We study photonic band gaps in a one-dimensional optical lattice of la
ser-cooled trapped atoms. We solve for the self-consistent equilibrium
positions of the atoms, accounting for the backaction of the atoms on
the trapping beams. This solution depends strongly on the sign of the
trapping laser detuning. For red-detuned trapping lasers, the resulti
ng lattice exhibits a one-dimensional photonic band gap for frequencie
s between the trapping laser frequency and the atomic resonance. For b
lue detuning the stop band extends symmetrically about resonance, typi
cally for hundreds of atomic linewidths, except for the small region b
etween atomic resonance and the lattice frequency, which is excluded.
We calculate the reflection spectrum for a lattice of Cs atoms for var
ious trapping laser detunings and interpret its behavior as a function
of the lattice size and density. For a mean density of 10(11) cm(-3),
and 1000 planes, 55% reflection of a weak probe beam should be observ
ed. We also consider Bragg scattering in a three-dimensional optical l
attice as a means of probing the long-range order in the atomic densit
y correlation function.