Generalized perfect optical vortices along arbitrary trajectories

Abstract

Perfect optical vortices (POVs) are a type of vortex beams with infinitely narrow rings and fixed radii independent of their topological charges. Here we propose the concept of generalized perfect optical vortices (GPOVs) along arbitrary curves beyond the regular shapes of circle and ellipse. GPOVs also share similar properties as POVs, such as defined only along infinitely narrow curves and owning topological charges independent of scales. Using a rigorous mathematical derivation in a curvilinear coordinate, we reveal theoretically that the GPOVs have the topological charge proportional to the area of the swept sector in tracing the curve, suggesting a unique mode for optical vortex beams. Experimentally, the complex-amplitude masks to generate the GPOVs are realized by using a pure-amplitude digital micro-mirror device (DMD) with the super-pixel encoding technique. The phase profiles of the generated GPOVs are retrieved experimentally through a self-built interferometry and exhibit the good agreement with the simulations. We also derive a properly modified formula to yield the intensity-uniform GPOVs along predesigned curves, which might find applications in optical tweezers and communication.