Manipulation of sub-symmetry-protected topological bound states in the continuum

Topological bound states in the continuum (TBICs) are localized boundary states spectrally embedded in extended-mode continua and robust against weak symmetry-preserving perturbations. Sub-symmetry (SubSy) can protect these states even when global chiral symmetry is broken. Here, we propose a modified bilayer Su-Schrieffer-Heeger (SSH) photonic lattice with uniform sublattice detuning that preserves interlayer mirror symmetry and supports two complementary energy-referenced SubSy conditions. This enables selective control of multiple topological boundary states with distinct sublattice character, which can be shifted between band gaps and bulk continua without hybridization. Periodic longitudinal modulation enables transitions between in-gap Floquet edge states and Floquet TBICs. Compared with the standard bilayer SSH lattice, the detuned system maintains strongly localized Floquet boundary states over a broader driving range.