Dual-point-groups engineering enable multi-ultrahigh-Q resonances via Brillouin zone folding in tetramer metasurfaces

High-Q resonances based on bound states in the continuum provide a central route of enhancing light-matter interactions. Here, we present a dual-point group framework of constructing multiple ultrahigh-Q resonances within tetramer metasurfaces with a C4v symmetry via Brillouin zone folding. By selectively preserving or reducing the O- and S-group symmetries of super lattice, guided modes below light cone can be converted into guided resonances or bound states in the continuum with controlled degeneracy lifting, Q-factor scaling, eigenfield profiles, and mode splitting. Besides, applying rectangular lattice provides an alternative way of tuning the Q-factors and mode splitting. Finally, we experimentally demonstrate such two types of high-Q resonances in the tetramer metasurfaces. Measurement results show that the mode splitting can be tuned from 0 nm to 70 nm while the Q-factors are modulated from 300 to 20,000 by varying the asymmetry parameters. This work establishes a symmetry-addressed route for programmable multi-resonant high-Q metasurfaces. A dual-point group framework of constructing multiple ultrahigh-Q resonances within tetramer metasurfaces with a C4v symmetry via Brillouin zone folding is developed, enabling high-performance nanophotonic devices like sum frequency generation and laser.