# Population Inversion

**Population Inversion:**** **It is well-known that the process of spontaneous emission is independent of external radiations. Einstein proved theoretically that transition probability of absorption is equal to transition probability of induced emission between same two levels. If the number of atoms N_{1} in lower state (energy E_{1)} is more than the number of atoms N_{2} in the upper state (energy E_{2}) then in the presence of external radiations of frequency (E_{2} – E_{1})/h, the absorption dominates over emission. On the other hand, if N_{1} is less than N_{2} then the emission dominates. In general at room temperature N_{1} is greater than N_{2}, so the absorption is more than emission. In some materials if the life time of any upper state (level) is of the order of 10–3 sec, called metastable state, then it is possible to have that material with N_{2} > N_{1}. If this happens, then the population inversion takes place in the medium. These materials are called active materials and they can be used for lasing transition. Thus for laser action population inversion is necessary. Population of a particular energy level of atoms is given by Maxwell-Boltzmann distribution function as

where N is the number of atoms in the state whose energy is E, T is the temperature of the material and k is the Boltzmann constant. Using this relation we get

Since E_{2} > E_{1}, therefore N_{2} < N_{1} under normal conditions. As mentioned above for laser action N_{2} should be more than N_{1}.

The process by which atoms are raised from lower level to upper level is called the pumping. Following are the commonly used methods of laser pumping:

(a) Optical pumping

(b) Electrical pumping

(c) Chemical pumping.

(a) Optical Pumping: In this process the population inversion is achieved by using strong sourcen of light such as gaseous discharge, flash lamp or arc lamp. This process keeps more atoms in the upper excited (metastable) state. This process is suited to solid state (e.g. Ruby) and liquid (e.g., dye) lasers.

(b) Electrical Pumping: In this process the population inversion is achieved by using an intense electrical discharge in the medium which is in the gaseous form. This process is suited to gas lasers and semiconductors. The discharge converts the gas into plasma and the population of the upper level also

increases.

(c) Chemical Pumping: In this process the population inversion is achieved by using suitable chemical reaction in the absence of any other source of energy. For example, in the reaction A B → AB*, AB* is the excited vibrational state of AB molecule.