beam steering devices光束转向装置

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BEAMSTEERINGDEVICEST.Kranjc1andJ.Pirš2,1FacultyofEducation,UniversityofLjubljana,Slovenia2Institute“JožefStefan”,Ljubljana,SloveniaCorrespondingauthor’se-mail:tomaz.kranjc@pef.uni-lj.si1IntroductionSomeinterestingtopicsconcerningphysicsofliquidcrystals(LC)andtheirtechnologicalusefulnessmaybepresentedinphysicsinstructionalreadyinthesecondaryschoolandinintroductoryuniversitycourses.Theymayservetointroducesomeimportantphysicsconcepts(atomicstructureandmicroscopicconfigurations,orderandorderparameters,symmetry,thermalmotionetc.)inordertoillustratephysicalpropertiesofmatterandtoshowhowphysicslawscanbeusedandappliedtopracticalsituations.LCsareparticularlyappropriatetodemonstrateseveralopticalpropertiesofmatterandunderlyingphysicsprinciples.Forexample,inmatchingvariouslightbeams,thedesiredopticalpathdifferencesmaybeachievedeitherbyadjustingthethicknessofanopticalmediumoritsindexorrefraction.TheindexofrefractionofLCscanbeeasilychangedandproperlyadjusted.AnimportantpartofmodernopticaltechnologiesisbasedonopticalpropertiesofLCswhichinturndependonaspecialinternalorderofLCmaterialaswellasingenuoustechnicalsolutions.Inopticalcommunicationsoververylongdistances,opticalbeamswithverysmalldivergencearerequired.Furthermore,withhighlycollimatedlightbeamsanultra-precisionalignmentisnecessary.Atpresent,typicalhighprecisionopto-mechanicaldevicesuseveryexpensiveopticalelements(precision(“l/10”)mirrors,galvo-motorsandotherprecisionmicro-mechanicalpositioningdevices).Suchelementsareexpensiveandtheirtimeresponseisratherslow(whichisinadequateformanyapplications).However,newtechnologicalsolutionsareemerging,basedonanentirelydifferentconcept,whichdoesnotrequireexpensiveprecisionmechanicalandopticalcomponents.Thesenewprecisionbeamsteeringdevicesarebasedontheuseofmatrixarraysofreflectivetype“micro”LClightmodulators(~5μm×5μm)usingstandardLConsilicondisplaytechnology(LiquidCrystalOnSilicon–LCOS).Byaproperelectricallycontrolledadjustmentoftheeffective“opticalpathvalue”foreachoftheLCmatrixelementsonecannotonlydirectthelaserbeamintherequireddirectionwiththedynamicslimitedonlybythedynamicsoftheLCdirector,butcanalsoefficientlycompensatefortheoptical“imperfection”ofthebuilt-inreflectiveelectrodesaswellasfortherestoftheopticalsystem.Thepresentationisintendedtoshowtheconceptoftheliquidcrystalprecisionbeamsteeringdevice.2Theneedofhigh-precisioninstrumentsInopticalcommunicationsoververylongdistances,opticalbeamswithverysmalldivergencearerequired.Example:Consideraparallellightbeamofcrosssection1dm2whichisreflectedfromaplanemirror.Ifthemirrorisnotcompletelyeven,thereisaslightspread-outofthereflected beam.Whatisthespreadofthebeamoveradistanceof40.000km,ifthedeviationfromthedesireddirection(α)is0.1°(Fig.1)?Answer:Thecrosssectionofthefinalbeamisabout15.000km2andthelightintensityisreducedbyafactorof~1012.Fig1.Spreadingoutofalightbeamonanunevenmirror.Thisshowsthataveryslightunevennessproducesanunacceptablylargedispersionofthebeam.Theproblemishowtomanufacturealow-costpreciseplanemirror.Thisisapartofamoregeneralproblem:howtoachieveaveryfinesteeringofabeamtobecollimatedanddirectedpreciselyinthedesireddirection.Ifthemirrorsurfaceisnotaperfectplane,acollimatedbeamisnotreflectedasacollimatedbeam.If,however,thephaseofthelightraysateverysmallregionofthemirrorplaneisadjustedinanappropriateway,abeamofthedesireddirectionandcollimationcanbeproduced.ThedeviceabletoproduceahighcollimationanddirectionprecisionofthelaserbeamisbasedonHuygens-Fresnelprinciple:Allpointsonawavefrontactaspointsourcesfortheproductionofsphericalsecondarywaves(wavelets),whichspreadoutwardswithspeedscharacteristicofwavesinthatmediumandinterferewitheachother.Aftersometime,thenewpositionofthewavefrontisthesurfacetangenttothewavelets.Theprinciplehasamoregeneraluse:Opticalaberrationsofany(complicated)opticalsystemofinsufficientqualitymaybecorrectedforatafinalreflectiononamirrorbyanappropriatephaseadjustmentofthelightbeam.2BasicdesignoffinesteerdevicesTheprinciplesofabeamsteeringdevicemaybeillustratedbyasimpleprism(Fig.2).IfalightbeamisdirectedperpendicularlytoanisotropicprismwithindexofrefractionnasshowninFig.2left,thenthebeamisredirectedbyasteeringangleδ.Thisangledepends,obviously,ontheprismangleα:sinδ=nsinα–α.Fig2.Left:aprismmayservetodeflectalightbeam.Right:birefringent-isotropicbi-prism. Aslightlymoresophisticateddeviceisobtainedbyabirefringent-isotropicbi-prism.Here,twoprismsareputtogetherasshownonFig.2right.Theindexofrefractionofthetopisotropicprismisequaltonoofthebottombirefringentprism.Inthisway,theordinaryrayisnotdeflected.UsingSnell’slaw,itiseasytodeterminethesteeringangleδfortheextraordinaryray:sinδ=[nosin(arcsin((ne/no)sinα)–α)].Thereisanalternativewaytodeflectalightbeam.Insteadofarefractivemediumintheformofprism,itispossibletousealayerwithparallelsurfaces,ofvaryingindexofrefraction.ThisisillustratedinFig.3.Thepassageofthelightbeamthroughthedeviceisbestseenbydrawingwavefrontsofthelight.Fig3.Left:deflectionbyaprism.Right:deflectionbyvariableindexofrefraction.TheoperatingprincipleofatransmissionLCopticalphasearray(OPA)beamsteererforfineanglebeamadjustmentisbasedonvariableindexofrefractionoftheLClayer.Intheopticalelement,thereisanarrayofequallyspacedphaseshifters.Ineachphaseshifter(Fig.4left),aseriesofelectrodesdeterminesthetiltanglealongthecoordinatex.TheappliedvoltageonanelectrodehastoexceedthethresholdvaluefortheFreedericksztransition.Aproperlyadjustedvoltageproducesthedesiredindexofrefractionatthecoordinateoftheelectrode.Avariableindexofrefractionalongxcanthereforebeobtainedbytheappliedvoltagevaluesontheelectrodes;thisdeterminesthetiltangle.Toachievetheshiftalongabroadersurface,anarrayofcoordinatedsingleshiftersisnecessary(Fig.4right,aswillbeexplainedbellow.Duetoagradientintheindexofrefraction,thewavefrontslightlychangesdirection(Fig.5,top).ByappropriatelyorientingtheLCdirectorfieldandcreatingtherightindexgradient,thedesiredbeamdeflectionmaybeachieved.Fig4.Arrayofphaseshifters.Withanappropriatevoltageinthesequenceofelectrodes,thetiltangleandconsequentlyavaryingindexofrefractioninthephaseshiftercanbeset.ThelimitationoftheLCdeviceisonlybythedynamicsoftheLCdirector.IntheLClayer,theindexofrefractionmaychangebetweenthetwoextremevalues,ne(extraordinaryray)andno(ordinaryray).InanidealLCOPA,thegradientintheindexis designedtochangelinearly:n(x)=Δn(x/L)+no,Δn=ne–no.Inordertoachievesuchagradient,theorderparameterconfigurationN(x)mustassumetherightspatialdependence.Theaveragerefractiveindexmayberelatedtothetiltangleθ(x)ofthedirector.Therefractiveindexintermsofthetiltangleisgivenby[2]n2(x)=(neno)2/[no2+(ne2–no2)sin2θ(x)],fromwhichthetiltprofileisobtainedtobesin2θ(x)=[(nenoL)2/((L–x)no+xne)2)–no2]/(ne2–no2).Forasteeringangleθ,thepathdifference(D)acrosstheapertureofwidthwisgivenbyD=wsinθ.Fig5.Agradientintheindexofrefractioncausesthewavefronttodeviatefromtheoriginaldirection.Thesurfaceiscomposedofalargenumberofsegmentsthatinturncomprisemanypixels.Tosteerthelightbeamoverthesurface,itisnecessarytocoordinateallthepixelsinallthesegmentstoproduce,afterareflection,ahighlyparallelbeamoflight(Fig.6).Thepathdifferencebetweenadjacentsegmentsshouldbesuchastomatchthewaves,allpropagatinginthedesireddirection.Thismeansthatthepathdifferenceovertheapertureshouldbemλ,mbeingthenumberofsegments,andλthewavelength.Fig6.Inordertomatchthewavesemergingfromadjacentsegments,theiropticalpathdifferenceshouldbeawavelength. Moreelectrodesperareaintheapertureproducegreaterlocalphasegradient,whichinturnproducesgreaterabilitytocorrectawavefrontdirection.Themaximalsteeringanglethereforedependsonthenumberofelectrodes(N).Itturnsoutthatforhighdiffractionefficiency,about10electrodesperwaveoftheopticalpathdifferencearenecessary.LettherebeNelectrodeseachofwidthweacrosstheaperturew.If10electrodesarerequiredforonewavelengthopticalpathdifference,thenλ=10wesinθ.Inthiscase,themaximalsteeringangleissinθ=λ/10weand(w=Nwe)sinθ=Nλ/10w.Withincreasingsteeringangle,theprecisionofsteeringdecreases.Fig.7bellowshowstherapiddecreaseintheefficiencyasthesteeringangleapproaches10-2rad(=0.5º).Fig7.SteeringefficiencyofaLCOSdeviceasfunctionofsteeringangle..3ConclusionsWiththeaidofLCsitispossibletoproduceperfectlyplanemirrorsbyappropriatelyadjustingthedirectorconfigurationofthesegmentsofthemirrorplane.Inthisway,highlypreciseopticallyplanesurfacemaybeachieved.TheopticalprinciplesofbothclassicalsteeringdevicesaswellasLCdevicesmaybepresentedinphysicsclassesandexplainedinaqualitativeway.Thismayserveasastimulatingillustrationofsomeoftheimportantopticalprinciplesandtheirtechnologicaluse.Afulleraccountofthepedagogicalissuesandproblemsnottoucheduponinthearticlewillbepresentedelsewhere.4References[1]BosPandWangX2004SomeNon-DisplayElectro-opticalApplicationsofLiquidCrystalsApplicationsTutorials,20thInternationalLiquidCrystalConference(Ljubljana)[2]BornMandWolfE1980PrinciplesofOptics(Oxford:Pergamon)p698