4 Level Laser System





Figure 3.




As seen in Figure 3 above, there is four energy levels, with energies E1, E2, E3, E4 with populations of N1, N2, N3, N4 respectively. There energies increase for each level so that E1 < E2 < E3 < E4.

In this system, optical pumping from the ground state (E1) into the pump band (E4) excites the atoms. From this level the atoms decay by a fast, radiationless transition into the level 3 (E3). The lifetime of the laser transition from E3 E2 is long compared to that of E4 E3, a population accumulates in this level 3 (lasing level). Here the atoms relax and start to create laser transitions through spontaneous and stimulated emissions into level 2 (E2). At this level, like level 4 has a fast decay into the ground state. Like before this quickly de-excited atom leads to a negligible population in E2. This is significant, as the highly populated E3 level will then form a population inversion with the E2 level. Specifically as long as the population of level3 N3 is greater then 0. Therefore optical amplification and laser operation can take place.

Since only a small number of atoms need to be excited in the upper lasing level E3 to form population inversion, it proves that a 4 level laser is much more efficient and practical then the 3 level laser.





  Rate Equations for 4 level laser System


dN4  = Wp(N1 N4) (γ43 + γ42 + γ41)N4


                                    = Wp(N1 N4) N4



         dN3 = γ43*N4  - (γ32 + γ31)N3 = N4 N3

          dt                                                 τ43    τ31

dN2  = γ42N4 + γ32N3 + γ21N2 = N4 + N3  N3

           dt                                                τ42    τ32   τ21

Pumping into level 3 is irrelevant due to weak absorption and narrow band.


        N3 = τ3 *N4


 N2 = τ21  + τ43τ21 *N3  = βN3

      τ32     τ42τ3

           β = N2 = τ21  + τ43 τ21  

                 N3      τ32          τ42τ3