Spectral-spatial diffusion in inhomogeneously broadened systems

Most phonon-assisted spectral transfer rates across an inhomogeneously broadened line are proportional to the inverse square of the energy change. The time-dependent optical emission profile is calculated exactly for a rectangular line shape for these processes. Numerical solutions are required for other line shapes (e.g., a Gaussian as found in ruby). They are exhibited as a function of time for a variety of initial excitation energies at different positions across the optical line.