光学相干和光子统计Word格式文档下载.docx

光学相干和光子统计Word格式文档下载.docx

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OpticalCoherenceandPhotonStatistics

Thefieldofoptics,afterseemingtohavereachedasortofmaturity,isbeginningtoundergosomerapidandrevolutionarychanges.Thesechangesareconnectedwiththingswhichwehave,asamatterofprinciple,knownaboutformanyyears,buttheextenttowhichwecouldputourknowledgeintopracticehas,untiljustafewyearsago,beenextremelylimited.Thustheelectromagneticcharacteroflightwaveshasbeenfamiliarknowledgesincethelastcentury.Avastbodyoftheoryandtechniqueconcerningthegenerationofelectromagneticwaveshasbeenbuiltupduringtheseyears,butvirtuallyallofithasdealtwithradiofrequencyfields.Lightwavesofcourse,areofthesameelectromagneticcharacterasradiowaves.Butbecausetheonlywayswehadofgeneratingtheminthepastwereextremelyclumsy（inasenseweshallpresentlydiscussatsomelength）therehasbeenverylittleoccasionuntilrecentlytoapplytheinsightsofradio-frequencytheoryinoptics.Asimplephysicalreason,asweshallsee,liesatthebottomofthis:

allofthetraditionaltypesofopticalsourcespossessacertainchaoticqualityincommon.Theyarewhataradioengineerwouldrefertoasnoisegenerators,andallofthedelicateandingenioustechniquesofopticsareexercisesintheconstructiveuseofnoise.Theinventionoftheopticalmaserliasremovedthisbarrierwithalmostasinglestroke.Itallowsustopresumethatwewillsomedaybeabletocontrolfieldsoscillatingatopticalorhigherfrequencieswiththesamesortofprecisionandversatilitythathavebecomefamiliarinradiofrequencytechnology.

Anotherrecentchangeisthedevelopmentofdetectorswhichrespondstronglytoindividualquantaoflight.Thesehavepermittedustoexplorethecorpuscularcharacterofopticalfields.Allofthetraditionalopticalexperimentshavenotonlydealtwithextremelycrudesources,buthavepaidverylittleattentiontothedetectionofindividuallightquanta.Thedetectorsusedweretopicallysensitiveonlytosubstantialnumbersofphotonsandwerequiteslowinactionsothatwemeasuredonlyintensitieswhichhadbeenaveragedoverrelativelylongperiodsoftime.Thenewlightdetectorsenableustoaskmoresubtlequestionsthanjustonesaboutaverageintensities;

wecanforexample,askquestionsaboutthecountingofpairsofquanta,andcanmakemeasurementsoftheprobabilitythatthequantaarepresentatanarbitrarypairofspacepoints,atanarbitrarypairoflimes.

Iftheinstrumentationinopticshasmadelongstridesinthedirectionofdealingwithphotons,itisworthmentioningthattheinstrumentationintheradiofrequencyfieldisleadinginthatdirectionaswell.Theenergiesofradiofrequencyphotonsareextremelysmall,muchsmallerthanthethermalfluctuationenergykT（T=noisetemperature～roomtemperatureformostamplifiers）.Therehasconsequentlynotbeenmuchneedinradiofrequencytechnologytodatetopayattentiontothecorpuscularstructureofthefield.Therecentinvention,however,oflownoiseamplifiers,suchasthemicrowavemaser,hasloweredthenoisetemperatureofthedetectingdevicetosuchadegreethatwithfurtherprogressitseemsnotimpossiblethatindividualphotonsmaybedetected.So,eveninthemicrowaveregion,thereisnowacertainamountofattentionbeingpaidtothecorpuscularstructureoflight.

Itisinteresting,inanycase,toinvestigatethecorpuscularnatureofelectromagneticfields,becauseitwillsettheultimatelimitationtothepossibilityoftransmittinginformationbymeansoffields.Wewillnotdiscussinformationtheoryinthisarticle,butwewillhavesomethingstocaywhicharerelatedtonoisetheory.Noisetheoryistheclassicalformofthetheoryoffluctuationsoftheelectromagneticfieldandisquitenaturallyrelatedtothetheoryofquantumfluctuationsofthefield.Allofthesesubjectsfallunderageneralheadingwhichwemightcallphotonstatistics.Coherencetheorytoo,isproperlyspeaking,arathersmallareaofthesamegeneralsubject.Itspurposeissimplytoformulatesomeusefulwaysofclassifyingthestatisticalbehaviouroffields.

Theproblemtowhichweshalladdressourselvesinthisarticleistheconstructionofafairlyrigorousandgeneraltreatmentoftheproblemsofphotonstatistics.Thereisnoneed,indoingit,tomakeanymaterialdistinctionbetweenradiofrequencyandopticalfields（orbetweentheseandX-rayfieldsforthatmatter）.Apartoftheformalism,thatwhichhastodowiththedefinitionofcoherence,issuggestedinfactasawayofunifyingtheratherdifferentconceptsofcoherence,whichhavecharacterizedtheseareasinthepast.

