Analytical solutions of partially coherent beams propagating in photonic lattices

The analytical solution for partially coherent beams propagating in one-dimensional (1D) uniform or binary periodic photonic environments is presented. The cross-spectral density (CSD) of a partially coherent Gaussian-Schell model (GSM) beam and a partially coherent Hermite-Gaussian correlated Schell-model (HGCSM) beam in uniform periodic photonic lattices is derived in detail. These analytical expressions demonstrate that the evolution of the spectral density is determined not only by the characteristics of the light sources, such as the coherence or correlation function structure, but also by the properties of the photonic lattices, specifically the coupling coefficient. Our findings pave the way for the analytical study of the propagation of partially coherent beams in photonic lattices.