Generation of spatial transverse optical vortices via 4π tight focusing radially polarized light

Spatial transverse optical vortices (STOVs), characterized by possessing transverse orbital angular momentum, offer new degrees of freedom for optical manipulation. However, since the vortex phase circulation of STOVs is the spatiotemporal plane (x-t plane), traditional phase modulation methods based on the x-y transverse plane are no longer applicable. Therefore, exploring new methods for generating STOVs has become a significant challenge. Here, a 4π tight focusing system with overlapped phase from two counter-propagating radially polarized beams is proposed to generate STOVs. First, by independently designing the phase wavefronts of counter-propagating beams, uniform nano-scale spherical spots are generated in the focal region. Then, treating spherical spots as spatial trajectory units and superimposing a time-dependent helical phase factor exp(–ilφst), precise control over the spot’s spatial position and motion trajectory is achieved. When the temporal step is sufficiently small, i.e., under high temporal resolution, smooth STOVs emerge. Through simultaneous modulation of temporal and spatial factor, STOVs with distinct radii r can be generated. This approach ultimately enables precise customization of STOVs in size, smoothness, and geometry, facilitating high-precision advancements in fields such as super-resolution microscopy, quantum manipulation and subwavelength nonlinear optical effects.