Characterization of partially polarized light fields PDF
Preview Characterization of partially polarized light fields
SpringerSeriesin OPTICAL SCIENCES 147 foundedbyH.K.V.Lotsch Editor-in-Chief: W.T.Rhodes,Atlanta EditorialBoard: A.Adibi,Atlanta T.Asakura,Sapporo T.W.Hänsch,Garching T.Kamiya,Tokyo F.Krausz,Garching B.Monemar,Linköping H.Venghaus,Berlin H.Weber,Berlin H.Weinfurter,Munich SpringerSeriesin OPTICAL SCIENCES The Springer Series in Optical Sciences, under the leadership of Editor-in-Chief William T. Rhodes, Georgia Institute of Technology, USA, provides an expanding selection of research monographs in allmajorareasofoptics:lasersandquantumoptics,ultrafastphenomena,opticalspectroscopytech- niques,optoelectronics,quantuminformation,informationoptics,appliedlasertechnology,industrial applications,andothertopicsofcontemporaryinterest. Withthisbroadcoverageoftopics,theseriesisofusetoallresearchscientistsandengineerswhoneed up-to-datereferencebooks. The editors encourage prospective authors to correspond with them in advance of submitting a manuscript.SubmissionofmanuscriptsshouldbemadetotheEditor-in-ChieforoneoftheEditors. Seealsowww.springer.com/series/624 Editor-in-Chief WilliamT.Rhodes GeorgiaInstituteofTechnology SchoolofElectricalandComputerEngineering Atlanta,GA30332-0250,USA E-mail:[email protected] EditorialBoard AliAdibi BoMonemar GeorgiaInstituteofTechnology DepartmentofPhysics SchoolofElectricalandComputerEngineering andMeasurementTechnology Atlanta,GA30332-0250,USA MaterialsScienceDivision E-mail:[email protected] LinköpingUniversity ToshimitsuAsakura 58183Linköping,Sweden E-mail:[email protected] Hokkai-GakuenUniversity FacultyofEngineering HerbertVenghaus 1-I,Minami-26,Nishi11,Chuo-ku FraunhoferInstitutfürNachrichtentechnik Sapporo,Hokkaido064-0926,Japan Heinrich-Hertz-Institut E-mail:[email protected] Einsteinufer37 TheodorW.Hänsch 10587Berlin,Germany E-mail:[email protected] Max-Planck-InstitutfürQuantenoptik Hans-Kopfermann-StraßeI HorstWeber 85748Garching,Germany TechnischeUniversitätBerlin E-mail:[email protected] OptischesInstitut TakeshiKamiya Straßedes17.Juni135 10623Berlin,Germany MinistryofEducation,Culture,Sports E-mail:[email protected] ScienceandTechnology NationalInstitutionforAcademicDegrees HaraldWeinfurter 3-29-1Otsuka,Bunkyo-ku Ludwig-Maximilians-UniversitätMünchen Tokyo112-0012,Japan SektionPhysik E-mail:[email protected] Schellingstraße4/III FerencKrausz 80799München,Germany E-mail:[email protected] Ludwig-Maximilians-UniversitätMünchen LehrstuhlfürExperimentellePhysik AmCoulombwall1 85748Garching,Germany and Max-Planck-InstitutfürQuantenoptik Hans-Kopfermann-Straße1 85748Garching,Germany E-mail:[email protected] · · Rosario Martínez-Herrero Pedro M. Mejías Gemma Piquero Characterization of Partially Polarized Light Fields 123 Prof.RosarioMartínez-Herrero Prof.PedroM.Mejías UniversidadComplutensedeMadrid UniversidadComplutensedeMadrid FacultyofPhysics FacultyofPhysics OpticsDepartment,28040Madrid OpticsDepartment,28040Madrid Spain Spain r.m-h@fis.ucm.es pmmejias@fis.ucm.es Dr.GemmaPiquero UniversidadComplutensedeMadrid FacultyofPhysics OpticsDepartment,28040Madrid Spain piquero@fis.ucm.es ISSN0342-4111 e-ISSN1556-1534 ISBN978-3-642-01326-3 e-ISBN978-3-642-01327-0 DOI10.1007/978-3-642-01327-0 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2009927003 ©Springer-VerlagBerlinHeidelberg2009 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:eStudioCalamarS.L.,Gerona,Spain Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Polarization involves the vectorial nature of light. In theoretical topics and tech- nological applications of current interest in optical science, the