Random polarization dynamics in a resonant optical medium

Random optical-pulse polarization switching along an active optical medium in the $\mathrm{\Lambda }$-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte-Carlo numerical simulations.