Partially coherent J0-correlated Schell-model beams beyond the paraxial approximation

The concept of partially coherent J(0)-correlated Schell-Model (JSM) beams is extended to the nonparaxial regime. By using the generalized Rayleigh-Sommerfeld diffraction integral, analytical propagation equations of nonparaxial JSM beams in free space are derived. Under the paraxial approximation our results reduce to the corresponding paraxial ones. The free-space propagation properties of nonparaxial JSM beams are illustrated with numerical examples. A comparison with paraxial JSM beams shows that the nonparaxial approach should be used if the parameters f and sigma are not small.