Stimulated emission 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: formula_6. Otherwise there is net absorption and the power of the wave is reduced during passage through the medium. The special condition formula_7 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
Stimulated emission frequency, phase, polarization, and direction of propagation as the incident photons. The photons involved are thus mutually coherent. When a population inversion (formula_6) is present, therefore, optical amplification of incident radiation will take place. Although energy generated by stimulated emission is always at the exact frequency of the field which has stimulated it, the above rate equation refers only to excitation at the particular optical frequency formula_9 corresponding to the energy of the transition. At frequencies offset from formula_9 the strength of stimulated (or spontaneous) emission will be decreased according to the so-called line shape. Considering only homogeneous broadening affecting