光電子學(xué)-第七講-黑體輻射及其他

SummaryBlackbodyradiationEinsteinCoefficientsHomogeneousBroadening:LimitedlifetimeintheupperlevelLorentzianlineshapeIndistinguishableinteractiontoatomsLinewidthusuallyinMHzrangeInhomogeneousBroadening:DopplerbroadeningGaussianlineshapeDistinguishableinteractiontoatomsLinewidthusuallyinGHzrangePopulationInversion§4.5GainSaturationinHomogeneousLaserMediaInpractice,thepopulationinversioniscausedbya“Pumping”process,suchaselectriccurrentininjectionlasers,flashlamplightinpulsedrubylasers,ortheenergeticelectronsinplasma-dischargegaslasers…GainConstantNow,wearegoingtoderivegainconstantinpresenceofanopticalfield210UpperlevelLowerlevelGroundlevelR1R21/t201/t11/tspWi(n)R1,R2:Pumpratet20:nonradiativerelaxationt2,t1:lifetimeWi(n):inducedemissionrate§4.5GainSaturationinHomogeneousLaserMediaI.RateEquationsAtsteadystate:Iftheopticalfieldisabsent,i.e.:§4.5GainSaturationinHomogeneousLaserMediaInanefficientlasersystem:andSaturationintensity:Gainconstant:Smallsignalgainconstant:II.PopulationInversionSaturation§4.5GainSaturationinHomogeneousLaserMedia:Populationinversionhasnorelationwithintensity10.50:Atsaturationintensitypoint,inducedradiationrateiscomparablewithotherrelaxationprocesses,andcausestheinversiontodroptoonehalfofitsnonsaturatedvalue.§4.5GainSaturationinHomogeneousLaserMediaandandThatis,themoreclosertoresonant,thesmallerthesaturationintensityWhileatthesameincidentintensity,thesmallersaturationintensitymeansthepopulationinversiondropsmore,thesaturationismoreserious.Sowhenincidentlaserfrequencyisclosetotheresonant,thesaturationeffectgetsstronger;whilelaserfrequencyisfarawayfromtheresonant,thesaturationeffectgetsweaker.§4.5GainSaturationinHomogeneousLaserMediaLorentzianlineshapepopulationinversionOnlyinthisregion,saturationeffectisobviousnn0DNIII.GainSaturation§4.5GainSaturationinHomogeneousLaserMediaSmallsignalgainconstant:GainconstantinLorentzianlineshapehomogeneouslasermediaGainconstantuniformlydropsinhomogeneousbroadeningcase§4.5GainSaturationinHomogeneousLaserMediaNowweconsiderahigherintensitylightwithfrequencyn1,howdoesanotherweakerlightwithfrequencyn2gainconstantchange?Thehigherintensitylightnotonlychangesitselfgainconstant,butalsochangesotherfrequencyweakerlightgainconstantinsamedegree.nn0gn1§4.6GainSaturationinInhomogeneousLaserMediaAssumetheinhomogeneousmediumismadeofclassesofatomseachdesignatedbyacontinuousvariablex.Moreover,defineafunctionf(x)sothataprioriprobabilitythatanatomhasitsparameterbetweenxandx+dxisp(x)dx,andsatisfy:Theatomswithinagivenclassxaresuchconsideredashomogeneouslybroadening,havingalineshapefunctionthatisnormalizedas:So,§4.6GainSaturationinInhomogeneousLaserMediaI.RateEquationsSteadystatesolution:§4.6GainSaturationinInhomogeneousLaserMediaSummingoveralltheclasses:Totalpoweremittedbyinducedtransitionsperunitvolumebyatomsinclassx:OrII.GainConstant§4.6GainSaturationinInhomogeneousLaserMediaSmallsignalgainconstant:IntheabsenceofsaturationthegainconstantofahomogenousandaninhomogeneousatomicsystemareidenticalOthercases:Ineachclass,alltheatomsareidenticalandarehomogeneousbroadeningSubstituteaboveequationtothegainexpressionforinhomogeneousmedia§4.6GainSaturationinInhomogeneousLaserMediaIntheextremeinhomogeneouscase,thewidthofp(n)ismuchlargerthanthatofgx

(n).Gainconstantininhomogeneouslasermedia§4.6GainSaturationinInhomogeneousLaserMediaIII.GainSaturationSmallsignalgainconstant:IftheinhomogeneousbroadeningisDopplerBroadening,thenGainconstantinaDopplerbroadeninglasermediaSaturationintensity§4.6GainSaturationinInhomogeneousLaserMediaIV.SpectralHoleBurningEffect對于非均勻加寬，表現(xiàn)中心頻率為n的粒子發(fā)射一條中心頻率為v，線寬為Dv的均勻加寬譜線。因而這部分粒子的飽和行為可以用均勻加寬情況下的增益飽和來描述。WhenandWhensaturationeffectgetsweaker,Whenandsaturationeffectcanbeignored,§4.6GainSa