光學101：1級理論基礎

Optics101:Level1TheoreticalFoundationsOpticsisthebranchofphysicsthatdealswithlightanditspropertiesandbehavior.Itisavastsciencecoveringmanysimpleandcomplexsubjectsrangingfromthereflectionoflightoffametallicsurfacetocreateanimage,totheinteractionofmultiplelayersofcoatingtocreateahighopticaldensityrugatenotchfilter.Assuch,itisimportanttolearnthebasictheoreticalfoundationsgoverningtheelectromagneticspectrum,interference,reflection,refraction,dispersion,anddiffractionbeforepickingthebestcomponentforone'soptics,imaging,and/orphotonicsapplications.THEELECTROMAGNETICSPECTRUMLightisatypeofelectromagneticradiationusuallycharacterizedbythelengthoftheradiationofinterest,specifiedintermsofwavelength,orlambdaA).Wavelengthiscommonlymeasuredinnm(109meters)orpm(106meters).Theelectromagneticspectrumencompassesallwavelengthsofradiationrangingfromlongwavelengths(radiowaves)toveryshortwavelengths(gammarays);Figure1illustratesthisvastspectrum.Themostrelevantwavelengthstoopticsaretheultraviolet,visible,andinfraredranges.Ultraviolet(UV)rays,definedas1-400nm,areusedintanningbedsandareresponsibleforsunburns.Visiblerays,definedas400-750nm,comprisethepartofthespectrumthatcanbeperceivedbythehumaneyeandmakeupthecolorspeoplesee.ThevisiblerangeisresponsibleforrainbowsandthefamiliarROYGBIV-themnemonicmanylearninschooltohelpmemorizethewavelengthsofvisiblelightstartingwiththelongestwavelengthtotheshortest.Lastly,infrared(IR)rays,definedas750nm-1000pm,areusedinheatingapplications.IRradiationcanbebrokenupfurtherintonear-infrared(750nm-3pm),mid-waveinfrared(3-30pm)andfar-infrared(30-1000pm).INTERFERENCEFigure1:ElectromagneticSpectrumIsaacNewton(1643-1727)wasoneofthefirstphysiciststoproposethatlightwascomprisedofsmallparticles.Acenturylater,ThomasYoung(1773-1829)proposedanewtheoryoflightwhichdemonstratedlight'swavequalities.Inhisdouble-slitexperiment,Youngpassedlightthroughtwocloselyspacedslitsandfoundthatthelightinterferedwithitself(Figure2).Thisinterferencecouldnotbeexplainediflightwaspurelyaparticle,butcouldiflightwasawave.Thoughlighthasbothparticleandwavecharacteristics,knownasthewave-particleduality,thewavetheoryoflightisimportantinopticswhiletheparticletheoryinotherbranchesofphysics.Figure3:ConstructiveandDestructiveInterferenceInterferenceoccurswhentwoormorewavesoflightaddtogethertoformanewpattern.Constructiveinterferenceoccurswhenthetroughsofthewavesalignwitheachother,whiledestructiveinterferenceoccurswhenthetroughsofonewavealignwiththepeaksoftheother(Figure3).InFigure3,thepeaksareindicatedwithblueandthetroughswithredandyellow.Constructiveinterferenceoftwowavesresultsinbrighterbandsoflight,whereasdestructiveinterferenceresultsindarkerbands.Intermsofsoundwaves,constructiveinterferencecanmakesoundlouderwhiledestructiveinterferencecancausedeadspotswheresoundcannotbeheard.Interferenceisanimportanttheoreticalfoundationinoptics.Thinkingoflightaswavesofradiationsimilartoripplesinwatercanbeextremelyuseful.Inaddition,understandingthiswavenatureoflightmakestheconceptsofreflection,refraction,dispersionanddiffractiondiscussedinthefollowingsectionseasiertounderstand.

