Module 8 : Laser- II
Lecture   : Rate equations for Lasers
 

If $ W_p$is the pumping induced transition rate for $ g\rightarrow u$or $ u\rightarrow g$and $ \tau$is the natural lifetime of atoms in the upper level, the rate equation for the two levels may be written as follows :

$\displaystyle \frac{dN_u}{dt}=-\frac{dN_g}{dt} = W_p(N_g-N_u) - \frac{N_u}{\tau}$

where $ N_g+N_u = N=\ {\rm constant}$. In the steady state, the time derivatives vanish, and we have

$\displaystyle N_u = N\frac{W_p\tau}{1+2W_p\tau}$

In order that a population inversion may take place, we must have $ N_u> N/2$. However, one sees that as the intensity is increased the population in the upper level at best approaches this number as its maximum. Thus population inversion is not possible in a two level system.

   
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Three Level Laser:

For optical frequencies, population inversion cannot be achieved in a two level system. In 1956 Bloembergen proposed a mechanism in which atoms are pumped into an excited state $ u$by an external source of energy ( such as by an electric pulse or by optical illumination).
   
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