Title: Thick-medium model of transverse pattern formation in optically excited cold two-level atoms with a feedback mirror,
Abstract: We study a pattern forming instability in a laser driven optically thick
cloud of cold two-level atoms with a planar feedback mirror. A theoretical
model is developed, enabling a full analysis of transverse patterns in a medium
with saturable nonlinearity, taking into account diffraction within the medium,
and both the transmission and reflection gratings. Focus of the analysis is on
combined treatment of nonlinear propagation in a diffractively- and
optically-thick medium and the boundary condition given by feedback. We
demonstrate explicitly how diffraction within the medium breaks the degeneracy
of Talbot modes inherent in thin slice models. Existence of envelope curves
bounding all possible pattern formation thresholds is predicted. The importance
of envelope curves and their interaction with threshold curves is illustrated
by experimental observation of a sudden transition between length scales as
mirror displacement is varied.