Local-nonlocal assisted multifunctional photonic crystals.

Metasurfaces excel at local, spatially varying control of wavefronts, whereas photonic crystals (PhCs) are admired for their nonlocal resonances such as bound states in the continuum (BICs). These two regimes-local control and nonlocal collective response-have long been viewed as difficult to integrate within a single platform. Here, we introduce local-nonlocal assisted multifunctional PhCs unifying wavefront shaping and BICs by embedding meta-notches within PhC pillars. The locally tunable notches generate spectral-zero-assisted topological phase for efficient 2π coverage, while the strongly confined BIC modes remain largely unperturbed, preserving high-Q nonlocal resonances. This constructive local-nonlocal integration synthesizes the design freedom of metasurfaces with the dispersive resonance of PhCs in a single planar device. Our approach extends the capabilities of flat optics, enabling multifunctional PhCs and opening pathways toward higher-order topologies, advanced imaging, communication, and analogue optical computing.