Maximum achievable population inversion in finite volumes

A calculation is made of the steady-state population inversion distribution in homogeneously pumped active media of spherical or cylindrical form. It is assumed that reflections from the boundaries of the active medium have been completely eliminated and it is shown that the inversion decrease, caused by the amplification of spontaneously emitted radiation, is mainly a function of the overall volume of the active medium. For active media of equal volume, the stored inversion is minimal for a sphere.