Fig. 2. Topological force distribution around BIC in momentum space with untwisted PhCS.

BIC induces a force singular point (force zero, F = 0) at Γ point with topological distribution of optical force calculated by integrating MST surrounding a sphere 1000 nm above the PhCS for the (A) upper band and (B) lower band. (A) The upper band has optical forces converging toward the center, Γ point. (B) The lower band has optical forces radiating away from the center. Insets plot maps of the angle of the force vector ϕ_F(k) showing topological winding feature of optical force around BIC in momentum space. The converging and radiating force patterns are of rotation symmetry with a degree of 180. Lower-band Poynting vector and electric field profile around the nanosphere with (C) k_x = 0, k_y < 0 (D) k_x < 0, k_y = 0, (E) k_x < 0, k_y > 0, and (F) k_x > 0, k_y < 0. Here, E₀ is equal to 1 × 10⁶V/m. (G) Comparison between magnitude of the converging force with a 10 × 10 PhCS and without PhCS by shining a Gaussian beam with a frequency of 186 THz, a beam width of 287 nm, and a focal plane at z = 850 nm.