Tight focusing Lorenz–Gaussian vortex beams modulated by power order space-variant phase

The aim of this paper is to investigate the focusing properties of linearly polarized Lorenz–Gaussian vortex beams modulated with power order space-variant (POSV) phase, which is based on vector diffraction theory. The results show that the shape of focal spot can be adjusted by changing the POSV parameter \(n\) $n$ . In addition, the adjustable phase parameter \(C\) $C$ can flexibly control the position of the focus on the \(X\) $X$ -axis. Immediately after that, it is revealed that with the increase of topological charge number \(m\) $m$ , the focused pattern can be separated along \(y = x\) $y=x$ direction. Even more interesting is the fact that the waist width \(\omega \) $\omega$ is inversely proportional to the length of the bar focusing peak. Specifically, when the value of waist width \(\omega \) $\omega$ is increased, the length of the strip-shaped focusing peak is continuously shortened. And the value of \(NA\) $\mathit{NA}$ is inversely proportional to the size of the circular spot. A range of focal properties were acquired through the introduction of a space-variant phase with a power order. These new properties hold potential applications within various fields, including particle manipulation, optical modulation, and particle confinement.