Dark focal spot shaping is investigated by vector diffraction theory in the focal region of a hyperbolic-cosine beam that contains one on-axis spiral optical vortex. Results show that a dark focal shape can be altered considerably by the decentered parameters in cosh parts of the beam and topological charge of the vortex. Many novel and interesting dark focal shapes may appear, including rhombic, quadrangular, cross-shaped, and foursquare dark foci. Some dark focal spot chains can also occur. In addition, the numerical aperture of the focusing system can also affect dark focal shapes remarkably, which may lead to dark focal spots that disappear or change focal shape due to the depolarization effect for a high numerical aperture. All of the above dark focal shapes can be used in an optical manipulation system to construct alterable optical traps.
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