Answer to Question #92957 in Optics for ROHIT SHARMA

Question

An atomic system, consisting of two energy levels with population of higher energy
level less than that of the lower level, is in thermal equilibrium. Show that the
absorption of radiation dominates stimulated emission if radiation of appropriate
frequency is introduced into the system. Comment on the consequences of this fact
for laser action.

Answer 1

There are three processes through which light can mediate transitions between atomic energy levels.

1)   spontaneous emission;

2)   absorption;

3)   stimulated emission.

In the first case, an atom in the upper state spontaneously decays to the lower state, while simultaneously emitting a photon with energy. In the second case, an atom in the lower state is excited to the upper state by the absorption of a photon. In the third case, an incident photon with energy hω21 stimulates an atom in the upper state todecay to the lower state by the emission of a second photon of energy.

Stimulated emission depends on the number of atoms in the excited level as well as on the energy density of the incident radiation. The higher energy state N₂ has a greater population than the lower energy state N₁: N2> N1. In this way, the emission process dominates.

Accordingly, we can write:

$\frac{N_2}{N_1}> 1$

In this sense, a population inversion is required for laser operation.

The stimulated photon is emitted in the same “radiation mode” as the incident photon, and hence has the exact same frequency, direction, phase,and polarisation of the incident photon.