Coherent and incoherent combinations of partially coherent beams beyond the paraxial approximation

The concept of coherent and incoherent combinations of partially coherent beams is described and interpreted physically. Taking the Gaussian Schell-model (GSM) beam as a typical example of a partially coherent beam, the analytical propagation expressions for the coherent and incoherent combinations of GSM beams beyond the paraxial approximation are derived and illustrated numerically. Some special cases of the general results are analyzed.