Investigation of control characteristics in tightly focused systems: self-focusing circular Airyprime-Gaussian vortex beams.

This study investigates the intricate properties of linearly polarized circular Airyprime-Gaussian vortex beams (CApGVBs) in tightly focused optical systems. We explore the relationship between self-focusing and tight focusing of CApGVBs by adjusting the main ring radius. By refining vortex pair parameters, we show that the intensity distribution depends significantly on whether the arrangement is axial or off-axis. Additionally, we present various scenarios demonstrating the generation of light bottle modes by linearly polarized CApGVBs. Our analysis explores the Gouy phase difference between the orientation of the spin density vector and the longitudinal and transverse electric field components of the vector beam across different optical distribution factors. We recognize the dual roles of orbital and spin angular momentum (SAM) in vortex beams. Furthermore, we show how the three-dimensional dynamics of the spin density vector during propagation can lead to the formation of a three-dimensional polarized elliptical topology. These findings provide critical insights into the flexible tunability of multi-focusing states, advance the understanding of the unique properties of CApGVBs and their potential applications in micro-optical systems and particle manipulation, while highlighting the potential of CApGVBs to enhance the precision of light capture and control systems.