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 an atomic or molecular resonance, the spectral line shape function is described as a Lorentzian distribution where formula_12 is the full width at half maximum or FWHM bandwidth. The peak value of the Lorentzian line shape occurs at the line center, formula_13. A line shape function can be normalized so that its value at formula_9 is unity; in the case of a Lorentzian we obtain Thus stimulated emission at frequencies away from formula_9 is reduced by this factor. In practice there may also be broadening of the line shape due to inhomogeneous broadening, most notably due to the Doppler effect