laser3-研深深圳大学高等激光物理学期末复习课(精)

1、Unit 3Amplification of Light Optical gain Population inversion Iwo-level system Three-level system Four-level system.An n2 nAOptical gainG(v)dNA/ =- /?= WdtA/ = (ji2B2Xp(v) - nxBnp(yy) A v AzB1 =B2A21_g兀屁A/ = B2Xp(y)hvn2-q)Az=恥心TLA/9(v) =01=)gQQGg 空字IZ)dzG(v) =A/(C)/(z) AzG=4l b2i(Wo)h v6|(人勺)=2 胡3)

2、c62，%) =告 yge)1巾(5)=77玮如Optical gainG(v)The difference in populationso(v): gain cross-section Parameters: related to the atomic transitions. describes the strength of the transition for the givenatom (molecule, etc)Area dimensions.Population inversionI(z) = I(0)exp(Gz)H V叫the medium absorbsn2= n, op

3、tical transparencythe medium is neither absorbing nor amplifying.It is perfectly transparent. n2 n, the medium amplifies.Population inversion is a necessary condition for light amplification (orlaser action) to occur. #An= n2nxTwo-level systemAssuming only two energy7levels5E2andBy optical pumping m

4、eansThe population of the levels cannot be inverted Tlie reason is stimulated emission and absorption willalways balance each other.At best, equal populations of atoms in Ej and E2#hhv (laihal ifMe)Three-level systemthe parameters are right and pump is hard enough bycontinuous pumping.the population

5、 inversion can be achieved between levels 2and 1.In an efficient laser medium, the lifetime of state 2 islong Level 2 to be显slow state-Level 3 with long lifetimes metastable states #Two-level system -sixjlt-livcd lcc；tjjdecay)-jz long hved (meiaitabk) le. elbi gw)tii(山w)EiF grtMUid stateThree-level

6、systemPopulation inversion.Conditions1. the spontaneous lifetime ofE2(t2i) be large relative to the other lifetimes.E2is a metastable state2. Tlie decay from level 3 to level 2 should be highlyprobable,t32is short relative to t3PThe first laser built by Maimaii was a 3 level system,t21103s ; t321012

7、s.The first laser一die ruby laser#JThree-level systemthe rate equations(mpd decoyE：-.-Jcup-hved (mefastable) leveltn (slow)E.wew2i=B21g(v)p=B21g(v)hvNW12=B12g(v)p=B12g(v)hv N1警=心仏_AZ% dtrRln:单位体积工作物质内的总粒子数The problem with three-level systemsThe lower state of the lasing transition is the ground state

8、.The ground state is always very heavily populated (it is the lowestpossible state)It takes a lot of energy to invert the population of other states relative tothe ground state.Three-level systems are inefficient.Four-level system is an efficient laser medium. #the rate equations= nW3-n3(S32A3l)Inve

9、rted population：AH=nL LSidt1 )21 (匕卜。-斤2 ( A? + 52| ) +比3$32dtHj+H2+H3= nnl)a2i(v,v0)vNlTRIFour-level system In a four-level system, the final state of the lasingtransition is an excited state, not the ground state asshown in the diagram below:-E3t32 (rapid decay)w- Ej (E metasrable )十 Ei (Final sta

10、te of awphtier)tio (rapid decay)-& (ground stare)Four-level systemiii an efficient laser medium,the lifetime of state 2 is longthe population of this state can grow and an inversion canbe created.t10and t32are much shorter than t21.E g Nd:YAG laser four-level systemt3210_7s, t1010_8s and t2110_3s.Four-level devices are more efficient than three-levelMost practical laser four-level system. #Four-level systemUnit 3Amplification of LightLearning outcomes: derive an expression for the gain coefficient using therat