashlinemarksthefrequencywherediffractionis
firstexpectedtooccuratnormalincidence.
sectionofthesapphiresampleisshowninperspectiveinFig-
ure6.Azoomedversionshowninprojectionalongthezaxisis
inFigure7.
Using the optical images we measured the parameters of
themachinedsurfacesintendifferentlocationsforeachofthe
alumina and sapphire samples. In each location we image a
squareconsistingofapproximatelytwopyramidsonasideand
Figure2: Thefillfraction f(z)(bluesolid)andeffectiveindex
extractthegeometricparametersofthemachinedsamples.The
n (z)(greendashed)forthedesigngeometryonaluminawith
eff average values across all these spatial locations are given in
ns =3.1(seeFigure1andTable2).Theeffectiveindexiscalcu- Table 2. Because groove depth is not uniform - grooves are
latedusingEMT(seetext).
deepestatgroovecrossings-theremaybeambiguityaboutthe
heightmeasurement. Tomeasureheightwefirstcalculatethe
fill fraction as a function of z in steps of 5 µm and set z = 0
whenthefillfractionis1.maximumheightisdefinedbythez
positionwherethefillfractionis0.ForallvaluesinTable2,the
errorsquotedarethestandarddeviationinthemeasurements
acrossthedifferentareasandprovideameasureofstructure
uniformity.
Wecharacterizethesymmetryofthestructuresbycomparing
1-dimensionalheightprofilesintwoorthogonaldirectionsthat
are parallel to the grooves. These 1-dimensional profiles on
sapphire(alumina)areillustratedinFigure7(9)andareplotted
inFigure8(10).WediscussthesemeasurementsinSection5.
ResearchArticle 4
Figure11:Diagramoftheexperimentalsetup.Aperturediametersforsapphirewerea=3cmandb>10cm.Foraluminaa=1.5cm
andb>10cm.
Figure5:Scanningelectronmicroscopeimageofpyramidsona
testsapphiresampleafterNpablationscans. Forthesapphire
sampleusedforthetransmissionmeasurements(Fig.12)we
usedNp =50becausetherewasonlyminorevolutioninstruc-
Figure 4: The ablation pattern consists of Np identical scans tureshapeforsubsequentpasses.
acrossthesurface. Ineachscanthelasermakesasingleraster
passofthehorizontallines(blue)thentheverticallines(red).
Thegroupsofblue/redlinesbecomethegroovesbetweenthe B. Transmission
pyramids.Withaluminathelinesare27mmlongandNp =200. Transmissionismeasuredatroomtemperatureusingamillime-
Withsapphireeachlineis3.3mmlong,andthesampleismade
terwavesourceandapowerdetector.Aschematicdiagramof
up of square sub-areas machined separately; Np = 50. The thesetupisshowninFigure11.Twoadjustable-frequencymm-
progressionoftheablationonsapphireisshowninFigure5.
wavemultipliersareusedtoup-converttheGHzsignalofthe
generatortobandsbetween75and110GHz,and90to140GHz.
Pyramidalhornswith3dBbeam divergenceof ∼25degrees
couplethelinearlypolarizedmm-wavesignaltofreespace.The
Table2:GeometricparametersofSWS.
sourceischoppedwithamechanicalbladeproducingamodu-
Sample height(µm) pitch(µm) peakwidth(µm) latedsignalat10Hz.Weusealock-inamplifierattheoutputof
thedetector.Thesampleiscontainedwithinaboxthathastwo
Designed
aperturesandislinedwithmm-waveabsorbingmaterial.The
All 810 330 60 polarizationaxisofthemm-wavesourceisalignedparallelto
oneoftheprincipaldirectionsoftheSWS-ARC,asdefinedby
Measureda
theorientationofthegrooves.Thesamplecanberotatedby90
Alumina 790±60 313±4 66±8 degreestoenabletransmissionmeasurementsattwoorthogonal
polarizations.
