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

$\displaystyle N_4 = \frac{W_p\tau_4}{1+W_p\tau_4}N_1$

(4)


From Eqn. (2), we get

$\displaystyle N_3 = \frac{\tau_3}{\tau_{4,3}}N_4$

(5)


Eqn. (3) gives,

$\displaystyle N_2$

$\displaystyle =$

$\displaystyle \frac{\tau_{2,1}}{\tau_{4,2}}N_4 + \frac{\tau_{2,1}}{\tau_{3,2}} N_3$

 

 

$\displaystyle =$

$\displaystyle \left( \frac{\tau_{2,1}}{\tau_{4,2}}\frac{\tau_{4,3}}{\tau_3} + \frac{\tau_{2,1}}{\tau_{3,2}}\right)N_3\equiv \beta N_3$

(6)

where

$\displaystyle \left( \frac{\tau_{2,1}}{\tau_{4,2}}\frac{\tau_{4,3}}{\tau_3} + \frac{\tau_{2,1}}{\tau_{3,2}}\right)$

(7)

1