REFLECTION0iIncidentLightReflectedLightFirstSurfaceisCoatedSubstrateSecondSurfaceisUncoatedFigure4ReflectionfromaFirstSurfaceMirrorReflectionisthechangeindirectionofawavefrontwhenithitsanobjectandreturnsatanangle.Thelawofreflectionstatesthattheangleofincidence(angleatwhichlightapproachesthesurface)isequaltotheangleofreflection(angleatwhichlightleavesthesurface).Figure4illustratesreflectionfromafirstsurfacemirror.Ideally,ifthereflectingsurfaceissmooth,allofthereflectedrayswillbeparallel,definedasspecular,orregular,reflection.Ifthesurfaceisrough,therayswillnotbeparallel;thisisreferredtoasdiffuse,orirregular,reflection.Mirrorsareknownfortheirreflectivequalitieswhicharedeterminedbythematerialusedandthecoatingapplied.REFLECTION0iIncidentLightReflectedLightFirstSurfaceisCoatedSubstrateREFRACTIONWhilereflectioncausestheangleofincidencetoequaltheangleofreflection,refractionoccurswhenthewavefrontchangesdirectionasitpassesthroughamedium.Thedegreeofrefractionisdependentuponthewavelengthoflightandtheindexofrefractionofthemedium.Indexofrefraction(n)istheratioofthespeedoflightinavacuum(c)tothespeedoflightwithinagivenmedium(v).ThiscanbemathematicallyexpressedbyEquationIndexofrefractionisameansofquantifyingtheeffectoflightslowingdownasitentersahighindexmediumfromalowindexmedium(Figure5).

wherenistheindexoftheincidentmedium,0istheangleoftheincidentray,nistheindexoftherefracted/reflectedmedium,and0istheangleoftherefracted/reflected2ray.Iftheangleofincidenceisgreaterthanacriticalangle0(whentheangleofrefraction=90°),thenlightisreflectedinsteadofrefracted.Thisprocessisreferredtoastotalinternalreflection(TIR).Figure6illustratesTIRwithinagivenmedium.Figure5:Figure5:LightRefractionfromaLowIndextoaHighIndexMediumFigure6:TotalInternalReflectionRaythatDemonstratesTIRRaythatDemonstratesSnell'sLawandNoTIRTIRismathematicallyexpressedbyEquation3:Figure6:TotalInternalReflectionsin(5)=—

TotalInternalReflectionisresponsibleforthesparkleoneseesindiamonds.Duetotheirhighindexofrefraction,diamondsexhibitahighdegreeofTIRwhichcausesthemtoreflectlightatavarietyofangles,orsparkle.AnothernotableexampleofTIRisinfiberopticswherelightenteringoneendofaglassorplasticfiberopticwillundergoseveralreflectionsthroughoutthefiber'slengthuntilitexitstheotherend(Figure7$inceTIRoccursforacriticalangle,fiberopticshavespecificacceptanceanglesandminimumbendradiiwhichdictatethelargestangleatwhichlightcanenterandbereflectedandthesmallestradiithefiberscanbebenttoachieveTIR.InddentAcceptance[HalfAngle'InddentAcceptance[HalfAngle'Jacket—-Clad(LowerIndex)Core(HigherIndex)"Figure7TotalInternalRefractioninaSingleFiberOpticDISPERSIONlightmoreitbyAbbeatthefwithlowdispersion.Onewaytoquantifydispersionistoexpressnumber(v)isafunctionoftherefractiveindexofamateriald(587.6nm),andc(656.3nm)wavelengthsoflight(Equation4).Dispersionisameasureofhowmuchtheindexofrefractionofamaterialchangeswithrespecttowavelength.Dispersionalsodeterminestheseparationofwavelengthsknownaschromaticaberration(Figure8).Aglasswithhighdispersionwillseparatethanaglassnumber.Abbe(486.1nm),d⑷Thechromaticaberrationcausedbydispersionisresponsibleforthefamiliarrainboweffectoneseesinopticallenses,prisms,andlightmoreitbyAbbeatthefwithlowdispersion.Onewaytoquantifydispersionistoexpressnumber(v)isafunctionoftherefractiveindexofamateriald(587.6nm),andc(656.3nm)wavelengthsoflight(Equation4).WhiteLiAngleofMinimumDeviationFigure8:DispersionthroughaPrismDIFFRACTIONTheinterferencepatternscreatedbyThomasYoung'sdouble-slitexperimentcanalsobecharacterizedbythephenomenonknownasdiffraction.Diffractionusuallyoccurswhenwavespassthroughanarrowslitoraroundasharpedge.Ingeneral,thegreaterthedifferencebetweenthesizeofthewavelengthoflightandthewidthoftheslitorobjectthewavelengthencounters,thegreaterthediffraction.Thebestexampleofdiffractionisdemonstratedusingdiffractiongratings.Adiffractiongrating'scloselyspaced,parallelgroovescauseincidentmonochromaticlighttobend,ordiffract.Thedegreeofdiffractioncreatesspecificinterferencepatterns.Figures9and10illustratevariouspatternsachievedwithdiffractiveoptics.Diffractionistheunderlyingtheoreticalfoundationbehindmanyapplicationsusingdiffractiongratings,spectrometersmonochrometers,laserWhiteLiAngleofMinimu