Light scattering from three-level systems: The T matrix of a point dipole with gain

In the description of the interaction of atomic ensembles with light, the atoms are often treated in the electric dipole approximation, and are therefore effectively considered to be point dipoles. The advantages of the point-dipole formalism are twofold. First, the d-function potential associated with point scatterers allows for significant mathematical simplifications compared to finite-size scatterers f1g. Second, the point-scatterer formalism allows for a transparent description of many multiple-scattering phenomena, mimicking most of the associated relevant physics f2g. The light scattering properties of point dipoles can be expressed by means of their T matrix T J which is related to the dynamic polarizability aJ by