We demonstrate that particles confined to two dimensions (2D) and subjected
to a one-dimensional (1D) periodic potential exhibit a rich phase diagram,
with both "locked floating solids" and smectic phases. The resulting phase
s and phase transitions are studied as a function of temperature and potent
ial strength. We find rerntrant melting as a function of the potential stre
ngth. Our results lead to universal predictions consistent with recent expe
riments on 2D colloids in the presence of a laser-induced 1D periodic poten
tial.