Population inversion field, to use quantum coherence effects to reduce the likelihood of an excited-state to ground-state transition. This technique, known as lasing without inversion, allows optical amplification to take place without producing a population inversion between the two states. Stimulated emission was first observed in the microwave region of the electromagnetic spectrum, giving rise to the acronym MASER for Microwave Amplification by Stimulated Emission of Radiation. In the microwave region, the Boltzmann distribution of molecules among energy states is such that, at room temperature all states are populated almost equally. To create a population inversion under these conditions, it is necessary
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