Orbital angular momentum, or OAM, is an important degree of freedom in wave physics. It has attracted broad interest for applications ranging from particle manipulation to optical communications. While integer OAM modes are generally stable, fractional orbital angular momentum modes are much more fragile. Because their phase is intrinsically multivalued, a single fractional vortex tends to lose its identity during propagation and break into ordinary integer-charge components.
A research team from Xiamen University and Shantou University has now proposed a new way to stabilize these fragile fractional wave states. Instead of relying on conventional momentum-space topology, the team engineered the topology of real space itself. Their work introduces a real-space topological framework based on optical conformal mapping and multi-sheeted Riemann surfaces.
The idea is conceptually similar to quark confinement in particle physics. Quarks carry fractional charges and cannot exist freely in isolation; they must combine into integer-charged particles such as mesons or baryons. In the new wave system, fractional OAM elements behave in an analogous way. A single fractional vortex is unstable, but several fractional elements can be geometrically confined and stitched together into a stable composite state with an overall integer OAM charge.
To realize this concept, the researchers used power conformal mappings to create effective multi-sheeted real-space connectivity. In one design, two half-order fractional OAM elements were confined into a meson-like composite mode. In another design, three one-third-order elements were combined into a baryon-like composite mode. Although each local element retains a fractional phase feature, the entire wave field forms a stable integer-OAM state. This “locally fractional, globally integer” behavior provides a new route to control fractional vortices.
The team first verified the mechanism through numerical simulations. The simulated fields showed clear fractional phase structures near the designed branch points, while the overall OAM spectrum was dominated by an integer OAM mode. These results confirmed that the real-space topology can protect fractional wave features by organizing them into stable composite states.
The researchers then demonstrated the concept experimentally using an elastic flexural wave platform. They fabricated two 3D-printed plates with gradient thickness profiles, which produced the required effective refractive-index distributions for flexural waves. Multiple transducers were used to generate stepped-phase excitations, and a laser Doppler vibrometer measured the resulting out-of-plane displacement fields.
The experimental measurements agreed well with the simulations. For the two-sheet design, two half-order fractional elements were observed and combined into a stable meson-like mode. For the three-sheet design, three one-third-order elements formed a baryon-like mode. The system also showed broadband performance, because the mechanism is based on geometry-level wave manipulation rather than narrow-band resonance.
This work extends topological protection from conventional momentum-space eigenmodes to real-space non-eigenmode wave structures. Although the experimental demonstration was performed with elastic waves, the underlying principle is governed by universal wave equations. The framework may therefore be transferable to other platforms, including acoustics, integrated photonics and optical metamaterials.
The findings provide a new way to manipulate fractional vortices and may inspire future applications in on-chip topological encoding, high-dimensional wave communication, acoustic manipulation and advanced photonic devices.
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Experimental study