Module 8 : Laser- II
Lecture   : Rate equations for Lasers
2.9.1 Rate Equations for a Three Level System :
 

In a three level system, the laser transition is from the metastable state $ m$to the ground state $ g$. In the following analysis, we will ignore the effects of degeneracy.

As in the case of two level system, we denote by $ W_p$, the transition rate induced by pumping from the ground state ( $ g$) to the top level $ m$or vice versa. $ W_p$is clearly proportional to the pumping rate. As the metastable state is long lived, we assume that $ \tau_{u,m}$is much smaller than either $ \tau_{u,g}$or $ \tau_{m,g}$, where $ \tau_{i,j}$denotes the lifetime of transition $ i\rightarrow j$. As a result, the population of the upper level is nearly zero, and correspondingly,

$\displaystyle N = N_u+N_m+N_g\simeq N_m+N_g$
  \includegraphics{laser7e.eps}
 

The rate equation for the level $ u$may be written as

$\displaystyle \frac{dN_u}{dt} = W_p(N_g-N_u)-\frac{N_u}{\tau_{u,m}}$
1