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


Define lineshape function $ g(\nu)$such that $ g(\nu)d\nu$gives the probability that a transition between two levels is an emission (or absorption) of photon whose frequency lies in the range $ \nu$and $ \nu+d\nu$. Normalization demands

$\displaystyle \int_0^\infty g(\nu) d\nu = 1$
 

If $ N$is the number of atoms in a given energy level, the spectral distribution of population in the level is given by $ N(\nu) = g(\nu)N$, i.e., $ N(\nu)d\nu$is the number of atoms in the levels within frequency range $ \nu$and $ \nu+d\nu$, so that

$\displaystyle \int_0^\infty N(\nu)d\nu = N\int_0^\infty g(\nu)d\nu = N$
 

Using the above, one can rewrite the equation defining Einstein's A - coefficient for spontaneous emission

$\displaystyle \frac{\partial N_2}{\partial t} = - AN_2$
as

$\displaystyle \frac{\partial N_2(\nu)}{\partial t} = - AN_2g(\nu)d\nu$
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