Bilayer metasurfaces offer abundant degrees of freedom and remarkable design flexibility for tailoring bound states in the continuum (BICs) through both interlayer and intralayer coupling compared with a single-layer metasurface. In this work, we present a comprehensive investigation of topological dynamics of BICs in bilayer metasurfaces. By appropriately adjusting the interlayer spacing, Fabry-Pérot BICs (FP-BICs) are successfully constructed at the $\mathrm{\Gamma }$ point in momentum space, which correspond to merging BICs carrying different topological charges whose quality factors ($Q$ factors) follow the scaling law $Q\propto k^{-4}$ or $Q\propto k^{-6}$. We investigate topological charge evolution of BICs for bonding and antibonding modes under both transverse electric (TE) and transverse magnetic (TM) polarizations in bilayer metagratings. A viable approach of achieving customized BICs at prescribed $k_x$ and $k_y$ in momentum space is proposed by simply tuning the interlayer distance. Furthermore, we show that bilayer metasurfaces and photonic crystal slabs serve as powerful platforms for exploiting rich topological dynamics of BICs. In particular, degenerate merging FP-BICs are demonstrated in bilayer metasurfaces with $C_{4v}$ symmetry, where distinct merging dynamics are strongly dependent on the eigenfield distributions. When reducing the $C_{4v}$ symmetry to $C_{2v}$, the degeneracy of BICs can be removed. In addition, we also show that an in-plane displacement between the two layers provides a convenient route for tailoring circularly polarized points in momentum space. Our results provide general guidance for designing BICs with unique topological dynamics in momentum space, and hold great promise for developing applications in nanophotonics.

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• Bound states in the continuum
• Fano resonance
• Metamaterials
• Metasurfaces
• Photonic crystals