Longitudinal topological manipulations of vortex fields via nested spiral arrays.

Vortex beams, characterized by their helical phase wavefronts, hold great promise in optical information science and light-matter interactions. However, current research predominantly focuses on static transverse properties, leaving a critical knowledge gap in the longitudinal mechanisms. This study systematically investigates the longitudinal evolution of vortex beams by constructing a nested spiral array configuration with gradient-distributed topological charges. Through a wavefront modulation scheme and a parametric topological charge regulation, we established a theoretical framework for longitudinal vortex field propagation, enabling quantitative characterization of annular intensity profiles, phase evolution patterns, and topological state transitions. Numerical simulations reveal propagation-dependent intensity enhancement followed by attenuation, while the phase maintains azimuthal rotational symmetry. Notably, the topological charge manifests a stepwise decrement pattern proportional to the spiral array number. This multidimensional vortex modulation mechanism provides theoretical foundations for advancing orbital angular momentum multiplexing technologies and developing multiple degree of freedom manipulation systems for microparticles in optical tweezers.