A fireworks algorithm based Gerchberg–Saxton algorithm for the design of diffractive optical element for beam shaping

In this paper, a fireworks algorithm based Gerchberg–Saxton (GS) algorithm for the design of diffractive optical element is developed, named FW-GS algorithm, in which, the explosion mechanism of the fireworks algorithm is introduced to efficiently find the initial phase, thereby ensuring a superior phase solution for the subsequent GS algorithm. By employing this approach to shape a Gaussian beam into a square beam, the results illustrated the notable improvement of 16.10 % in RMSE and 3.29 % in diffractive efficiency when compared to the traditional GS algorithm, while exhibiting stable optimization performance. Furthermore, the proposed algorithm demonstrated adaptability to various shaping targets, with RMSE improved by about 16 % and diffractive efficiency improved by more than 3 % for shaping to circular, annular, and rectangular beams.