Quark-like modes of fractional orbital angular momentum.

Orbital angular momentum (OAM) expands the Hilbert space for wave-based information processing. While integer OAM is robust, fractional orbital angular momentum (FOAM) suffers from intrinsic topological instability and disintegrates in free space. Conventional k-space topology is limited to protecting eigenmodes, leaving non-eigenmode FOAM unprotected. We overcome this limitation by introducing a real-space topology framework via the optical conformal mapping method. By engineering topological connectivity, we stitch discontinuous fractional phases into globally stable, integer-charged composite states, conceptually analogous to quark confinement. We experimentally validate this mechanism on an elastic flexural wave platform. This work establishes a universal paradigm to extend topological protection from k-space eigenmodes to real-space non-eigenmodes, offering a versatile framework for manipulating fractional vortices across diverse wave systems, ranging from acoustics to integrated photonics.