Propagation invariance and self-imaging in variable-coherence optics

The concept of propagation invariance in partially coherent optics is introduced. Explicit expressions are given for the cross-spectral density and the angular correlation function (cross-angular spectrum) characterizing a class of fields that are propagation invariant in the sense that their correlation properties in the space-frequency domain are exactly the same in every transverse plane. The so-called diffraction-free beams are shown to be members of this new, wider class of wave fields, which itself is a subset of a generalized class of partially coherent self-imaging fields. The existence of partially coherent propagation-invariant fields with a sharp correlation peak is verified experimentally by considering radiation from a planar J0 Bessel-correlated source.