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

The ratio of spontaneous emission probability to the stimulated emission probability is

$\displaystyle \frac{A}{Bu(\nu)}= e^{h\nu/kT}-1$

so that for low temperatures, when $ h\nu/kT \gg 1$, spontaneous emission is much more probable than induced emission and the latter may be neglected. For high enough temperatures, stimulated emission probability can be significant though for optical frequencies, this requires very high temperature. For microwave frequencies the stimulated emission processes may be significant even at room temperatures.

  Exercise :
  Find the ratio of the probability of spontaneous emission to stimulated emission at 300 K for (a) microwave photons ( $ \nu = 10^{13}$Hz.) and (b) optical photons ( $ \nu = 10^{15}$Hz).(Ans. (a) $ 0.17$(b) $ \sim 10^{7}$.)
   
2.4 Population Inversion :
 
We have seen that when atoms are in equilibrium with the surrounding, the population of atoms in the ground state is more than that in any of the excited states. Population of excited states can be increased by absorption of radiation. However, the life time in the excited states being typically of the order of $ 10^{-8}$seconds, atoms which make transitions to the excited states fall back to the ground state soon thereafter. This is also indicated by the ratios of the Einstein coefficients. It is, therefore, not possible to keep the population in the excited states higher than that in the ground state.
The basic principle involved in the operation of laser is population inversion , a situation in which the population of the excited state is kept higher than that of the ground state.
  When $ N_u<N_l$, i.e., the population in the upper level is less than that in the lower level, the number of transitions from the lower to the upper level with absorption of radiation is more than that with emission and hence the radiation is attenuated. If, on the other hand, $ N_u>N_l$, emissions are more than absorption and the radiation is amplified as it passes through the material.
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