  Motivated by a recent experiment by Zelevinsky et al. [Phys. Rev. Lett. 96,
203201], we present the theory for photoassociation and optical Feshbach
resonances of atoms confined in a tight one-dimensional (1D) or two-dimensional
(2D) optical lattice. In the case of an alkaline-earth intercombination
resonance, the narrow natural width of the line makes it possible to observe
clear manifestations of the dimensionality, as well as some sensitivity to the
scattering length of the atoms. Among possible applications, a 2D lattice may
be used to increase the spectroscopic resolution by about one order of
magnitude. Furthermore, a 1D lattice induces a shift which provides a new way
of determining the strength of a resonance by spectroscopic measurements.
