Longitudinal evolution of phase vortices generated by rotationally interleaved multi-spiral.

Phase vortices exhibit significant applications and hold promising prospects across various scientific fields. However, while extensive attention has been devoted to the two-dimensional transverse plane of these vortices, their longitudinal properties have received comparatively limited exploration. Our study focuses on the longitudinal evolution of phase vortices, encompassing an investigation of variational topological charges and phase distributions. The investigation employs the rotationally interleaved multi-spiral, characterized by multiple identical spirals arranged in an azimuthally symmetric rotation, to modulate phase distributions by the variable spiral radius versus the azimuthal angle. Initially, we analyze the modulation effect theoretically, delving into propagation properties and vortex formations. Subsequently, through numerical simulations of vortices generated by both single and multi-spiral setups, we examine the longitudinal evolution of topological charges and phase distributions. The analyses reveal a step-wise reductant topological charges and a tortuous increasing spatial variations of phase singularities in transmission direction, with the dependency on both propagation distance and number of multi-spiral. The outcomes hold significant potential applications in optical communications and optical tweezers.