Sculpting isolated optical vortex knots on demand

The rapid development of optical technologies, including optical trapping, enhanced imaging, and microscopy, necessitates fundamentally new approaches to higher-dimensional optical beam shaping. We introduce a rigorous theoretical approach for sculpting three-dimensional, topological particle-like objects, such as optical knots or links, including precise control of their individual parts. Universally applicable to knots created using braided zero lines, our method is validated through theoretical analysis and experimental measurements. The proposed approach enables new degrees of freedom in multi-dimensional singularities shaping, including rotations, shifts, and rescaling of their parts for enhanced stability in complex media. These results may find applications in the fields of three-dimensional optical trapping, manipulation, and subwavelength microscopy, as well as probing and imaging through atmospheric or underwater turbulence.