Spatial correlation properties and phase singularity annihilation of Gaussian Schell-model beams in the focal region

By using the generalized Debye diffraction integral, this paperstudies the spatial correlation properties and phase singularityannihilation of apertured Gaussian Schell-model (GSM) beams in thefocal region. It is shown that the width of the spectral degree ofcoherence can be larger, less than or equal to the correspondingwidth of spectral density, which depends not only on the scalarcoherence length of the beams, but also on the truncation parameter.With a gradual increase of the truncation parameter, a pair of phasesingularities of the spectral degree of coherence in the focal planeapproaches each other, resulting in subwavelength structures.Finally, the annihilation of pairs of phase singularities takesplace at a certain value of the truncation parameter. Withincreasing scalar coherence length, the annihilation occurs at thelarger truncation parameter. However, the creation process of phasesingularities outside the focal plane is not found for GSM beams.