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

If $ \beta <1$, there will be more population in the upper laser level than in the lower one, leading to a population inversion. Using the above, and after straight forward simplification, we get

$\displaystyle N = \frac{1+2W_p\tau_4 + (1+\beta)W_p\frac{\tau_4\tau_3}{\tau_{4,3}}} {1+W_p\tau_4}N_1$

and the population difference $ N_3-N_2 = \Delta N$given by

$\displaystyle \Delta N = (1-\beta)\frac{\tau_3}{\tau_{4,3}}\frac{W_p\tau_4}{1+W_p\tau_4} N_1$

Combining the above two equations

$\displaystyle \boxed{\frac{\Delta N}{N} = \frac{(1-\beta)W_p\frac{\tau_3\tau_4}... ...+\beta)+ 2\frac{\tau_{4,3}}{\tau_3}\right]W_p\frac{\tau_4\tau_3} {\tau_{4,3}}}}$

Let us define Quantum Efficiency $ \eta$as the fraction of atoms excited from the ground state (1) which ultimately results in stimulated emission. $ \eta$is thus a product of the fraction which arrives at the upper laser level (3) and the fraction of atoms in the upper laser level which make radiative transition to the lower laser level (2).

1