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 The PPT/PDF document "Investigation of a Blazed Reection Grati..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
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,theblazeangleisdenedastheangleatwhichboththeincidentlighthitsthegratingandthedi ractedlightisre ected,relativetothegratingnormal,whentheinci-dentlightwavelengthisequaltotheblazewavelength.[7]Inotherwords,theblazeangleistheanglethatsat-isesequation(1)forbothinandmfor=b,andmisorderofwhichevermaximatowhichthelightisdirected.Forthegratingusedinthisexperiment,themanufacturerhasprovidedthatthegratingdirectsthemajorityofthelightintensityintotherstorderandthatb=250nm.Wemaythencalculatetheblazean-glenecessarytodi ractthelightintensityintotherstorder(m=1),beginningwiththegratingequation:sin(m)+sin(in)=m dsin()+sin()=1b d=arcsinb 2d:(2)EXPERIMENTThisequipmentusedinthisexperimentincludedaDi-mension3100AFM,anOriel77230re ectiongrating,andanopticalspectrometer.TheOrielre ectiongratingwasrststudiedbyatomicforcemicroscopy.TheAFMwastestedusingawafercontainingagridof55mwells.There ectiongratingwasthenscanned.Severalscansweretakenwithsizesofboth55mand11m.Thegratinghadbeenpreviouslyused,andwasthereforesomewhatscratched.Carewastakennottoscananareathatwasexessivelyscratched.TheAFMwascontrolledusingthenanoscopesoftware.Thegratingswerescannedsuchthatthetipmovementwasneverparalleltothegratingruling.DatacollectedfromthesescanswasthenimportedintothecomputerprogramIgorProCarbonv.4.05foranalysis.Theopticaldi ractivepropertiesofthegratingwerethenstudied.Aspectrometerwasusedinordertode-terminetheangleofincidenceandofdi ractionforthegratingtothenearestminuteofarc.ThelightsourcewaschosentobeaMercurylamp,becauseitemitsmul-tiplediscretewavelengthsoflight.Thisway,multipledi ractionmaximawereobserved.Theanglesoftheze-rothandrstorderdi ractionmaximawererecordedformultiplewavelengthsoflight.Fivemeasurementsweremadeforeachmaximainordertoensurereproducibility.Eachtime,thespectrometerapproachedthepeakfromtherightsoastominimizethepossibilityofsystematicerror.RESULTSANDANALYSISLineSpacingBecausethegratingwasproducedbyholography,itssurfaceshouldbeshapedasasinewave.Thus,anaver-ageestimateofthefrequencyofoscillationmaybedeter-minedbyttingasinewavetothecross-sectionalAFMdataasshowninFigure1.Thecrosssectionwaschosensothatwelookalmostdirectlydownthelengthofthegratinglines.Inotherwords,we\cut"perpendiculartothegratinglines.Thus,localinconsistenciesareaver-agedoutofthedata,andtheaveragedistancemaybedeterminedusingthefrequencyofoscillation.ThisdataissummarizedinTableI. FIG.1:Asinewavettedtothecrosssectionofascan.Usingequation(1),theanglesmeasuredusingthespectrometermaybeused,alongwiththewavelengthsoflightemittedbytheHglamp,todeterminethedis-tancebetweengratinglinesdandthusthelinesspacingS.TheseresultsaresummarizedinTableII.BlazeAngleThegratingstudiedherewasfabricatedsuchthatthereare2400lines/mm.Thisspecicationcorrespondstoa 3TABLEI:Spacingdataforthethreere ectiongratingscansamples,asdeterminedbysinewavets. 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.Byplottingasafunctionofb,usingequation(2)form=1,weobtainawaytodeterminetheblazeanglefromthemanufacturer'sblazewavelength(Figure2). FIG.2:Agraphofblazeangle,,versusblazewavelength,b.Byusingthemanufacturer'svaluefordandb,wemaysolveequation(2)fortheblazeangle.Forthegratingusedinthisexperiment,=17:5.Aspreviouslymentioned,foraruledre ectiongrating,theblazeanglewhicha ectstowhichorderlightisdirectedisdenedastheanglebetweenthelongfaceofthesawtooth-shapedsurfaceandtheplaneofthegrating.Withaholographicgrating,thesurfaceisshapedasasinewave.Byusingthedenitionoftheblazeangleforaruledgrating,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-tsinewavesgeneratedpreviouslytondthespacingd.TheseresultsaresummarizeinTableIIITABLEIII:Spacingdataforthere ectiongrating,asdeter-minedbyasinewavet. 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