electromagnetic descriptionofthelightdisturbanceandpolarization-relatedphenomenahaveturned out to be crucial. In fact, they have gained importance in recent years, attracting the attention of numerous scientists in the last decade. Photonics devices, biologi- caloptics,opticalcommunications,atmosphericoptics,andsensortechnologiesare examplesofresearchareaswherethevectorialfeaturesoflightarerelevant. In practice, optical radiation exhibits randomness and spatial nonuniformity of the polarization state. These kinds of realistic and general situations are most fre- quentlyencounteredintheliterature,anddrasticallydepartfromthesimplestmodel of harmonic plane waves. Keeping in mind the framework of classical optics, this bookdealswiththeanalyticalproblemofdescribingandcharacterizingthepolariza- tionandspatialstructureofnonuniformlypolarizedfields,alongwiththeirevolution whenlightpropagatesthroughopticalsystems.Thisistheaimofthiswork. In particular, the scope and the contents of the book are essentially focused on thecontributionsoftheauthorstofourmainissues,whichcorrespondtoapproach- ing the problem under study from different angles. Thus, in Chap. 1, after a short introductiontothemainstandardrepresentationsofthepolarization,weanalyzein some detail several recently proposed measurable parameters, of practical use for characterizing, in a global way, the polarization of nonuniformly polarized beam- like fields. Chapter 2 also proposes an overall description, but now the alternative formalismallowsacharacterizationofthepolarizationdistributionandtheshapeof partiallypolarized,partiallycoherentbeams.Afamilyofmeasurableandmeaning- ful parameters is defined, whose determination involves certain averages over the regionofthetransverseprofilewherethebeamirradianceissignificant. On the other hand, in recent years, the coherence theory, well established for scalar beams, has been investigated with regard to partially polarized fields. It has been shown that, for stochastic electromagnetic beams, the properties concerning coherenceandpolarizationfeaturesare,ingeneral,connectedwitheachother.Con- sequently, fundamental concepts, such as the degree of coherence and the fringe visibilityinYounginterferometers,shouldberevisited.Thisisdoneinsomedetail inChap.3. v vi Preface Finally, Chap. 4 is devoted to nonparaxial electromagnetic fields, which arise whenlightisstronglyfocusedandthebeamreachesawaistsizeevensmallerthan the wavelength. The theoretical analysis deals with certain kinds of nonparaxial exactsolutionsoftheMaxwellequations.Theirpolarizationfeaturesarediscussed and,inthosecasesinwhichtheevanescentwavesaresignificant(highlynonparaxial regime),theirfieldstructureisalsodescribed. Although short surveys are provided to review some basic formalisms, the reader is assumed to be familiar with well-known concepts treated in many optics textbooks. Theresearchworkleadingtotheresultsreportedinthisbookhavebeenobtained in collaboration with a number of researchers. We would like to acknowledge here their fundamental contribution. We also thank Prof. H. Weber for his inter- est, helpful suggestions and continuous kindness, which include support during all the experimental work described in Sect. 2.4.3 and performed at the Optisches Institut of the Technische Universität in Berlin. We are indebted to Prof. F. Gori, Dr.M.SantarsieroandDr.R.Borghi,attheUniversityofRome3,forhelpfuldis- cussionsconcerningpartiallypolarizedGaussianSchell-modelbeams.Inaddition, we are also grateful to Dr. M. Santarsiero and Profs. S. Bosch and A. Carnicer, at BarcelonaUniversity,fortheirkindreadingofChaps.3and4. This work was supported by the Ministerio de Educación y Ciencia of Spain, Project FIS2007-63396, and by the Comunidad de Madrid, Project: CCG07- UCM/ESP-3070. Contents 1 RepresentationsofthePolarizationofBeamlikeFields . