in energies between the two states as a photon. The photon will have frequency ν0 and energy hν0, given by: where h is Planck's constant. Alternatively, if the excited-state atom is perturbed by an electric field of frequency ν0, 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 N2, the rate at which stimulated emission occurs is given by where the proportionality constant B21 is known as the Einstein B coefficient for that particular transition, and ρ(ν) is the radiation density of the incident field at frequency ν. The rate of emission is thus proportional to the number of atoms in the excited state N2, and to the density of incident photons. At the same time, there will be a process of atomic absorption which removes energy from the field while raising electrons from the lower state to the upper state. Its rate is given by an essentially identical equation, The rate of absorption is thus proportional to the number of atoms in the lower state, N1. Einstein showed that the coefficient for this transition must be identical to that for stimulated emission: Thus absorption and stimulated emission are reverse processes proceeding at somewhat different rates. Another way of viewing this is to look at the net stimulated emission or absorption viewing it as a single process. The net rate of transitions from E2 to E1 due to this combined process can be found by adding their respective rates, given above: Thus a net power is released into the electric field equal to the photon energy hν times this net transition rate. In order for this to be a positive number, indicating net stimulated emission, there must be more atoms in the excited state than in the lower level: . Otherwise there is net absorption and the power of the wave is reduced during passage through the medium. The special condition is known as a population inversion, a rather unusual condition that must be effected in the gain medium of a laser. The notable characteristic of stimulated emission compared to everyday light sources (which depend on spontaneous emission) is that the emitted photons have the same frequency, phase,