Direct Mapping of Intrinsic Topology of Bound States in the Continuum via Nonlinear Emission

The direct mapping of the intrinsic topology in a leaky photonic band is crucial and challenging in topological photonics. For instance, observables in bound states in the continuum (BICs) feature complex topological textures such as a polarization vortex in momentum space, which nonetheless is difficult to be characterized in far-field scattering, especially considering the dominant direct channel. Here, we propose and experimentally demonstrate a hybrid nonlinear metasurface that enables a direct visualization of the intrinsic topology in BICs via second-harmonic generation (SHG). The enhanced local-source of SHG from the ultrathin indium tin oxide can effectively excite the emissions from the eigenmodes of a TiO2 photonics crystal slab, achieving three-order enhancement of SHG magnitudes. Importantly, these enhanced SH emissions carry topological polarization textures of BICs to the far field. With this, we can directly construct polarization vector maps of symmetry-protected BICs and chiral symmetry-broken quasi-BICs, clearly visualizing the winding structure around V points, the generation and evolution of chiral C points. This work provides a universal approach for characterizing topological photonic systems via coherent nonlinearity processes, opening new avenues for studying topological phenomena in non-Hermitian photonic systems.