Beams originated by J(0)-correlated Schell-model planar sources

We analyse the behaviour in propagation of the beams originated by J(0)-correlated Schell-model planar sources. Using the theory of coherence in the space-frequency domain, we find that, if the intensity profile across the source plane is Gaussian, the modes are the Bessel-Gauss beams. Then we work out an analytical expression for the cross-spectral density of the beam in free propagation. All the beam features are deduced from this quantity. Profiles of the intensity and of the degree of coherence in propagation are analysed. We find that the intensity profile has properties analogous to those of the Bessel-Gauss beams but the degree of coherence does not keep the J(0)(x) profile nor shift-invariance