清华激光原理

第7讲,四能级系统单模速率方程的建立多模速率方程的建立均匀加宽工作介质的增益系数从速率方程出发推导小信号增益系数表达式小信号增益曲线增益线宽均匀加宽工作介质的增益饱和大信号增益系数、强光作用下的弱光增益系数非均匀加宽工作介质增益系数,作业：4-7、4-13、4-20,laser,laser,Two,three,fourlevellasers,2,1,0,3,2,1,3,2,1,0,He+eHe*21S0，23S1He*+NeNe*+He+DE,100ns,10ns,与管壁碰撞,铒离子能级图,0.98nm,4.3Rateequationsexamples(three,fourlevelssystem)DifferentialequationsdescribingthedynamicsofpopulationandphotondensityofvariouslevelsPhysicalbasicforrateequations:Einsteinrelationship,Redruby,Er3+dopedfiber,He-Ne,Nd:YAG,1.Fourlevelssystem1)singlemodeoscillation(lthmode,n),没有包括A21引起的光子数？,(ignoreS30),（4.4.13）,RateequationsforpracticallaseraresetupaccordingtothevariousphysicalprocessesDifferentexpressionsofrateequationsforasamelaser,R1,R2isatomdensitypumpedpersecondintoE1andE2,respectively.t1,t2islifetimeatE1,E2,respectively;t21isspontaneousemission(荧光fluorescence）lifetimeforE2E1.,E2,E1,R2,R1,t2,t1,t21,Considerlossonly,Photonlifetime光子寿命,（2.1.14）,Lasertransition,E2,E1,R2,R1,t2,t1,t21,Pumptransitions,Lasertransition,2)RateequationsformultimodeoscillationSerialnumberofmodeFrequencyofmodePhotonnumberofserialmode,Method:对应每个模式分别建立一个速率方程,序数相应变化,SimplificationsLineshapefunctionrectangle(矩形)Sameloss,samelifetimeofphotonforeachmode,矩形面积原谱线面积,ReasonsofsimplificationDonotneedtoconsiderdifferencesofthemodesforstudyingquestionNeglectthedifferenceofdiffractionlossinthemodes,Accordingtotheabovesimplifiedmodel,multimoderateequationsforfourlevelssystemasfollowing,Ntotalphotondensityforallmodes,泵浦效率,Multimoderateequationsforfourlevelslasersystem,荧光量子效率,Pumpingefficiency:thefractionofthetotalpumppowerthatisusefulincreatingthepopulationinversion,Fluorescence(quantum)efficiencyfromE2E1,dependssolelyoncharacteristicsofmedium,itistheupperlimitforperformanceofanylaser.,RateequationsExpressionofgaincoefficient(effectingfactors)behaviorofgainsaturation(增益饱和)(forhomogeneousandinhomogeneousmedium)4.5Gaincoefficientinhomogeneousbroadeningmedium1、Smallsignalgaincoefficientforsteadystate(fourlevels）,I=Nhnv,dz=vdt,不计损耗,*1)GaincoefficientisproportionaltopopulationinversionDn(fourlevelssystemasexample),Gaincoefficient,Discussingkeyfactorsdependentongaincoefficient,*Reason:opticalintensityinmediumisverysmall,thechangeofDnintroducedbySTEcanbeneglectedinsmallsignalcase,Insmallsignalcase,Dn0alsoindependentonopticalintensity,dependentonpumpingrateW03Dn0,稳态,Smallsignal(unsaturated)gaincoefficientg0isdependentonDn0,independentonopticalintensity,review：如何理解小信号情况？,小信号,2)Gaincurve-g0varyingwithfrequency,Smallsignalgaincurvedependsonspectrumlineshape(小信号增益曲线的形状完全取决于谱线线型函数),Smallsignalgaincoefficient,=s21,STEcrosssectionatn0,增益线宽荧光线宽F（自发辐射线宽H）,3)g0(n0)isproportionaltol02,inverselyproportionaltospectralwidth,2、GainSaturation（增益饱和）大信号情况,UndertheactionofincidencelightwithIn1,atn1(consideringSTEprocess),1)Saturationofinversionpopulation,Whatisgainsaturation？GaincoefficientisdecreasedasSTEintensitybecomesstrong.Reasonofgainsaturation：Whentheintensityisstrongenough,稳态,=1/Is(n),saturationofinversionpopulation,Saturationintensityatn0,大信号情况,（4.5.7）,小信号情况,Populationn2isbarelyaffectedbySTE(即可忽略受激辐射的影响),Incidencelightatsamefrequencywithdifferentintensity,differenteffectonsaturationofDn,Incidentlightwithsameintensityatdifferentfrequency,differenteffectonsaturationofDn,(Stimulatingwave),Atcentralfrequencyn0,STEprobabilityisbiggest,saturationactionisstrongest.Thefrequencydepartfromn0,STEprobabilityisreduced,saturationactionbecomesweak.,2)Saturationgaincoefficientinhomogeneousmedium(均匀加宽介质的饱和（大信号）增益系数),Gaincoefficientofquasi-monochromaticlightatfrequencyn1,withtheintensityofIn1,Saturationgaincoefficient,(4.5.5),where,(4.5.12),Saturationgaincoefficientisdroppedtoonehalfofun-saturatedgainwhen,Gainandsaturationeffectisveryweak,(canbeneglected),ifthefrequencyisoutsidetherangeof,思考题：大信号增益曲线宽度与小信号增益曲线宽度是否相等？,讨论此命题的物理背景:激光器中某一模式频率首先起振,成为强光；别的模式刚起振(弱光),强光模式对刚起振的弱光模式的影响,3.在强光In1作用下的弱光n增益系数,频率为n1,光强为In1强光,同时有一频率为n的弱光入射求强光对弱光增益系数的影响，即弱光增益系数会如何变化？,定性分析,定量分析,强光作用下的反转粒子数,强光不仅使自身增益系数下降,而且使弱光增益系数也以同一比例下降,其结果是整个增益曲线下降（为什么？增益线宽是否改变）,复习：注意理解并区分强光增益及强光作用下弱光增益变化,强光作用下的弱光增益系数,弱光增益曲线,(4.5.16),（饱和增益）,4.6非均匀加宽工作介质的增益系数及增益饱和非均匀加宽小信号增益曲线为高斯线型,1、非均匀加宽大信号增益系数:思路：Dn按表观中心频率分类,这部分粒子发射中心频率为线宽为的均匀加宽谱线。这部分粒子对频率n1，光的增益贡献为dg按均匀加宽增益系数计算(4.5.12),表观中心频率小信号增益系数,大信号增益系数(4-5-12),(4-5-14),1,的粒子发射中心频率为n0,线宽为DnH的谱线,(4-6-1),(4-6-2),非均匀加宽介质大信号增益系数,大信号情况,增益饱和,大信号增益系数,非均匀加宽,均匀加宽,思考：此式物理意义，如何理解在非均匀加宽情况下，饱和效应的强弱与频率无关,入射时的大信号增益为小信号增益的,以中心频率处两种加宽机制的饱和效应相比，非均匀加宽的饱和效应弱些,非均匀加宽大信号情况，增益饱和效应强弱与频率无关,2、强光In1作用下,弱光n增益系数烧孔效应(HoleBurning),1,2,强光(n1,In1)入射,造成表观中心频率的粒子饱和-AA1,BB1,反转粒子数饱和,烧孔深度,烧孔宽度,烧孔面积,增益曲线烧孔效应,g0(n),g(n,In1),g,dn