Abstract
In this paper, we investigate the propagation properties of radially polarized rectangular-symmetric cosine-Gaussian Schell-model (RCGSM) beam with multiple off-axis vortex phases by using Fourier transform and convolution method based on the unified theory of coherence and polarization. The results indicate that the radially polarized RCGSM beam has self-splitting properties and can be split into four identical lobes due to its unique spatial coherence structure. Furthermore, the modulation of multiple off-axis vortex phases can be acted on each lobe. For high coherence, the spot arrays with triangular or square hollow light intensity distribution can be generated in the focal plane by modulating the number of off-axis vortices (<i>N</i><sub>0</sub>) and the beam order, and the corresponding state of polarization on each lobe presents an inverted triangular or oblique square elliptic distribution. However, for small coherence, the modulation effect of multiple off-axis vortex phases disappears and the light intensity of each lobe degenerates into a quasi-Gaussian distribution, whereas its state of polarization keeps invariant, which is independent of the beam order and coherence length. In addition, the beam still has a certain self-healing ability for one of the off-axis vortex phases partially blocked by an obstacle, but it will be destroyed for completely blocking, resulting in a notch on each lobe.
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