Bound states in the continuum (BICs) are states that exist within the continuous spectrum of radiation modes but remain perfectly localized — they don't radiate despite having the energy to do so. They're trapped by symmetry or destructive interference, existing as dark modes in a sea of bright ones. BICs are topological objects in momentum space: they carry quantized topological charges that protect them from perturbation. The charges are vortices in the polarization field — points in momentum space where the far-field polarization is undefined.
Zhao, Chen, Wang, and collaborators (arXiv 2602.22634, February 2026) show that the topological structure of BICs doesn't stay in momentum space. It projects into real space.
A gyromagnetic photonic crystal slab — a periodic dielectric structure doped with magnetic material — provides the platform. Applying a magnetic field breaks time-reversal symmetry. Without the field, the BICs come in degenerate pairs related by time reversal. With the field, the pairs split into chiral BICs: one with right circular polarization, one with left. Each carries a topological charge of opposite sign.
Near-field scanning microscopy reveals the real-space consequences. Phase vortices with quantized topological charges appear in the near-field distribution — the electromagnetic field near the surface carries imprints of the momentum-space topology. The vortex charges are integers, protected by the same topology that protects the BIC. The near-field chirality is spatially distributed — regions of predominantly right-circular and left-circular polarization form patterns that map the chiral BIC's structure onto the crystal surface.
Most remarkably, the Stokes vector field — the four-component description of polarization state at each point in space — forms skyrmionic textures. Skyrmions are topological objects originally discovered in nuclear physics and later observed in magnetic materials, where the spin direction wraps smoothly around a sphere. Here, the polarization state wraps around the Poincaré sphere as you move across the crystal surface. The skyrmion is controlled by the applied magnetic field: changing the field changes the skyrmion number.
The topology has moved from an abstract parameter space (momentum) into a directly observable physical space (the electromagnetic field near the surface). What was a mathematical property of the band structure becomes a measurable texture of light.
The gyromagnetic photonic crystal provides the critical ingredient: time-reversal symmetry breaking. Without it, the chiral BICs would be degenerate and their real-space projections would cancel. The magnetic field splits them, making each chiral component individually observable. The symmetry breaking makes the topology visible.