  The optomechanical coupling and transverse stability of a co-propagating
monochromatic electromagnetic wave and mono-energetic beam of two-level atoms
is investigated in the collisionless regime. The coupled dynamics are studied
through a Landau stability analysis of the coupled gas- kinetic and paraxial
wave equations, including the effect of the electronic nonlinearity. The
resulting dispersion relation captures the interaction of kinetic and
saturation effects and shows that for blue detuning the combined nonlinear
interaction is unstable below a critical wavenumber which reduces to the result
of Bespalov and Talanov in the limit of a negligible kinetic nonlinearity. For
red detuning we find that under a saturation parameter threshold exists whereby
the system stabilizes unconditionally. With negligible saturation, an
optomechanical form of Landau damping stabilizes all wavenumbers above a
critical wavenumber determined by the combined strength of the kinetic and
refractive optomechanical feedback. The damping is mediated primarily by atoms
traveling along the primary diagonals of the Talbot carpet.
