Population inversion atoms in the ground and excited states are equal, the rate of stimulated emission is equal to the rate of absorption for a given radiation density. The critical detail of stimulated emission is that the induced photon has the same frequency and phase as the incident photon. In other words, the two photons are coherent. It is this property that allows optical amplification, and the production of a laser system. During the operation of a laser, all three light-matter interactions described above are taking place. Initially, atoms are energized from the ground state to the excited state by a process
Stimulated emission difference in energies between the two states as a photon. The photon will have frequency "ν" and energy "hν", given by: where "h" is Planck's constant. Alternatively, if the excited-state atom is perturbed by an electric field of frequency "ν", it may emit an additional photon of the same frequency and in phase, thus augmenting the external field, leaving the atom in the lower energy state. This process is known as stimulated emission. 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