Study on optical hierarchical sorting of particles based on the Fraunhofer diffraction field of spiral phase plate array

Optical hierarchical sorting has attracted significant attention in recent years. The existing approaches use either complex numerical calculation or computer-aided experimental tools for optical hierarchical sorting. We proposed a method to perform hierarchical sorting, which is computationally simple and does not need computer aid. In particular, we employed a focused optical vortices array (FOVA), which is generated and focused by a spiral phase plate array (SPPA) and a microlens array, respectively. We designed different heights for the spiral phase plate in different columns of the SPPA. This enabled different columns of the FOVA to carry different topological charges and consequently possess different capture capabilities. To realize hierarchical sorting, we exploited the properties of FOVA by deploying it in a microfluidic chamber containing particles of various sizes. The four columns of the FOVA formed four corresponding capture regions in the flow area of the particles. From our theoretical analysis and numerical results, we observed that particle sizes in the range of 1 to 582 nm could be sorted. Our approach provides a theoretical framework that can be readily employed in experiments for optical hierarchical sorting.