Emerging Multidimensional Real-Space Topological Structures at Chiral Bound States in the Continuum

Abstract

As widely studied topological singularities, bound states in the continuum (BICs) have revealed rich physical properties through their momentum-space topology. Here, we reveal and experimentally demonstrate that magnetically induced chiral BICs possess multidimensional topological structures extending into real space. We design and realize a gyromagnetic photonic crystal slab where magnetic field breaks the time-reversal symmetry and lifts the degeneracy of BICs, creating a pair of chiral BICs with opposite circular polarizations. Near-field scanning measurements reveal phase vortices with quantized topological charges, spatially distributed near-field chirality, and skyrmionic Stokes textures arising from magnetic control. Our work unveils a previously unexplored dimension of BIC topology and establishes gyromagnetic photonic crystals as versatile platforms for manipulating complex topological states.

Figures (5)

• Figure 1: (a) Upper panel: a unit cell of the PhC slab, where the gray plane indicates where the near-field distributions are evaluated in later discussions. Lower panel: the relative permeability tensor $\overset{\leftrightarrow}{\mu}_r$ of YIG. (b) Top: evolution of the BICs with $\kappa$. Bottom: representative photonic band structures for $\kappa=\pm 0.3$. Red/blue/gray dots denote L-BIC/R-BIC/D-BIC, respectively. (c) Real-space topological textures in a unit cell associated with the chiral BICs, evaluated at the gray plane shown in (a). From top to bottom: (i) phase distributions, (ii) chirality distributions, and (iii) Stokes vector distributions. Reversing the magnetic field swaps the two chiral BICs and their associated topological textures. (d) Schematic real-space topological structures of the R-BIC across the PhC slab.
• Figure 2: (a) Photo of the experimental sample. (b) Simulated and measured co-polarized transmission spectra under circularly polarized incidence for the sample magnetized in the positive B direction. Upper row: LCP incidence; Lower row: RCP incidence. Dashed curves mark bands whose handedness matches that of the incident light. (c) Measured co-polarized transmission spectra under reversed magnetization.
• Figure 3: (a) Schematic view of the near-field scanning setup. (b) The measured near-field Fourier components of the $E_z$ amplitude, showing the two bands of interest. The gray region denotes the light cone. (c)-(d) Measured amplitude (c) and phase (d) of the electric field for the R-BIC. (e) The phase vortices in the unit cell for the R-BIC and L-BIC, where the L-BIC has opposite phase winding compared to the R-BIC.
• Figure 4: (a) The left-handed circular (left panel) and right-handed circular (right panel) components of the near-field electric field of chiral BICs. (b) The normalized third Stokes parameter ($S_3/S_0$) of chiral BICs in the near field. (c) The distribution of Stokes vectors, showing skyrmionic textures. From top to bottom: measured results of R-BIC and L-BIC.
• Figure 5: Upon reversing the magnetic field, the BIC on the upper band transforms from R-BIC to L-BIC, with its near-field topological structures switching correspondingly.