Transverse Focal Shift in Vortex Beams

The transverse focal shift (TFS) is a phenomenon that the maximum of a focused field does not occur at the geometrical focus, but is moved a short distance transversely in the focal plane. In this paper, the TFS of vortex beams in a high numerical aperture system is investigated. Four typical types of incident vortex beams are selected and the intensity distributions and the vortices behaviors in the focal region are discussed analytically and numerically. It is found that there are three main parameters, the topological charge, the initial positions of the vortices, and the semiaperture angle influencing the TFS in different ways, and the TFS even can be observed when the vortices annihilate in the focal plane. Our results also show that the intensity maximum can move from the $y$-axis, $x$-axis to the geometrical focus, or move from $+y$-axis to $-y$ -axis in different cases, which may have implications in optical trapping.