  We investigate the interaction between a light beam and a two-dimensional
photonic lattice that is photo-induced in a photorefractive crystal using
partially coherent light. We demonstrate that this interaction process is
associated with a host of new phenomena including lattice dislocation, lattice
deformation, and creation of structures akin to optical polarons. In addition,
two-dimensional discrete solitons are realized in such partially coherent
photonic lattices.
