Fig. 1. Schematic model of the optical field manipulation based on the dual-spiral arrays. (a) Model setup, consisting of a laser, dual-spiral arrays, and a detector. (b) Front view of the dual-spiral arrays. The dual-spiral arrays are composed of an inner spiral and an outer spiral, with each spiral consisting of multiple pinholes represented by white dots. The blue arrows indicate the radii of the spirals, denoted as r₁ and r₂, respectively. (c) Intensity field generated by the dual-spiral arrays

Fig. 2. Schematic of the optical field modulated by dual-spiral arrays with first-order topological charges. (a) Structures of dual-spiral arrays, each characterized by varying spiral radii. (b) Sequentially presents the intensity and phase distributions progressing from the inner to the outer layer. Sequences (a1)–(a12) and (b1)–(b12) correspond in terms of the arrangement direction, collectively showcasing 12 datasets with different spiral radius variations linked to intensity and phase distributions. Each set of images rotates according to the directions indicated by the arrows on the inner and outer circles. In the intensity and phase distribution maps shown in (b), the white dotted arrows denote the azimuthal direction of the optical field

Fig. 3. Schematic of the optical field modulated by dual-spiral arrays with third-order topological charges. (a) Structures of dual-spiral arrays with different spiral radii. (b) Sequentially presents the intensity and phase distributions progressing from the inner to the outer layer. The images in (a1)–(a12) and (b1)–(b12) are arranged in the corresponding directions, collectively displaying 12 datasets with different spiral radius differences and their corresponding intensity and phase distributions. Each set of images rotates according to the directions indicated by the arrows on the inner and outer circles. In the intensity and phase distribution maps shown in (b), the white dotted arrows denote the azimuthal direction of the optical field

Fig. 4. (a) Radial difference of the dual-spiral arrays as a function of the azimuthal angle of the optical field, with the linear fit lines of the purple line representing spirals with a first-order topological charge and the blue line representing spirals with a third-order topological charge. (b) and (c) show the sector plots of the azimuthal variation of the optical field for topological charges l = 1 and l = 3, respectively, with sector plots spanning from 0° to 360°