Sapphire 715±24 325±4 57±6
Ameasurementconsistsofarelativenormalizationstagein
a
Errorquotedisthestandarddeviationformeasurementsin10locations.Indi- whichthesampleisnotpresent,butthesamplemountandall
vidualmeasurementerrorsare±2µmforpitchand±4µmforheightandpeak
aperturesareincluded,andadatatakingstagewiththesample.
width.
Duringthenormalizationstagetheoutputofthepowerdetector
ResearchArticle 5
Figure8: 1-dimensionalheightprofilesonsapphire. Thepro-
filesareproducedfromcutsthroughpeakcenters,asshownin
Figure7,for6locationsacrossthesample. Cutsatconstanty
areingreen;constantxareinblue. Theyhavebeenmanually
translatedtoalignverticallyandhorizontallytoenablevisual
comparisonofstructureuniformity.
Figure6:OpticalimageofSWS-ARConsapphirereconstructed
fromaseriesof2-dimensionalimagestakenalongthezaxis.
Figure9: HeightmapofSWSonalumina. The1-dimensional
Figure7:HeightmapofSWSonsapphire. The1-dimensional heightprofilesthatareshowninFigure10aremarkedhereas
heightprofilesthatareshowninFigure8aremarkedhereas broadblueandgreenlines.Thewidthofeachlinecorresponds
broadblueandgreenlines.Thewidthofeachlinecorresponds to the portion of the height map averaged to produce the 1-
to the portion of the height map averaged to produce the 1- dimensionalprofile.
dimensionalprofile.
ResearchArticle 6
Figure10: 1-dimensionalheightprofilesonalumina. Thepro-
filesareproducedfromcutsthroughpeakcenters,asshownin
Figure9,for5locationsacrossthesample. Cutsatconstanty
areingreen;constantxareinblue. Theyhavebeenmanually
translatedtoalignverticallyandhorizontallytoenablevisual
comparisonofstructureuniformity.
Figure12:Measuredtransmissionasafunctionoffrequencyfor
sapphireattwofrequencybandsbetween75and110GHz(red)
andbetween90and140GHz(cyan). Alldataweretakenata
isloggedasafunctionofthesourcefrequencyνanddetector
positionalongthez-axis.Therangeofsamplinginzisslightly singlepolarizationstate.WeshowHFSSpredictionsforasample
thatisablatedononesideandassumingallSWSaremadewith
largerthanonewavelength. Thesearethenormalizationdata
N(ν). Thesampleistheninsertedintoitsholderanddataare thetallest(h=740µm,blue)andshortest(h=680µm,green)
retakenatthesamesourcefrequenciesandzpositions. These profilesmeasuredin10differentlocationsacrossthesample.
arethedataD(ν).ForeachfrequencyνbothNandDarefitto ThedataarenormalizedtotheblueHFSScurveat87GHz.
models
N(ν,z)= N (ν)+N (ν)sin(N (ν)z+N (ν)), (1)
0 1 2 3
and
D(ν,z)=D (ν)+D (ν)sin(D (ν)z+D (ν)), (2)
0 1 2 3
whereN, D (i=0,1,2,3)arethefitparameters.Thetransmis-
i i
siondatawereportis
D (ν)
T(ν)=C 0 , (3)
N (ν)
0
whereCisaconstantusedtonormalizeTtotheEM-FEApre-
dictions,asdiscussedinSection5.Thez-dependentsinusoidal
fitsaccountforstandingwavesbetweenthesourceanddetector.
ThetransmissiondataforthetwosamplesisshowninFigures12
and13alongwithHFSSpredictions,whicharediscussedinSec-
tion5.Generally,dataweretakenatonepolarizationstate.With
aluminadataatthehigherfrequencybandwasrecordedattwo
polarizationstates.
