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

Using the Boltzmann facor $ N_2/N_1 = (g_2/g_1) \exp(-h\nu/kT)$, and simplifying, we get

$\displaystyle u(\nu) = \frac{A_{21}\frac{g_2}{g_1}}{B_{12}e^{h\nu/kT}-B_{21}\fr... ...1}} = \frac{A_{21}/B_{21}}{\frac{g_1}{g_2}e^{h\nu/kT}\frac{B_{12}}{B_{21}}-1} $

If we regard the matter to be a blackbody and compare the above expression for the energy density with the corresponding energy density expression derived for the blackbody radiation, viz.,

$\displaystyle u(\nu) = \frac{8\pi h\nu^3}{c^3}\frac{1}{e^{h\nu/kT}-1}$

we get

$\displaystyle \frac{A_{21}}{B_{21}} = \frac{8\pi h\nu^3}{c^3}$

and

                                                                                          $\displaystyle \frac{B_{21}}{B_{12}}= \frac{g_1}{g_2}$
The last equation shows that n the absence of degeneracy, the probability of stimulated emission is equal to that of absorption. In view of this we replace the two coefficients by a single coefficient $ B$and term them as $ B$- coefficient. The spontaneous emission coefficient will be called the $ A$- coefficient.

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