CWlaserbehaviorPPT課件

1、ReviewReviewProperties of LaserInteraction between Material and Radiation Blackbody radiation(2.2)Spontaneous and stimulated emission, absorbtion(1.1)(Einstein Coefficients)The laser idea(1.2-1.3)Lineshape function, Natural Broadening, collision broadening, Doppler broadening)第1頁/共14頁ReviewReviewRay

2、 and wave propagation through optical media(chapet4)ABCD martix(4.2)Fabry-perot interferometer(Longitudinal modes )Gaussian BeamsPassive optical resonators(5.1-5.5)Typical resonator Stability conditionsStable resonators (eigenmodes and eigenvalus)第2頁/共14頁Continuous Wave Laser Behavior第3頁/共14頁Introdu

3、ctionWhat we concern:- Behavior of continuous wave laser-Rate equation approximation( on the basis of a simple notion that there should be a balance between the total number of atoms undergoing a transition and the total number of photons being created or annihilated.)第4頁/共14頁7.2 Rate EquationsFour-

4、level laser Ionic crystal lasers( with the exception of ruby laser)Gas lasers, such as CO2 , Ar+, He-Ne, Cu vapor, etc.Quasi-three-level laser( the lower level laser level is a sublevel of the ground state)Many rare-earth ions in various crystal or glass hosts, such as Yb, Er and Yb:Er, Ho etc. for

5、its shortest wavelength transition.第5頁/共14頁典型激光器速率方程典型激光器速率方程表征激光器腔內(nèi)光子數(shù)和工作物質(zhì)各有關(guān)能級上的原子數(shù)隨時間變化的微分方程組，稱為激光器速率方程組(rate equations)。歸納共性，針對一些簡化的、具有代表性的模型列出速率方程組，所謂的三能級和四能級系統(tǒng)。激光速率方程理論的出發(fā)點是原子的自發(fā)輻射、受激輻射和受激吸收幾率的基本關(guān)系式。第6頁/共14頁愛因斯坦得到的光和物質(zhì)相互作用的關(guān)系式22122212212111211212321121212321()(),(),8,spstabndNA NdtdNW N WBdtd

6、NW N WBdtAhB gB gBc 第7頁/共14頁7.2.1Four-Level LaserWe assume that there is only one pump level or band (band 3) and relaxation from the pump band to the upper laser level 2 as well as relaxation from the lower laser level 1 to the ground level proceeds very rapidly.We consider the case of space-indepe

7、ndent rate equations. (oscillating on only one cavity mode and pumping and mode energy densities are uniform within the laser material.013 NN2, N21, N1pumplaserFast decay3, N3Fast decay0, Ng第8頁/共14頁7.2.1Four-Level Laser222()pdNNRB Ndt013 NN2acdV B NdtRp: pumping rateB: stimulated emission coefficien

8、t per photon per mode: total number of photons oscillating only on one cavity mode:the life time of the upper-laser levelVa: mode volume within the active mediumc:the photon lifetime,accounts for the removal of photons due to cavity loss2, N21, N1pumplaserFast decay3, N3Fast decay0, Ng第9頁/共14頁7.2.1F

9、our-Level LaserOnly concern TEM00 mode420lwVamedium active theoflength : lsizespot central :0w某一模式的模體積描述該模式在腔內(nèi)所擴展的空間范圍模體積大，對該模式的振蕩有貢獻的激發(fā)態(tài)粒子數(shù)就多，也就可能獲得大的輸出功率。第10頁/共14頁7.2.1Four level laserTwo observations: (1) Level 3 can be considered empty if its decay rate is much faster than the pump rate33pgNRN32

10、NN(2) The term accounting for spontaneous emission has been neglectedWhen spontaneous emission is taken into account, 2aV B N2221aaaV B NV BNV BNFor simplicity, the extra photon will not be introduced 第11頁/共14頁7.2.1 Four level laserIntensity of one wave:2dIN Idzsection crossn transitio:A resonator o

11、f length L in which an active medium of length l and the refractive index n is inserted.Round-trip intensity change:21221222111exp 21 1(1) (1)iiiITTTNNlIwhereTaL Transmission losses (logarithmic transmission losses per pass):111lnT221lnT1mirror ofsmission power tran :1T2mirror ofsmission power tran :2T122i第12頁/共14頁7.2.1 Four level laserAssume: 21N l22IN lI 2,(1) (the optical length of the resonator)eeLtLLnlc 2eedIlccNIdtLL V=()eaaeL