5. DISCUSSION
Figure13: Measuredtransmissionasafunctionoffrequency
A. Geometry foraluminaattwofrequencybandsbetween75and110GHz
(red,asinglepolarizationstate)andbetween90and140GHz
Thespatiallyaveragedshapeparametersofbothsamplesmatch
(cyanforonepolarizationstate,andpurplefortheorthogonal
thenominaldesigntobetterthan12%;theheightofthesapphire
polarizationstate).WeshowHFSSpredictionsforasamplethat
pyramidsisconsistentlyshortby12%andthewidthofthealu-
is ablated on one side and assuming all SWS are made with
minatipsaretoowideby11%,althoughthereisasimilarlevel
thetallest(h=875µm,blue)andshortest(h=715µm,green)
ofspatialdispersionacrossthesample,seeTable2.Otherwise
profilesmeasuredin10differentlocationsacrossthesample,
theshapeparametersagreewithin5%.Thislevelofagreement
with the design was achieved with a small number of trials. andforns =3.16(darkblueandgreen)andns =3.04(lightblue
andgreen). ThedataarenormalizedtothedarkgreenHFSS
Noextensiveattemptsweremadetodecreasediscrepanciesbe-
simulationat85GHz.
tweenthedesignedandablatedstructures.Withsinglecrystals
likesapphirebetteragreementisachievableandwehavenot
identifiedanylimitationthatwouldpreventevenmoreaccurate
ResearchArticle 7
ablation. Aluminaissinteredmaterialanditspropertiesmay Withtallerstructures,thenonAR-coatedpartofthesampleis
showvariationsbetweendifferentsamples.Thisaspectrequires thinner,resultinginalowerfrequencyfringepattern.
furtherinvestigation. Variationinlaserpowerisnotalikely Withsapphirethedataandmeasuredshapevariabilitymatch
causeforthe∼10%spatialdispersionofthemeasuredparame- EM-FEApredictionsclosely.Thedataisbracketedbyprediction
tersaspowerwasstabletobetterthan0.1%overthe5-6hoursit withthetallestandshorteststructuresmeasured. Thisisnot
tooktoablateeachsample. thecasewithaluminaforwhichthedataisoutsidetherange
The ablated SWS have square tops and they transition to ofshortesttotallestpredictionsmadewiththemeasuredindex
approximatelycircularbases.Thestructuresareslightlyasym- ofns =3.04;seelightgreentoblueinFigure13. Wenotethat
metric;saddlesbetweenpeaksinoneorientationareonaverage reportedmeasurementsoftheindexofaluminahavelargervari-
slightlydeeperthanintheorthogonaldirection,seeFigures8 abilitythanthosewithsapphire[19]andthatourmeasurement
and10.Suchasymmetry,whileavoidablewithbettertuningof wascarriedoutonadifferentsamplethantheoneablated.The
ablationparameters,maybeimportantforpolarimetricstudies. indexofaluminathatbettermatchesourdataisns =3.16and
Wequantifythesymmetryofthepyramidsbycalculatingthe thisvalueiswithintherangeofvariabilityreportedinthelitera-
fullwidthathalfheight(FWHH)andthesaddledepthsdforx ture[19].Predictionswiththisindexfortheshortestandtallest
andyslicesateachofthetenimagelocationsonthesamples.We structuresmeasuredareshownasboldinFigure13.
