Propagation of partially coherent light in non-Hermitian lattices

Band theory for partially coherent light is introduced by using the formalism of second-order classical coherence theory. It is demonstrated that the cross-spectral density function can have bands and gaps and form a correlation band structure. The propagation of a partially coherent beam in non-Hermitian periodic structures is considered to elucidate the interplay between the degree of coherence and the gain or loss present in the lattice. We apply the formalism to study partially coherent Bloch oscillations in lattices having parity-time symmetry.