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Generalized Perfect Optical Vortex along Arbitrary Trajectories

Perfect optical vortex (POV) is a type of vortex beam with an infinite thin ring and a fixed radius independent of its topological charge. Here we propose the concept of generalized perfect optical vortex along arbitrary curves beyond the regular shapes of circle and ellipse. Generalized perfect optical vortices also share the similar properties as POVs, such as defined only along infinite thin curves and owning topological charges independent of scales. Notably, they naturally degenerate to the POVs and elliptic POVs along circles and ellipses, respectively. We also experimentally generated the generalized perfect optical vortices through a digital micromirror device (DMD) and measured the phase distributions by interferometry, exhibiting good agreements with the simulations. Moreover, we derive a proper modified formula to yield the generalized perfect optical vortices with uniform intensity distribution along predesigned curves. The generalized perfect optical vortices might find the potential applications in optical tweezers and communication.