Tailoring angular momentum density via Mandelbrot fractal polarization singularities

Structured light with engineered polarization singularities (PSs) provides unprecedented control over spin and orbital angular momentum (SAM/OAM) densities; however, conventional PSs often exhibit limited spatial complexity for advanced light-matter interactions. We propose Mandelbrot fractal polarization singularities (MFPSs) - a novel class of structured light that leverages multifractal geometry to tailor the angular momentum density. Through a robust common-path interferometric strategy employing spatially modulated fractal phase encoding, we experimentally generated MFPSs with hierarchical polarization singularities. We characterized their non-uniform SAM/OAM separation in the focal region. Crucially, the fractal-driven non-uniform angular momentum density enables optical manipulation surpassing conventional singular beams. The selective directional transport and configurable multi-particle trapping of microparticles via tailored angular momentum landscapes were realized. These results not only establish MFPSs as a versatile platform for angular momentum engineering but also bridge singular optics with optical micromanipulation, offering promising solutions for further studies of light-matter interactions.