Investigation of a Blazed Reection Grating Daniel E - PDF document

Investigation of a Blazed Reection Grating Daniel E
Investigation of a Blazed Reection Grating Daniel E

Investigation of a Blazed Reection Grating Daniel E - Description


Shai Department of Physics The College of Wooster Wooster Ohio 44691 USA Dated May 9 2004 A re64258ection grating was studied via two di64256erent experimental measurement techniques Initially the di64256ractive properties of the grating were used t ID: 61979 Download Pdf

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2Twoprominentmethodsofmanufacturinggratingsareviaeitherrulingorholographictechniques.Inbothcases,averyaccurate\master"gratingismadeandthensubse-quentgratingsarereproducedfromthismastertemplate.Ruledgratingstakeontheformofasawtooth,whileholographicgratingsmorecloselyresemblesinewaves.Forasawtoothgrating,theanglebetweenthelongsideoftheruledsurfaceandtheplaneofthegratingisknownastheblazeangle.Itisthisanglethatdeterminesintowhichorderthedi ractedlightwillbedirected.Holo-graphicgratings,ontheotherhand,cannotbeblazedaseasilyandthereforeproducemuchlowerecienciesthanruledgratings.Whenthewavelengthoftheincidentlight,however,isontheorderofthegratingspacing,theeciencyincreasestothepointthatitiscomparabletothatofaruledgrating.Thiswavelengthofmaximumeciencyiscalledtheblazewavelength.FortheOrielgratingusedinthisexperiment,theblazewavelengthis250nm.[6]Forasinusoidallyshapedholographicgrating,theblazeangleisde nedastheangleatwhichboththeincidentlighthitsthegratingandthedi ractedlightisre ected,relativetothegratingnormal,whentheinci-dentlightwavelengthisequaltotheblazewavelength.[7]Inotherwords,theblazeangle istheanglethatsat-is esequation(1)forbothinandmfor=b,andmisorderofwhichevermaximatowhichthelightisdirected.Forthegratingusedinthisexperiment,themanufacturerhasprovidedthatthegratingdirectsthemajorityofthelightintensityintothe rstorderandthatb=250nm.Wemaythencalculatetheblazean-glenecessarytodi ractthelightintensityintothe rstorder(m=1),beginningwiththegratingequation:sin(m)+sin(in)=m dsin( )+sin( )=1b d =arcsinb 2d:(2)EXPERIMENTThisequipmentusedinthisexperimentincludedaDi-mension3100AFM,anOriel77230re ectiongrating,andanopticalspectrometer.TheOrielre ectiongratingwas rststudiedbyatomicforcemicroscopy.TheAFMwastestedusingawafercontainingagridof55mwells.There ectiongratingwasthenscanned.Severalscansweretakenwithsizesofboth55mand11m.Thegratinghadbeenpreviouslyused,andwasthereforesomewhatscratched.Carewastakennottoscananareathatwasexessivelyscratched.TheAFMwascontrolledusingthenanoscopesoftware.Thegratingswerescannedsuchthatthetipmovementwasneverparalleltothegratingruling.DatacollectedfromthesescanswasthenimportedintothecomputerprogramIgorProCarbonv.4.05foranalysis.Theopticaldi ractivepropertiesofthegratingwerethenstudied.Aspectrometerwasusedinordertode-terminetheangleofincidenceandofdi ractionforthegratingtothenearestminuteofarc.ThelightsourcewaschosentobeaMercurylamp,becauseitemitsmul-tiplediscretewavelengthsoflight.Thisway,multipledi ractionmaximawereobserved.Theanglesoftheze-rothand rstorderdi