Stimulated emission can be modelled mathematically by considering an atom which may be in two electronic energy states, the ground state (1) and the excited state (2), with energies E1 and E2 respectively.
If the atom is in the excited state, it may decay into the ground state by the process of spontaneous emission, releasing the difference in energies between the two states as a photon. The photon will have frequency ν and energy hν, given by:
Alternatively, if the excited-state atom is perturbed by the electric field of a photon with frequency ν, it may release a second photon of the same frequency, in phase with the first photon. The atom will again decay into the ground state. This process is known as stimulated emission.
An energy level diagram illustrating the process is shown below:
In a group of such atoms, if the number of atoms in the excited state is given by N, the rate at which stimulated emission occurs is given by:
The critical detail of stimulated emission is that the emitted photon is identical to the stimulating photon in that it has the same frequency, phase and polarisation (thus the two photons are totally coherent). It is this property that allows optical amplification to take place.