Module 7 : Laser- I
Lecture   : Introduction - Basics of stimulated emission
 

where $ \tau = 1/A_{12}$gives the average $ {\it life time}$of an atom in the excited level before the atom returns to the ground state. Thus the spontaneous emission depends on the lefetime of the atom in the excited state. The process is statistical and the emitted quanta bear no phase relationship with one another, i.e. the emission is incoherent .

  • Stimulated Emission - Stimulated or induced emission depends on the number of atoms in the excited level as well as on the energy density of the incident radiation. If $ B_{21}$be the transition be the transition probability per unit time per unit energy density of radiation, the rate of decrease of the population of the excited state is $ B_{21}u(\nu)N_2$.

The rate equation for the population of the upper level is

$\displaystyle \frac{dN_2}{dt} = B_{12}u(\nu)N_1 - [A_{21}+B_{21}u(\nu)]N_2$

Since $ N_1+N_2 =$constant,

$\displaystyle \frac{\partial N_2}{\partial t}= - \frac{\partial N_1}{\partial t}$
  The emitted quanta under stimulated emission are coherent with the impressed field. The spontaneous emission, being incoherent, is a source of noise in lasers. When equilibrium is reached, the population of the levels remains constant, so that $ dN_2/dt=0$and the rate of emission equals rate of absorption, so that
$\displaystyle B_{12}u(\nu)N_1 = [A_{21}+B_{21}u(\nu)]N_2$
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