Lasing in a random amplifying medium: Spatiotemporal characteristics and nonadiabatic atomic dynamics

We study the dynamics of lasing from photonic paints excited by short, localized, optical pulses, using a time-dependent diffusion model for light propagating in the medium containing active atoms. The full time-dependent, nonadiabatic nonlinear response of the atomic system to the local optical field intensity is described using the Einstein rate equations for absorption and emission of light. Solving the time-dependent diffusion equation for the light intensity in the medium with nonlinear gain and loss, we derive detailed information on the spectral, spatial, and temporal properties of the emitted laser light. Our model recaptures the effects of scatterers to narrow the emission spectral linewidth and to narrow the emitted pulse duration, at a specific threshold pump intensity. Our model also describes how this threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results.