findtheglobalmaximumofeachimage,excludingthehighest We can asses the expected broadband performance of the
1%ofpointstoavoidoutliers,andthedepthofeachsaddlefor fabricatedSWSbyextendingtheHFSSsimulationsto350GHz
eachslice(sd),thendeterminethewidthofeachpyramidatthe andassumingthatthesapphireandaluminasamplesarecoated
halfwaypointbetweenthemaximumandthesaddle(FWHH). onbothsides. Thesimulationsassumethemeasuredsapphire
TheprocedureproducesvaluesforFWHHx,sdx,FWHHy,and (alumina)pyramidshapewithaheightof740µm(715µm)and
sdy.Weformaratio followthesameproceduredescribedearliertocreateperiodic
boundaryconditions.ThepredictionsareshowninFigures14
rsym = FWHHx, (4) and15,eachfortwoincidentpolarizationstates.Startingatlow
FWHHy frequencies,reflectiondecreaseswithincreasingfrequency,drop-
pingbelow3%at170GHzforbothpolarizationsandbothma-
sosymmetricstructureshaversym = 1. Table3givesaverage terials.OnSapphire,atotalbandwidthof130GHzisachieved
valuesandstandarddeviationsforrsymandsd.Somestructure withbandaveragedreflectionof1.0%.Thehighfrequencyside
asymmetryisexpectedwhenidenticalablationparametersare is limited by sharp reflection features that are introduced by
usedforthetwoorthogonaldirections.Relativetothefirstpass, diffraction. Wediscussthesebelow. Thereisaslightlylarger
thepassintheorthogonaldirectionwillproduceonaverage effective bandwidth of 140 GHz on alumina because it has a
deepergrooves.Thisasymmetrycanbemitigatedbytuningthe smaller pitch, moving the sharp reflection features to higher
scanspeedornumberofscanrepeats. frequencies.Thebandaveragedreflectionofaluminabetween
170and310GHz,isalso1.0%.Forcomparison,astandardλ/4
coatingoptimizedfor250GHz,alsoshownintheFigures(light
Table3: Averagesymmetryparameterrsym andsaddledepth gray),hasabandwidthofonly60GHz. Rosenetal.[9]report
sdx,y forthetwosamples. The1σstandarddeviationsreflect bandwidths∆ν/νof92%and104%withreflectionbelow10%
spatialvariationsacrossthesample. withtwo-andthree-layerARConaluminausinglayeredepox-
rsym sdx(µm) sdy(µm) ies.Theircenterfrequencyis∼150GHz.Withthisfirstroundof
laserablation,ouraluminasamplehas∆ν/ν=74%,centered
Alumina 1.042±0.035 545±50 525±25 on225GHz,withreflectionsbelow10%.
Sapphire 0.950±0.015 500±10 450±10 Atfrequenciesbetween100and170GHzthereflectionex-
pectedfromthefabricatedstructuresishigherthanpredictions
based on the design geometry; compare to Figure 3. This is
because the design geometry has a uniform pyramid height
B. Transmission
of810µm;inotherwordsthegrooveshaveuniformdepthof
ThemeasuredtransmissionforeachsampleisplottedinFig- 810µmrelativetothetips. Yetwiththeablatedstructuresthe
ures12and13alongwithEM-FEAsimulations.Thesimulated maximumgroovedepthisachievedoverasmallerfractionof
transmissioniscalculatedbyimportingthemeasuredheight groovelength. Theaveragegroovedepthrelativetothepeaks
mapofasinglepeakintoHFSS,mirroringitacrossthex-axis, is∼550µm(600µm)onsapphire(alumina),whichisafactor
andthenmirroringtheresultingpairacrossthey-axistocreate of1.5(1.4)shorterthantheoriginaldesign. Recallingthatthe
anarrayoffourpeakswhoseopposingboundariesareidenti- lowerbandcut-offfrequencyisproportionalto1/hweshould
cal.Thisallowsustoimplementperiodicboundaryconditions findthatthelowerfrequencyedgeofthebandisafactorof∼1.5
andsimulatethesampleasaninfiniteplane.1 Foreachsample higherthantheanticipated110GHz,ingoodagreementwith
weindicateapossiblerangeofpredictionsbysimulatingthe theEM-FEMcalculations.
