Population Inversion

Population inversion is a state of a system, for example a laser gain medium, where a higher-lying energy level is more strongly populated than a lower-lying level. This cannot occur under conditions of thermal equilibrium, where the level populations are described by a Boltzmann distribution. However, a population inversion is often easily achieved by optical pumping at a suitable optical wavelength.

Formally, population inversion is sometimes described as a state with a negative temperature. This is because a Boltzmann distribution would lead to such a situation for negative temperatures. Note that the concept of a temperature fundamentally applies to thermal equilibrium states, while population inversion is a non-equilibrium state.

In the simplest case, a laser transition involves only two (nondegenerate) energy levels of the active atoms or ions of the gain medium: an upper and a lower laser level. The transition cross-sections for absorption and for stimulated emission are then necessarily the same (for any given wavelength). The net gain on the laser transition can be calculated as the gain resulting from the upper-state population (enabling stimulated emission) minus the absorption caused by the lower-state population. A positive net gain (i.e., more gain than absorption) can occur only when the population in the upper laser level is higher than that of the lower level (i.e. more laser-active atoms or ions are in the higher level). In other words, positive laser gain is possible only when achieving a population inversion.

In most solid-state lasers, however, the concept of population inversion is not directly applicable because the upper and lower energy levels actually consist of large numbers of slightly different energy levels. Typical models involve upper level and lower level manifolds, each consisting of different Stark levels, which can in addition be subject to inhomogeneous broadening. Within each level manifold, thermal equilibrium is reached within picoseconds due to the strong coupling via phonons. It is then convenient to use effective transition cross-sections, which take into account the thermal population distribution within the manifolds and are in general different for absorption and stimulated emission. This shows that population inversion in the sense of > 50% inversion is not required for obtaining optical amplification: for long wavelengths, where the emission is typically much stronger than the absorption, gain is achieved even for fairly low excitation levels.

The latter phenomenon should not be confused with lasing without inversion, where laser amplification is achieved in a simple atomic system by means of quantum coherence.