Investigation of a Blazed Reection Grating Daniel E - PDF document

Presentation on theme: "Investigation of a Blazed Reection Grating Daniel E"— Presentation transcript

2Twoprominentmethodsofmanufacturinggratingsareviaeitherrulingorholographictechniques.Inbothcases,averyaccurate\master"gratingismadeandthensubse-quentgratingsarereproducedfromthismastertemplate.Ruledgratingstakeontheformofasawtooth,whileholographicgratingsmorecloselyresemblesinewaves.Forasawtoothgrating,theanglebetweenthelongsideoftheruledsurfaceandtheplaneofthegratingisknownastheblazeangle.Itisthisanglethatdeterminesintowhichorderthediractedlightwillbedirected.Holo-graphicgratings,ontheotherhand,cannotbeblazedaseasilyandthereforeproducemuchlowerecienciesthanruledgratings.Whenthewavelengthoftheincidentlight,however,isontheorderofthegratingspacing,theeciencyincreasestothepointthatitiscomparabletothatofaruledgrating.Thiswavelengthofmaximumeciencyiscalledtheblazewavelength.FortheOrielgratingusedinthisexperiment,theblazewavelengthis250nm.[6]Forasinusoidallyshapedholographicgrating,theblazeangleisdenedastheangleatwhichboththeincidentlighthitsthegratingandthediractedlightisre ected,relativetothegratingnormal,whentheinci-dentlightwavelengthisequaltotheblazewavelength.[7]Inotherwords,theblazeangleistheanglethatsat-isesequation(1)forbothinandmfor=b,andmisorderofwhichevermaximatowhichthelightisdirected.Forthegratingusedinthisexperiment,themanufacturerhasprovidedthatthegratingdirectsthemajorityofthelightintensityintotherstorderandthatb=250nm.Wemaythencalculatetheblazean-glenecessarytodiractthelightintensityintotherstorder(m=1),beginningwiththegratingequation:sin(m)+sin(in)=m
 dsin()+sin()=1
b d=arcsinb 2
d:(2)EXPERIMENTThisequipmentusedinthisexperimentincludedaDi-mension3100AFM,anOriel77230re ectiongrating,andanopticalspectrometer.TheOrielre ectiongratingwasrststudiedbyatomicforcemicroscopy.TheAFMwastestedusingawafercontainingagridof55mwells.There ectiongratingwasthenscanned.Severalscansweretakenwithsizesofboth55mand11m.Thegratinghadbeenpreviouslyused,andwasthereforesomewhatscratched.Carewastakennottoscananareathatwasexessivelyscratched.TheAFMwascontrolledusingthenanoscopesoftware.Thegratingswerescannedsuchthatthetipmovementwasneverparalleltothegratingruling.DatacollectedfromthesescanswasthenimportedintothecomputerprogramIgorProCarbonv.4.05foranalysis.Theopticaldiractivepropertiesofthegratingwerethenstudied.Aspectrometerwasusedinordertode-terminetheangleofincidenceandofdiractionforthegratingtothenearestminuteofarc.ThelightsourcewaschosentobeaMercurylamp,becauseitemitsmul-tiplediscretewavelengthsoflight.Thisway,multiplediractionmaximawereobserved.Theanglesoftheze-rothandrstorderdiractionmaximawererecordedformultiplewavelengthsoflight.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:Summaryoflinespacingasdeterminedbyopticaldiraction. 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whichaectstowhichorderlightisdirectedisde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.Thisdierencecouldbecausedbythreesources.First,itispossiblethatsomesortofsystematicerrorwasinvolvedintheAFMmeasurement.TheAFMwasperhapsnotcalibratedproperly.Inaddition,asecondsourceoferrorcouldbethesteepnessofthegratinglines.Whenthetiptravelsalongthegratingsurface,itcannotaccuratelymeasuresteepslopes.Thistypeoferrorwouldresultin