Module 7 : Laser- I
Lecture   : Introduction - Basics of stimulated emission
  where $ g_1$and $ g_2$, respectively, are the multiplicities of the levels $ E_1$and $ E_2$.
2.3
Einstein Relations - A and B Coefficients:
 

The distribution of atoms in the two energy levels will change by absorption or emission of radiation. Einstein introduced three empirical coefficients to quantify the change of population of the two levels.

  • Absorption - If $ B_{12}$is the probability (per unit time) of absorption of radiation, the population of the upper level increases. The rate is clearly proportional to the population of atoms in the lower level and to the energy density $ u(\nu)$of radiation in the system. Thus the rate of increase of population of the excited state is given by
    $\displaystyle \frac{\partial N_2}{\partial t}= B_{12} u(\nu) N_1$
    where $ B_{12}$is a constant of proportionality with dimensions m$ ^3$/s $ ^2$-J.
  • Spontaneous Emission - The population of the upper level will decrease due to spontaneous transition to the lower level with emission of radiation. The rate of emission will depend on the population of the upper level. If $ A_{12}$is the probability that an atom in the excited state will spontaneously decay to the ground state,

                     $\displaystyle \frac{\partial N_2}{\partial t}= -A_{12} N_2$
The equation above has the solution

$\displaystyle N_2(t) = N_2(0)e^{-t/\tau}$
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