Abstract
In this paper, we investigate the focusing properties and focal shift of a partially coherent vortex cosine-hyperbolic-Gaussian beam (PCvChGB) passing through a lens system. Based on the extended Collins formula, the analytical expression for a PCvChGB propagating through a thin lens is derived in detail. By using the obtained formula, the influences of the spatial coherence length, the Fresnel number, and the initial beam parameters on the focusing properties and the focal shift of a PCvChGB are discussed numerically. It is shown that the average intensity distribution in the focal region and the focal shift of the focused PCvChGB are strongly affected by the above factors. The obtained results could be beneficial for applications of vortex cosine-hyperbolic-Gaussian beam (vChGB) beams in beam shaping and atom optics.
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