Production of triangular helix beams with the hexagonal array

In this paper, we demonstrate triangular helix beams with a hexagonal array, which are formed by the superposition of propagation-invariant triangular spots and triangular vortex beams arranged in a hexagonal array. Both spots array and vortex beams array can be obtained through the interference of six plane waves with identical transverse wave vectors, where adjacent plane waves maintain a π phase difference. When the transverse wave vectors of these two arrays satisfy specific conditions, they can achieve complete spatial overlap. Furthermore, by precisely controlling the difference in longitudinal wave vectors between the vortex arrays and spot arrays, their superposition forms triangular spiral beams with hexagonal array. As the distance along the z-axis increases, adjacent helices exhibit opposite rotation directions, which results from adjacent vortices possessing opposite topological charges. Both simulation and experimental results confirm the feasibility of this method.