ractionmaximawererecordedformultiplewavelengthsoflight.Fivemeasurementsweremadeforeachmaximainordertoensurereproducibility.Eachtime,thespectrometerapproachedthepeakfromtherightsoastominimizethepossibilityofsystematicerror.RESULTSANDANALYSISLineSpacingBecausethegratingwasproducedbyholography,itssurfaceshouldbeshapedasasinewave.Thus,anaver-ageestimateofthefrequencyofoscillationmaybedeter-minedby ttingasinewavetothecross-sectionalAFMdataasshowninFigure1.Thecrosssectionwaschosensothatwelookalmostdirectlydownthelengthofthegratinglines.Inotherwords,we\cut"perpendiculartothegratinglines.Thus,localinconsistenciesareaver-agedoutofthedata,andtheaveragedistancemaybedeterminedusingthefrequencyofoscillation.ThisdataissummarizedinTableI. FIG.1:Asinewave ttedtothecrosssectionofascan.Usingequation(1),theanglesmeasuredusingthespectrometermaybeused,alongwiththewavelengthsoflightemittedbytheHglamp,todeterminethedis-tancebetweengratinglinesdandthusthelinesspacingS.TheseresultsaresummarizedinTableII.BlazeAngleThegratingstudiedherewasfabricatedsuchthatthereare2400lines/mm.Thisspeci cationcorrespondstoa 3TABLEI:Spacingdataforthethreere ectiongratingscansamples,asdeterminedbysinewave ts. Scan# Spacing(Lines/mm) 1 24244 2 23152 3 23152 Average 235151() TABLEII:Summaryoflinespacingasdeterminedbyopticaldi raction. Trial Sspacing(Lines/mm) 1 24006 2 24006 3 24006 4 24036 5 24016 Average 24016 linespacingd=416:7nm.Byplotting asafunctionofb,usingequation(2)form=1,weobtainawaytodeterminetheblazeanglefromthemanufacturer'sblazewavelength(Figure2). FIG.2:Agraphofblazeangle, ,versusblazewavelength,b.Byusingthemanufacturer'svaluefordandb,wemaysolveequation(2)fortheblazeangle .Forthegratingusedinthisexperiment, =17:5.Aspreviouslymentioned,foraruledre ectiongrating,theblazeangle whicha ectstowhichorderlightisdirectedisde nedastheanglebetweenthelongfaceofthesawtooth-shapedsurfaceandtheplaneofthegrating.Withaholographicgrating,thesurfaceisshapedasasinewave.Byusingthede nitionoftheblazeangleforaruledgrating,wemayapproximatetheblazeangleforaholographicgratingbyassumingthatthesinewaveisapproximatelyatriangularwave.AsillustratedinFigure3,ifwemakethisassumption,calculationoftheblazeanglebecomespossible. FIG.3:Approximateblazeangleforaholographicgrating.Ifweassumethattheheightofthe\triangle"issimplytheheightofthesinewave,thentheverticalsideofthetriangleissimplytwicetheamplitude.Also,wemayassumethatthewidthofthetriangleisonehalfoftheperiodofthewave.Usinggeometry,wemaycalculatetheapproximateblazeangle:tan =2A d=2 =arctan4A d(3)UsingEquation(3)theaprroximateblazeanglewascal-culatedforthebest- tsinewavesgeneratedpreviouslyto ndthespacingd.TheseresultsaresummarizeinTableIIITABLEIII:Spacingdataforthere ectiongrating,asdeter-minedbyasinewave t. ScanFilename (degrees) `refgrat2.004' 12:40:1 `refgrat2.007' 12:80:2 `refgrat2.009' 11:90:2 Average 12:40:4() Thecalculatedvalueof17:5isconsistentlylargerthanthoseapproximatedusingatomicforcemicroscopy.Thisdi erencecouldbecausedbythreesources.First,itispossiblethatsomesortofsystematicerrorwasinvolvedintheAFMmeasurement.TheAFMwasperhapsnotcalibratedproperly.Inaddition,asecondsourceoferrorcouldbethesteepnessofthegratinglines.Whenthetiptravelsalongthegratingsurface,itcannotaccuratelymeasuresteepslopes.Thistypeoferrorwouldresultin

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