transmissionforasamplemadewiththetallestandshortest ThebandwidthoftheSWS-ARCisextendabletolowerfre-
structuresfoundbyimaging10locationsonthesamples. The quenciesbyincreasingtheheightofthestructuresandtohigher
phaseandamplitudeofthetransmissioninterferencefringes frequenciesbydecreasingthepitch. Ausefulfigureofmerit
varybetweenthetwocases, withthephasedifferenceshow- is the aspect ratio a = h/p. The current value of a, using
inglargersensitivitytoheightdifference.Thefrequencyofthe h = 550 µmand p = 315 µmis1.7. Increasingthedepth
eff
fringepatternissensitivetothetotalthicknessofthematerial. toh =1100µm,thusdoublingtheaspectratio,wouldhalve
eff
the low frequency edge of the band giving a useful band be-
1Themirroringoperationproducesarepetitionofstructuresonalengthscales tween∼85and300GHz. Thesameaspectratiobutproduced
of2p. Thisartificialperiodicitycreatesdiffractionfeaturesatafrequencyν =
2c/(pns),whichwemanuallyremovefromtheFigures. withhalfthepitchwouldgiveabandbetween170and600GHz.
ResearchArticle 8
Weseenophysicallimitationforincreasingtheaspectratiobya
factorof5-10.
ThesimulationsshowninFigures 14and15reflecttheheight
andsymmetrydifferencesbetweenthesamples.Thesomewhat
higherasymmetrywiththesapphiresamplegivesrisetoasome-
whatstrongerdifferentialreflection,asnotedprimarilybythe
phasedifferenceinthereflectionfringesbetweenthetwopo-
larizationstates. However,averagingovera∆ν/ν=0.3band
thatiscenteredon235GHz,aswouldbeexpectedwithabroad-
bandinstrumentobservinginthatband,wefindadifferential
reflectionoflessthan0.1%forbothmaterials.
TheoryandHFSSsimulationsindicatethatatnormalinci-
dence diffraction at wavelengths shorter than λu ∼ pns pro-
ducesstrongreflectionfeatures. Thedensityofthesefeatures
increaseswithincreasingfrequency.Atoff-normalincidencean-
glestheonsetofthereflectionfeaturesshiftstolowerfrequencies.
Toavoidsuchreflections,experimentsusingSWS-ARCshould
implementlowpassfilterstoblockhighfrequencyradiation.
Figure15: SimulatedreflectionofourmachinedARCapplied
tobothsidesofanaluminaflat. Thegreencurvecorresponds
6. SUMMARY tothestructuresandpolarizationplottedingreeninFigure13.
Theorthogonalpolarizationfortheseisinred.Verticalredline
We have demonstrated the first use of laser ablation to pro-
ducemillimeter-waveSWSARConhard,difficult-to-machine indicatesthepointwhere p = λ/ns andthestructurescanno
longerbeconsideredsub-wavelength.
aluminaandsapphire. Theablationiscarriedoutinregular
atmospheric conditions and involves no additional chemical
etchants. Structureswithaspectratioof1.7,averageheightof ACKNOWLEDGEMENT
∼550µm, andmaximumheightof∼800µmwerefabricated
ononesideof∼5cmdiametersampleswithinabout5hours. TheauthorsacknowledgeuseofresourcesprovidedbytheMin-
nesotaNanofabricationCenter(http://nfc.umn.edu),theUniver-
Measurementsoftransmissionareincloseagreementwithelec-
sityofMinnesotaImagingCenter(http://uic.umn.edu),andthe
tromagnetic simulations. The simulations indicate that with
MinnesotaSupercomputingInstitute(http://www.msi.umn.edu).
SWSARContwosidesthesesampleshavereflectionsofless
TMthanksProf. M.Hasegawaforuseofthemillimeter-wave
than3%overabandbetween170and300GHz,afractionalband-
widthof∆ν/νcenter =0.55.Significantlylargerbandwidthsand source.ThisworkwaspartiallysupportedbyJSPSKAKENHI
grantnumbers24740182and15H05441,theMitsubishifounda-
fasterablationratesarepossiblebyappropriatelytuninglaser
tion(grantnumber24inJFY2015inScienceandtechnology)
parameters.AcompanionpaperbySchützet.al[15]givesmore
and by the ISAS strategic development fund of the steering
informationaboutthelaserablationprocess.
committeeforspacescience.
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