Population inversion _versus pumping in an \"upper-level\" three-level laser sys- tem. It is possible (though not likely in practice) to have a three-level laser system which is pumped on the 1 + 3 transition and in which cw laser action takes place on the 3 : 2 rather then the 2 r 1 transition (no such real system is known). Suppose that level 3 in such a system is longlived with lifetime T3; level 2 has a short relaxation time to the ground state; and the system is pumped with transition probability WP on the l -+ 3 transition. Carry through the rateequation analysis (in the optical approximation) necessary to nd the pepulation inversion on the 3 - 2 transition as a function of pumping power WP. Compare the N versus WP curve for this system to to those for the four-level and three-level models shown in Figure 6.4. Four-level Three-level system system Laser threshold inversion FIGURE 6.4 AN Inverted population 0 Laser population inversion 2 versus normalized pumping Normalized pump rate, WIT rate for idealized four-level and three-level laser systems. -N