Production of longitudinal equidistant misaligned helix beams with the hexagonal array

In this study, we successfully generated helix beams with a hexagonal array by combining propagation-invariant vortex beams and spots with the hexagonal array. Propagation-invariant vortex beams with a hexagonal array were achieved through the interference of six symmetric plane beams with adjacent phase steps of π/3 in either the clockwise or anticlockwise direction. These vortex units with the hollow dark center have identical phase and intensity distributions. Similarly, the propagation-invariant spots with a hexagonal array were produced by the interference of three symmetric plane beams with identical initial phase. The generated spots have the same intensity distribution, and adjacent spots have a phase difference of ±2π/3. The adjacent helix beams have an equidistant longitudinal pitch for the special phase distribution of the spots. Our simulation and experimental results have demonstrated the feasibility of this method.