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1、习题1(a)Consideranopticalgainmediumconsistingofidealisedatoms,withtwonon-broadenedenergylevels1and2,havingpopulationsN1andN2anddegeneraciesg1andg2respectively.i.Writedowntherateofchangeofthephotondensity,resultingfromabsorption,spontaneousemissionandstimulatedemission.ii
2、.Whycanweneglectthespontaneousemissioninthederivationofthegaincoefficientinalaser?iii.GivenEinstein'srelations(g1B12=g2B21andA21/B21=8phn3/c3),findthechangeinintensityoftheradiationfieldwithdistanceofpropagationthroughthegainmedium,andhencefindanexpressionforthegaincoe
3、fficient.(b)Illustratewiththeaidofanenergy-leveldiagramtheoperatingprincipleofa4-levellaser.Whataretheadvantagescomparedtoa2-levellaser?Writedownapproximateconditionspertaininginanideal4-levellaser.(c)Whatisthepopulationofthelowerlasinglevelinanideal4-levellaser?Derive
4、anexpressionforthesaturationintensity.Solution:(a)Theenergyoflevel1isE1,theenergyoflevel2isE2,andthephotonenergyishn=E1-E2.Theradiationenergydensityisr(n)andA21,B12andB21aretheusualEinsteincoefficients(or,constantsofproportionalitydefinedbytherateequations).(i)Forinduc
5、edabsorption,thetransitionratefromlevel1to2isW12andisgivenby.Forspontaneousemission,thetransitionratefromlevel2to1isWspandisgivenby.Forstimulatedemission,thetransitionratefromlevel2to1isW21andisgivenby.Thephotondensityfisthenumberofphotonsperunitvolume,wherethephotonsa
6、recreated/destroyedbytheaboveprocesses.Hence.(i)Inalaseroscillator,thephotondensityisdominatedbystimulatedemissionofphotonsintoafew(orasingle)cavitymode(s).Spontaneousemissionisisotropic,andonlyasmallfractionofemittedphotonscoupleintocavitymodes.Thereforespontaneousemi
7、ssionisnegligibleintherateequations.(However,itisanessentialprocessininitiatingthelaseroscillation…)(ii)First,realizethatyouarebeingaskedtofinddI/dz,whereIistheradiationintensityandzisthedistanceofpropagationinthematerial(giveninthequestion).Second,recallthatthelightin
8、tensity(whichdependsonthelightfrequencyinthegeneralcase)isrelatedtotheenergydensitybyI(n)=c·r(n).[Usetheunitstohelpyo
