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

Abstract

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