Longitudinal dynamics of optical vortices based on multi-spiral arrays

Optical vortices, possessing orbital angular momentum (OAM) and spiral wavefronts, have become indispensable carriers for high-dimensional classical and quantum information. While transverse vortex properties are extensively characterized, the longitudinal dynamics of vortex fields, crucial for understanding complex light propagation, remain relatively unexplored. To address this, we introduce a phase-encoded methodology utilizing multi-spiral arrays (MSAs) to enable systematic spatial control and analysis of longitudinal vortex dynamics. Through a comprehensive theoretical framework, we derive vortex field expressions across ultra-near-field, near-field, and far-field regimes, and establish analytic formulations for longitudinal properties. Numerical simulations reveal fundamental longitudinal dynamics, as a monotonic decay of OAM coupled with progressive attenuation of Poynting vector. Quantitative analysis via circumferential averaging at intensity maxima conclusively reveals the dual dependence of vortex dynamics on spiral structure and propagation depth. The MSA-based modulation paradigm provides a fundamental theoretical framework essential for advancing structured light applications demanding precise spatial control over optical vortices. • Presents the first systematic theoretical framework for 3D spatial dynamics of optical vortices. • Phase-encoded multi-spiral arrays enable flexibly longitudinal control of vortex dynamics. • Derives analytical expressions for transverse fields and longitudinal evolutions in full-space. • Longitudinal vortex decay, as monotonic orbital-angular-momentum reduction coupled with Poynting vector attenuation. • Dual dependence of vortex dynamics on spiral topology and propagation depth.