A general phase-modulating solution for generating optical array with arbitrary dimensions via mapping space

It is of great significance to control the energy, location, topological charge, and other parameters of each beam in three-dimensional space. Thus, optical array is proposed and widely used in processing, communication, microscopy, storage, and other fields. However, the current methods to generate optical array are only effective in specific scenarios. In this work, we present an efficient and general method, which separates iterative calculation and parameter selection by introducing a special mapping space, allowing the generation of optical arrays with arbitrary dimensions, optional parameters, and any energy ratios. This method is compared with traditional methods from both simulation and experiment and is superior in diffraction efficiency, focus amount, and calculation speed. Additionally, a five-dimensional optical array with specially designed parameters is produced to show the versatility for different parameters. It shows advantages in beam shaping and parallelization and will be instrumental for applications in information storage, industrial processing, and three-dimensional imaging.