2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/84120We report the discovery of a "dark area theorem," a new quantum optical relation for propagation of unmatched pulses in thick three-level $Λ$-type media. We define dark area and derive the dark area theorem for a coherently prepared and inhomogeneously broadened lambda medium. We also obtain the first equation for the spatial evolution of the dark state amplitude prior to pulse-matching.8 pages, 4 figuresOpticstext