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 StandardRepresentationsofthePolarization . . . . . . . . . . . 1 1.2.1 TheJonesCalculus . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Coherence-PolarizationMatrices . . . . . . . . . . . . . 4 1.2.3 TheStokes-MüllerCalculus . . . . . . . . . . . . . . . . 6 1.2.4 LocalDegreeofPolarization . . . . . . . . . . . . . . . 8 1.3 WeightedDegreeofPolarization . . . . . . . . . . . . . . . . . 10 1.4 Linear and Circular Polarization Content of Totally PolarizedBeams . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 KeyDefinitionsandPhysicalMeaning . . . . . . . . . . 12 1.4.2 ApplicationtoanExample. . . . . . . . . . . . . . . . . 13 1.4.3 Measurability . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 RadialandAzimuthalPolarizationContentofTotally PolarizedBeams . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5.1 KeyDefinitions . . . . . . . . . . . . . . . . . . . . . . 16 1.5.2 RelationswiththeStokesParameters . . . . . . . . . . . 19 1.5.3 Relations with the Output of Radial andAzimuthalPolarizers . . . . . . . . . . . . . . . . . 20 1.5.4 Measurability . . . . . . . . . . . . . . . . . . . . . . . 21 1.6 PartiallyPolarizedGaussianSchell-ModelBeams . . . . . . . . 24 1.6.1 GaussianSchell-ModelBeams:ScalarCase . . . . . . . 24 1.6.2 GaussianSchell-ModelBeams:VectorialCase . . . . . . 26 1.6.3 TheVanCittert-ZernikeTheorem . . . . . . . . . . . . . 28 1.6.4 ExperimentalSynthesisofGSMfields . . . . . . . . . . 31 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2 Second-OrderOverallCharacterizationofNon-uniformly PolarizedLightBeams . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 Second-OrderOverallCharacterization:ScalarCase . . . . . . . 38 2.2.1 FormalismandKeyDefinitions . . . . . . . . . . . . . . 38 vii viii Contents 2.2.2 PropagationandMeasurementoftheIrradiance Moments . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3 Second-OrderOverallCharacterization:VectorialCase . . . . . 44 2.3.1 TheWignerMatrix. . . . . . . . . . . . . . . . . . . . . 44 2.3.2 TheStokesMatrices . . . . . . . . . . . . . . . . . . . . 45 2.3.3 PropagationLawsandMeasurement . . . . . . . . . . . 48 2.3.4 InvariantParameters . . . . . . . . . . . . . . . . . . . . 51 2.4 GeneralizedDegreeofPolarization . . . . . . . . . . . . . . . . 54 2.4.1 DefinitionandPropertiesofGeneralizedDegree ofPolarization . . . . . . . . . . . . . . . . . . . . . . . 54 2.4.2 PhysicalMeaningandMeasurement . . . . . . . . . . . 55 2.4.3 GeneralizedDegreeofPolarizationofBeams EmergingfromOptically-PumpedNd:YAGRods . . . . 58 2.4.4 ClassificationSchemeofPartiallyPolarizedBeams . . . 62 2.5 BeamQualityParameterofPartiallyPolarizedfields . . . . . . . 63 2.6 OverallParametricCharacterizationofPGSMBeams . . . . . . 65 2.7 BeamQualityImprovement:GeneralConsiderations . . . . . . . 69 2.8 BeamQualityImprovementAfterPropagationThrough OpticalPhaseDevices . . . . . . . . . . . . . . . . . . . . . . . 75 2.8.1 PropagationThroughAnisotropicPure-PhasePlates . . . 76 2.8.2 Propagation of Radially and Azimuthally PolarizedBeamsThroughQuarticPhasePlates . . . . . . 78 2.8.3 PropagationThroughSpiralPhaseElements . . . . . . . 82 2.9 GlobalBeamShapingwithNon-uniformlyPolarizedBeams . . . 84 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3 PolarizationandCoherenceofRandomElectromagneticFields . . 93 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.2 ScalarFramework . