Supplementary Material 1

The supplementary material 1 presents comprehensive derivations of the radiation force and further elucidates the proposed approach for the simultaneous trapping and manipulation of multiple high-refractive-index particles under low spatial coherence conditions. In addition, a dedicated section is included to analyze the relationship between trapping stiffness and coherence length for particles with varying refractive indices, providing further quantitative insights into the stability of the proposed optical tweezers arrays.