In this paper, we generalize the concept of classical spiral zone plates (SZPs) to fractional spiral zone plates (FSZPs). By using an SZP with a fractional topological charge and controlling the starting orientation, we can break down the symmetry of the focusing process to give orientation-selective anisotropic vortex foci. Numerical results show that its binary structure gives additional high-order foci on the optical axis and the intensities in the foci can be controlled by properly choosing the fractional topological charge. Our study reveals the feasibility to control the intensity in the foci by means of FSZPs.
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