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.2.1 SpectralDegreeofCoherence . . . . . . . . . . . . . . . 94 3.2.2 Young’sInterferenceExperiment . . . . . . . . . . . . . 96 3.3 VectorialFramework:KeyDefinitions . . . . . . . . . . . . . . 98 3.3.1 Young’sExperimentRevisited . . . . . . . . . . . . . . . 98 3.3.2 Degrees of Coherence of Random ElectromagneticFields. . . . . . . . . . . . . . . . . . . 100 3.3.3 Relation Between Degrees of Coherence of ElectromagneticFields. . . . . . . . . . . . . . . . . . . 103 3.4 MaximumVisibilityUnderUnitaryTransformations . . . . . . . 107 3.5 Position-IndependentStochasticBehaviorofRandom ElectromagneticFields. . . . . . . . . . . . . . . . . . . . . . . 112 3.6 Mean-SquareCoherentLight:MaximumYoung’sFringe VisibilityThroughReversibleDevices . . . . . . . . . . . . . . 118 3.7 Comparing Special Types of Random ElectromagneticFields. . . . . . . . . . . . . . . . . . . . . . . 122 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Contents ix 4 Non-ParaxialElectromagneticBeams . . . . . . . . . . . . . . . . 127 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.2 FormalismandKeyDefinitions . . . . . . . . . . . . . . . . . . 128 4.2.1 AngularPlane-WaveSpectrum . . . . . . . . . . . . . . 128 4.2.2 PropagatingandEvanescentWaves . . . . . . . . . . . . 131 4.2.3 TE-andTM-DecompositionofthePropagatingField . . 131 4.2.4 SignificanceoftheLongitudinalFieldComponent . . . . 134 4.3 Propagation of Non-paraxial Beams with Radial or AzimuthalPolarizationDistributionataTransversePlane . . . . 136 4.3.1 RadialandAzimuthalComponents . . . . . . . . . . . . 136 4.3.2 RadialCase:Free-SpacePropagation . . . . . . . . . . . 138 4.3.3 AzimuthalCase:Free-SpacePropagation . . . . . . . . . 142 4.3.4 ApplicationtoaParticularSetofFields . . . . . . . . . . 145 4.3.5 Radially-PolarizedFieldsatAnyTransversePlane . . . . 148 4.4 ClosestField . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.4.1 DefinitionandMeaning . . . . . . . . . . . . . . . . . . 151 4.4.2 ApplicationtotheUniformly-PolarizedGaussianModel . 152 4.4.3 TransversePolarizationStructureoftheClosest FieldAssociatedtotheGaussianModel. . . . . . . . . . 157 4.4.4 OtherExamples . . . . . . . . . . . . . . . . . . . . . . 161 4.5 Evanescent Waves Associated to Highly Non-paraxialBeams . . . . . . . . . . . . . . . . . . . . . . . . 165 4.5.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.5.2 NumericalExamples . . . . . . . . . . . . . . . . . . . . 167 4.6 PartiallyCoherentElectromagneticTE-Fields . . . . . . . . . . 172 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Notation Symbol Name First appearancein thetext (Subsection) [αβ]ij,i,j=s,p; 2.3.2 α,β=x,y,u,v Det determinantofamatrix 1.2.1 E electricfieldvector 1.2.1 ˜ ˜ E,H spatialFouriertransformofEandH 4.2.1 e1(φ),e2(ρ,φ) 4.2.3 E˜0(ρ,φ) 4.2.1 Eazim azimuthallypolarizedfield 4.3.3 Eclosest,Hclosest closestelectricandmagneticfields 4.4.2 eev(ρ,φ) 4.5.1 Epr,Eev propagatingandevanescenttermsofE 4.2.2 ER,Eθ radialandazimuthalcomponentsofE 1.5.1 Erad radiallypolarizedfield 4.3.2 Es,Ep transversecomponentsofE 1.2.1 ETE,ETM transverse-electricandtransverse-magnetictermsofE 4.2.3 (cid:7)(r1,r2,τ) mutualcoherencefunction 1.2.2 (cid:7)ˆ(r1,r2,τ) 1.2.2 g12≡g(r1,r2) 3.4 H magneticfieldvector 4.2.1 HTE,HTM transverse-electricandtransverse-magnetictermsofH 4.2.3 h(r,η,z) Wignerdistributionfunction 2.2.1 Hˆ(r˜,η˜,z) Wignermatrix 2.3.1 Jˆ Jonesmatrix 1.2.1 ˆ J(r1,r2,z) coherence-polarizationmatrix 1.2.2 j(r1,r2) complexdegreeofcoherence 1.6.1 Jsc(r1,r2) mutualintensity 1.6.1 k wavenumber 1.2.1 K Kurtosisparameter 2.9 λ wavelength 1.2.1 M2 beampropagationfactor 2.5 xi
The list of books you might like
