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LightandMatterTimFreegardeSchoolofPhysics&AstronomyUniversityofSouthamptonControllinglightwithmatterOpticalpolarizationforanywavevector,therearetwofieldcomponentslightisatransversewave:perpendiculartoanywavemaybewrittenasasuperpositionofthetwopolarizations2TheFresnelequationreturntoderivationofelectromagneticwaveequationconsideroscillatorywavesofdefinitepolarizationaωapplyvectoridentitytwiceandsimplify3TheFresnelequationreturntoderivationofelectromagneticwaveequationconsideroscillatorywavesofdefinitepolarizationaωapplyvectoridentitytwiceandsimplify4TheFresnelequationforisotropicmediaelectromagneticwavesaretransversethePoyntingvectorisparalleltothewavevector5Characterizingtheopticalpolarizationwavevectorinsufficienttodefineelectromagneticwavewemustadditionallydefinethepolarizationvectore.g.linearpolarizationatangle6JonesvectorsnormalizedpolarizationvectorisknownastheJonesvectorrealfieldcorrespondstosuperpositionofexponentialformandcomplexconjugatedefinespolarizationstateofanywaveofgivenand7Categoriesofopticalpolarizationlinear(plane)polarizationcoefficientsdifferonlybyrealfactorcircularpolarizationcoefficientsdifferonlybyfactorellipticalpolarizationallothercases8Categoriesofopticalpolarizationlinear(plane)polarizationcoefficientsdifferonlybyrealfactorcircularpolarizationcoefficientsdifferonlybyfactorellipticalpolarizationallothercases9Polarizationnotationcircularpolarizationright-orleft-handedrotationwhenlookingtowardssourcelinear(plane)polarizationparallelorperpendiculartoplaneofincidenceRCPplaneofincidenceperpendicularparalleltracesoutright-orleft-handedthreadplaneofincidencecontainswavevectorandnormaltosurface10Categoriesofopticalpolarizationcomplexelectricfieldgivenbyrealelectricfieldcorrespondstosuperpositionwithcomplexconjugateformonochromaticfields,Jonesvectorisconstant11Polarizationoftime-varyingfieldscomplexpolychromaticelectricfieldgivenbybeatingbetweenfrequenciescausesfieldtovarywithtimeevenstabilizedlasershavelinewidthintheMHzrangeJonesvectormaythereforevaryonamicrosecondtimescale–orfaster12Stokesparameterswithpolychromaticlight,theJonesvectorvarieswethereforedescribepolarizationthroughaveragesandcorrelations:STOKESPARAMETERSaretheinstantaneousfieldcomponentsistheirrelativephase13Stokesparameterswithpolychromaticlight,theJonesvectorvarieswethereforedescribepolarizationthroughaveragesandcorrelations:STOKESPARAMETERSaretheinstantaneousfieldcomponentsistheirrelativephase14Stokesparameterstotalintensity,I1relatedtohorizontallypolarizedcomponent,I2…componentpolarizedat+45ºtohorizontal,I3…rightcircularlypolarizedcomponent,I415Unpolarized(randomlypolarized)lightaveragehorizontalcomponent=averageverticalcomponent
average+45ºcomponent=average-45ºcomponent
averageRCPcomponent=averageLCPcomponent…=halftotalintensityorthogonalpolarizationsareuncorrelated16Degreeofpolarizationforpartiallypolarizedlight,thequantity representsthedegreeofpolarization,whereunpolarized(randomlypolarized)completelypolarized17CompletelypolarizedlightconstantJonesvectorStokesparametersgivenbywhensimplydefiningthepolarizationstate,itiscommontodroptheintensityfactorI118ThePoincarésphere(a) rightcircularlypolarizedplottheStokesvector(b) leftcircularlypolarized(c) horizontallypolarized(d) verticallypolarized(e) polarizedat+45º(f) ellipticallypolarized(a)(b)(c)(d)(e)(f)(g) unpolarizedrightellipticallypolarized(g)leftellipticallypolarized[0,0,1][0,0,-1][1,0,0][-1,0,0][0,1,0][δ1,δ2,δ3]/δ0[0,0,0]19Polarizersmanyopticalelementsrestrictormodifythepolarizationstateoflightpolarization-dependenttransmission/reflectionpolarization-dependentrefractiveindexsheetpolarizers(Polaroid)Nicol,Wollastonprismsetcpolarizers,polarizingfilters,analyzerswaveplates,retardersfourcategoriesofphysicalphenomenapolarization-sensitiveabsorption(dichroism)polarization-sensitivedispersion(birefringence,opticalactivity)reflectionatinterfacesscattering20Polarizerseachmechanismmaydiscriminatebetweeneitherlinearorcircularpolarizationsmechanismsdependuponanasymmetryinthedeviceormediumplaneofincidenceperpendicularparallel21Linearpolarizationuponreflectionfornormalincidence,nodistinctionbetweenhorizontalandverticalpolarizationsifwavevectormakesanglewithinterfacenormal,s-andp-polarizationsaffecteddifferentlyweconsiderherethereflectionofp-polarizedlight;s-polarizedbeamsmaybetreatedsimilarlyweresolvetheelectricfieldintocomponentsparallelandnormaltotheinterfaceallmagneticfieldcomponentsareparalleltotheinterface22Linearpolarizationuponreflectionfornormalincidence,nodistinctionbetweenhorizontalandverticalpolarizationsifwavevectormakesanglewithinterfacenormal,s-andp-polarizationsaffecteddifferentlyweconsiderherethereflectionofp-polarizedlight;s-polarizedbeamsmaybetreatedsimilarlyweresolvetheelectricfieldintocomponentsparallelandnormaltotheinterfaceallmagneticfieldcomponentsareparalleltotheinterfacecombineforwardandreflectedwavestogivetotalfieldsforeachregionapplycontinuityconditionsforseparatecomponentshencederivefractionaltransmissionandreflection23Fresnelequationsp-polarizations-polarizationcombineforwardandreflectedwavestogivetotalfieldsforeachregionapplycontinuityconditionsforseparatecomponentshencederivefractionaltransmissionandreflection24LineardichroismconductivityofwiregriddependsuponfieldpolarizationelectricfieldsperpendiculartothewiresaretransmittedWIREGRIDPOLARIZERfieldsparalleltothewiresareabsorbed25LineardichroismcrystalsmaysimilarlyshowabsorptionwhichdependsuponlinearpolarizationabsorptionalsodependsuponwavelengthpolarizationthereforedeterminescrystalcolourTOURMALINEpleochroism,dichroism,trichroism26Circulardichroismabsorptionmayalsodependuponcircularpolarizationthescarabbeetlehaspolarization-sensitivevision,whichitusesfornavigationthebeetle’sowncolourdependsuponthecircularpolarizationSCARABBEETLELEFTCIRCULARPOLARIZEDLIGHTRIGHTCIRCULARPOLARIZEDLIGHT27PolarizationinnaturetheEuropeancuttlefishalsohaspolarization-sensitivevision…andcanchangeitscolourandpolarization!MAN’SVIEWCUTTLEFISHVIEW(red=horizontalpolarization)CUTTLEFISH(sepiaofficinalis)28Birefringenceasymmetryincrystalstructurecausespolarizationdependentrefractiveindexoppositepolarizationsfollowdifferentpathsthroughcrystalbirefringence,doublerefraction2938.5ºLinearpolarizers(analyzers)e-rayo-raye-rayo-rays-rayp-raybirefringenceresultsindifferentanglesofrefractionandtotalinternalreflectionmanydifferentdesigns,offeringdifferentgeometriesandacceptanceanglesasimilarfunctionresultsfrommultiplereflection30Waveplates(retarders)WAVEPLATEatnormalincidence,abirefringentmaterialretardsonepolarizationrelativetotheotherlinearlypolarizedlightbecomesellipticallypolarized31Compensatorsadjustfixedvariableavariablewaveplateusestwowedgestoprovideavariablethicknessofbirefringentcrystalafurthercrystal,orientedwiththefastandslowaxesinterchanged,allowstheretardationtobeadjustedaroundzeroSOLEILCOMPENSATORwithasingle,fixedfirstsection,thisisa‘singleorder’(or‘zeroorder’)waveplateforsmallconstantretardation32Opticalactivity(circularbirefringence)l-limonene(orange)r-limonene(lemon)CH2CH3HCH3CH2CH3HCH3CHIRALMOLECULESopticalactivityisbirefringenceforcircularpolarizationsanasymmetrybetweenrightandleftallowsopposingcircularpolarizationstohavedifferingrefractiveindicesopticalactivityrotatesthepolarizationplaneoflinearlypolarizedlightmaybeobservedinvapours,liquidsandsolids33JonesvectorcalculusifthepolarizationstatemayberepresentedbyaJonesvectorthentheactionofanopticalelementmaybedescribedbyamatrixJONESMATRIX34JonesvectorcalculusifthepolarizationstatemayberepresentedbyaJones
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