Module 7 : Laser- I
Lecture   : Line Broadening in Lasers
 

As the rate of spontaneous emission is much smaller than the rate of stimulated emission, we may neglect the former. Using Einstein's equation for the population of lower level, we have

$\displaystyle \frac{\partial N_1}{\partial t} = -B_{12}u(\nu)N_1+B_{21}u(\nu)N_2$

$\displaystyle =+B_{21}u(\nu)\left[N_2-\frac{g_2}{g_1}N_1\right]$

where $ \frac{B_{12}}{B_{21}}= \frac{g_2}{g_1}$

The number of atoms which interact with the laser signal at frequency $ \nu_s$is obtained by multiplying the above with the prob. function $ g(\nu_s,\nu_0)d\nu$. Thus

$\displaystyle \frac{\partial N_1}{\partial t}=+B_{21}u(\nu_s)\left[N_2-\frac{g_2}{g_1}N_1\right]g(\nu_s,\nu_0)d\nu\eqno(A)$

The equation may be rewritten using the following:

  1. Define the population densities of the two levels $ n_2=\frac{N_2}{V}$and $ n_1=\frac{N_1}{V}$.
  2. The rate of decrease of population of atoms in the lower level is also equal to the rate at which incident photons
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