Wehavealreadyremarkedthatopticalexperimentshaveonlyrarelydealtwithindividualphotons.Muchthesameobservationcanbemadeforopticaltheoryaswell.Ifthephotonhastosucharemarkabledegreeremainedastrangertoopticaltheorysomejustificationforthatfactsurelyliesinthegreatsuccessofthesimple,wavemodelsintheanalysisofopticalexperiments.Suchmodelsareusuallyspokenofasbeingclassicalincharactersincetheyproceedtypicallyfromsomekindofanalogytoclassicalelectromagnetictheoryandpayaslittleattentiontothecorpuscularcharacteroftheradiationastheexperimentalarrangementwillpermit.

Figure1

Intheseapproachesonetalkstypicallyaboutsomekindof“opticaldisturbancefunction”whichisassumedtoobeythewaveequationandperhapscertainboundaryconditionsaswell.Thefunctionmayrepresentthecomponentsofthoelectricvectororpossiblyotherfieldquantitiessuchasthevectorpotential,orthemagneticfield.Inmanyapplicationsinfactonedoesnotneedtobeveryspecificaboutwhatitreallydoesordoesnotrepresent.

LetusconsidertheYounginterferometer（Fig.1）inordertoillustratetheelementaryapproacheswearediscussing.Aplane,quasi-monochromaticwavecomingfromapointsourceσimpingesonthescreenΣwithtwoparallelslitsatthepositionsP1andP2.

ThetwowavesemergingfromtheslitsgiverisetoaninterferencepatternonthescreenΣ,whichwecanoftenseewiththeunaidedeye.Thesimplestwayofpredictingtheformoftheinterferencepatternistoignorethevectorcharacteroftheelectromagneticfieldandintroduceascalarfieldwhichispresumedtodescribethe“opticaldisturbance”.Wethentrytofindafunction.whichsatisfiesthewaveequationtogetherwithasetofboundaryconditionswhichwetaketorepresenttheeffectofthescreenΣ.Thatproblem,asyouremember,isingeneralagooddealtoodifficulttobesolvedexactly,anditiscustomarytomakeanumberofsimplifyingapproximationssuchasdealingverycrudelywiththeboundaryconditions,andmakinguseofHuygens’principle.Bythesefamiliarmethodswereachasimpleevaluationofthefielddistribution.onthescreenΣ..

Ofcourse,ifwearetopredicttheformoftheinterferencepattern,wemustatsomestagefacethequestionofattachingaphysicalinterpretationtothefields.Themostfamiliarapproachistoregardφ（r,t）asarealfieldandtoidentifyit,perhaps,withoneofthecomponentsoftheelectricfieldvector.Theexperimentalfringepatternisthenpredictedquiteaccurately,asweallknow,ifthelightintensityonthescreenisidentifiedwithφ2,thesquareofouropticalfield.Theidentificationpossessesthejustification,fromthestandpointofclassicaltheory,thatthePoyntingvector,whichtellsustheenergyflux,isindeedquadraticinthefieldstrength.Inspiteofthisevidentsupporttheidentificationisnotauniqueone,however;

itpaystoolittleattentiontothewayinwhichthelightisdetected.

Letussupposethatthelightintensityismeasuredbyusingaphotoncounteratthepositionofthescreen.Wethenaskhowwemaypredicttheresponseofthecounterasitisusedtoprobethepattern.Althoughtheuseofthewaveequationtofindthefieldamplitudedidnotintroduceanydistinctionsbetweentheclassicalandthequantumtheoreticalapproachestothediffractionproblem,theuseofaphotoncounterasadetectordoesintroduceadistinction.Thephotoncounterisanintrinsicallyquantummechanicalinstrument.Itsoutputisonlypredictableintermsofstatisticalaveragesevenwhenthestateofthefieldisspecifiedprecisely.Ifwearetopredictthisaverageresponsewemustberathermorespecificthanwehavethusfarbeenaboutthefieldwhichthecounterseesandwemusttreatthedetectionmechanisminafullyquantummechanicalway.Whatwefindwhenwedothesethingsisthatthecountermaybemoreaccuratelythoughtofasrespondingtoacomplexfieldφ+ratherthantherealfield.,andashavinganoutputproportional,nottoφ2,butto|φ+|2,（Thedistinctionisnotatrivialonephysically,sinceinamonochromaticfieldφ2oscillatesrapidlyinmagnitudewhile|φ+|2remainsconstant.）Oncethisanswerisknownitcanbeusedasacruderuleforbypassingtheexplicitdiscussionofthedetectionmechanisminapplicationstootherdetectionproblems.

Theuseofsuchrulesasameansofavoidingtheexplicituseofquantummechanicshasseveraltimesbeencalledthe“semi-classicalapproach”.Whileapproachesofthistypeclearlyneedaruleofsomesorttobridgethegapbetweentheirdescriptionsofthewaveandparticlebehaviorsofphotonstheymayremainperfectlycorrectapproachesinaquantummechanicalsenseaslongastherulehasbeenchosencorrectly.Thefactthatamistakenformofthisruleliasbeenusedrepeatedlyin“semi-classical”discussionsisagoodindicationthatthefullyquantummechanicaldiscussionisnotentirelybesidethepoint.

Oneofthepropertiesofthe“se